Patent Publication Number: US-2023139102-A1

Title: Method and system for quantifying limitations in coronary artery blood flow during physical activity in patients with coronary artery disease

Description:
TECHNICAL FIELD 
     Embodiments include methods and systems for modeling of fluid flow and more particularly methods and systems for patient-specific modeling of blood flow. 
     BACKGROUND 
     Coronary artery disease may produce coronary lesions in the blood vessels providing blood to the heart, such as a stenosis (abnormal narrowing of a blood vessel). As a result, blood flow to the heart may be restricted. A patient suffering from coronary artery disease may experience chest pain, referred to as chronic stable angina during physical exertion or unstable angina when the patient is at rest. A more severe manifestation of disease may lead to myocardial infarction, or heart attack. 
     A need exists to provide more accurate data relating to coronary lesions, e.g., size, shape, location, functional significance (e.g., whether the lesion impacts blood flow), etc. Patients suffering from chest pain and/or exhibiting symptoms of coronary artery disease may be subjected to one or more tests that may provide some indirect evidence relating to coronary lesions. For example, noninvasive tests may include electrocardiograms, biomarker evaluation from blood tests, treadmill tests, echocardiography, single positron emission computed tomography (SPECT), and positron emission tomography (PET). These noninvasive tests, however, typically do not provide a direct assessment of coronary lesions or assess blood flow rates. The noninvasive tests may provide indirect evidence of coronary lesions by looking for changes in electrical activity of the heart (e.g., using electrocardiography (ECG)), motion of the myocardium (e.g., using stress echocardiography), perfusion of the myocardium (e.g., using PET or SPECT), or metabolic changes (e.g., using biomarkers). 
     For example, anatomic data may be obtained noninvasively using coronary computed tomographic angiography (CCTA). CCTA may be used for imaging of patients with chest pain and involves using computed tomography (CT) technology to image the heart and the coronary arteries following an intravenous infusion of a contrast agent. However, CCTA also cannot provide direct information on the functional significance of coronary lesions, e.g., whether the lesions affect blood flow. In addition, since CCTA is purely a diagnostic test, it cannot be used to predict changes in coronary blood flow, pressure, or myocardial perfusion under other physiologic states, e.g., exercise, nor can it be used to predict outcomes of interventions. 
     Thus, patients may also require an invasive test, such as diagnostic cardiac catheterization, to visualize coronary lesions. Diagnostic cardiac catheterization may include performing conventional coronary angiography (CCA) to gather anatomic data on coronary lesions by providing a doctor with an image of the size and shape of the arteries. CCA, however, does not provide data for assessing the functional significance of coronary lesions. For example, a doctor may not be able to diagnose whether a coronary lesion is harmful without determining whether the lesion is functionally significant. Thus, CCA has led to what has been referred to as an “oculostenotic reflex” of some interventional cardiologists to insert a stent for every lesion found with CCA regardless of whether the lesion is functionally significant. As a result, CCA may lead to unnecessary operations on the patient, which may pose added risks to patients and may result in unnecessary heath care costs for patients. 
     During diagnostic cardiac catheterization, the functional significance of a coronary lesion may be assessed invasively by measuring the fractional flow reserve (FFR) of an observed lesion. FFR is defined as the ratio of the mean blood pressure downstream of a lesion divided by the mean blood pressure upstream from the lesion, e.g., the aortic pressure, under conditions of increased coronary blood flow, e.g., induced by intravenous administration of adenosine. The blood pressures may be measured by inserting a pressure wire into the patient. Thus, the decision to treat a lesion based on the determined FFR may be made after the initial cost and risk of diagnostic cardiac catheterization has already been incurred. 
     Thus, a need exists for a method for assessing coronary anatomy, myocardial perfusion, and coronary artery flow noninvasively. Such a method and system may benefit cardiologists who diagnose and plan treatments for patients with suspected coronary artery disease. In addition, a need exists for a method to predict coronary artery flow and myocardial perfusion under conditions that cannot be directly measured, e.g., exercise, and to predict outcomes of medical, interventional, and surgical treatments on coronary artery blood flow and myocardial perfusion. 
     Moreover, patients with known coronary artery disease may be subject to limitations in physical activity or exercise due to reductions in blood flow or perfusion pressure, or concerns of plaque disruption related to elevated blood pressure or elevated plaque stress. Thus, a need exists for a method for assessing coronary anatomy, myocardial perfusion, and coronary artery flow noninvasively during physical activity in patients with coronary artery disease. A need further exists for a method to predict coronary artery flow and myocardial perfusion under conditions and intensity levels of physical activity or exercise, such as aerobic and/or anerobic exercise, and to predict outcomes of medical, interventional, and surgical treatments on coronary artery blood flow and myocardial perfusion during such physical activity. With the assistance of such a method, patient risk of physical activity during cardiac rehabilitation may be assessed. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosure. 
     SUMMARY 
     In accordance with an embodiment, a system for determining cardiovascular information for a patient with coronary artery disease includes at least one computer system configured to receive patient-specific data regarding a geometry of the patient&#39;s heart; create a model representing at least a portion of the patient&#39;s heart based on the patient-specific data; create a physics-based model of blood flow through the patient&#39;s heart simulated during a selected level of physical activity; determine one or more values of at least one blood flow characteristic within the patient&#39;s heart during the simulated level of physical activity based on the model and the physics-based model; normalize the determined one or more values of the at least one blood flow characteristic during the simulated level of physical activity; and compare the one or more normalized values of the at least one blood flow characteristic during the simulated level of physical activity to a threshold to determine whether the level of the physical activity exceeds a level identified as an acceptable level of risk. If the one or more normalized values of the at least one blood flow characteristic are above the threshold, the at least one computer system is configured to identify a level of physical activity at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk. Optionally, at least one computer system may be further configured to recommend a level of physical activity appropriate for the patient. If the one or more normalized values of the at least one blood flow characteristic are at or below the threshold, the at least one computer system is configured to increase the simulated level of physical activity. In that case, the at least one computer system may be configured to update the physics-based model of blood flow through the patient&#39;s heart simulated during the increased level of physical activity. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, a method for determining cardiovascular information for a patient with coronary artery disease using at least one computer system includes inputting into the at least one computer system patient-specific data regarding a geometry of the patient&#39;s heart; creating, using the at least one computer system, a model representing at least a portion of the patient&#39;s heart based on the patient-specific data; creating, using the at least one computer system, a physics-based model of blood flow through the patient&#39;s heart simulated during a selected level of physical activity; determining, using the at least one computer system, one or more values of the at least one blood flow characteristic within the patient&#39;s heart during the simulated level of physical activity based on the model and the physics-based model; normalizing the determined one or more values of the at least one blood flow characteristic during the simulated level of physical activity; and comparing the one or more normalized values of the at least one blood flow characteristic during the simulated level of physical activity to a threshold to determine whether the level of physical activity exceeds a level identified as an acceptable level of risk. If the one or more normalized values of the at least one blood flow characteristic are above the threshold, the method comprises identifying a level of physical activity at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk. Optionally, the method may further comprise recommending a level of physical activity appropriate for the patient. If the one or more normalized values of the at least one blood flow characteristic are at or below the threshold, the method further comprises increasing the simulated level of physical activity. In that case, the method may further comprise updating the physics-based model of blood flow through the patient&#39;s heart simulated during the increased level of physical activity. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, the present disclosure relates to a non-transitory computer readable medium for use on at least one computer system containing computer-executable programming instructions for performing a method for determining cardiovascular information for a patient with coronary artery disease, wherein the method includes receiving patient-specific data regarding a geometry of the patient&#39;s heart; creating a model representing at least a portion of the patient&#39;s heart based on the patient-specific data; creating a physics-based model of blood flow through the patient&#39;s heart simulated during the level of physical activity; determining one or more values of at least one blood flow characteristic within the patient&#39;s heart during the simulated level of physical activity based on the model and the physics-based model; normalizing the determined one or more values of the at least one blood flow characteristic during the simulated level of physical activity; and comparing the one or more normalized values of the at least one blood flow characteristic during the simulated level of physical activity to a threshold to determine whether the level of physical activity exceeds a level identified as an acceptable level of risk. If the one or more normalized values of the at least one blood flow characteristic are above the threshold, the method further comprises identifying a level of physical activity at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk. Optionally, the method may further comprise recommending a level of physical activity appropriate for the patient. If the one or more normalized values of the at least one blood flow characteristic are at or below the threshold, the method further comprises increasing the simulated level of physical activity. In that case, the method may further comprise updating the physics-based model of blood flow through the patient&#39;s heart simulated during the increased level of physical activity. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, the present disclosure relates to a system for evaluating risk associated with physical activity in a patient, wherein the system includes at least one computer system configured to receive data regarding geometry of the patient&#39;s heart; create a three-dimensional, geometric model representing the geometry of at least a portion of the patient&#39;s heart; receive a first physical activity intensity level of the patient; create a physics-based model of blood flow through the patient&#39;s heart simulated at the first physical activity intensity level; calculate at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first physical activity intensity level based on the three-dimensional, geometric model and the physics-based model; and compare the at least one value to a threshold to determine whether the first physical activity intensity level exceeds the threshold. If the at least one value is above the threshold, the at least one computer system is further configured to identify the first physical activity intensity level as exceeding an acceptable level of risk and optionally recommend a third physical activity intensity level appropriate for the patient. If the at least one value is at or below the threshold, the at least one computer system is further configured to receive a second physical activity intensity level of the patient, wherein the second physical activity intensity level is increased relative to the first physical activity intensity level. In that case, the at least one computer system may be configured to update the physics-based model of blood flow through the patient&#39;s heart simulated during the second physical activity intensity level. 
     In accordance with another embodiment, the present disclosure relates to a method for evaluating risk associated with physical activity in a patient using at least one computer system, wherein the method includes inputting into the at least one computer system data regarding geometry of the patient&#39;s heart; creating, using the at least one computer system and the data, a three-dimensional, geometric model representing the geometry of at least a portion of the patient&#39;s heart; selecting a first physical activity intensity level of the patient; creating, using the at least one computer system, a physics-based model of blood flow through the patient&#39;s heart simulated at the selected first physical activity intensity level; calculating, using the at least one computer system, at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first physical activity intensity level based on the three-dimensional, geometric model and the physics-based model; and comparing the at least one value to a threshold to determine whether the first physical activity intensity level exceeds the threshold. If the at least one value is above the threshold, the method further comprises identifying the first physical activity intensity level as exceeding an acceptable level of risk and optionally recommending a third physical activity intensity level appropriate for the patient. If the at least one normalized value is at or below the threshold, the method further comprises selecting a second physical activity intensity level of the patient, wherein the second physical activity intensity level is increased relative to the first physical activity intensity level. In that case, the method may further comprise updating the physics-based model of blood flow through the patient&#39;s heart simulated during the second physical activity intensity level. 
     In accordance with another embodiment, the present disclosure relates to a non-transitory computer readable medium for use on at least one computer system containing computer-executable programming instructions for performing a method for evaluating risk associated with physical activity in a patient, wherein the method includes receiving data regarding geometry of the patient&#39;s heart; creating a three-dimensional, geometric model, using the data, representing the geometry of at least a portion of the patient&#39;s heart; receiving a first physical activity intensity level of the patient; creating a physics-based model of blood flow through the patient&#39;s heart simulated at the first physical activity intensity level; calculating at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first physical activity intensity level based on the three-dimensional, geometric model and the physics-based model; and comparing the at least one value to a threshold to determine whether the first physical activity intensity level exceeds the threshold. If the at least one value is above the threshold, the method further comprises identifying the first physical activity intensity level as exceeding an acceptable level of risk and optionally recommending a third physical activity intensity level appropriate for the patient. If the at least one value is at or below the threshold, the method further comprises receiving a second physical activity intensity level of the patient, wherein the second physical activity intensity level is increased relative to the first physical activity intensity level. In that case, the method may further comprise updating the physics-based model of blood flow through the patient&#39;s heart simulated during the second physical activity intensity level. 
     In accordance with another embodiment, the present disclosure relates to a system for quantifying limitations in coronary artery blood flow during exercise in a patient with coronary artery disease, wherein the system includes at least one computer system configured to create a model representing at least a portion of a patient&#39;s heart, using patient-specific data regarding a geometry of the patient&#39;s heart; create a physics-based model of blood flow through the patient&#39;s heart simulated during a first level of exercise; determine at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first level of exercise based on the model and the physics-based model; normalize the at least one value by relating it to at least one hypothetical value of the at least one blood flow characteristic were the patient without coronary artery disease; and compare the at least one normalized value to at least one threshold value to determine whether the at least one normalized value is above the at least one threshold value, and selectively classify the first exercise level as one at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk. If the at least one normalized value is above the at least one threshold value, the at least one computer system is further configured to recommend a level of exercise appropriate for the patient. If the at least one normalized value is at or below the at least one threshold value, the at least one computer system is further configured to update the physics-based model of blood flow through the patient&#39;s heart simulated during a second level of exercise. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, the present disclosure relates to a method for quantifying limitations in coronary artery blood flow during exercise in a patient with coronary artery disease using at least one computer system, wherein the method includes creating a model representing at least a portion of a patient&#39;s heart, using the at least one computer system and patient-specific data regarding a geometry of the patient&#39;s heart; creating, using the at least one computer system, a physics-based model of blood flow through the patient&#39;s heart simulated during a first level of exercise; determining, using the at least one computer system, at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first level of exercise based on the model and the physics-based model; normalizing the at least one value by relating it to at least one hypothetical value of the at least one blood flow characteristic were the patient without coronary artery disease; and comparing the at least one normalized value to at least one threshold value to determine whether the at least one normalized value is above the at least one threshold value, and selectively classify the first level of exercise as one at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk. If the at least one normalized value is above the at least one threshold value, the method further comprises recommending a level of exercise appropriate for the patient. If the at least one normalized value is at or below the at least one threshold value, the method further includes updating the physics-based model of blood flow through the patient&#39;s heart simulated during a second level of exercise. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, the present disclosure relates to a non-transitory computer readable medium for use on at least one computer system containing computer-executable programming instructions for quantifying limitations in coronary artery blood flow during exercise in a patient with coronary artery disease, wherein the method includes creating a model representing at least a portion of a patient&#39;s heart, using patient-specific data regarding a geometry of the patient&#39;s heart; creating a physics-based model of blood flow through the patient&#39;s heart simulated during a first level of exercise; determining at least one value of at least one blood flow characteristic within the patient&#39;s heart at the first level of exercise based on the model and the physics-based model; normalizing the at least one value by relating it to at least one hypothetical value of the at least one blood flow characteristic were the patient without coronary artery disease; and comparing the at least one normalized value to at least one threshold value to determine whether the at least one normalized value is above the at least one threshold value, and selectively classify the first level of exercise as one at which the at least one blood flow characteristic exceed a level identified as within an acceptable level of risk. If the at least one normalized value is above the at least one threshold value, the method further comprises recommending a level of exercise appropriate for the patient. If the at least one normalized value is at or below the at least one threshold value, the method further includes updating the physics-based model of blood flow through the patient&#39;s heart simulated during a second level of exercise. In at least one embodiment, the model may, for example, include a lumped parameter model, a one-dimensional model, or a three-dimensional model. 
     In accordance with another embodiment, a system for determining cardiovascular information for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry of the patient&#39;s heart and create a three-dimensional model representing at least a portion of the patient&#39;s heart based on the patient-specific data. The at least one computer system is further configured to create a physics-based model relating to a blood flow characteristic of the patient&#39;s heart and determine a fractional flow reserve within the patient&#39;s heart based on the three-dimensional model and the physics-based model. 
     In accordance with another embodiment, a method for determining patient-specific cardiovascular information using at least one computer system includes inputting into the at least one computer system patient-specific data regarding a geometry of the patient&#39;s heart, and creating, using the at least one computer system, a three-dimensional model representing at least a portion of the patient&#39;s heart based on the patient-specific data. The method further includes creating, using the at least one computer system, a physics-based model relating to a blood flow characteristic of the patient&#39;s heart, and determining, using the at least one computer system, a fractional flow reserve within the patient&#39;s heart based on the three-dimensional model and the physics-based model. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on at least one computer system containing computer-executable programming instructions for performing a method for determining patient-specific cardiovascular information is provided. The method includes receiving patient-specific data regarding a geometry of the patient&#39;s heart and creating a three-dimensional model representing at least a portion of the patient&#39;s heart based on the patient-specific data. The method further includes creating a physics-based model relating to a blood flow characteristic in the patient&#39;s heart and determining a fractional flow reserve within the patient&#39;s heart based on the three-dimensional model and the physics-based model. 
     In accordance with another embodiment, a system for planning treatment for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry of an anatomical structure of the patient and create a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The at least one computer system is further configured to determine first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physics-based model relating to the anatomical structure of the patient, modify the three-dimensional model, and determine second information regarding the blood flow characteristic within the anatomical structure of the patient based on the modified three-dimensional model. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for planning treatment for a patient is provided. The method includes receiving patient-specific data regarding a geometry of an anatomical structure of the patient and creating a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method further includes determining first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physics-based model relating to the anatomical structure of the patient, and determining second information regarding the blood flow characteristic within the anatomical structure of the patient based on a desired change in geometry of the anatomical structure of the patient. 
     In accordance with another embodiment, a method for planning treatment for a patient using a computer system includes inputting into at least one computer system patient-specific data regarding a geometry of an anatomical structure of the patient and creating, using the at least one computer system, a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method further includes determining, using the at least one computer system, first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physics-based model relating to the anatomical structure of the patient. The method also includes modifying, using the at least one computer system, the three-dimensional model, and determining, using the at least one computer system, second information regarding the blood flow characteristic within the anatomical structure of the patient based on the modified three-dimensional model. 
     In accordance with another embodiment, a system for planning treatment for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry of an anatomical structure of the patient and create a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The at least one computer system is also configured to determine first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and information regarding a physiological condition of the patient, modify the physiological condition of the patient, and determine second information regarding the blood flow characteristic within the anatomical structure of the patient based on the modified physiological condition of the patient. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for planning treatment for a patient is provided. The method includes receiving patient-specific data regarding a geometry of an anatomical structure of the patient and creating a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method further includes determining first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and information regarding a physiological condition of the patient, and determining second information regarding the blood flow characteristic within the anatomical structure of the patient based on a desired change in the physiological condition of the patient. 
     In accordance with another embodiment, a method for planning treatment for a patient using at least one computer system includes inputting into at least one computer system patient-specific data regarding a geometry of an anatomical structure of the patient, and creating, using the at least one computer system, a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method also includes determining, using the at least one computer system, first information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and information regarding a physiological condition of the patient. The method further includes modifying, using the at least one computer system, the physiological condition of the patient, and determining, using the at least one computer system, second information regarding the blood flow characteristic within the anatomical structure of the patient based on the modified physiological condition of the patient. 
     In accordance with another embodiment, a system for determining patient-specific cardiovascular information includes at least one computer system configured to receive patient-specific data regarding a geometry of an anatomical structure of the patient and create a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The at least one computer system is also configured to determine a total resistance associated with a total flow through the portion of the anatomical structure of the patient and determine information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model, a physics-based model relating to the anatomical structure of the patient, and the determined total resistance. 
     In accordance with another embodiment, a method for determining patient-specific cardiovascular information using at least one computer system includes inputting into the at least one computer system patient-specific data regarding a geometry of an anatomical structure of the patient, and creating, using at least one computer, a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method also includes determining, using at least one computer, a total resistance associated with a total flow through the portion of the anatomical structure of the patient, and determining, using at least one computer, information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model, a physics-based model relating to the anatomical structure of the patient, and the determined total resistance. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for determining patient-specific cardiovascular information is provided. The method includes receiving patient-specific data regarding a geometry of an anatomical structure of the patient and creating a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method also includes determining a total resistance associated with a total flow through the portion of the anatomical structure of the patient and determining information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model, a physics-based model relating to the anatomical structure of the patient, and the determined total resistance. 
     In accordance with another embodiment, a system for providing patient-specific cardiovascular information using a web site includes at least one computer system configured to allow a remote user to access a web site, receive patient-specific data regarding at least a portion of a geometry of an anatomical structure of the patient, create a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data, and determine information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physiological condition of the patient. The at least one computer system is also configured to communicate display information regarding a first three-dimensional simulation of at least the portion of the anatomical structure of the patient to the remote user using the web site. The three-dimensional simulation includes the determined information regarding the blood flow characteristic. 
     In accordance with another embodiment, a method for providing patient-specific cardiovascular information using a web site includes allowing, using at least one computer system, a remote user to access a web site, and receiving, using the at least one computer system, patient-specific data regarding a geometry of an anatomical structure of the patient. The method also includes creating, using the at least one computer system, a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data, and determining, using the at least one computer system, information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physiological condition of the patient. The method further includes communicating, using the at least one computer system, display information regarding a first three-dimensional simulation of at least the portion of the anatomical structure of the patient to the remote user using the web site. The three-dimensional simulation includes the determined information regarding the blood flow characteristic. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for providing patient-specific cardiovascular information using a web site is provided. The method includes allowing a remote user to access a web site, receiving patient-specific data regarding a geometry of an anatomical structure of the patient, and creating a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method also includes determining information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physics-based model relating to the anatomical structure of the patient, and communicating display information regarding a first three-dimensional simulation of at least the portion of the anatomical structure of the patient to the remote user using the web site. The three-dimensional simulation includes the determined information regarding the blood flow characteristic. 
     In accordance with another embodiment, a system for determining patient-specific time-varying cardiovascular information includes at least one computer system configured to receive time-varying patient-specific data regarding a geometry of at least a portion of an anatomical structure of the patient at different times and create a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The at least one computer system is also configured to determine information regarding a change in a blood flow characteristic over time within the anatomical structure of the patient based on the three-dimensional model and a physics-based model relating to the anatomical structure of the patient. 
     In accordance with another embodiment, a method for determining patient-specific time-varying cardiovascular information using at least one computer system includes receiving, using at least one computer system, time-varying patient-specific data regarding a geometry of an anatomical structure of the patient at different times. The method also includes creating, using the at least one computer system, a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data. The method further includes determining, using the at least one computer system, information regarding a change in a blood flow characteristic over time within the anatomical structure of the patient based on the three-dimensional model and the information regarding a physics-based model relating to the anatomical structure of the patient. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for determining patient-specific time-varying cardiovascular information is provided. The method includes receiving time-varying patient-specific data regarding a geometry of an anatomical structure of the patient at different times, creating a three-dimensional model representing at least a portion of the anatomical structure of the patient based on the patient-specific data, and determining information regarding a change in a blood flow characteristic over time within the anatomical structure of the patient based on the three-dimensional model and the information regarding a physics-based model relating to the anatomical structure of the patient. 
     In accordance with another embodiment, a system for determining cardiovascular information for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry and at least one material property of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a blood vessel. The at least one computer system is further configured to create a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, and determine information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physiological condition of the patient. The at least one computer system is also configured to identify a location of a plaque within the blood vessel. 
     In accordance with another embodiment, a method for determining cardiovascular information for a patient using at least one computer system includes receiving, using at least one computer system, patient-specific data regarding a geometry and at least one material property of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a blood vessel. The method also includes creating, using the at least one computer system, a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, and determining, using the at least one computer system, information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physiological condition of the patient. The method further includes identifying, using the at least one computer system, a plaque within the blood vessel. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for determining cardiovascular information for a patient is provided. The method includes receiving patient-specific data regarding a geometry and at least one material property of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a blood vessel. The method also includes creating a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, determining information regarding a blood flow characteristic within the anatomical structure of the patient based on the three-dimensional model and a physiological condition of the patient, and identifying a location of a plaque within the blood vessel. 
     In accordance with another embodiment, a system for determining cardiovascular information for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a plurality of arteries and tissue connected to at least a portion of the plurality of arteries. The at least one computer system is further configured to create a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, divide at least a portion of the three-dimensional model representing the tissue into segments, and determine information regarding a blood flow characteristic associated with at least one of the segments based on the three-dimensional model and a physiological condition of the patient. 
     In accordance with another embodiment, a method for determining cardiovascular information for a patient using at least one computer system includes receiving, using at least one computer system, patient-specific data regarding a geometry of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a plurality of arteries and tissue connected to at least a portion of the plurality of arteries. The method also includes creating, using the at least one computer system, a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, and extending, using the at least one computer system, the three-dimensional model to form an augmented model. The method further includes dividing, using the at least one computer system, at least a portion of the augmented model representing the tissue into segments, and determining, using the at least one computer system, information regarding a blood flow characteristic associated with at least one of the segments based on the augmented model and a physiological condition of the patient. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on a computer system containing computer-executable programming instructions for performing a method for determining cardiovascular information for a patient is provided. The method includes receiving patient-specific data regarding a geometry of at least a portion of an anatomical structure of the patient. The anatomical structure includes at least a portion of a plurality of arteries and tissue connected to at least a portion of the plurality of arteries. The method also includes creating a three-dimensional model representing the anatomical structure of the patient based on the patient-specific data, dividing at least a portion of the three-dimensional model representing the tissue into segments, and determining information regarding a blood flow characteristic associated with at least one of the segments based on the three-dimensional model and a physics-based model relating to the anatomical structure. 
     In accordance with another embodiment, a system for determining cardiovascular information for a patient includes at least one computer system configured to receive patient-specific data regarding a geometry of the patient&#39;s brain. The at least one computer system is further configured to create a three-dimensional model representing at least a portion of the patient&#39;s brain based on the patient-specific data, and determine information regarding a blood flow characteristic within the patient&#39;s brain based on the three-dimensional model and a physics-based model relating to the patient&#39;s brain. 
     In accordance with another embodiment, a method for determining patient-specific cardiovascular information using at least one computer system includes inputting into the at least one computer system patient-specific data regarding a geometry of at least a portion of a plurality of cerebral arteries of the patient. The method also includes creating, using the at least one computer system, a three-dimensional model representing at least the portion of the cerebral arteries of the patient based on the patient-specific data, and determining, using the at least one computer system, information regarding a blood flow characteristic within the cerebral arteries of the patient based on the three-dimensional model and a physics-based model relating to the cerebral arteries of the patient. 
     In accordance with another embodiment, a non-transitory computer readable medium for use on at least one computer system containing computer-executable programming instructions for performing a method for determining patient-specific cardiovascular information is provided. The method includes receiving patient-specific data regarding a geometry of the patient&#39;s brain, creating a three-dimensional model representing at least a portion of the patient&#39;s brain based on the patient-specific data, and determining information regarding a blood flow characteristic within the patient&#39;s brain based on the three-dimensional model and a physics-based model relating to the patient&#39;s brain. 
     Additional embodiments and advantages will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the disclosure. The embodiments and advantages will be realized and attained by means of the elements and combinations particularly pointed out below. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate several embodiments and together with the description, serve to explain the principles of the disclosure. 
         FIG.  1    is a schematic diagram of a system for providing various information relating to coronary blood flow in a specific patient, according to an exemplary embodiment; 
         FIG.  2    is a flow chart of a method for providing various information relating to blood flow in a specific patient, according to an exemplary embodiment; 
         FIG.  3    is a flow chart showing the substeps of the method of  FIG.  2   ; 
         FIG.  4    shows imaging data obtained noninvasively from a patient, according to an exemplary embodiment; 
         FIG.  5    shows an exemplary three-dimensional model generated using the imaging data of  FIG.  4   ; 
         FIG.  6    shows a portion of a slice of the imaging data of  FIG.  4    including seeds for forming a first initial model; 
         FIG.  7    shows a portion of the first initial model formed by expanding the seeds of  FIG.  6   ; 
         FIG.  8    shows a trimmed solid model, according to an exemplary embodiment; 
         FIG.  9    shows an exemplary computed FFR (cFFR) model when the patient is at rest; 
         FIG.  10    shows an exemplary cFFR model when the patient is under maximum hyperemia; 
         FIG.  11    shows an exemplary cFFR model when the patient is under maximum exercise; 
         FIG.  12    shows a portion of a trimmed solid model provided for forming a lumped parameter model, according to an exemplary embodiment; 
         FIG.  13    shows a portion of the centerlines for the trimmed solid model of  FIG.  12   , provided for forming a lumped parameter model; 
         FIG.  14    shows segments formed based on the trimmed solid model of  FIG.  12   , provided for forming a lumped parameter model; 
         FIG.  15    shows the segments of  FIG.  14    replaced by resistors, provided for forming a lumped parameter model; 
         FIG.  16    shows exemplary lumped parameter models representing the upstream and downstream structures at the inflow and outflow boundaries of a solid model, according to an exemplary embodiment; 
         FIG.  17    shows a three-dimensional mesh prepared based on the solid model of  FIG.  8   ; 
         FIGS.  18  and  19    show portions of the three-dimensional mesh of  FIG.  17   ; 
         FIG.  20    shows a model of the patient&#39;s anatomy including blood flow information with certain points on the model identified by individual reference labels; 
         FIG.  21    is a graph of simulated blood pressure over time in the aorta and at some of the points identified in  FIG.  20   ; 
         FIG.  22    is a graph of simulated blood flow over time at each of the points identified in  FIG.  20   ; 
         FIG.  23    is a finalized report, according to an exemplary embodiment; 
         FIG.  24 A  is a flow chart of a method for providing various information relating to coronary blood flow in a specific patient, according to an exemplary embodiment; 
         FIG.  24 B  is a flow chart of a method for providing various information relating to coronary blood flow in a specific patient during physical activity, according to an exemplary embodiment; 
         FIG.  25    shows a modified cFFR model determined based on a solid model created by widening a portion of the left anterior descending (LAD) artery and a portion of the LCX artery, according to an exemplary embodiment; 
         FIG.  26    shows an example of a modified simulated blood flow model after widening a portion of the LAD artery and a portion of the left circumflex (LCX) artery, according to an exemplary embodiment; 
         FIG.  27    is a flow chart of a method for simulating various treatment options using a reduced order model, according to an exemplary embodiment; 
         FIG.  28    is a flow chart of a method for simulating various treatment options using a reduced order model, according to another exemplary embodiment; 
         FIG.  29    is a flow chart of a method for providing various information relating to myocardial perfusion in a specific patient, according to an exemplary embodiment; 
         FIG.  30    is a flow chart of a method for providing various information relating to myocardial perfusion in a specific patient, according to another exemplary embodiment; 
         FIG.  31    shows a patient-specific model providing various information relating to myocardial perfusion, according to an exemplary embodiment; 
         FIG.  32    is a flow chart of a method for providing various information relating to myocardial perfusion in a specific patient, according to a further exemplary embodiment; 
         FIG.  33    is a cross-sectional view of plaque built up along a blood vessel wall; 
         FIG.  34    shows a patient-specific model providing various information relating to plaque vulnerability, according to an exemplary embodiment; 
         FIG.  35    is a flow chart of a method for providing various information relating to assessing plaque vulnerability, myocardial volume risk, and myocardial perfusion risk in a specific patient, according to an exemplary embodiment; 
         FIG.  36    is a schematic diagram showing information obtained from the method of  FIG.  35   , according to an exemplary embodiment; 
         FIG.  37    is a diagram of cerebral arteries; 
         FIG.  38    is a flow chart of a method for providing various information relating to intracranial and extracranial blood flow in a specific patient, according to an exemplary embodiment; 
         FIG.  39    is a flow chart of a method for providing various information relating to cerebral perfusion in a specific patient, according to an exemplary embodiment; 
         FIG.  40    is a flow chart of a method for providing various information relating to cerebral perfusion in a specific patient, according to another exemplary embodiment; 
         FIG.  41    is a flow chart of a method for providing various information relating to cerebral perfusion in a specific patient, according to a further exemplary embodiment; and 
         FIG.  42    is a flow chart of a method for providing various information relating to assessing plaque vulnerability, cerebral volume risk, and cerebral perfusion risk in a specific patient, according to an exemplary embodiment. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Reference will now be made in detail to exemplary embodiments, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers will be used throughout the drawings to refer to the same or like parts. This description is organized according to the following outline:
         I. Overview   II. Obtaining and Preprocessing Patient-Specific Anatomical Data   III. Creating The Three-Dimensional Model Based On Obtained Anatomical Data   IV. Preparing The Model For Analysis and Determining Boundary Conditions
           A. Preparing the Model For Analysis   B. Determining Boundary Conditions
               i. Determining Reduced Order Models   ii. Exemplary Lumped Parameter Models   
               C. Creating the Three-Dimensional Mesh   
           V. Performing The Computational Analysis And Outputting Results
           A. Performing the Computational Analysis   B. Displaying Results for Blood Pressure, Flow, and cFFR   C. Verifying Results   D. Another Embodiment of a System and Method for Providing Coronary Blood Flow Information   E. Exemplary Embodiment of a System and Method for Providing Coronary Blood Flow Information in a Patient During Physical Activity   
           VI. Providing Patient-Specific Treatment Planning
           A. Using Reduced Order Models to Compare Different Treatment Options   
           VII. Other Results
           A. Assessing Myocardial Perfusion   B. Assessing Plaque Vulnerability   
           VIII. Other Applications
           A. Modeling Intracranial and Extracranial Blood Flow
               i. Assessing Cerebral Perfusion   ii. Assessing Plaque Vulnerability   
               
               

     I. Overview 
     In an exemplary embodiment, a method and system determines various information relating to blood flow in a specific patient using information retrieved from the patient noninvasively. The determined information may relate to blood flow in the patient&#39;s coronary vasculature. Alternatively, as will be described below in further detail, the determined information may relate to blood flow in other areas of the patient&#39;s vasculature, such as carotid, peripheral, abdominal, renal, and cerebral vasculature. The coronary vasculature includes a complex network of vessels ranging from large arteries to arterioles, capillaries, venules, veins, etc. The coronary vasculature circulates blood to and within the heart and includes an aorta  2  ( FIG.  5   ) that supplies blood to a plurality of main coronary arteries  4  ( FIG.  5   ) (e.g., the left anterior descending (LAD) artery, the left circumflex (LCX) artery, the right coronary (RCA) artery, etc.), which may further divide into branches of arteries or other types of vessels downstream from the aorta  2  and the main coronary arteries  4 . Thus, the exemplary method and system may determine various information relating to blood flow within the aorta, the main coronary arteries, and/or other coronary arteries or vessels downstream from the main coronary arteries. Although the aorta and coronary arteries (and the branches that extend therefrom) are discussed below, the disclosed method and system may also apply to other types of vessels. 
     In an exemplary embodiment, the information determined by the disclosed methods and systems may include, but is not limited to, various blood flow characteristics or parameters, such as blood flow velocity, pressure (or a ratio thereof), flow rate, and FFR at various locations in the aorta, the main coronary arteries, and/or other coronary arteries or vessels downstream from the main coronary arteries. This information may be used to determine whether a lesion is functionally significant and/or whether to treat the lesion. This information may be determined using information obtained noninvasively from the patient. As a result, the decision whether to treat a lesion may be made without the cost and risk associated with invasive procedures. 
       FIG.  1    shows aspects of a system for providing various information relating to coronary blood flow in a specific patient, according to an exemplary embodiment. A three-dimensional model  10  of the patient&#39;s anatomy may be created using data obtained noninvasively from the patient as will be described below in more detail. Other patient-specific information may also be obtained noninvasively. In an exemplary embodiment, the portion of the patient&#39;s anatomy that is represented by the three-dimensional model  10  may include at least a portion of the aorta and a proximal portion of the main coronary arteries (and the branches extending or emanating therefrom) connected to the aorta. 
     Various physiological laws or relationships  20  relating to coronary blood flow may be deduced, e.g., from experimental data as will be described below in more detail. Using the three-dimensional anatomical model  10  and the deduced physiological laws  20 , a plurality of equations  30  relating to coronary blood flow may be determined as will be described below in more detail. For example, the equations  30  may be determined and solved using any numerical method, e.g., finite difference, finite volume, spectral, lattice Boltzmann, particle-based, level set, finite element methods, etc. The equations  30  may be solvable to determine information (e.g., pressure, velocity, FFR, etc.) about the coronary blood flow in the patient&#39;s anatomy at various points in the anatomy represented by the model  10 . 
     The equations  30  may be solved using a computer  40 . Based on the solved equations, the computer  40  may output one or more images or simulations indicating information relating to the blood flow in the patient&#39;s anatomy represented by the model  10 . For example, the image(s) may include a simulated blood pressure model  50 , a simulated blood flow or velocity model  52 , a computed FFR (cFFR) model  54 , etc., as will be described in further detail below. The simulated blood pressure model  50 , the simulated blood flow model  52 , and the cFFR model  54  provide information regarding the respective pressure, velocity, and cFFR at various locations along three dimensions in the patient&#39;s anatomy represented by the model  10 . cFFR may be calculated as the ratio of the blood pressure at a particular location in the model  10  divided by the blood pressure in the aorta, e.g., at the inflow boundary of the model  10 , under conditions of increased coronary blood flow, e.g., conventionally induced by intravenous administration of adenosine. 
     In an exemplary embodiment, the computer  40  may include one or more non-transitory computer-readable storage devices that store instructions that, when executed by a processor, computer system, etc., may perform any of the actions described herein for providing various information relating to blood flow in the patient. The computer  40  may include a desktop or portable computer, a workstation, a server, a personal digital assistant, or any other computer system. The computer  40  may include a processor, a read-only memory (ROM), a random access memory (RAM), an input/output (I/O) adapter for connecting peripheral devices (e.g., an input device, output device, storage device, etc.), a user interface adapter for connecting input devices such as a keyboard, a mouse, a touch screen, a voice input, and/or other devices, a communications adapter for connecting the computer  40  to a network, a display adapter for connecting the computer  40  to a display, etc. For example, the display may be used to display the three-dimensional model  10  and/or any images generated by solving the equations  30 , such as the simulated blood pressure model  50 , the simulated blood flow model  52 , and/or the cFFR model  54 . 
       FIG.  2    shows aspects of a method for providing various information relating to blood flow in a specific patient, according to another exemplary embodiment. The method may include obtaining patient-specific anatomical data, such as information regarding the patient&#39;s anatomy (e.g., at least a portion of the aorta and a proximal portion of the main coronary arteries (and the branches extending therefrom) connected to the aorta), and preprocessing the data (step  100 ). The patient-specific anatomical data may be obtained noninvasively, e.g., by CCTA, as will be described below. 
     A three-dimensional model of the patient&#39;s anatomy may be created based on the obtained anatomical data (step  200 ). For example, the three-dimensional model may be the three-dimensional model  10  of the patient&#39;s anatomy described above in connection with  FIG.  1   . 
     The three-dimensional model may be prepared for analysis and boundary conditions may be determined (step  300 ). For example, the three-dimensional model  10  of the patient&#39;s anatomy described above in connection with  FIG.  1    may be trimmed and discretized into a volumetric mesh, e.g., a finite element or finite volume mesh. The volumetric mesh may be used to generate the equations  30  described above in connection with  FIG.  1   . 
     Boundary conditions may also be assigned and incorporated into the equations  30  described above in connection with  FIG.  1   . The boundary conditions provide information about the three-dimensional model  10  at its boundaries, e.g., the inflow boundaries  322  ( FIG.  8   ), the outflow boundaries  324  ( FIG.  8   ), the vessel wall boundaries  326  ( FIG.  8   ), etc. The inflow boundaries  322  may include the boundaries through which flow is directed into the anatomy of the three-dimensional model, such as at an end of the aorta near the aortic root (e.g., end A shown in  FIG.  16   ). Each inflow boundary  322  may be assigned, e.g., with a prescribed value or field for velocity, flow rate, pressure, or other characteristic, by coupling a heart model and/or a lumped parameter model to the boundary, etc. The outflow boundaries  324  may include the boundaries through which flow is directed outward from the anatomy of the three-dimensional model, such as at an end of the aorta near the aortic arch (e.g., end B shown in  FIG.  16   ), and the downstream ends of the main coronary arteries and the branches that extend therefrom (e.g., ends a-m shown in  FIG.  16   ). Each outflow boundary can be assigned, e.g., by coupling a lumped parameter or distributed (e.g., a one-dimensional wave propagation) model, as will be described in detail below. The prescribed values for the inflow and/or outflow boundary conditions may be determined by noninvasively measuring physiologic characteristics of the patient, such as, but not limited to, cardiac output (the volume of blood flow from the heart), blood pressure, myocardial mass, etc. The vessel wall boundaries may include the physical boundaries of the aorta, the main coronary arteries, and/or other coronary arteries or vessels of the three-dimensional model  10 . 
     The computational analysis may be performed using the prepared three-dimensional model and the determined boundary conditions (step  400 ) to determine blood flow information for the patient. For example, the computational analysis may be performed with the equations  30  and using the computer  40  described above in connection with  FIG.  1    to produce the images described above in connection with  FIG.  1   , such as the simulated blood pressure model  50 , the simulated blood flow model  52 , and/or the cFFR model  54 . 
     The method may also include providing patient-specific treatment options using the results (step  500 ). For example, the three-dimensional model  10  created in step  200  and/or the boundary conditions assigned in step  300  may be adjusted to model one or more treatments, e.g., placing a coronary stent in one of the coronary arteries represented in the three-dimensional model  10  or other treatment options. Then, the computational analysis may be performed as described above in step  400  in order to produce new images, such as updated versions of the blood pressure model  50 , the blood flow model  52 , and/or the cFFR model  54 . These new images may be used to determine a change in blood flow velocity and pressure if the treatment option(s) are adopted. 
     The systems and methods disclosed herein may be incorporated into a software tool accessed by physicians to provide a noninvasive means to quantify blood flow in the coronary arteries and to assess the functional significance of coronary artery disease. In addition, physicians may use the software tool to predict the effect of medical, interventional, and/or surgical treatments on coronary artery blood flow. The software tool may prevent, diagnose, manage, and/or treat disease in other portions of the cardiovascular system including arteries of the neck (e.g., carotid arteries), arteries in the head (e.g., cerebral arteries), arteries in the thorax, arteries in the abdomen (e.g., the abdominal aorta and its branches), arteries in the arms, or arteries in the legs (e.g., the femoral and popliteal arteries). The software tool may be interactive to enable physicians to develop optimal personalized therapies for patients. 
     For example, the software tool may be incorporated at least partially into a computer system, e.g., the computer  40  shown in  FIG.  1    used by a physician or other user. The computer system may receive data obtained noninvasively from the patient (e.g., data used to create the three-dimensional model  10 , data used to apply boundary conditions or perform the computational analysis, etc.). For example, the data may be input by the physician or may be received from another source capable of accessing and providing such data, such as a radiology or other medical lab. The data may be transmitted via a network or other system for communicating the data, or directly into the computer system. The software tool may use the data to produce and display the three-dimensional model  10  or other models/meshes and/or any simulations or other results determined by solving the equations  30  described above in connection with  FIG.  1   , such as the simulated blood pressure model  50 , the simulated blood flow model  52 , and/or the cFFR model  54 . Thus, the software tool may perform steps  100 - 500 . In step  500 , the physician may provide further inputs to the computer system to select possible treatment options, and the computer system may display to the physician new simulations based on the selected possible treatment options. Further, each of steps  100 - 500  shown in  FIG.  2    may be performed using separate software packages or modules. 
     Alternatively, the software tool may be provided as part of a web-based service or other service, e.g., a service provided by an entity that is separate from the physician. The service provider may, for example, operate the web-based service and may provide a web portal or other web-based application (e.g., run on a server or other computer system operated by the service provider) that is accessible to physicians or other users via a network or other methods of communicating data between computer systems. For example, the data obtained noninvasively from the patient may be provided to the service provider, and the service provider may use the data to produce the three-dimensional model  10  or other models/meshes and/or any simulations or other results determined by solving the equations  30  described above in connection with  FIG.  1   , such as the simulated blood pressure model  50 , the simulated blood flow model  52 , and/or the cFFR model  54 . Then, the web-based service may transmit information relating to the three-dimensional model  10  or other models/meshes and/or the simulations so that the three-dimensional model  10  and/or the simulations may be displayed to the physician on the physician&#39;s computer system. Thus, the web-based service may perform steps  100 - 500  and any other steps described below for providing patient-specific information. In step  500 , the physician may provide further inputs, e.g., to select possible treatment options or make other adjustments to the computational analysis, and the inputs may be transmitted to the computer system operated by the service provider (e.g., via the web portal). The web-based service may produce new simulations or other results based on the selected possible treatment options, and may communicate information relating to the new simulations back to the physician so that the new simulations may be displayed to the physician. 
     It is to be understood that one or more of the steps described herein may be performed by one or more human operators (e.g., a cardiologist or other physician, the patient, an employee of the service provider providing the web-based service or other service provided by a third party, other user, etc.), or one or more computer systems used by such human operator(s), such as a desktop or portable computer, a workstation, a server, a personal digital assistant, etc. The computer system(s) may be connected via a network or other method of communicating data. 
       FIG.  3    shows further aspects of the exemplary method for providing various information relating to blood flow in a specific patient. The aspects shown in  FIG.  3    may be incorporated into the software tool that may be incorporated at least partially into a computer system and/or as part of a web-based service. 
     II. Obtaining and Preprocessing Patient-Specific Anatomical Data 
     As described above in connection with step  100  shown in  FIG.  2   , the exemplary method may include obtaining patient-specific anatomical data, such as information regarding the patient&#39;s heart, and preprocessing the data. In an exemplary embodiment, step  100  may include the following steps. 
     Initially, a patient may be selected. For example, the patient may be selected by the physician when the physician determines that information about the patient&#39;s coronary blood flow is desired, e.g., if the patient is experiencing symptoms associated with coronary artery disease, such as chest pain, heart attack, etc. 
     Patient-specific anatomical data may be obtained, such as data regarding the geometry of the patient&#39;s heart, e.g., at least a portion of the patient&#39;s aorta, a proximal portion of the main coronary arteries (and the branches extending therefrom) connected to the aorta, and the myocardium. The patient-specific anatomical data may be obtained noninvasively, e.g., using a noninvasive imaging method. For example, CCTA is an imaging method in which a user may operate a computer tomography (CT) scanner to view and create images of structures, e.g., the myocardium, the aorta, the main coronary arteries, and other blood vessels connected thereto. The CCTA data may be time-varying, e.g., to show changes in vessel shape over a cardiac cycle. CCTA may be used to produce an image of the patient&#39;s heart. For example, 64-slice CCTA data may be obtained, e.g., data relating to 64 slices of the patient&#39;s heart, and assembled into a three-dimensional image.  FIG.  4    shows an example of a three-dimensional image  120  produced by the 64-slice CCTA data. 
     Alternatively, other noninvasive imaging methods, such as magnetic resonance imaging (MRI) or ultrasound (US), or invasive imaging methods, such as digital subtraction angiography (DSA), may be used to produce images of the structures of the patient&#39;s anatomy. The imaging methods may involve injecting the patient intravenously with a contrast agent to enable identification of the structures of the anatomy. The resulting imaging data (e.g., provided by CCTA, MRI, etc.) may be provided by a third-party vendor, such as a radiology lab or a cardiologist, by the patient&#39;s physician, etc. 
     Other patient-specific anatomical data may also be determined from the patient noninvasively. For example, physiological data such as the patient&#39;s blood pressure, baseline heart rate, height, weight, hematocrit, stroke volume, etc., may be measured. The blood pressure may be the blood pressure in the patient&#39;s brachial artery (e.g., using a pressure cuff), such as the maximum (systolic) and minimum (diastolic) pressures. 
     The patient-specific anatomical data obtained as described above may be transferred over a secure communication line (e.g., via a network). For example, the data may be transferred to a server or other computer system for performing the computational analysis, e.g., the computational analysis described above in step  400 . In an exemplary embodiment, the data may be transferred to a server or other computer system operated by a service provider providing a web-based service. Alternatively, the data may be transferred to a computer system operated by the patient&#39;s physician or other user. 
     Referring back to  FIG.  3   , the transferred data may be reviewed to determine if the data is acceptable (step  102 ). The determination may be performed by the user and/or by the computer system. For example, the transferred data (e.g., the CCTA data and other data) may be verified by a user and/or by the computer system, e.g., to determine if the CCTA data is complete (e.g., includes sufficient portions of the aorta and the main coronary arteries) and corresponds to the correct patient. 
     The transferred data (e.g., the CCTA data and other data) may also be preprocessed and assessed. The preprocessing and/or assessment may be performed by a user and/or by the computer system and may include, e.g., checking for misregistration, inconsistencies, or blurring in the CCTA data, checking for stents shown in the CCTA data, checking for other artifacts that may prevent the visibility of lumens of the blood vessels, checking for sufficient contrast between the structures (e.g., the aorta, the main coronary arteries, and other blood vessels) and the other portions of the patient, etc. 
     The transferred data may be evaluated to determine if the data is acceptable based on the verification, preprocessing, and/or assessment described above. During the verification, preprocessing, and/or assessment described above, the user and/or computer system may be able to correct certain errors or problems with the data. If, however, there are too many errors or problems, then the data may be determined to be unacceptable, and the user and/or computer system may generate a rejection report explaining the errors or problems necessitating the rejection of the transferred data. Optionally, a new CCTA scan may be performed and/or the physiological data described above may be measured from the patient again. If the transferred data is determined to be acceptable, then the method may proceed to step  202  described below. 
     Accordingly, step  102  shown in  FIG.  3    and described above may be considered as a substep of step  100  of  FIG.  2   . 
     III. Creating the Three-Dimensional Model Based on Obtained Anatomical Data 
     As described above in connection with step  200  shown in  FIG.  2   , the exemplary method may include creating the three-dimensional model based on the obtained anatomical data. In an exemplary embodiment, step  200  may include the following steps. 
     Using the CCTA data, a three-dimensional model of the coronary vessels may be generated.  FIG.  5    shows an example of the surface of a three-dimensional model  220  generated using the CCTA data. For example, the model  220  may include, e.g., at least a portion of the aorta, at least a proximal portion of one or more main coronary arteries connected to that portion of the aorta, at least a proximal portion of one or more branches connected to the main coronary arteries, etc. The modeled portions of the aorta, the main coronary arteries, and/or the branches may be interconnected and treelike such that no portion is disconnected from the rest of the model  220 . The process of forming the model  220  is called segmentation. 
     Referring back to  FIG.  3   , the computer system may automatically segment at least a portion of the aorta (step  202 ) and the myocardium (or other heart tissue, or other tissue connected to the arteries to be modeled) (step  204 ). The computer system may also segment at least a portion of the main coronary arteries connected to the aorta. In an exemplary embodiment, the computer system may allow the user to select one or more coronary artery root or starting points (step  206 ) in order to segment the main coronary arteries. 
     Segmentation may be performed using various methods. Segmentation may be performed automatically by the computer system based on user inputs or without user inputs. For example, in an exemplary embodiment, the user may provide inputs to the computer system in order to generate a first initial model. For example, the computer system may display to the user the three-dimensional image  120  ( FIG.  4   ) or slices thereof produced from the CCTA data. The three-dimensional image  120  may include portions of varying intensity of lightness. For example, lighter areas may indicate the lumens of the aorta, the main coronary arteries, and/or the branches. Darker areas may indicate the myocardium and other tissue of the patient&#39;s heart. 
       FIG.  6    shows a portion of a slice  222  of the three-dimensional image  120  that may be displayed to the user, and the slice  222  may include an area  224  of relative lightness. The computer system may allow the user to select the area  224  of relative lightness by adding one or more seeds  226 , and the seeds  226  may serve as coronary artery root or starting points for segmenting the main coronary arteries. At the command of the user, the computer system may then use the seeds  226  as starting points to form the first initial model. The user may add seeds  226  in one or more of the aorta and/or the individual main coronary arteries. Optionally, the user may also add seeds  226  in one or more of the branches connected to the main coronary arteries. Alternatively, the computer system may place the seeds automatically, e.g., using extracted centerline information. The computer system may determine an intensity value of the image  120  where the seeds  226  have been placed and may form the first initial model by expanding the seeds  226  along the portions of the image  120  having the same intensity value (or within a range or threshold of intensity values centered at the selected intensity value). Thus, this method of segmentation may be called “threshold-based segmentation.” 
       FIG.  7    shows a portion  230  of the first initial model that is formed by expanding the seeds  226  of  FIG.  6   . Accordingly, the user inputs the seeds  226  as starting points for the computer system to begin forming the first initial model. This process may be repeated until the entire portions of interest, e.g., the portions of the aorta and/or the main coronary arteries, are segmented. Alternatively, the first initial model may be generated by the computer system without user inputs. 
     Alternatively, segmentation may be performed using a method called “edge-based segmentation.” In an exemplary embodiment, both the threshold-based and edge-based segmentation methods may be performed, as will be described below, to form the model  220 . 
     A second initial model may be formed using the edge-based segmentation method. With this method, the lumen edges of the aorta and/or the main coronary arteries may be located. For example, in an exemplary embodiment, the user may provide inputs to the computer system, e.g., the seeds  226  as described above, in order to generate the second initial model. The computer system may expand the seeds  226  along the portions of the image  120  until the edges are reached. The lumen edges may be located, e.g., by the user visually, and/or by the computer system (e.g., at locations where there is a change in intensity value above a set threshold). The edge-based segmentation method may be performed by the computer system and/or the user. 
     The myocardium or other tissue may also be segmented based on the CCTA data in step  204 . For example, the CCTA data may be analyzed to determine the location of the internal and external surfaces of the myocardium, e.g., the left and/or right ventricles. The locations of the surfaces may be determined based on the contrast (e.g., relative darkness and lightness) of the myocardium compared to other structures of the heart in the CCTA data. Thus, the geometry of the myocardium may be determined. 
     The segmentation of the aorta, the myocardium, and/or the main coronary arteries may be reviewed and/or corrected, if necessary (step  208 ). The review and/or correction may be performed by the computer system and/or the user. For example, in an exemplary embodiment, the computer system may automatically review the segmentation, and the user may manually correct the segmentation if there are any errors, e.g., if any portions of the aorta, the myocardium, and/or the main coronary arteries in the model  220  are missing or inaccurate. 
     For example, the first and second initial models described above may be compared to ensure that the segmentation of the aorta and/or the main coronary arteries is accurate. Any areas of discrepancy between the first and second initial models may be compared to correct the segmentation and to form the model  220 . For example, the model  220  may be an average between the first and second initial models. Alternatively, only one of the segmentation methods described above may be performed, and the initial model formed by that method may be used as the model  220 . 
     The myocardial mass may be calculated (step  240 ). The calculation may be performed by the computer system. For example, the myocardial volume may be calculated based on the locations of the surfaces of the myocardium determined as described above, and the calculated myocardial volume may be multiplied by the density of the myocardium to calculate the myocardial mass. The density of the myocardium may be preset. 
     The centerlines of the various vessels (e.g., the aorta, the main coronary arteries, etc.) of the model  220  ( FIG.  5   ) may be determined (step  242 ). In an exemplary embodiment, the determination may be performed automatically by the computer system. 
     The centerlines determined in step  242  may be reviewed and/or corrected, if necessary (step  244 ). The review and/or correction may be performed by the computer system and/or the user. For example, in an exemplary embodiment, the computer system may automatically review the centerlines, and the user may manually correct the centerlines if there are any errors, e.g., if any centerlines are missing or inaccurate. 
     Calcium or plaque (causing narrowing of a vessel) may be detected (step  246 ). In an exemplary embodiment, the computer system may automatically detect the plaque. For example, the plaque may be detected in the three-dimensional image  120  and removed from the model  220 . The plaque may be identified in the three-dimensional image  120  since the plaque appears as areas that are even lighter than the lumens of the aorta, the main coronary arteries, and/or the branches. Thus, the plaque may be detected by the computer system as having an intensity value below a set value or may be detected visually by the user. After detecting the plaque, the computer system may remove the plaque from the model  220  so that the plaque is not considered as part of the lumen or open space in the vessels. Alternatively, the computer system may indicate the plaque on the model  220  using a different color, shading, or other visual indicator than the aorta, the main coronary arteries, and/or the branches. 
     The computer system may also automatically segment the detected plaque (step  248 ). For example, the plaque may be segmented based on the CCTA data. The CCTA data may be analyzed to locate the plaque (or a surface thereof) based on the contrast (e.g., relative darkness and lightness) of the plaque compared to other structures of the heart in the CCTA data. Thus, the geometry of the plaque may also be determined. 
     The segmentation of the plaque may be reviewed and/or corrected, if necessary (step  250 ). The review and/or correction may be performed by the computer system and/or the user. For example, in an exemplary embodiment, the computer system may automatically review the segmentation, and the user may manually correct the segmentation if there are any errors, e.g., if any plaque is missing or shown inaccurately. 
     The computer system may automatically segment the branches connected to the main coronary arteries (step  252 ). For example, the branches may be segmented using similar methods for segmenting the main coronary arteries, e.g., as shown in  FIGS.  6  and  7    and described above in connection with step  206 . The computer system may also automatically segment the plaque in the segmented branches using similar methods as described above in connection with steps  248  and  250 . Alternatively, the branches (and any plaque contained therein) may be segmented at the same time as the main coronary arteries (e.g., in step  206 ). 
     The segmentation of the branches may be reviewed and/or corrected, if necessary (step  254 ). The review and/or correction may be performed by the computer system and/or the user. For example, in an exemplary embodiment, the computer system may automatically review the segmentation, and the user may manually correct the segmentation if there are any errors, e.g., if any portions of the branches in the model  220  are missing or inaccurate. 
     The model  220  may be corrected if any misregistration, stents, or other artifacts are located (e.g., during the review of the CCTA data in step  102 ) (step  256 ). The correction may be performed by a user and/or by the computer system. For example, if a misregistration or other artifact (e.g., inconsistency, blurring, an artifact affecting lumen visibility, etc.) is located, the model  220  may be reviewed and/or corrected to avoid an artificial or false change in the cross-sectional area of a vessel (e.g., an artificial narrowing). If a stent is located, the model  220  may be reviewed and/or corrected to indicate the location of the stent and/or to correct the cross-sectional area of the vessel where the stent is located, e.g., based on the size of the stent. 
     The segmentation of the model  220  may also be independently reviewed (step  258 ). The review may be performed by a user and/or by the computer system. For example, the user and/or computer system may be able to identify certain errors with the model  220 , such as correctable errors and/or errors that may require the model  220  to be at least partially redone or resegmented. If such errors are identified, then the segmentation may be determined to be unacceptable, and certain steps, e.g., one or more of steps  202 - 208 ,  240 - 256 , depending on the error(s), may be repeated. 
     If the segmentation of the model  220  is independently verified as acceptable, then, optionally, the model  220  may be output and smoothed (step  260 ). The smoothing may be performed by the user and/or by the computer system. For example, ridges, points, or other discontinuous portions may be smoothed. The model  220  may be output to a separate software module to be prepared for computational analysis, etc. 
     Accordingly, steps  202 - 208  and  240 - 260  shown in  FIG.  3    and described above may be considered as substeps of step  200  of  FIG.  2   . 
     IV. Preparing the Model for Analysis and Determining Boundary Conditions 
     As described above in connection with step  300  shown in  FIG.  2   , the exemplary method may include preparing the model for analysis and determining boundary conditions. In an exemplary embodiment, step  300  may include the following steps. 
     A. Preparing the Model for Analysis 
     Referring back to  FIG.  3   , the cross-sectional areas of the various vessels (e.g., the aorta, the main coronary arteries, and/or the branches) of the model  220  ( FIG.  5   ) may also be determined (step  304 ). In an exemplary embodiment, the determination may be performed by the computer system. 
     The model  220  ( FIG.  5   ) may be trimmed (step  306 ) and a solid model may be generated.  FIG.  8    shows an example of the trimmed solid model  320  prepared based on a model similar to the model  220  shown in  FIG.  5   . The solid model  320  is a three-dimensional patient-specific geometric model. In an exemplary embodiment, the trimming may be performed by the computer system, with or without a user&#39;s input. Each of the inflow boundaries  322  and outflow boundaries  324  may be trimmed such that the surface forming the respective boundary is perpendicular to the centerlines determined in step  242 . The inflow boundaries  322  may include the boundaries through which flow is directed into the anatomy of the model  320 , such as at an upstream end of the aorta, as shown in  FIG.  8   . The outflow boundaries  324  may include the boundaries through which flow is directed outward from the anatomy of the model  320 , such as at a downstream end of the aorta and the downstream ends of the main coronary arteries and/or branches. 
     B. Determining Boundary Conditions 
     Boundary conditions may be provided to describe what is occurring at the boundaries of the model, e.g., the three-dimensional solid model  320  of  FIG.  8   . For example, the boundary conditions may relate to at least one blood flow characteristic associated with the patient&#39;s modeled anatomy, e.g., at the boundaries of the modeled anatomy, and the blood flow characteristic(s) may include blood flow velocity, pressure, flow rate, FFR, etc. By appropriately determining the boundary conditions, a computational analysis may be performed to determine information at various locations within the model. Examples of boundary conditions and methods for determining such boundary conditions will now be described. 
     In an exemplary embodiment, the determined boundary conditions may simplify the structures upstream and downstream from the portions of the vessels represented by the solid model  320  into a one- or two-dimensional reduced order model. An exemplary set of equations and other details for determining the boundary conditions are disclosed, for example, in U.S. Patent Application Publication No. 2010/0241404 and U.S. Provisional Application No. 61/210,401, which are both entitled “Patient-Specific Hemodynamics of the Cardiovascular System” and hereby incorporated by reference in their entirety. 
     Boundary conditions may vary depending on the physiological condition of the patient since blood flow though the heart may differ depending on the physiological condition of the patient. For example, FFR is typically measured under the physiological condition of hyperemia, which generally occurs when the patient is experiencing increased blood flow in the heart, e.g., due to stress, etc. The FFR is the ratio of the coronary pressure to aortic pressure under conditions of maximum stress. Hyperemia may also be induced pharmacologically, e.g., with adenosine.  FIGS.  9 - 11    show examples of a calculated FFR (cFFR) model that indicates the change in the ratio of coronary pressure to aortic pressure in the model  320 , depending on the physiological condition of the patient (at rest, under maximum hyperemia, or under maximum exercise).  FIG.  9    shows minimal variation in the ratio of coronary pressure to aortic pressure throughout the model  320  when the patient is at rest.  FIG.  10    shows greater variation in the ratio of coronary pressure to aortic pressure throughout the model  320  when the patient is undergoing maximum hyperemia.  FIG.  11    shows even greater variation in the ratio of coronary pressure to aortic pressure throughout the model  320  when the patient is undergoing maximum exercise. 
     Referring back to  FIG.  3   , boundary conditions for hyperemia conditions may be determined (step  310 ). In an exemplary embodiment, the effect of adenosine may be modeled using a decrease in coronary artery resistance by a factor of 1-5 fold, a decrease in aortic blood pressure of approximately 0-20%, and an increase in heart rate of approximately 0-20%. For example, the effect of adenosine may be modeled using a decrease in coronary artery resistance by a factor of 4 fold, a decrease in aortic blood pressure of approximately 10%, and an increase in heart rate of approximately 10%. Although the boundary conditions for hyperemia conditions are determined in the exemplary embodiment, it is understood that boundary conditions for other physiological states, such as rest, varying degrees of hyperemia, varying degrees of exercise, exertion, stress, or other conditions, may be determined. 
     Boundary conditions provide information about the three-dimensional solid model  320  at its boundaries, e.g., the inflow boundaries  322 , the outflow boundaries  324 , vessel wall boundaries  326 , etc., as shown in  FIG.  8   . The vessel wall boundaries  326  may include the physical boundaries of the aorta, the main coronary arteries, and/or other coronary arteries or vessels of the model  320 . 
     Each inflow or outflow boundary  322 ,  324  may be assigned a prescribed value or field of values for velocity, flow rate, pressure, or other blood flow characteristic. Alternatively, each inflow or outflow boundary  322 ,  324  may be assigned by coupling a heart model to the boundary, a lumped parameter or distributed (e.g. one-dimensional wave propagation) model, another type of one- or two-dimensional model, or other type of model. The specific boundary conditions may be determined based on, e.g., the geometry of the inflow or outflow boundaries  322 ,  324  determined from the obtained patient-specific information, or other measured parameters, such as cardiac output, blood pressure, the myocardial mass calculated in step  240 , etc. 
     i. Determining Reduced Order Models 
     The upstream and downstream structures connected to the solid model  320  may be represented as reduced order models representing the upstream and downstream structures. For example,  FIGS.  12 - 15    show aspects of a method for preparing a lumped parameter model from three-dimensional patient-specific anatomical data at one of the outflow boundaries  324 , according to an exemplary embodiment. The method may be performed separately from and prior to the methods shown in  FIGS.  2  and  3   . 
       FIG.  12    shows a portion  330  of the solid model  320  of one of the main coronary arteries or the branches extending therefrom, and  FIG.  13    shows the portion of the centerlines determined in step  242  of the portion  330  shown in  FIG.  12   . 
     The portion  330  may be divided into segments  332 .  FIG.  14    shows an example of the segments  332  that may be formed from the portion  330 . The selection of the lengths of the segments  332  may be performed by the user and/or the computer system. The segments  332  may vary in length, depending, for example, on the geometry of the segments  332 . Various techniques may be used to segment the portion  330 . For example, diseased portions, e.g., portions with a relatively narrow cross-section, a lesion, and/or a stenosis (an abnormal narrowing in a blood vessel), may be provided in one or more separate segments  332 . The diseased portions and stenoses may be identified, e.g., by measuring the cross-sectional area along the length of the centerline and calculating locally minimum cross-sectional areas. 
     The segments  332  may be approximated by a circuit diagram including one or more (linear or nonlinear) resistors  334  and/or other circuit elements (e.g., capacitors, inductors, etc.).  FIG.  15    shows an example of the segments  332  replaced by a series of linear and nonlinear resistors  334 . The individual resistances of the resistors  334  may be determined, e.g., based on an estimated flow and/or pressure across the corresponding segment  332 . 
     The resistance may be constant, linear, or non-linear, e.g., depending on the estimated flow rate through the corresponding segment  332 . For more complex geometries, such as a stenosis, the resistance may vary with flow rate. Resistances for various geometries may be determined based on a computational analysis (e.g., a finite difference, finite volume, spectral, lattice Boltzmann, particle-based, level set, isogeometric, or finite element method, or other computational fluid dynamics (CFD) analytical technique), and multiple solutions from the computational analysis performed under different flow and pressure conditions may be used to derive patient-specific, vessel-specific, and/or lesion-specific resistances. The results may be used to determine resistances for various types of features and geometries of any segment that may be modeled. As a result, deriving patient-specific, vessel-specific, and/or lesion-specific resistances as described above may allow the computer system to recognize and evaluate more complex geometry such as asymmetric stenosis, multiple lesions, lesions at bifurcations and branches and tortuous vessels, etc. 
     Capacitors may be also included, and capacitance may be determined, e.g., based on elasticity of the vessel walls of the corresponding segment. Inductors may be included, and inductance may be determined, e.g., based on inertial effects related to acceleration or deceleration of the blood volume flowing through the corresponding segment. 
     The individual values for resistance, capacitance, inductance, and other variables associated with other electrical components used in the lumped parameter model may be derived based on data from many patients, and similar vessel geometries may have similar values. Thus, empirical models may be developed from a large population of patient-specific data, creating a library of values corresponding to specific geometric features that may be applied to similar patients in future analyses. Geometries may be matched between two different vessel segments to automatically select the values for a segment  332  of a patient from a previous simulation. 
     ii. Exemplary Lumped Parameter Models 
     Alternatively, instead of performing the steps described above in connection with  FIGS.  12 - 15   , the lumped parameter models may be preset. For example,  FIG.  16    shows examples of lumped parameter models  340 ,  350 ,  360  representing the upstream and downstream structures at the inflow and outflow boundaries  322 ,  324  of the solid model  320 . End A is located at the inflow boundary  322 , and ends a-m and B are located at the outflow boundaries. 
     A lumped parameter heart model  340  may be used to determine the boundary condition at the end A at the inflow boundary  322  of the solid model  320 . The lumped parameter heart model  340  may be used to represent blood flow from the heart under hyperemia conditions. The lumped parameter heart model  340  includes various parameters (e.g., P LA , R AV , L AV , R V-Art , L V-Art , and E(t)) that may be determined based on known information regarding the patient, e.g., an aortic pressure, the patient&#39;s systolic and diastolic blood pressures (e.g., as determined in step  100 ), the patient&#39;s cardiac output (the volume of blood flow from the heart, e.g., calculated based on the patient&#39;s stroke volume and heart rate determined in step  100 ), and/or constants determined experimentally. 
     A lumped parameter coronary model  350  may be used to determine the boundary conditions at the ends a-m at the outflow boundaries  324  of the solid model  320  located at the downstream ends of the main coronary arteries and/or the branches that extend therefrom. The lumped parameter coronary model  350  may be used to represent blood flow exiting from the modeled vessels through the ends a-m under hyperemia conditions. The lumped parameter coronary model  350  includes various parameters (e.g., R a , C a , R a-micro , C im , and R V ) that may be determined based on known information regarding the patient, e.g., the calculated myocardial mass (e.g., as determined in step  240 ) and terminal impedance at the ends a-m (e.g., determined based on the cross-sectional areas of the vessels at the ends a-m as determined in step  304 ). 
     For example, the calculated myocardial mass may be used to estimate a baseline (resting) mean coronary flow through the plurality of outflow boundaries  324 . This relationship may be based on an experimentally-derived physiological law (e.g., of the physiological laws  20  of  FIG.  1   ) that correlates the mean coronary flow Q with the myocardial mass M (e.g., as determined in step  240 ) as Q∝Q o M α , where α is a preset scaling exponent and Q o  is a preset constant. The total coronary flow Q at the outflow boundaries  324  under baseline (resting) conditions and the patient&#39;s blood pressure (e.g., as determined in step  100 ) may then be used to determine a total resistance R at the outflow boundaries  324  based on a preset, experimentally-derived equation. 
     The total resistance R may be distributed among the ends a-m based on the respective cross-sectional areas of the ends a-m (e.g., as determined in step  304 ). This relationship may be based on an experimentally-derived physiological law (e.g., of the physiological laws  20  of  FIG.  1   ) that correlates the respective resistance at the ends a-m as R i ∝R i,o d i   β  where R i  is the resistance to flow at the i-th outlet, and R i,o  is a preset constant, d i  is the diameter of that outlet, and β is a preset power law exponent, e.g., between −3 and −2, −2.7 for coronary flow, −2.9 for cerebral flow, etc. The coronary flow through the individual ends a-m and the mean pressures at the individual ends a-m (e.g., determined based on the individual cross-sectional areas of the ends a-m of the vessels as determined in step  304 ) may be used to determine a sum of the resistances of the lumped parameter coronary model  350  at the corresponding ends a-m (e.g., R a +R a-micro +R V ). Other parameters (e.g., R a /R a-micro , C a , C im ) may be constants determined experimentally. 
     A Windkessel model  360  may be used to determine the boundary condition at the end B at the outflow boundary  324  of the solid model  320  located at the downstream end of the aorta toward the aortic arch. The Windkessel model  360  may be used to represent blood flow exiting from the modeled aorta through the end B under hyperemia conditions. The Windkessel model  360  includes various parameters (e.g., R p , R d , and C) that may be determined based on known information regarding the patient, e.g., the patient&#39;s cardiac output described above in connection with the lumped parameter heart model  340 , the baseline mean coronary flow described above in connection with the lumped parameter coronary model  350 , an aortic pressure (e.g., determined based on the cross-sectional area of the aorta at the end B as determined in step  304 ), and/or constants determined experimentally. 
     The boundary conditions, e.g., the lumped parameter models  340 ,  350 ,  360  (or any of the constants included therein) or other reduced order model, may be adjusted based on other factors. For example, resistance values may be adjusted (e.g., increased) if a patient has a lower flow to vessel size ratio due to a comparatively diminished capacity to dilate vessels under physiologic stress. Resistance values may also be adjusted if the patient has diabetes, is under medication, has undergone past cardiac events, etc. 
     Alternate lumped parameter or distributed, one-dimensional network models may be used to represent the coronary vessels downstream of the solid model  320 . Myocardial perfusion imaging using MRI, CT, PET, or SPECT may be used to assign parameters for such models. Also, alternate imaging sources, e.g., magnetic resonance angiography (MRA), retrospective cine gating or prospective cine gating computed tomography angiography (CTA), etc., may be used to assign parameters for such models. Retrospective cine gating may be combined with image processing methods to obtain ventricular chamber volume changes over the cardiac cycle to assign parameters to a lumped parameter heart model. 
     Simplifying a portion of the patient&#39;s anatomy using the lumped parameter models  340 ,  350 ,  360 , or other reduced order one- or two-dimensional model allows the computational analysis (e.g., step  402  of  FIG.  3    described below) to be performed more quickly, particularly if the computational analysis is performed multiple times such as when evaluating possible treatment options (e.g., step  500  of  FIG.  2   ) in addition to the untreated state (e.g., step  400  of  FIGS.  2  and  3   ), while maintaining high accuracy with the final results. 
     In an exemplary embodiment, the determination of the boundary conditions may be performed by the computer system based on the user&#39;s inputs, such as patient-specific physiological data obtained in step  100 . 
     C. Creating the Three-Dimensional Mesh 
     Referring back to  FIG.  3   , a three-dimensional mesh may be generated based on the solid model  320  generated in step  306  (step  312 ).  FIGS.  17 - 19    show an example of a three-dimensional mesh  380  prepared based on the solid model  320  generated in step  306 . The mesh  380  includes a plurality of nodes  382  (meshpoints or gridpoints) along the surfaces of the solid model  320  and throughout the interior of the solid model  320 . The mesh  380  may be created with tetrahedral elements (having points that form the nodes  382 ), as shown in  FIGS.  18  and  19   . Alternatively, elements having other shapes may be used, e.g., hexahedrons or other polyhedrons, curvilinear elements, etc. In an exemplary embodiment, the number of nodes  382  may be in the millions, e.g., five to fifty million. The number of nodes  382  increases as the mesh  380  becomes finer. With a higher number of nodes  382 , information may be provided at more points within the model  320 , but the computational analysis may take longer to run since a greater number of nodes  382  increases the number of equations (e.g., the equations  30  shown in  FIG.  1   ) to be solved. In an exemplary embodiment, the generation of the mesh  380  may be performed by the computer system, with or without a user&#39;s input (e.g., specifying a number of the nodes  382 , the shapes of the elements, etc.). 
     Referring back to  FIG.  3   , the mesh  380  and the determined boundary conditions may be verified (step  314 ). The verification may be performed by a user and/or by the computer system. For example, the user and/or computer system may be able to identify certain errors with the mesh  380  and/or the boundary conditions that require the mesh  380  and/or the boundary conditions to be redone, e.g., if the mesh  380  is distorted or does not have sufficient spatial resolution, if the boundary conditions are not sufficient to perform the computational analysis, if the resistances determined in step  310  appear to be incorrect, etc. If so, then the mesh  380  and/or the boundary conditions may be determined to be unacceptable, and one or more of steps  304 - 314  may be repeated. If the mesh  380  and/or the boundary conditions are determined to be acceptable, then the method may proceed to step  402  described below. 
     In addition, the user may check that the obtained patient-specific information, or other measured parameters, such as cardiac output, blood pressures, height, weight, the myocardial mass calculated in step  240 , are entered correctly and/or calculated correctly. 
     Accordingly, steps  304 - 314  shown in  FIG.  3    and described above may be considered as substeps of step  300  of  FIG.  2   . 
     V. Performing the Computational Analysis and Outputting Results 
     As described above in connection with step  400  shown in  FIG.  2   , the exemplary method may include performing the computational analysis and outputting results. In an exemplary embodiment, step  400  may include the following steps. 
     A. Performing the Computational Analysis 
     Referring to  FIG.  3   , the computational analysis may be performed by the computer system (step  402 ). In an exemplary embodiment, step  402  may last minutes to hours, depending, e.g., on the number of nodes  382  in the mesh  380  ( FIGS.  17 - 19   ), etc. 
     The analysis involves generating a series of equations that describe the blood flow in the model  320  from which the mesh  380  was generated. As described above, in the exemplary embodiment, the desired information relates to the simulation of blood flow through the model  320  under hyperemic conditions. 
     The analysis also involves using a numerical method to solve the three-dimensional equations of blood flow using the computer system. For example, the numerical method may be a known method, such as finite difference, finite volume, spectral, lattice Boltzmann, particle-based, level set, isogeometric, or finite element methods, or other computational fluid dynamics (CFD) numerical techniques. 
     Using these numerical methods, the blood may be modeled as a Newtonian, a non-Newtonian, or a multiphase fluid. The patient&#39;s hematocrit or other factors measured in step  100  may be used to determine blood viscosity for incorporation in the analysis. The blood vessel walls may be assumed to be rigid or compliant. In the latter case, equations for wall dynamics, e.g., the elastodynamics equations, may be solved together with the equations for blood flow. Time-varying three-dimensional imaging data obtained in step  100  may be used as an input to model changes in vessel shape over the cardiac cycle. An exemplary set of equations and steps for performing the computational analysis are disclosed in further detail, for example, in U.S. Pat. No. 6,236,878, which is entitled “Method for Predictive Modeling for Planning Medical Interventions and Simulating Physiological Conditions,” and U.S. Patent Application Publication No. 2010/0241404 and U.S. Provisional Application No. 61/210,401, which are both entitled “Patient-Specific Hemodynamics of the Cardiovascular System,” all of which are hereby incorporated by reference in their entirety. 
     The computational analysis using the prepared model and boundary conditions may determine blood flow and pressure at each of the nodes  382  of the mesh  380  representing the three-dimensional solid model  320 . For example, the results of the computational analysis may include values for various parameters at each of the nodes  382 , such as, but not limited to, various blood flow characteristics or parameters, such as blood flow velocity, pressure, flow rate, or computed parameters, such as cFFR, as described below. The parameters may also be interpolated across the three-dimensional solid model  320 . As a result, the results of the computational analysis may provide the user with information that typically may be determined invasively. 
     Referring back to  FIG.  3   , the results of the computational analysis may be verified (step  404 ). The verification may be performed by a user and/or by the computer system. For example, the user and/or computer system may be able to identify certain errors with the results that require the mesh  380  and/or the boundary conditions to be redone or revised, e.g., if there is insufficient information due to an insufficient number of nodes  382 , if the analysis is taking too long due to an excessive number of nodes  382 , etc. 
     If the results of the computational analysis are determined to be unacceptable in step  404 , then the user and/or computer system may determine, for example, whether and how to revise or refine the solid model  320  generated in step  306  and/or the mesh  380  generated in step  312 , whether and how to revise the boundary conditions determined in step  310 , or whether to make other revisions to any of the inputs for the computational analysis. Then, one or more steps described above, e.g., steps  306 - 314 ,  402 , and  404  may be repeated based on the determined revisions or refinements. 
     B. Displaying Results for Blood Pressure, Flow, and cFFR 
     Referring back to  FIG.  3   , if the results of the computational analysis are determined to be acceptable in step  404 , then the computer system may output certain results of the computational analysis. For example, the computer system may display images generated based on the results of the computational analysis, such as the images described above in connection with  FIG.  1   , such as the simulated blood pressure model  50 , the simulated blood flow model  52 , and/or the cFFR model  54 . As noted above, these images indicate the simulated blood pressure, blood flow, and cFFR under simulated hyperemia conditions, e.g., since the boundary conditions determined in step  310  were determined with respect to hyperemia conditions. 
     The simulated blood pressure model  50  ( FIG.  1   ) shows the local blood pressure (e.g., in millimeters of mercury or mmHg) throughout the patient&#39;s anatomy represented by the mesh  380  of  FIGS.  17 - 19    under simulated hyperemia conditions. The computational analysis may determine the local blood pressure at each node  382  of the mesh  380 , and the simulated blood pressure model  50  may assign a corresponding color, shade, or other visual indicator to the respective pressures such that the simulated blood pressure model  50  may visually indicate the variations in pressure throughout the model  50  without having to specify the individual values for each node  382 . For example, the simulated blood pressure model  50  shown in  FIG.  1    shows that, for this particular patient, under simulated hyperemia conditions, the pressure may be generally uniform and higher in the aorta (as indicated by the darker shading), and that the pressure gradually and continuously decreases as the blood flows downstream into the main coronary arteries and into the branches (as shown by the gradual and continuous lightening in shading toward the downstream ends of the branches). The simulated blood pressure model  50  may be accompanied by a scale indicating the specific numerical values for blood pressure, as shown in  FIG.  1   . 
     In an exemplary embodiment, the simulated blood pressure model  50  may be provided in color, and a color spectrum may be used to indicate variations in pressure throughout the model  50 . The color spectrum may include red, orange, yellow, green, blue, indigo, and violet, in order from highest pressure to lowest pressure. For example, the upper limit (red) may indicate approximately 110 mmHg or more (or 80 mmHg, 90 mmHg, 100 mmHg, etc.), and the lower limit (violet) may indicate approximately 50 mmHg or less (or 20 mmHg, 30 mmHg, 40 mmHg, etc.), with green indicating approximately 80 mmHg (or other value approximately halfway between the upper and lower limits). Thus, the simulated blood pressure model  50  for some patients may show a majority or all of the aorta as red or other color towards the higher end of the spectrum, and the colors may change gradually through the spectrum (e.g., towards the lower end of the spectrum (down to violet)) towards the distal ends of the coronary arteries and the branches that extend therefrom. The distal ends of the coronary arteries for a particular patient may have different colors, e.g., anywhere from red to violet, depending on the local blood pressures determined for the respective distal ends. 
     The simulated blood flow model  52  ( FIG.  1   ) shows the local blood velocity (e.g., in centimeters per second or cm/s) throughout the patient&#39;s anatomy represented by the mesh  380  of  FIGS.  17 - 19    under simulated hyperemia conditions. The computational analysis may determine the local blood velocity at each node  382  of the mesh  380 , and the simulated blood flow model  52  may assign a corresponding color, shade, or other visual indicator to the respective velocities such that the simulated blood flow model  52  may visually indicate the variations in velocity throughout the model  52  without having to specify the individual values for each node  382 . For example, the simulated blood flow model  52  shown in  FIG.  1    shows that, for this particular patient, under simulated hyperemia conditions, the velocity is generally higher in certain areas of the main coronary arteries and the branches (as indicated by the darker shading in area  53  in  FIG.  1   ). The simulated blood flow model  52  may be accompanied by a scale indicating the specific numerical values for blood velocity, as shown in  FIG.  1   . 
     In an exemplary embodiment, the simulated blood flow model  52  may be provided in color, and a color spectrum may be used to indicate variations in velocity throughout the model  52 . The color spectrum may include red, orange, yellow, green, blue, indigo, and violet, in order from highest velocity to lowest velocity. For example, the upper limit (red) may indicate approximately 100 (or 150) cm/s or more, and the lower limit (violet) may indicate approximately 0 cm/s, with green indicating approximately 50 cm/s (or other value approximately halfway between the upper and lower limits). Thus, the simulated blood flow model  52  for some patients may show a majority or all of the aorta as a mixture of colors towards the lower end of the spectrum (e.g., green through violet), and the colors may change gradually through the spectrum (e.g., towards the higher end of the spectrum (up to red)) at certain locations where the determined blood velocities increase. 
     The cFFR model  54  ( FIG.  1   ) shows the local cFFR throughout the patient&#39;s anatomy represented by the mesh  380  of  FIGS.  17 - 19    under simulated hyperemia conditions. As noted above, cFFR may be calculated as the ratio of the local blood pressure determined by the computational analysis (e.g., shown in the simulated blood pressure model  50 ) at a particular node  382  divided by the blood pressure in the aorta, e.g., at the inflow boundary  322  ( FIG.  8   ). The computational analysis may determine the cFFR at each node  382  of the mesh  380 , and the cFFR model  54  may assign a corresponding color, shade, or other visual indicator to the respective cFFR values such that the cFFR model  54  may visually indicate the variations in cFFR throughout the model  54  without having to specify the individual values for each node  382 . For example, the cFFR model  54  shown in  FIG.  1    shows that, for this particular patient, under simulated hyperemia conditions, cFFR may be generally uniform and approximately 1.0 in the aorta, and that cFFR gradually and continuously decreases as the blood flows downstream into the main coronary arteries and into the branches. The cFFR model  54  may also indicate cFFR values at certain points throughout the cFFR model  54 , as shown in  FIG.  1   . The cFFR model  54  may be accompanied by a scale indicating the specific numerical values for cFFR, as shown in  FIG.  1   . 
     In an exemplary embodiment, the cFFR model  54  may be provided in color, and a color spectrum may be used to indicate variations in pressure throughout the model  54 . The color spectrum may include red, orange, yellow, green, blue, indigo, and violet, in order from lowest cFFR (indicating functionally significant lesions) to highest cFFR. For example, the upper limit (violet) may indicate a cFFR of 1.0, and the lower limit (red) may indicate approximately 0.7 (or 0.75 or 0.8) or less, with green indicating approximately 0.85 (or other value approximately halfway between the upper and lower limits). For example, the lower limit may be determined based on a lower limit (e.g., 0.7, 0.75, or 0.8) used for determining whether the cFFR measurement indicates a functionally significant lesion or other feature that may require intervention. Thus, the cFFR model  54  for some patients may show a majority or all of the aorta as violet or other color towards the higher end of the spectrum, and the colors may change gradually through the spectrum (e.g., towards the higher end of the spectrum (up to anywhere from red to violet) towards the distal ends of the coronary arteries and the branches that extend therefrom. The distal ends of the coronary arteries for a particular patient may have different colors, e.g., anywhere from red to violet, depending on the local values of cFFR determined for the respective distal ends. 
     After determining that the cFFR has dropped below the lower limit used for determining the presence of a functionally significant lesion or other feature that may require intervention, the artery or branch may be assessed to locate the functionally significant lesion(s). The computer system or the user may locate the functionally significant lesion(s) based on the geometry of the artery or branch (e.g., using the cFFR model  54 ). For example, the functionally significant lesion(s) may be located by finding a narrowing or stenosis located near (e.g., upstream) from the location of the cFFR model  54  having the local minimum cFFR value. The computer system may indicate or display to the user the portion(s) of the cFFR model  54  (or other model) that includes the functionally significant lesion(s). 
     Other images may also be generated based on the results of the computational analysis. For example, the computer system may provide additional information regarding particular main coronary arteries, e.g., as shown in  FIGS.  20 - 22   . The coronary artery may be chosen by the computer system, for example, if the particular coronary artery includes the lowest cFFR. Alternatively, the user may select the particular coronary artery. 
       FIG.  20    shows a model of the patient&#39;s anatomy including results of the computational analysis with certain points on the model identified by individual reference labels (e.g., LM, LAD1, LAD2, LAD3, etc.). In the exemplary embodiment shown in  FIG.  21   , the points are provided in the LAD artery, which is the main coronary artery having the lowest cFFR for this particular patient, under simulated hyperemia conditions. 
       FIGS.  21  and  22    show graphs of certain variables over time at some or all of these points (e.g., LM, LAD1, LAD2, LAD3, etc.) and/or at certain other locations on the model (e.g., in the aorta, etc.).  FIG.  21    is a graph of the pressure (e.g., in millimeters of mercury or mmHg) over time in the aorta and at points LAD1, LAD2, and LAD3 indicated in  FIG.  20   . The top plot on the graph indicates the pressure in the aorta, the second plot from the top indicates the pressure at point LAD1, the third plot from the top indicates the pressure at point LAD2, and the bottom plot indicates the pressure at point LAD3.  FIG.  22    is a graph of the flow (e.g., in cubic centimeters per second or cc/s) over time at points LM, LAD1, LAD2, and LAD3 indicated in  FIG.  20   . In addition, other graphs may be provided, such as a graph of shear stress over time at some or all of these points and/or at other points. The top plot on the graph indicates the flow at point LM, the second plot from the top indicates the flow at point LAD1, the third plot from the top indicates the flow at point LAD2, and the bottom plot indicates the flow at point LAD3. Graphs may also be provided that show the change in these variables, e.g., blood pressure, flow, velocity, or cFFR, along the length of a particular main coronary artery and/or the branches extending therefrom. 
     Optionally, the various graphs and other results described above may be finalized in a report (step  406 ). For example, the images and other information described above may be inserted into a document having a set template. The template may be preset and generic for multiple patients, and may be used for reporting the results of computational analyses to physicians and/or patients. The document or report may be automatically completed by the computer system after the computational analysis is completed. 
     For example, the finalized report may include the information shown in  FIG.  23   .  FIG.  23    includes the cFFR model  54  of  FIG.  1    and also includes summary information, such as the lowest cFFR values in each of the main coronary arteries and the branches that extend therefrom. For example,  FIG.  23    indicates that the lowest cFFR value in the LAD artery is 0.66, the lowest cFFR value in the LCX artery is 0.72, the lowest cFFR value in the RCA artery is 0.80. Other summary information may include the patient&#39;s name, the patient&#39;s age, the patient&#39;s blood pressure (BP) (e.g., obtained in step  100 ), the patient&#39;s heart rate (HR) (e.g., obtained in step  100 ), etc. The finalized report may also include versions of the images and other information generated as described above that the physician or other user may access to determine further information. The images generated by the computer system may be formatted to allow the physician or other user to position a cursor over any point to determine the value of any of the variables described above, e.g., blood pressure, velocity, flow, cFFR, etc., at that point. 
     The finalized report may be transmitted to the physician and/or the patient. The finalized report may be transmitted using any known method of communication, e.g., a wireless or wired network, by mail, etc. Alternatively, the physician and/or patient may be notified that the finalized report is available for download or pick-up. Then, the physician and/or patient may log into the web-based service to download the finalized report via a secure communication line. 
     C. Verifying Results 
     Referring back to  FIG.  3   , the results of the computational analysis may be independently verified (step  408 ). For example, the user and/or computer system may be able to identify certain errors with the results of the computational analysis, e.g., the images and other information generated in step  406 , that require any of the above described steps to be redone. If such errors are identified, then the results of the computational analysis may be determined to be unacceptable, and certain steps, e.g., steps  100 ,  200 ,  300 ,  400 , substeps  102 ,  202 - 208 ,  240 - 260 ,  304 - 314 , and  402 - 408 , etc., may be repeated. 
     Accordingly, steps  402 - 408  shown in  FIG.  3    and described above may be considered as substeps of step  400  of  FIG.  2   . 
     Another method for verifying the results of the computational analysis may include measuring any of the variables included in the results, e.g., blood pressure, velocity, flow, cFFR, etc., from the patient using another method. In an exemplary embodiment, the variables may be measured (e.g., invasively) and then compared to the results determined by the computational analysis. For example, FFR may be determined, e.g., using a pressure wire inserted into the patient as described above, at one or more points within the patient&#39;s anatomy represented by the solid model  320  and the mesh  380 . The measured FFR at a location may be compared with the cFFR at the same location, and the comparison may be performed at multiple locations. Optionally, the computational analysis and/or boundary conditions may be adjusted based on the comparison. 
     D. Another Embodiment of a System and Method for Providing Coronary Blood Flow Information 
     Another embodiment of a method  600  for providing various information relating to coronary blood flow in a specific patient is shown in  FIG.  24 A . The method  600  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . The method  600  may be performed using one or more inputs  610 , and may include generating one or more models  620  based on the inputs  610 , assigning one or more conditions  630  based on the inputs  610  and/or the models  620 , and deriving one or more solutions  640  based on the models  620  and the conditions  630 . 
     The inputs  610  may include medical imaging data  611  of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and heart, such as CCTA data (e.g., obtained in step  100  of  FIG.  2   ). The inputs  610  may also include a measurement  612  of the patient&#39;s brachial blood pressure and/or other measurements (e.g., obtained in step  100  of  FIG.  2   ). The measurements  612  may be obtained noninvasively. The inputs  610  may be used to generate the model(s)  620  and/or determine the condition(s)  630  described below. 
     As noted above, one or more models  620  may be generated based on the inputs  610 . For example, the method  600  may include generating one or more patient-specific three-dimensional geometric models of the patient&#39;s anatomy (e.g., the aorta, coronary arteries, and branches that extend therefrom) based on the imaging data  611  (step  621 ). For example, the geometric model may be the solid model  320  of  FIG.  8    generated in step  306  of  FIG.  3   , and/or the mesh  380  of  FIGS.  17 - 19    generated in step  312  of  FIG.  3   . 
     Referring back to  FIG.  24 A , the method  600  may also include generating one or more physics-based blood flow models (step  622 ). The blood flow models may include a model that relates to blood flow through the patient-specific geometric model generated in step  621 , heart and aortic circulation, distal coronary circulation, etc. The blood flow models may relate to at least one blood flow characteristic associated with the patient&#39;s modeled anatomy, e.g., blood flow velocity, pressure, flow rate, FFR, etc. The blood flow models may be assigned as boundary conditions at the inflow and outflow boundaries  322 ,  324  of the three-dimensional geometric model. The blood flow model may include the reduced order models or other boundary conditions described above in connection with step  310  of  FIG.  3   , e.g., the lumped parameter heart model  340 , the lumped parameter coronary model  350 , the Windkessel model  360 , etc. 
     As noted above, one or more conditions  630  may be determined based on the inputs  610  and/or the models  620 . The conditions  630  include the parameters calculated for the boundary conditions determined in step  622  (and step  310  of  FIG.  3   ). For example, the method  600  may include determining a condition by calculating a patient-specific ventricular or myocardial mass based on the imaging data  611  (e.g., as determined in step  240  of  FIG.  3   ) (step  631 ). 
     The method  600  may include determining a condition by calculating, using the ventricular or myocardial mass calculated in step  631 , a resting coronary flow based on the relationship Q=Q o M α , where α is a preset scaling exponent, M is the ventricular or myocardial mass, and Q o  is a preset constant (e.g., as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   ) (step  632 ). Alternatively, the relationship may have the form Q∝Q o M α , as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   . 
     The method  600  may also include determining a condition by calculating, using the resulting coronary flow calculated in step  632  and the patient&#39;s measured blood pressure  612 , a total resting coronary resistance (e.g., as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   ) (step  633 ). 
     The method  600  may also include determining a condition by calculating, using the total resting coronary resistance calculated in step  633  and the models  620 , individual resistances for the individual coronary arteries (and the branches that extend therefrom) (step  634 ). For example, as described above in connection with step  310  of  FIG.  3   , the total resting coronary resistance calculated in step  633  may be distributed to the individual coronary arteries and branches based on the sizes (e.g., determined from the geometric model generated in step  621 ) of the distal ends of the individual coronary arteries and branches, and based on the relationship R=R o d β , where R is the resistance to flow at a particular distal end, and R o  is a preset constant, d is the size (e.g., diameter of that distal end), and β is a preset power law exponent, as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   . 
     Referring back to  FIG.  24 A , the method  600  may include adjusting the boundary conditions based on one or more physical conditions of the patient (step  635 ). For example, the parameters determined in steps  631 - 634  may be modified based on whether the solution  640  is intended to simulate rest, varying levels of hyperemia, varying levels of exercise or exertion, different medications, etc. Based on the inputs  610 , the models  620 , and the conditions  630 , a computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine the solution  640  that includes information about the patient&#39;s coronary blood flow under the physical conditions selected in step  635  (step  641 ). Examples of information that may be provided from the solution  640  will now be described. 
     The combined patient-specific anatomic (geometric) and physiologic (physics-based) model may be used to determine the effect of different medications or lifestyle changes (e.g., cessation of smoking, changes in diet, or increased physical activity) that alters heart rate, stroke volume, blood pressure, or coronary microcirculatory function on coronary artery blood flow. Such information may be used to optimize medical therapy or avert potentially dangerous consequences of medications. The combined model may also be used to determine the effect on coronary artery blood flow of alternate forms and/or varying levels of physical activity or risk of exposure to potential extrinsic force, e.g., when playing football, during space flight, when scuba diving, during airplane flights, etc. Such information may be used to identify the types and level of physical activity that may be safe and efficacious for a specific patient. The combined model may also be used to predict a potential benefit of percutaneous coronary interventions on coronary artery blood flow in order to select the optimal interventional strategy, and/or to predict a potential benefit of coronary artery bypass grafting on coronary artery blood flow in order to select the optimal surgical strategy. 
     The combined model may also be used to illustrate potential deleterious effects of an increase in the burden of arterial disease on coronary artery blood flow and to predict, using mechanistic or phenomenological disease progression models or empirical data, when advancing disease may result in a compromise of blood flow to the heart muscle. Such information may enable the determination of a “warranty period” in which a patient observed to be initially free from hemodynamically significant disease using noninvasive imaging may not be expected to require medical, interventional, or surgical therapy, or alternatively, the rate at which progression might occur if adverse factors are continued. 
     The combined model may also be used to illustrate potential beneficial effects on coronary artery blood flow resulting from a decrease in the burden of coronary artery disease and to predict, using mechanistic or phenomenological disease progression models or empirical data, when regression of disease may result in increased blood flow through the coronary arteries to the heart muscle. Such information may be used to guide medical management programs including, but not limited to, changes in diet, increased physical activity, prescription of statins or other medications, etc. 
     E. Exemplary Embodiment of a System and Method for Estimating Coronary Blood Flow Information in a Patient During Physical Activity 
     As noted above, patients with known coronary artery disease may be subject to limitations in physical activity or exercise due to reductions in blood flow or perfusion pressure, or concerns of plaque disruption related to elevated blood pressure or elevated plaque stress. Nevertheless, patients with coronary artery disease may be undergoing cardiac rehabilitation, which often includes a physical activity program. A method and system for quantifying risk associated with elevated coronary artery blood flow during physical activity would enable providers to assess a patient&#39;s risk of myocardial infarction or other injury, and accordingly make recommendations, for instance, for a cardiac rehab program. Moreover, the methods and systems described herein may be applied to patients without coronary artery disease to likewise investigate the effect of physical activity on blood flow, perfusion pressure, and/or plaque stress resulting from physical activity in order to assess those patients&#39; risk of myocardial infarction or other injury and make physical activity or exercise recommendations. 
     One embodiment of a method  1300  for quantifying limitations in coronary artery blood flow during physical activity is shown in  FIG.  24 B . Method  1300  includes using at least one computer system to input into the at least one computer system patient-specific data regarding a geometry of the patient&#39;s heart (step  1301 ). Such data may include image data and be obtained noninvasively, for example, using cCTA. Method  1300  also includes creating, using the at least one computer system, a model, such as a one-dimensional, two-dimensional, or three-dimensional model, representing at least a portion of the patient&#39;s heart based on the patient-specific data (step  1302 ). In at least one embodiment, the model is a three-dimensional model. In at least one embodiment, the model is a geometric model. Method  1300  includes creating a physics-based model of blood flow through the patient&#39;s heart during a selected level of physical activity, a first selected physical activity intensity level, or a first level of exercise (step  1303 ). Non-limiting examples of physical activity or exercise include aerobic and anerobic activity. Physical activity or exercise may also include intimacy. 
     Method  1300  further includes determining, using the at least one computer system, one or more values of at least one blood flow characteristic within the patient&#39;s heart during the simulated level of physical activity, the first selected physical activity intensity level, or the first level of exercise, based on the model and the physics-based model (step  1304 ). The at least one blood flow characteristic may be chosen, for example, from coronary blood flow, blood pressure, plaque stress, myocardial perfusion, plaque vulnerability, FFR, and territory at risk. Method  1300  also includes normalizing the determined one or more values of the at least one blood flow characteristic during the simulated level of physical activity, the first selected physical activity intensity level, or the first level of exercise (step  1305 ). For example, limitations in coronary blood flow or an increase in blood pressure within the patient may be normalized by relating each, respectively, to blood flow or blood pressure in a hypothetical case where the patient&#39;s coronary arteries are not diseased and/or not treated with an intervention (e.g., a stent or bypass). Method  1300  further includes comparing the one or more normalized values of the at least one blood flow characteristic during the simulated level of physical activity, the first selected physical activity intensity level, or the first level of exercise to a threshold or threshold value (step  1306 ). In at least one embodiment, the threshold or threshold value may be, or derived from, a hypothetical normal state or a population norm, for example. This comparison may be accomplished, for example, by comparing the patient&#39;s blood flow to that of other subjects of similar age and/or fitness level. If the one or more normalized values of the at least one blood flow characteristic are above the threshold (step  1307 ), method  1300  further comprises identifying a level of physical activity, the first selected physical activity intensity level, or the first level of exercise at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk (step  1308 ). Using this information, a recommendation optionally may be made to the patient regarding an appropriate (e.g., a maximum) level of physical activity, intensity, or exercise (optional step  1309 ). 
     If the one or more normalized values of the at least one blood flow characteristic are at or below the threshold, the method  1300  further comprises increasing the simulated level of physical activity to a second level physical activity intensity level or second level of exercise (step  1310 ). The simulated level of physical activity may be increased, for example, by reducing the resistance of blood flow at the myocardium. Once an increased level of physical activity, a second level physical activity intensity level, or second level of exercise is selected, method  1300  comprises updating the physics-based model of blood flow through the patient&#39;s heart simulated during the increased level of physical activity, the second level physical activity intensity level, or the second level of exercise (step  1303 ). Method  1300  may then be repeated until, for example, the one or more normalized values of the at least one blood flow characteristic are above the threshold (step  1307 ), and a level of physical activity, intensity, or exercise at which the at least one blood flow characteristic exceeds a level identified as within an acceptable level of risk (step  1308 ) is identified. 
     Alternatively, in at least one embodiment, the systems and methods disclosed herein may be applied to a patient without coronary artery disease. In such an embodiment, the systems and methods do not include normalizing the one or more values of the at least one blood flow characteristic before comparing to a threshold or threshold value. Rather, the calculated at least one value of the at least one blood flow characteristic is compared to the threshold or threshold value to determine if the first physical activity intensity level exceeds the threshold. 
     In at least one embodiment, a physical activity recommendation may be made after consulting a library or other collection of exercises which have been grouped according to activity level. For example, exercises may be categorized as “light,” “moderate, or “vigorous” in intensity. By simulating at least one blood flow characteristic during physical exertion according to the method described herein, a maximum physical activity level at which the patient would experience a maximum at least one blood flow characteristic event (e.g., a maximum FFR event) may be determined. The patient with coronary artery disease might therefore receive a recommendation to engage in exercises below the patient-specific maximum physical activity level (for example, those deemed “light” or “moderate” in the library) and avoid those at or above the patient-specific maximum physical activity level (for example, those deemed “vigorous”) as too risky for the patient. 
     Risk of physical activity to a patient with coronary artery disease may include risk of stroke and limitations in physical activity due to peripheral artery disease. Thus, one of ordinary skill in the art would understand that use of the systems and methods disclosed herein are not limited to patients with coronary artery disease, but may be applied to patients without coronary artery disease, patients at risk of stroke, and/or patients with peripheral artery disease, among others. 
     VI. Providing Patient-Specific Treatment Planning 
     As described above in connection with step  500  shown in  FIG.  2   , the exemplary method may include providing patient-specific treatment planning. In an exemplary embodiment, step  500  may include the following steps. Although  FIG.  3    does not show the following steps, it is understood that these steps may be performed in conjunction with the steps shown in  FIG.  3   , e.g., after steps  406  or  408 . 
     As described above, the cFFR model  54  shown in  FIGS.  1  and  23    indicates the cFFR values throughout the patient&#39;s anatomy represented by the mesh  380  of  FIGS.  17 - 19    in an untreated state and under simulated hyperemia conditions. Using this information, the physician may prescribe treatments to the patient, such as an increase in exercise, a change in diet, a prescription of medication, surgery on any portion of the modeled anatomy or other portions of the heart (e.g., coronary artery bypass grafting, insertion of one or more coronary stents, etc.), etc. 
     To determine which treatment(s) to prescribe, the computer system may be used to predict how the information determined from the computational analysis would change based on such treatment(s). For example, certain treatments, such as insertion of stent(s) or other surgeries, may result in a change in geometry of the modeled anatomy. Accordingly, in an exemplary embodiment, the solid model  320  generated in step  306  may be revised to indicate a widening of one or more lumens where a stent is inserted. 
     For example, the cFFR model  54  shown in  FIGS.  1  and  23    indicates that the lowest cFFR value in the LAD artery is 0.66, the lowest cFFR value in the LCX artery is 0.72, the lowest cFFR value in the RCA artery is 0.80. Treatment may be proposed if a cFFR value is, for example, less than 0.75. Accordingly, the computer system may propose to the user revising the solid model  320  to indicate a widening of the LAD artery and the LCX artery to simulate inserting stents in these coronary arteries. The user may be prompted to choose the location and amount of widening (e.g., the length and diameter) corresponding to the location and size of the simulated stent. Alternatively, the location and amount of widening may be determined automatically by the computer system based on various factors, such as the location of the node(s) with cFFR values that are less than 0.75, a location of a significant narrowing of the vessels, sizes of conventional stents, etc. 
       FIG.  25    shows an example of a modified cFFR model  510  determined based on a solid model created by widening a portion of the LAD artery at location  512  and a portion of the LCX artery at location  514 . In an exemplary embodiment, any of the steps described above, e.g., steps  310 - 314  and  402 - 408 , may be repeated using the modified solid model. In step  406 , the finalized report may include the information relating to the untreated patient (e.g., without the stents), such as the information shown in  FIG.  23   , and information relating to the simulated treatment for the patient, such as the information shown in  FIGS.  25  and  26   . 
       FIG.  25    includes the modified cFFR model  510  and also includes summary information, such as the lowest cFFR values in the main coronary arteries and the branches that extend therefrom for the modified solid model associated with the proposed treatment. For example,  FIG.  25    indicates that the lowest cFFR value in the LAD artery (and its downstream branches) is 0.78, the lowest cFFR value in the LCX artery (and its downstream branches) is 0.78, the lowest cFFR value in the RCA artery (and its downstream branches) is 0.79. Accordingly, a comparison of the cFFR model  54  of the untreated patient (without stents) and the cFFR model  510  for the proposed treatment (with stents inserted) indicates that the proposed treatment may increase the minimum cFFR in the LAD artery from 0.66 to 0.78 and would increase the minimum cFFR in the LCX artery from 0.72 to 0.76, while there would be a minimal decrease in the minimum cFFR in the RCA artery from 0.80 to 0.79. 
       FIG.  26    shows an example of a modified simulated blood flow model  520  determined after widening portions of the LAD artery at location  512  and of the LCX artery at location  514  as described above.  FIG.  26    also includes summary information, such as the blood flow values at various locations in the main coronary arteries and the branches that extend therefrom for the modified solid model associated with the proposed treatment. For example,  FIG.  26    indicates blood flow values for four locations LAD1, LAD2, LAD3, and LAD4 in the LAD artery and for two locations LCX1 and LCX2 in the LCX artery for the untreated patient (without stents) and for the treated patient (with stents inserted).  FIG.  26    also indicates a percentage change in blood flow values between the untreated and treated states. Accordingly, a comparison of the simulated blood flow model  52  of the untreated patient and the simulated blood flow model  520  for the proposed treatment indicates that the proposed treatment may increase the flow through the LAD artery and LCX artery at all of the locations LAD1-LAD4, LCX1, and LCX2 by 9% to 19%, depending on the location. 
     Other information may also be compared between the untreated and treated states, such as coronary artery blood pressure. Based on this information, the physician may discuss with the patient whether to proceed with the proposed treatment option. 
     Other treatment options may also involve modifying the solid model  320  in different ways. For example, coronary artery bypass grafting may involve creating new lumens or passageways in the solid model  320  and removing a lesion may also involve widening a lumen or passage. Other treatment options may not involve modifying the solid model  320 . For example, an increase in exercise or exertion, a change in diet or other lifestyle change, a prescription of medication, etc., may involve changing the boundary conditions determined in step  310 , e.g., due to vasoconstriction, dilation, decreased heart rate, etc. For example, the patient&#39;s heart rate, cardiac output, stroke volume, blood pressure, coronary microcirculation function, the configurations of the lumped parameter models, etc., may depend on the medication prescribed, the type and frequency of exercise adopted (or other exertion), the type of lifestyle change adopted (e.g., cessation of smoking, changes in diet, etc.), thereby affecting the boundary conditions determined in step  310  in different ways. 
     In an exemplary embodiment, modified boundary conditions may be determined experimentally using data from many patients, and similar treatment options may require modifying the boundary conditions in similar ways. Empirical models may be developed from a large population of patient-specific data, creating a library of boundary conditions or functions for calculating boundary conditions, corresponding to specific treatment options that may be applied to similar patients in future analyses. 
     After modifying the boundary conditions, the steps described above, e.g., steps  312 ,  314 , and  402 - 408 , may be repeated using the modified boundary conditions, and in step  406 , the finalized report may include the information relating to the untreated patient, such as the information shown in  FIG.  23   , and information relating to the simulated treatment for the patient, such as the information shown in  FIGS.  25  and  26   . 
     Alternatively, the physician, the patient, or other user may be provided with a user interface that allows interaction with a three-dimensional model (e.g., the solid model  320  of  FIG.  8   ). The model  320  may be divided into user-selectable segments that may be edited by the user to reflect one or more treatment options. For example, the user may select a segment with a stenosis (or occlusion, e.g., an acute occlusion) and adjust the segment to remove the stenosis, the user may add a segment to the model  320  to serve as a bypass, etc. The user may also be prompted to specify other treatment options and/or physiologic parameters that may alter the boundary conditions determined above, e.g., a change in a cardiac output, a heart rate, a stroke volume, a blood pressure, an exercise or exertion level, a hyperemia level, medications, etc. In an alternate embodiment, the computer system may determine or suggest a treatment option. 
     The user interface may allow interaction with the three-dimensional model  320  to allow the user to simulate a stenosis (or occlusion, e.g., an acute occlusion). For example, the user may select a segment for including the stenosis, and the computer system may be used to predict how the information determined from the computational analysis would change based on the addition of the stenosis. Thus, the methods described herein may be used to predict the effect of occluding an artery. 
     The user interface may also allow interaction with the three-dimensional model  320  to simulate a damaged artery or removal of an artery, which may occur, for example, in certain surgical procedures, such as when removing cancerous tumors. The model may also be modified to simulate the effect of preventing blood flow through certain arteries in order to predict the potential for collateral pathways for supplying adequate blood flow for the patient. 
     A. Using Reduced Order Models to Compare Different Treatment Options 
     In an exemplary embodiment, the computer system may allow the user to simulate various treatment options more quickly by replacing the three-dimensional solid model  320  or mesh  380  with a reduced order model.  FIG.  27    shows a schematic diagram relating to a method  700  for simulating various treatment options using a reduced order model, according to an exemplary embodiment. The method  700  may be implemented in the computer system described above. 
     One or more patient-specific simulated blood flow models representing blood flow or other parameters may be output from the computational analysis described above (step  701 ). For example, the simulated blood flow models may include the simulated blood pressure model  50  of  FIG.  1   , the simulated blood flow model  52  of  FIG.  1   , the cFFR model  54  of  FIG.  1   , etc., provided using the methods described above and shown in  FIGS.  2  and  3   . As described above, the simulated blood flow model may include a three-dimensional geometrical model of the patient&#39;s anatomy. 
     Functional information may be extracted from the simulated blood flow models in order to specify conditions for a reduced order model (step  702 ). For example, the functional information may include the blood pressure, flow, or velocity information determined using the computational analysis described above. 
     A reduced order (e.g., zero-dimensional or one-dimensional) model may be provided to replace the three-dimensional solid model  320  used to generate the patient specific simulated blood flow models generated in step  701 , and the reduced order model may be used to determine information about the coronary blood flow in the patient (step  703 ). For example, the reduced order model may be a lumped parameter model generated as described above in connection with step  310  of  FIG.  3   . Thus, the lumped parameter model is a simplified model of the patient&#39;s anatomy that may be used to determine information about the coronary blood flow in the patient without having to solve the more complex system of equations associated with the mesh  380  of  FIGS.  17 - 19   . 
     Information determined from solving the reduced order model in step  703  may then be mapped or extrapolated to a three-dimensional solid model (e.g., the solid model  320 ) of the patient&#39;s anatomy (step  704 ), and the user may make changes to the reduced order model as desired to simulate various treatment options and/or changes to the physiologic parameters for the patient, which may be selected by the user (step  705 ). The selectable physiologic parameters may include cardiac output, exercise or exertion level, level of hyperemia, types of medications, etc. The selectable treatment options may include removing a stenosis, adding a bypass, etc. 
     Then, the reduced order model may be modified based on the treatment options and/or physiologic parameters selected by the user, and the modified reduced order model may be used to determine information about the coronary blood flow in the patient associated with the selected treatment option and/or physiologic parameter (step  703 ). Information determined from solving the reduced order model in step  703  may then be mapped or extrapolated to the three-dimensional solid model  320  of the patient&#39;s anatomy to predict the effects of the selected treatment option and/or physiologic parameter on the coronary blood flow in the patient&#39;s anatomy (step  704 ). 
     Steps  703 - 705  may be repeated for various different treatment options and/or physiologic parameters to compare the predicted effects of various treatment options to each other and to the information about the coronary blood flow in the untreated patient. As a result, predicted results for various treatment options and/or physiologic parameters may be evaluated against each other and against information about the untreated patient without having to rerun the more complex analysis using the three-dimensional mesh  380 . Instead, a reduced order model may be used, which may allow the user to analyze and compare different treatment options and/or physiologic parameters more easily and quickly. 
       FIG.  28    shows further aspects of the exemplary method for simulating various treatment options using a reduced order model, according to an exemplary embodiment. The method  700  may be implemented in the computer system described above. 
     As described above in connection with step  306  of  FIG.  3   , a patient-specific geometric model may be generated based on imaging data for the patient (step  711 ). For example, the imaging data may include the CCTA data obtained in step  100  of  FIG.  2   , and the geometric model may be the solid model  320  of  FIG.  8    generated in step  306  of  FIG.  3   , and/or the mesh  380  of  FIGS.  17 - 19    generated in step  312  of  FIG.  3   . 
     Using the patient-specific three-dimensional geometric model, the computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine information about the patient&#39;s coronary blood flow (step  712 ). The computational analysis may output one or more three-dimensional patient-specific simulated blood flow models representing blood flow or other parameters, e.g., the simulated blood pressure model  50  of  FIG.  1   , the simulated blood flow model  52  of  FIG.  1   , the cFFR model  54  of  FIG.  1   , etc. 
     The simulated blood flow model may be segmented (e.g., as described above in connection with  FIG.  14   ) based on the anatomical features of the model (step  713 ). For example, branches extending from the main coronary arteries may be provided in separate segments (step  714 ), portions with stenosis or diseased areas may be provided in separate segments (step  716 ), and portions between the branches and the portions with stenosis or diseased areas may be provided in separate segments (step  715 ). Varying degrees of resolution may be provided in segmenting the simulated blood flow model such that each vessel may include a plurality of short, discrete segments or longer segments, e.g., including the entire vessel. Also, various techniques may be provided for segmenting the simulated blood flow model, including generating centerlines and sectioning based on the generated centerlines, or detecting branch points and sectioning based on the detected branch points. The diseased portions and stenoses may be identified, e.g., by measuring the cross-sectional area along the length of the centerline and calculating locally minimum cross-sectional areas. Steps  711 - 716  may be considered as substeps of step  701  of  FIG.  27   . 
     The segments may be replaced by components of a lumped parameter model, such as resistors, capacitors, inductors, etc., as described above in connection with  FIG.  15   . The individual values for the resistance, capacitance, inductance, and other variables associated with other electrical components used in the lumped parameter model may be derived from the simulated blood flow models provided in step  712 . For example, for branches and portions between the branches and the portions with stenosis or diseased areas, information derived from the simulated blood flow model may be used to assign linear resistances to the corresponding segments (step  717 ). For portions with complex geometry, such as a stenosis or diseased area, resistance may vary with flow rate. Thus, multiple computational analyses may be used to obtain simulated blood flow models for various flow and pressure conditions to derive patient-specific, vessel-specific, and lesion-specific resistance functions for these complex geometries, as described above in connection with  FIG.  15   . Accordingly, for portions with stenosis or diseased areas, information derived from these multiple computational analyses or models derived from previous data may be used to assign non-linear, flow-dependent resistances to corresponding segments (step  718 ). Steps  717  and  718  may be considered as substeps of step  702  of  FIG.  27   . 
     Using the resistances determined in steps  717  and  718 , a reduced order (e.g., zero-dimensional or one-dimensional) model may be generated (step  719 ). For example, the reduced order model may be a lumped parameter model generated as described above in connection with step  310  of  FIG.  3   . Thus, the lumped parameter model is a simplified model of the patient&#39;s anatomy that may be used to determine information about the coronary blood flow in the patient without having to solve the more complex system of equations associated with the mesh  380  of  FIGS.  17 - 19   . 
     A user interface may be provided that allows the user to interact with the reduced order model created in step  719  (step  720 ). For example, the user may select and edit different segments of the reduced order model to simulate different treatment options and/or may edit various physiologic parameters. For example, intervention, such as insertion of a stent to repair of a diseased region, may be modeled by decreasing the resistance of the segment where the stent is to be inserted. Forming a bypass may be modeled by adding a segment having a low resistance parallel to a diseased segment. 
     The modified reduced order model may be solved to determine information about the coronary blood flow in the patient under the treatment and/or change in physiologic parameters selected in step  720  (step  721 ). The solution values for flow and pressure in each segment determined in step  721  may then be compared to the three-dimensional solution determined in step  712 , and any difference may be minimized by adjusting the resistance functions of the segments (e.g., as determined in steps  717  and  718 ) and resolving the reduced order model (e.g., step  721 ) until the solutions match. As a result, the reduced order model may be created and then solved with a simplified set of equations that allows for relatively rapid computation (e.g., compared to a full three-dimensional model) and may be used to solve for flow rate and pressure that may closely approximate the results of a full three-dimensional computational solution. The reduced order model allows for relatively rapid iterations to model various different treatment options. 
     Information determined from solving the reduced order model in step  721  may then be mapped or extrapolated to a three-dimensional solid model of the patient&#39;s anatomy (e.g., the solid model  320 ) (step  722 ). Steps  719 - 722  may be similar to steps  703 - 705  of  FIG.  27    and may be repeated as desired by the user to simulate different combinations of treatment options and/or physiologic parameters. 
     Alternatively, rather than calculating the resistance along segments from the three-dimensional model (e.g., as described above for steps  717  and  718 ), flow and pressure at intervals along the centerline may be prescribed into a lumped parameter or one-dimensional model. The effective resistances or loss coefficients may be solved for under the constraints of the boundary conditions and prescribed flow and pressure. 
     Also, the flow rates and pressure gradients across individual segments may be used to compute an epicardial coronary resistance using the solution derived from the reduced-order model (e.g., as described above for step  721 ). The epicardial coronary resistance may be calculated as an equivalent resistance of the epicardial coronary arteries (the portions of the coronary arteries and the branches that extend therefrom included in the patient-specific model reconstructed from medical imaging data). This may have clinical significance in explaining why patients with diffuse atherosclerosis in the coronary arteries may exhibit symptoms of ischemia (restriction in blood supply). Also, the flow per unit of myocardial tissue volume (or mass) and/or the flow per unit of cardiac work under conditions of simulated pharmacologically-induced hyperemia or varying exercise intensity may be calculated using data from the reduced-order models. 
     As a result, the accuracy of three-dimensional blood flow modeling may be combined with the computational simplicity and relative speed inherent in one-dimensional and lumped parameter modeling technologies. Three-dimensional computational methods may be used to numerically derive patient-specific one-dimensional or lumped parameter models that embed numerically-derived empirical models for pressure losses over normal segments, stenoses, junctions, and other anatomical features. Improved diagnosis for patients with cardiovascular disease may be provided, and planning of medical, interventional, and surgical treatments may be performed faster. 
     Also, the accuracy of three-dimensional computational fluid dynamics technologies may be combined with the computational simplicity and performance capabilities of lumped parameter and one-dimensional models of blood flow. A three-dimensional geometric and physiologic model may be decomposed automatically into a reduced-order one-dimensional or lumped parameter model. The three-dimensional model may be used to compute the linear or nonlinear hemodynamic effects of blood flow through normal segments, stenoses, and/or branches, and to set the parameters of empirical models. The one-dimensional or lumped parameter models may more efficiently and rapidly solve for blood flow and pressure in a patient-specific model, and display the results of the lumped parameter or one-dimensional solutions. 
     The reduced order patient-specific anatomic and physiologic model may be used to determine the effect of different medications or lifestyle changes (e.g., cessation of smoking, changes in diet, or increased physical activity) that alters heart rate, stroke volume, blood pressure, or coronary microcirculatory function on coronary artery blood flow. Such information may be used to optimize medical therapy or avert potentially dangerous consequences of medications. The reduced order model may also be used to determine the effect on coronary artery blood flow of alternate forms and/or varying levels of physical activity or risk of exposure to potential extrinsic force, e.g., when playing football, during space flight, when scuba diving, during airplane flights, etc. Such information may be used to identify the types and level of physical activity that may be safe and efficacious for a specific patient. The reduced order model may also be used to predict a potential benefit of percutaneous coronary interventions on coronary artery blood flow in order to select the optimal interventional strategy, and/or to predict a potential benefit of coronary artery bypass grafting on coronary artery blood flow in order to select the optimal surgical strategy. 
     The reduced order model may also be used to illustrate potential deleterious effects of an increase in the burden of arterial disease on coronary artery blood flow and to predict, using mechanistic or phenomenological disease progression models or empirical data, when advancing disease may result in a compromise of blood flow to the heart muscle. Such information may enable the determination of a “warranty period” in which a patient observed to be initially free from hemodynamically significant disease using noninvasive imaging may not be expected to require medical, interventional, or surgical therapy, or alternatively, the rate at which progression might occur if adverse factors are continued. 
     The reduced order model may also be used to illustrate potential beneficial effects on coronary artery blood flow resulting from a decrease in the burden of coronary artery disease and to predict, using mechanistic or phenomenological disease progression models or empirical data, when regression of disease may result in increased blood flow through the coronary arteries to the heart muscle. Such information may be used to guide medical management programs including, but not limited to, changes in diet, increased physical activity, prescription of statins or other medications, etc. 
     The reduced order model may also be incorporated into an angiography system to allow for live computation of treatment options while a physician examines a patient in a cardiac catheterization lab. The model may be registered to the same orientation as the angiography display, allowing side-by-side or overlapping results of a live angiographic view of the coronary arteries with simulated blood flow solutions. The physician may plan and alter treatment plans as observations are made during procedures, allowing for relatively rapid feedback before medical decisions are made. The physician may take pressure, FFR, or blood flow measurements invasively, and the measurements may be utilized to further refine the model before predictive simulations are performed. 
     The reduced order model may also be incorporated into a medical imaging system or workstation. If derived from a library of previous patient-specific simulation results, then the reduced order models may be used in conjunction with geometric segmentation algorithms to relatively rapidly solve for blood flow information after completing an imaging scan. 
     The reduced order model may also be used to model the effectiveness of new medical therapies or the cost/benefit of treatment options on large populations of patients. A database of multiple patient-specific lumped parameter models (e.g., hundreds, thousands, or more) may provide models to solve in relatively short amounts of time. Relatively quick iteration and optimization may be provided for drug, therapy, or clinical trial simulation or design. Adapting the models to represent treatments, patient responses to drugs, or surgical interventions may allow estimates of effectiveness to be obtained without the need to perform possibly costly and potentially risky large-scale clinical trials. 
     VII. Other Results 
     A. Assessing Myocardial Perfusion 
     Other results may be calculated. For example, the computational analysis may provide results that quantify myocardial perfusion (blood flow through the myocardium). Quantifying myocardial perfusion may assist in identifying areas of reduced myocardial blood flow, such as due to ischemia (a restriction in a blood supply), scarring, or other heart problems. 
       FIG.  29    shows a schematic diagram relating to a method  800  for providing various information relating to myocardial perfusion in a specific patient, according to an exemplary embodiment. The method  800  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  800  may be performed using one or more inputs  802 . The inputs  802  may include medical imaging data  803  of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and heart, such as CCTA data (e.g., obtained in step  100  of  FIG.  2   ). The inputs  802  may also include additional physiological data  804  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in step  100  of  FIG.  2   ). The additional physiological data  804  may be obtained noninvasively. The inputs  802  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s myocardial tissue may be created based on the imaging data  803  (step  810 ) and the geometric model may be divided into segments or volumes (step  812 ). For example,  FIG.  31    shows a three-dimensional geometric model  846  including a three-dimensional geometric model  838  of the patient&#39;s myocardial tissue divided into segments  842 . The sizes and locations of the individual segments  842  may be determined based on the locations of the outflow boundaries  324  ( FIG.  8   ) of the coronary arteries (and the branches extending therefrom), the sizes of the blood vessels in or connected to the respective segment  842  (e.g., the neighboring blood vessels), etc. The division of the geometric myocardial model  838  into segments  842  may be performed using various known methods, such as a fast marching method, a generalized fast marching method, a level set method, a diffusion equation, equations governing flow through a porous media, etc. 
     The three-dimensional geometric model may also include a portion of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom), which may be modeled based on the imaging data  803  (step  814 ). For example, the three-dimensional geometric model  846  of  FIG.  31    includes a three-dimensional geometric model  837  of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom) and the three-dimensional geometric model  838  of the patient&#39;s myocardial tissue created in step  810 . 
     Referring back to  FIG.  29   , a computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine a solution that includes information about the patient&#39;s coronary blood flow under a physical condition determined by the user (step  816 ). For example, the physical condition may include rest, a selected level of hyperemia, a selected level of exercise or exertion, or other conditions. The solution may provide information, such as blood flow and pressure, at various locations in the anatomy of the patient modeled in step  814  and under the specified physical condition. The computational analysis may be performed using boundary conditions at the outflow boundaries  324  ( FIG.  8   ) derived from lumped parameter or one-dimensional models. The one-dimensional models may be generated to fill the segments  842  as described below in connection with  FIG.  30   . 
     Based on the blood flow information determined in step  816 , the perfusion of blood flow into the respective segments  842  of the myocardium created in step  812  may be calculated (step  818 ). For example, the perfusion may be calculated by dividing the flow from each outlet of the outflow boundaries  324  ( FIG.  8   ) by the volume of the segmented myocardium to which the outlet perfuses. 
     The perfusion for the respective segments of the myocardium determined in step  818  may be displayed on the geometric model of the myocardium generated in step  810  or  812  (e.g., the three-dimensional geometric model  838  of the patient&#39;s myocardial tissue shown in  FIG.  31   ) (step  820 ). For example,  FIG.  31    shows that the segments  842  of the myocardium of the geometric model  838  may be illustrated with a different shade or color to indicate the perfusion of blood flow into the respective segments  842 . 
       FIG.  30    shows another schematic diagram relating to a method  820  for providing various information relating to myocardial perfusion in a specific patient, according to an exemplary embodiment. The method  820  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  820  may be performed using one or more inputs  832 , which may include medical imaging data  833  of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and heart, such as CCTA data (e.g., obtained in step  100  of  FIG.  2   ). The inputs  832  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s myocardial tissue may be created based on the imaging data  833  (step  835 ). The model may also include a portion of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom), which may also be created based on the imaging data  803 . For example, as described above,  FIG.  31    shows a three-dimensional geometric model  836  including the geometric model  837  of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom) and the geometric model  838  of the patient&#39;s myocardial tissue. Step  835  may include steps  810  and  814  of  FIG.  29    described above. 
     Referring back to  FIG.  30   , the geometric myocardial model  838  may be divided into volumes or segments  842  (step  840 ). Step  840  may include step  812  of  FIG.  29    described above. As described above,  FIG.  31    shows the three-dimensional geometric model  846  including the geometric model  838  of the patient&#39;s myocardial tissue divided into the segments  842 . 
     Referring back to  FIG.  30   , the geometric model  846  may be modified to include a next generation of branches  857  in the coronary tree (step  855 ). The location and size of the branches  857  (shown in dashed lines in  FIG.  31   ) may be determined based on centerlines for the coronary arteries (and the branches that extend therefrom). The centerlines may be determined, e.g., based on the imaging data  833  (step  845 ). An algorithm may also be used to determine the location and size of the branches  857  based on morphometric models (models used to predict vessel location and size downstream of the known outlets at the outflow boundaries  324  ( FIG.  8   )) and/or physiologic branching laws related to vessel size (step  850 ). The morphometric model may be augmented to the downstream ends of the coronary arteries (and the branches that extend therefrom) included in the geometric model  837 , and provided on the epicardial surface (the outer layer of heart tissue) or contained within the geometric model  838  of the myocardial wall. 
     The myocardium may be further segmented based on the branches  857  created in step  855  (step  860 ). For example,  FIG.  31    shows that segments  842  may be divided into subvolumes or subsegments  862 . 
     Additional branches  857  may be created in the subsegments  862 , and the subsegments  862  may be further segmented into smaller segments  867  (step  865 ). The steps of creating branches and sub-segmenting the volumes may be repeated until a desired resolution of volume size and/or branch size is obtained. The model  846 , which has been augmented to include new branches  857  in steps  855  and  865 , may then be used to compute coronary blood flow and myocardial perfusion into the subsegments, such as the subsegments  867  generated in step  865 . 
     Accordingly, the augmented model may be used to perform the computational analysis described above. The results of the computational analysis may provide information relating to the blood flow from the patient-specific coronary artery model, e.g., the model  837  of  FIG.  31   , into the generated morphometric model (including the branches  857  generated in steps  855  and  865 ), which may extend into each of the perfusion subsegments  867  generated in step  865 . The computational analysis may be performed using a static myocardial perfusion volume or a dynamic model incorporating data from coupled cardiac mechanics models. 
       FIG.  32    shows another schematic diagram relating to a method  870  for providing various information relating to myocardial perfusion in a specific patient, according to an exemplary embodiment. The method  870  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  870  may be performed using one or more inputs  872 . The inputs  872  may include medical imaging data  873  of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and heart, such as CCTA data (e.g., obtained in step  100  of  FIG.  2   ). The inputs  872  may also include additional physiological data  874  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in step  100  of  FIG.  2   ). The additional physiological data  874  may be obtained noninvasively. The inputs  872  may further include cardiac perfusion data  875  measured from the patient (e.g., using CT, PET, SPECT, etc.). The inputs  872  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom) may be created based on the imaging data  873  (step  880 ). For example,  FIG.  31    shows the three-dimensional geometric model  837  of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom). Step  880  may be similar to step  814  of  FIG.  29    described above. 
     A computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine a solution that includes information about the patient&#39;s coronary blood flow under a physical condition determined by the user (step  882 ). For example, the physical condition may include rest, a selected level of hyperemia, a selected level of exercise or exertion, or other conditions. The solution may provide information, such as blood flow and pressure, at various locations in the anatomy of the patient modeled in step  880  and under the specified physical condition. Step  882  may be similar to step  816  of  FIG.  29    described above. 
     Also, a three-dimensional geometric model of the patient&#39;s myocardial tissue may be created based on the imaging data  873  (step  884 ). For example, as described above,  FIG.  31    shows the three-dimensional geometric model  836  including the three-dimensional geometric model  838  of the patient&#39;s myocardial tissue (e.g., as created in step  884 ) and the three-dimensional geometric model  837  of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom) (e.g., as created in step  880 ). Step  884  may be similar to step  810  of  FIG.  29    described above. 
     The geometric model may be divided into segments or subvolumes (step  886 ). For example,  FIG.  31    shows the geometric model  846  including the model  838  of the patient&#39;s myocardial tissue divided into segments  842 . Step  886  may be similar to step  812  of  FIG.  29    described above. 
     Based on the blood flow information determined in step  882 , the perfusion of blood flow into the respective segments  842  of the myocardium created in step  886  may be calculated (step  888 ). Step  888  may be similar to step  818  of  FIG.  29    described above. 
     The calculated perfusion for the respective segments of the myocardium may be displayed on the geometric model of the myocardium generated in step  884  or  886  (e.g., the three-dimensional geometric model  838  of the patient&#39;s myocardial tissue shown in  FIG.  31   ) (step  890 ). For example,  FIG.  31    shows that the segments  842  of the myocardium of the geometric model  838  may be illustrated with a different shade or color to indicate the perfusion of blood flow into the respective segments  842 . Step  890  may be similar to step  820  of  FIG.  29    described above. 
     The simulated perfusion data mapped onto the three-dimensional geometric model of the myocardium in step  890  may be compared with the measured cardiac perfusion data  875  (step  892 ). The comparison may be performed, e.g., on a voxel-based representation of the myocardium or a different discrete representation of the myocardium, e.g. a finite element mesh. The comparison may indicate the differences in the simulated and measured perfusion data using various colors and/or shades on the three-dimensional representation of the myocardium. 
     The boundary conditions at the outlets of the three-dimensional geometric model created in step  880  may be adjusted to decrease the error between the simulated and measured perfusion data (step  894 ). For example, in order to reduce the error, the boundary conditions may be adjusted so that the prescribed resistance to flow of the vessels feeding a region (e.g., the segment  842 ,  862 , or  867 ) where the simulated perfusion is lower than the measured perfusion may be reduced. Other parameters of the boundary conditions may be adjusted. Alternatively, the branching structure of the model may be modified. For example, the geometric model created in step  880  may be augmented as described above in connection with  FIGS.  30  and  31    to create the morphometric model. The parameters of the boundary conditions and/or morphometric models may be adjusted empirically or systematically using a parameter estimation or data assimilation method, such as the method described in U.S. Patent Application Publication No. 2010/0017171, which is entitled “Method for Tuning Patient-Specific Cardiovascular Simulations,” or other methods. 
     Steps  882 ,  888 ,  890 ,  892 ,  894 , and/or other steps of  FIG.  32    may be repeated, e.g., until the error between the simulated and measured perfusion data is below a predetermined threshold. As a result, the computational analysis may be performed using a model that relates anatomical information, coronary blood flow information, and myocardial perfusion information. Such a model may be useful for diagnostic purposes and for predicting the benefits of medical, interventional, or surgical therapies. 
     As a result, coronary artery blood flow and myocardial perfusion under resting and/or stress conditions may be simulated in a patient-specific geometric model constructed from three-dimensional medical imaging data. Measured myocardial perfusion data may be used in combination with simulated myocardial perfusion results to adjust the boundary conditions until the simulated myocardial perfusion results match the measured myocardial perfusion data within a given tolerance (e.g., as described above in connection with  FIG.  32   ). More accurate patient-specific coronary artery blood flow computations may be provided, and cardiologists may be enabled to predict coronary artery blood flow and myocardial perfusion under circumstances where measured data may be unavailable, such as when simulating the patient under maximum exercise or exertion, simulated treatments, or other conditions. 
     The patient-specific three-dimensional model of the left and/or right ventricle myocardium may be divided into perfusion segments or subvolumes. Also, a patient-specific three-dimensional geometric model of the coronary arteries determined from medical imaging data may be combined with a morphometric model of a portion of the remaining coronary arterial tree on the epicardial surface or contained in the left and/or right ventricle myocardial wall represented by the perfusion subvolumes to form an augmented model. The percentage of the total myocardial volume downstream of a given, e.g. diseased, location in the augmented model may be calculated. The percentage of the total myocardial blood flow at a given, e.g., diseased, location in the augmented model may also be calculated. The augmented model may be used to compute coronary blood flow and myocardial perfusion. The coronary blood flow model may also be modified until the simulated perfusion matches a measured perfusion data within a prescribed tolerance. 
     B. Assessing Plaque Vulnerability 
     The computational analysis may also provide results that quantify patient-specific biomechanical forces acting on plaque that may build up in the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom), e.g., coronary atherosclerotic plaque. The biomechanical forces may be caused by pulsatile pressure, flow, and heart motion. 
       FIG.  33    shows an example of plaque  900  built up along a blood vessel wall  902 , such as a wall of one of the main coronary arteries or one of the branches that extends therefrom. The difference in pressure and/or surface area between the upstream and downstream ends of the plaque may produce a force  904  acting on the plaque  900  at least along the direction of the blood flow, e.g., caused by the blood flowing through the vessel. Another force  906  may act on a surface of the plaque  900  at least along the direction toward and perpendicular to the vessel wall  902 . The force  906  may be caused by the blood pressure of the blood flowing through the vessel. Yet another force  908  may act on the surface of the plaque  900  at least along the direction of the blood flow, and may be due to hemodynamic forces during rest, exercise, etc. 
     The results may also assess the risk of plaque rupture (e.g., when plaque accumulated on a vessel wall becomes unstable and breaks off or breaks open) and the myocardial volume that may be affected by such rupture. The results may be assessed under various simulated physiological conditions, such as resting, exercising, etc. The plaque rupture risk may be defined as a ratio of simulated plaque stress to a plaque strength estimated using material composition data derived from CCTA or MRI (e.g., determined in step  100  of  FIG.  2   ). 
     For example,  FIG.  34    shows an example of results that the computational analysis may output. The results may include the three-dimensional geometric model  846  of  FIG.  31   , which may include the three-dimensional geometric model  837  of the patient&#39;s aorta and coronary arteries (and the branches that extend therefrom) and the three-dimensional geometric model  838  of the patient&#39;s myocardial tissue divided into segments  842 . The results may also indicate a location  910  in one of the coronary arteries (of the branches that extend therefrom) where plaque may be determined to be vulnerable, and the location  910  may be identified based on the assessment of the risk of plaque rupture as will be described below in further detail and/or based on input from a user. Also, as shown in  FIG.  34   , a myocardial segment  912  (of the plurality of segments  842 ) may be identified as having a high probability of low perfusion due to the rupture of the plaque identified at location  910 . 
       FIGS.  35  and  36    are schematic diagrams showing aspects of a method  920  for providing various information relating to assessing plaque vulnerability, myocardial volume risk, and myocardial perfusion risk in a specific patient, according to an exemplary embodiment. The method  920  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . The method  920  may be performed using one or more inputs  922 , and may include generating one or more models  930  based on the inputs  922 , performing one or more biomechanical analyses  940  based on the one or more of the models  930 , and providing various results based on the models  930  and the biomechanical analyses  940 . 
     The inputs  922  may include medical imaging data  923  of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and heart, such as CCTA data (e.g., obtained in step  100  of  FIG.  2   ). The inputs  922  may also include additional physiological data  924  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in step  100  of  FIG.  2   ). The additional physiological data  924  may be obtained noninvasively. The inputs  922  may be used to generate the models  930  and/or perform the biomechanical analyses  940  described below. 
     As noted above, one or more models  930  may be generated based on the inputs  922 . For example, the method  920  may include generating a hemodynamic model  932  including computed blood flow and pressure information at various locations throughout a three-dimensional geometric model of the patient&#39;s anatomy. The model of the patient&#39;s anatomy may be created using the medical imaging data  923 , e.g., the solid model  320  of  FIG.  8    generated in step  306  of  FIG.  3   , and/or the mesh  380  of  FIGS.  17 - 19    generated in step  312  of  FIG.  3   , and, in an exemplary embodiment, the hemodynamic model  932  may be the simulated blood pressure model  50  ( FIG.  1   ), the simulated blood flow model  52  ( FIG.  1   ), the cFFR model  54  ( FIG.  1   ), or other simulation produced after performing a computational analysis, e.g., as described above in connection with step  402  of  FIG.  3   . Solid mechanics models, including fluid structure interaction models, may be solved with the computational analysis with known numerical methods. Properties for the plaque and vessels may be modeled as linear or nonlinear, isotropic or anisotropic. The solution may provide stress and strain of the plaque and the interface between the plaque and the vessel. In the exemplary embodiment shown in  FIG.  36   , the hemodynamic model  932  is the cFFR model  54 . 
     The method  920  may include performing a biomechanical analysis  940  using the hemodynamic model  932  by computing a pressure  906  ( FIG.  33   ) and shear stress  908  ( FIG.  33   ) acting on a plaque luminal surface due to hemodynamic forces at various physiological states, such as rest, varying levels of exercise or exertion, etc. (step  942 ). The pressure  906  and shear stress  908  may be calculated based on information from the hemodynamic model  932 , e.g., blood pressure and flow. 
     Optionally, the method  920  may also include generating a geometric analysis model  934  for quantifying vessel deformation from four-dimensional imaging data, e.g., imaging data obtained at multiple phases of the cardiac cycle, such as the systolic and diastolic phases. The imaging data may be obtained using various known imaging methods. The geometric analysis model  934  may include information regarding vessel position, deformation, orientation, and size, e.g., due to cardiac motion, at the different phases of the cardiac cycle. For example, various types of deformation of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and the plaque, such as longitudinal lengthening (elongation) or shortening, twisting (torsion), radial expansion or compression, and bending, may be simulated by the geometric analysis model  934 . 
     The method  920  may include performing a biomechanical analysis  940  using the geometric analysis model  934  by computing various deformation characteristics, such as longitudinal lengthening (elongation) or shortening, twisting (torsion), radial expansion or compression, and bending, etc., of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), and the plaque due to cardiac-induced pulsatile pressure (step  944 ). These deformation characteristics may be calculated based on information from the geometric analysis model  934 , e.g., a change in vessel position, orientation, and size, over multiple phases of the cardiac cycle. 
     The calculation of the deformation characteristics may be simplified by determining centerlines or surface meshes of the modeled geometry (e.g., the geometry of the patient&#39;s aorta, coronary arteries (and the branches that extend therefrom), the plaque, etc.). To determine a change in the modeled geometry between different phases, branch ostia, calcified lesions, and soft plaque may be used as landmarks. In the regions that have no landmarks, cross-sectional area profiles along a length of the modeled geometry may be used to identify corresponding locations between the two image frames (to “register” the two image frames). Deformable registration algorithms based on raw image data may be used to extract three-dimensional deformation fields. The calculated three-dimensional deformation field may then be projected to a curvilinear axis aligned with the modeled geometry (e.g., the vessel length) to compute tangential and normal components of the deformation field. The resulting difference in modeled geometry (e.g., vessel length), angle of branch separation, and curvature between systole and diastole may be used to determine the strain experienced by a vessel. 
     The method  920  may also include generating a plaque model  936  for determining plaque composition and properties from the medical imaging data  923 . For example, the plaque model  936  may include information regarding density and other material properties of the plaque. 
     The method  920  may also include generating a vessel wall model  938  for computing information about the plaque, the vessel walls, and/or the interface between the plaque and the vessel walls. For example, the vessel wall model  938  may include information regarding stress and strain, which may be calculated based on the plaque composition and properties included in the plaque model  936 , the pressure  906  and shear stress  908  calculated in step  942 , and/or the deformation characteristics calculated in step  944 . 
     The method  920  may include performing a biomechanical analysis  940  using the vessel wall model  938  by computing stress (e.g., acute or cumulative stress) on the plaque due to hemodynamic forces and cardiac motion-induced strain (step  946 ). For example, the flow-induced force  904  ( FIG.  33   ) acting on the plaque may be computed. The stress or force on the plaque due to hemodynamic forces and cardiac motion-induced strain may be calculated based on information from the vessel wall model  938 , e.g., stress and strain on the plaque. 
     The method  920  may include determining further information based on one or more of the models  930  and one or more of the biomechanical analyses  940  described above. 
     A plaque rupture vulnerability index may be calculated (step  950 ). The plaque rupture vulnerability index may be calculated, e.g., based on total hemodynamic stress, stress frequency, stress direction, and/or plaque strength or other properties. For example, a region surrounding a plaque of interest may be isolated from the three-dimensional model  930  of the plaque, such as the plaque model  936 . The strength of the plaque may be determined from the material properties provided in the plaque model  936 . A hemodynamic and tissue stress on the plaque of interest, due to pulsatile pressure, flow, and heart motion, may be calculated under simulated baseline and exercise (or exertion) conditions by using the hemodynamic stresses and motion-induced strains previously computed in step  946 . The vulnerability of the plaque may be assessed based on the ratio of plaque stress to plaque strength. 
     A myocardial volume risk index (MVRI) may also be calculated (step  952 ). The MVRI may be defined as a percentage of the total myocardial volume affected by a plaque rupture and occlusion (closure or obstruction) of a vessel at a given location in the arterial tree. The MVRI may be calculated based on the portion of the myocardium supplied by the vessels downstream of the given plaque, which may take into account the size of the plaque with respect to the size of the downstream vessels and the probability that the plaque may flow into different vessels based on the three-dimensional hemodynamic solution. 
     The myocardium may be modeled and divided into segments  842  supplied by each vessel in the hemodynamic simulation (e.g., as described in connection with steps  835  and  840  of  FIG.  30   ). The geometric model may be modified to include a next generation of branches  857  in the coronary tree (e.g., as described in connection with step  855  of  FIG.  30   ), and the myocardium may be further segmented (e.g., as described in connection with step  860  of  FIG.  30   ). Additional branches  857  may be created in the subsegments  862 , and the subsegments  862  may be further segmented into smaller segments  867  (e.g., as described in connection with step  865  of  FIG.  30   ). Physiologic relationships, as previously described, may be used to relate the size of a vessel to a proportional amount of myocardium supplied. 
     Potential paths for a ruptured plaque to follow may be determined. The hemodynamic solution may be used to determine a percent chance that a plaque fragment or embolus may flow into different downstream vessels. 
     The size of the ruptured plaque may be compared with the size of the downstream vessels to determine where the plaque may eventually create an impediment to flow. This information may be combined with the vulnerability index to provide a probability map of the volume of the myocardium that may potentially be affected by the ruptured plaque. The MVRI may be assigned to each potential affected segment.  FIG.  34    shows an example of a segment  912  where the vulnerable plaque at location  910  in a distal vessel has a high probability of affecting a small area of the myocardium. 
     A myocardial perfusion risk index (MPRI) may also be calculated (step  954 ). The MPRI may be defined as a percentage of the total myocardial blood flow affected by a plaque rupture and occlusion of a vessel at a given location in the arterial tree. For example, a rupture of plaque in a distal portion of the LAD artery would yield a lower MVRI and a lower MPRI than a rupture of plaque in a proximal portion of the LAD artery. These indices may differ, however, if a portion of the myocardial volume affected by a vulnerable plaque in a feeding vessel is not viable (e.g., due to scar tissue that may form subsequent to myocardial infarction). Thus, the MPRI indicates a potential loss of perfusion to the myocardium segments, rather than the volume affected as indicated by the MVRI. The perfusion rate to each segment  842 ,  862 , or  867  of FIG.  31  may be calculated, and the loss of perfusion may be calculated based on the vulnerability index, the hemodynamic solution, and the sizes of the plaque and vessels. 
     As a result, plaque stress due to pulsatile blood pressure, pulsatile blood flow, pulsatile blood shear stress, and/or pulsatile cardiac motion may be calculated, and plaque strength may be estimated based on medical imaging data, and indices relating to plaque vulnerability, myocardial volume risk, and myocardial perfusion risk may be quantified. 
     VIII. Other Applications 
     The embodiments described above are associated with assessing information about coronary blood flow in a patient. Alternatively, the embodiments may also be adapted to blood flow in other areas of the body, such as, but not limited to, the carotid, peripheral, abdominal, renal, femoral, popliteal, and cerebral arteries. 
     A. Modeling Intracranial and Extracranial Blood Flow 
     Embodiments relating to the cerebral arteries will now be described. Numerous diseases may influence or be affected by blood flow and pressure in the extracranial or intracranial arteries. Atherosclerotic disease in the extracranial, e.g. carotid and vertebral, arteries may restrict blood flow to the brain. A severe manifestation of atherosclerotic disease may lead to a transient ischemic attack or an ischemic stroke. Aneurysmal disease in the intracranial or extracranial arteries may pose a risk of embolization leading to ischemic stroke or aneurysm rupture leading to hemorrhagic stroke. Other conditions such as head trauma, hypertension, head and neck cancer, arteriovenous malformations, orthostatic intolerance, etc., may also affect cerebral blood flow. Furthermore, reductions in cerebral blood flow may induce symptoms such as syncope or impact chronic neurologic disorders such as dementia subsequent to Alzheimer&#39;s or Parkinson&#39;s disease. 
     Patients with known or suspected extracranial or intracranial arterial disease may typically receive one or more of the following noninvasive diagnostic tests: US, MRI, CT, PET. These tests, however, may not be able to efficiently provide anatomic and physiologic data for extracranial and intracranial arteries for most patients. 
       FIG.  37    is a diagram of cerebral arteries, including intracranial (within the cranium) and extracranial (outside the cranium) arteries. The methods for determining information regarding patient-specific intracranial and extracranial blood flow may be generally similar to the methods for determining information regarding patient-specific coronary blood flow as described above. 
       FIG.  38    is a schematic diagram showing aspects of a method  1000  for providing various information relating to intracranial and extracranial blood flow in a specific patient. The method  1000  may be implemented in a computer system, e.g., similar to the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . The method  1000  may be performed using one or more inputs  1010 , and may include generating one or more models  1020  based on the inputs  1010 , assigning one or more conditions  1030  based on the inputs  1010  and/or the models  1020 , and deriving one or more solutions  1040  based on the models  1020  and the conditions  1030 . 
     The inputs  1010  may include medical imaging data  1011  of the patient&#39;s intracranial and extracranial arteries, e.g., the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), vertebral arteries (shown in  FIG.  37   ), and brain, such as CCTA data (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The inputs  1010  may also include a measurement  1012  of the patient&#39;s brachial blood pressure, carotid blood pressure (e.g., using tonometry), and/or other measurements (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The measurements  1012  may be obtained noninvasively. The inputs  1010  may be used to generate the model(s)  1020  and/or determine the condition(s)  1030  described below. 
     As noted above, one or more models  1020  may be generated based on the inputs  1010 . For example, the method  1000  may include generating one or more patient-specific three-dimensional geometric models of the patient&#39;s intracranial and extracranial arteries based on the imaging data  1011  (step  1021 ). The three-dimensional geometric model  1021  may be generated using similar methods as described above for generating the solid model  320  of  FIG.  8    and the mesh  380  of  FIGS.  17 - 19   . For example, similar steps as steps  306  and  312  of  FIG.  3    may be used to generate a three-dimensional solid model and mesh representing the patient&#39;s intracranial and extracranial arteries. 
     Referring back to  FIG.  38   , the method  1000  may also include generating one or more physics-based blood flow models (step  1022 ). For example, the blood flow model may be a model that represents the flow through the patient-specific geometric model generated in step  1021 , heart and aortic circulation, distal intracranial and extracranial circulation, etc. The blood flow model may include reduced order models as described above in connection with step  310  of  FIG.  3   , e.g., the lumped parameter models or distributed (one-dimensional wave propagation) models, etc., at the inflow boundaries and/or outflow boundaries of the three-dimensional geometric model  1021 . Alternatively, the inflow boundaries and/or outflow boundaries may be assigned respective prescribed values or field for velocity, flow rate, pressure, or other characteristic, etc. As another alternative the inflow boundary may be coupled to a heart model, e.g., including the aortic arch. The parameters for the inflow and/or outflow boundaries may be adjusted to match measured or selected physiological conditions including, but limited to, cardiac output and blood pressure. 
     As noted above, one or more conditions  1030  may be determined based on the inputs  1010  and/or the models  1020 . The conditions  1030  include the parameters calculated for the boundary conditions determined in step  1022  (and step  310  of  FIG.  3   ). For example, the method  1000  may include determining a condition by calculating a patient-specific brain or head volume based on the imaging data  1011  (e.g., obtained in a similar manner as described above in connection with step  240  of  FIG.  3   ) (step  1031 ). 
     The method  1000  may include determining a condition by calculating, using the brain or head volume calculated in step  1031 , a resting cerebral blood flow Q based on the relationship Q=Q o M α , where α is a preset scaling exponent, M is the brain mass determined from the brain or head volume, and Q o  is a preset constant (e.g., similar to the physiological relationship described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   ) (step  1032 ). Alternatively, the relationship may have the form Q∝Q o M α , as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   . 
     The method  1000  may also include determining a condition by calculating, using the resulting coronary flow calculated in step  1032  and the patient&#39;s measured blood pressure  1012 , a total resting cerebral resistance (e.g., similar to the methods described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   ) (step  1033 ). For example, the total cerebral blood flow Q at the outflow boundaries of the three-dimensional geometric model  1021  under baseline (resting) conditions determined in step  1032  and the measured blood pressure  1012  may be used to determine a total resistance R at the outflow boundaries based on a preset, experimentally-derived equation. Resistance, capacitance, inductance, and other variables associated with various electrical components used in lumped parameter models may be incorporated into the boundary conditions (e.g., as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   ). 
     The method  1000  may also include determining a condition by calculating, using the total resting cerebral resistance calculated in step  1033  and the models  1020 , individual resistances for the individual intracranial and extracranial arteries (step  1034 ). For example, similar to the methods described above in connection with step  310  of  FIG.  3   , the total resting cerebral resistance R calculated in step  1033  may be distributed to the individual intracranial and extracranial arteries based on the sizes (e.g., determined from the geometric model generated in step  1021 ) of the distal ends of the individual intracranial and extracranial arteries, and based on the relationship R=R o d β , where R is the resistance to flow at a particular distal end, and R o  is a preset constant, d is the size (e.g., diameter of that distal end), and β is a preset power law exponent, as described above in connection with determining the lumped parameter model in step  310  of  FIG.  3   . 
     Referring back to  FIG.  38   , the method  1000  may include adjusting the boundary conditions based on one or more physical conditions of the patient (step  1035 ). For example, the parameters determined in steps  1031 - 1034  may be modified based on whether the solution  1040  is intended to simulate rest, varying levels of stress, varying levels of baroreceptor response or other autonomic feedback control, varying levels of hyperemia, varying levels of exercise, exertion, hypertension, or hypotension, different medications, postural change, and/or other conditions. The parameters (e.g., the parameters relating to the boundary conditions at the outflow boundaries) may also be adjusted based on a vasodilatory capacity of the intracranial and extracranial arteries (the ability of the blood vessels to widen), e.g., due to microvascular dysfunction or endothelial health. 
     Based on the inputs  1010 , the models  1020 , and the conditions  1030 , a computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine the solution  1040  that includes information about the patient&#39;s coronary blood flow under the physical conditions selected in step  1035  (step  1041 ). Examples of information that may be provided from the solution  1040  may be similar to the examples provided above in connection with  FIGS.  1  and  21 - 24   , e.g., a simulated blood pressure model, a simulated blood flow model, etc. The results may also be used to determine, e.g., flow rate, total brain flow, vessel wall shear stress, traction or shear force acting on vessel walls or atherosclerotic plaque or aneurysm, particle/blood residence time, vessel wall movement, blood shear rate, etc. These results may also be used to analyze where emboli leaving from a specific region in the vascular system may most likely travel due to blood circulation. 
     The computer system may allow the user to simulate various changes in geometry. For example, the models  1020 , e.g., the patient-specific geometric model generated in step  1021  may be modified to predict the effect of occluding an artery (e.g., an acute occlusion). In some surgical procedures, such as when removing cancerous tumors, one or more extracranial arteries may be damaged or removed. Thus, the patient-specific geometric model generated in step  1021  may also be modified to simulate the effect of preventing blood flow to one or more of the extracranial arteries in order to predict the potential for collateral pathways for supplying adequate blood flow for the patient. 
     The computer system may allow the user to simulate the results of various treatment options, such as interventional or surgical repair, e.g., of an acute occlusion. The simulations may be performed more quickly by replacing the three-dimensional solid model or mesh representing the intracranial and extracranial arteries, as described above, with reduced order models, as described above in connection with  FIGS.  27  and  28   . As a result, the reduced order models, such as one-dimensional or lumped parameter models, may more efficiently and rapidly solve for blood flow and pressure in a patient-specific model and display the results of solutions. 
     A response to vasodilatory stimuli by a specific patient may be predicted based on hemodynamic information for the patient at rest or based on population-based data for different disease states. For example, in a baseline (resting) simulation is run (e.g., as described above in step  1041 ) with flow distribution assigned based on power laws and brain mass (e.g., as described above in connection with step  1032 ). The resistance values (e.g., determined in steps  1033  and  1034 ) may be adjusted to allow adequate perfusion. Alternatively, data from patient populations with such factors as diabetes, medications, and past cardiac events are used to assign different resistances. The adjustment in resistance under resting conditions, alone or in combination with hemodynamic information (e.g., wall shear stress or a relationship of flow and vessel size), may be used to determine a remaining capacity for distal cerebral vessels to dilate. Patients requiring resistance reductions to meet resting flow requirements or patients with a high flow to vessel size ratio may have a diminished capacity to further dilate their vessels under physiologic stress. 
     Flow rates and pressure gradients across individual segments of the cerebral arteries (e.g., as determined in step  1041 ) may be used to compute a cerebral arterial resistance. The cerebral arterial resistance may be calculated as an equivalent resistance of the portions of the extracranial and intracranial arteries included in the patient-specific geometric model generated from medical imaging data (e.g., generated in step  1021 ). The cerebral arterial resistance may have clinical significance in explaining why patients with diffuse atherosclerosis in extracranial and/or intracranial arteries may exhibit symptoms of syncope (temporary loss of consciousness or posture, e.g., fainting) or ischemia (restriction in blood supply). 
     Also, the flow per unit of brain tissue volume (or mass) under baseline or altered physiologic conditions may be calculated, e.g., based on the flow information determined in step  1041  and the brain tissue volume or mass calculated in step  1031 . This calculation may be useful in understanding the impact of reductions in blood flow on chronic neurological disorders. This calculation may also be useful in selecting or refining medical therapies, e.g., dosage of antihypertensives. Additional results may include quantifying the effects of trauma, concussion, external physiologic stresses, excess G-forces, weightlessness, space flight, deep sea decompression (e.g., the bends), etc. 
     The combined patient-specific anatomic (geometric) and physiologic (physics-based) model may be used to determine the effect of different medications or lifestyle changes (e.g., cessation of smoking, changes in diet, or increased physical activity) that alters heart rate, stroke volume, blood pressure, or cerebral microcirculatory function on cerebral artery blood flow. The combined model may also be used to determine the effect on cerebral artery blood flow of alternate forms and/or varying levels of physical activity or risk of exposure to potential extrinsic force, e.g., when playing football, during space flight, when scuba diving, during airplane flights, etc. Such information may be used to identify the types and level of physical activity that may be safe and efficacious for a specific patient. The combined model may also be used to predict a potential benefit of percutaneous interventions on cerebral artery blood flow in order to select the optimal interventional strategy, and/or to predict a potential benefit of carotid endarterectomy or external-carotid-to-internal-carotid bypass grafting on cerebral artery blood flow in order to select the optimal surgical strategy. 
     The combined model may also be used to illustrate potential deleterious effects of an increase in the burden of arterial disease on cerebral artery blood flow and to predict, using mechanistic or phenomenological disease progression models or empirical data, when advancing disease may result in a compromise of blood flow to the brain. Such information may enable the determination of a “warranty period” in which a patient observed to be initially free from hemodynamically significant disease using noninvasive imaging may not be expected to require medical, interventional, or surgical therapy, or alternatively, the rate at which progression might occur if adverse factors are continued. 
     The combined model may also be used to illustrate potential beneficial effects on cerebral artery blood flow resulting from a decrease in the burden of disease and to predict, using mechanistic or phenomenological disease progression models or empirical data, when regression of disease may result in increased blood flow to the brain. Such information may be used to guide medical management programs including, but not limited to, changes in diet, increased physical activity, prescription of statins or other medications, etc. 
     The combined model may also be used to predict the effect of occluding an artery. In some surgical procedures, such as the removal of cancerous tumors, some extracranial arteries may be damaged or removed. Simulating the effect of preventing blood flow to one of the extracranial arteries may allow prediction of the potential for collateral pathways to supply adequate blood flow for a specific patient. 
     i. Assessing Cerebral Perfusion 
     Other results may be calculated. For example, the computational analysis may provide results that quantify cerebral perfusion (blood flow through the cerebrum). Quantifying cerebral perfusion may assist in identifying areas of reduced cerebral blood flow. 
       FIG.  39    shows a schematic diagram relating to a method  1050  for providing various information relating to cerebral perfusion in a specific patient, according to an exemplary embodiment. The method  1050  may be implemented in the computer system described above, e.g., similar to the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  1050  may be performed using one or more inputs  1052 . The inputs  1052  may include medical imaging data  1053  of the patient&#39;s intracranial and extracranial arteries, e.g., the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), vertebral arteries (shown in  FIG.  37   ), and brain, such as CCTA data (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The inputs  1052  may also include additional physiological data  1054  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The additional physiological data  1054  may be obtained noninvasively. The inputs  1052  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s brain tissue may be created based on the imaging data  1053  (step  1060 ) and the geometric model may be divided into segments or volumes (step  1062 ) (e.g., in a similar manner as described above in connection with  FIGS.  29 - 32   ). The sizes and locations of the individual segments may be determined based on the locations of the outflow boundaries of the intracranial and extracranial arteries, the sizes of the blood vessels in or connected to the respective segments (e.g., the neighboring blood vessels), etc. The division of the geometric model into segments may be performed using various known methods, such as a fast marching method, a generalized fast marching method, a level set method, a diffusion equation, equations governing flow through a porous media, etc. 
     The three-dimensional geometric model may also include a portion of the patient&#39;s intracranial and extracranial arteries, which may be modeled based on the imaging data  1053  (step  1064 ). For example, in steps  1062  and  1064 , a three-dimensional geometric model may be created that includes the brain tissue and the intracranial and extracranial arteries. 
     A computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine a solution that includes information about the patient&#39;s cerebral blood flow under a physical condition determined by the user (step  1066 ). For example, the physical condition may include rest, varying levels of stress, varying levels of baroreceptor response or other autonomic feedback control, varying levels of hyperemia, varying levels of exercise or exertion, different medications, postural change, and/or other conditions. The solution may provide information, such as blood flow and pressure, at various locations in the anatomy of the patient modeled in step  1064  and under the specified physical condition. The computational analysis may be performed using boundary conditions at the outflow boundaries derived from lumped parameter or one-dimensional models. The one-dimensional models may be generated to fill the segments of the brain tissue as described below in connection with  FIG.  40   . 
     Based on the blood flow information determined in step  1066 , the perfusion of blood flow into the respective segments of the brain created in step  1062  may be calculated (step  1068 ). For example, the perfusion may be calculated by dividing the flow from each outlet of the outflow boundaries by the volume of the segmented brain to which the outlet perfuses. 
     The perfusion for the respective segments of the brain determined in step  1068  may be displayed on the geometric model of the brain generated in step  1060  or  1062  (step  1070 ). For example, the segments of the brain shown in the geometric model created in step  1060  may be illustrated with a different shade or color to indicate the perfusion of blood flow into the respective segments. 
       FIG.  40    shows another schematic diagram relating to a method  1100  for providing various information relating to cerebral perfusion in a specific patient, according to an exemplary embodiment. The method  1100  may be implemented in the computer system described above, e.g., similar to the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  1100  may be performed using one or more inputs  1102 , which may include medical imaging data  1103  of the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), vertebral arteries (shown in  FIG.  37   ), and brain, such as CCTA data (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The inputs  1102  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s brain tissue may be created based on the imaging data  1103  (step  1110 ). The model may also include a portion of the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), and vertebral arteries (shown in  FIG.  37   ), which may also be created based on the imaging data  1103 . For example, as described above, a three-dimensional geometric model may be created that includes the brain tissue and the intracranial and extracranial arteries. Step  1110  may include steps  1060  and  1064  of  FIG.  39    described above. 
     The geometric brain tissue model created in step  1110  may be divided into volumes or segments (step  1112 ). Step  1112  may include step  1062  of  FIG.  39    described above. The geometric brain tissue model may also be further modified to include a next generation of branches in the cerebral tree (step  1118 ) (e.g., in a similar manner as described above in connection with  FIGS.  29 - 32   ). The location and size of the branches may be determined based on centerlines for the intracranial and extracranial arteries. The centerlines may be determined, e.g., based on the imaging data  1103  (step  1114 ). An algorithm may also be used to determine the location and size of the branches based on morphometric models (models used to predict vessel location and size downstream of the known outlets at the outflow boundaries) and/or physiologic branching laws related to vessel size (step  1116 ). The morphometric model may be augmented to the downstream ends of the intracranial and extracranial arteries included in the geometric model, and provided on the outer layer of brain tissue or contained within the geometric model of the brain tissue. 
     The brain may be further segmented based on the branches created in step  1118  (step  1120 ) (e.g., in a similar manner as described above in connection with  FIGS.  29 - 32   ). Additional branches may be created in the subsegments, and the subsegments may be further segmented into smaller segments (step  1122 ) (e.g., in a similar manner as described above in connection with  FIGS.  29 - 32   ). The steps of creating branches and sub-segmenting the volumes may be repeated until a desired resolution of volume size and/or branch size is obtained. The geometric model, which has been augmented to include new branches in steps  1118  and  1122 , may then be used to compute cerebral blood flow and cerebral perfusion into the subsegments, such as the subsegments generated in step  1122 . 
     Accordingly, the augmented model may be used to perform the computational analysis described above. The results of the computational analysis may provide information relating to the blood flow from the patient-specific cerebral artery model, into the generated morphometric model (including the branches generated in steps  1118  and  1122 ), which may extend into each of the perfusion subsegments generated in step  1122 . 
       FIG.  41    shows another schematic diagram relating to a method  1150  for providing various information relating to cerebral perfusion in a specific patient, according to an exemplary embodiment. The method  1150  may be implemented in the computer system described above, e.g., the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . 
     The method  1150  may be performed using one or more inputs  1152 . The inputs  1152  may include medical imaging data  1153  of the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), vertebral arteries (shown in  FIG.  37   ), and brain, such as CCTA data (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The inputs  1152  may also include additional physiological data  1154  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in step  100  of  FIG.  2   ). The additional physiological data  1154  may be obtained noninvasively. The inputs  1152  may further include brain perfusion data  1155  measured from the patient (e.g., using CT, PET, SPECT, MRI, etc.). The inputs  1152  may be used to perform the steps described below. 
     A three-dimensional geometric model of the patient&#39;s intracranial and extracranial arteries may be created based on the imaging data  1153  (step  1160 ). Step  1160  may be similar to step  1064  of  FIG.  39    described above. 
     A computational analysis may be performed, e.g., as described above in connection with step  402  of  FIG.  3   , to determine a solution that includes information about the patient&#39;s cerebral blood flow under a physical condition determined by the user (step  1162 ). For example, the physical condition may include rest, varying levels of stress, varying levels of baroreceptor response or other autonomic feedback control, varying levels of hyperemia, varying levels of exercise or exertion, different medications, postural change, and/or other conditions. The solution may provide information, such as blood flow and pressure, at various locations in the anatomy of the patient modeled in step  1160  and under the specified physical condition. Step  1162  may be similar to step  1066  of  FIG.  39    described above. 
     Also, a three-dimensional geometric model of the patient&#39;s brain tissue may be created based on the imaging data  1153  (step  1164 ). For example, in steps  1160  and  1164 , a three-dimensional geometric model may be created that includes the brain tissue and the intracranial and extracranial arteries. Step  1164  may be similar to step  1060  of  FIG.  39    described above. 
     The geometric model may be divided into segments or subvolumes (step  1166 ). Step  1166  may be similar to step  1062  of  FIG.  39    described above. 
     Based on the blood flow information determined in step  1162 , the perfusion of blood flow into the respective segments of the brain tissue created in step  1166  may be calculated (step  1168 ). Step  1168  may be similar to step  1068  of  FIG.  39    described above. 
     The calculated perfusion for the respective segments of the brain tissue may be displayed on the geometric model of the brain tissue generated in step  1164  or  1166  (step  1170 ). Step  1170  may be similar to step  1070  of  FIG.  39    described above. 
     The simulated perfusion data mapped onto the three-dimensional geometric model of the brain tissue in step  1170  may be compared with the measured cerebral perfusion data  1155  (step  1172 ). The comparison may indicate the differences in the simulated and measured perfusion data using various colors and/or shades on the three-dimensional representation of the brain tissue. 
     The boundary conditions at the outlets of the three-dimensional geometric model created in step  1160  may be adjusted to decrease the error between the simulated and measured perfusion data (step  1174 ). For example, in order to reduce the error, the boundary conditions may be adjusted so that the prescribed resistance to flow of the vessels feeding a region (e.g., the segments created in step  1166 ) where the simulated perfusion is lower than the measured perfusion may be reduced. Other parameters of the boundary conditions may be adjusted. Alternatively, the branching structure of the model may be modified. For example, the geometric model created in step  1160  may be augmented as described above in connection with  FIG.  40    to create the morphometric model. The parameters of the boundary conditions and/or morphometric models may be adjusted empirically or systematically using a parameter estimation or data assimilation method, such as the method described in U.S. Patent Application Publication No. 2010/0017171, which is entitled “Method for Tuning Patient-Specific Cardiovascular Simulations,” or other methods. 
     Steps  1162 ,  1168 ,  1170 ,  1172 ,  1174 , and/or other steps of  FIG.  41    may be repeated, e.g., until the error between the simulated and measured perfusion data is below a predetermined threshold. As a result, the computational analysis may be performed using a model that relates anatomical information, cerebral blood flow information, and cerebral perfusion information. Such a model may be useful for diagnostic purposes and for predicting the benefits of medical, interventional, or surgical therapies. 
     As a result, extracranial and intracranial arterial blood flow and cerebral perfusion under baseline conditions or altered physiologic states may be computed. Cerebral perfusion data may be used in combination with simulated cerebral perfusion results to adjust the boundary conditions of the intracranial artery blood flow computations until the simulated cerebral perfusion results match the measured cerebral perfusion data within a given tolerance. Thus, more accurate patient-specific extracranial and intracranial arterial blood flow computations may be provided and physicians may predict cerebral artery blood flow and cerebral perfusion when measured data may be unavailable, e.g., certain physical conditions such as exercise, exertion, postural changes, or simulated treatments. The patient-specific three-dimensional model of the brain may be divided into perfusion segments or subvolumes, and it may be determined whether a patient is receiving adequate minimum perfusion to various regions of the brain. 
     A patient-specific three-dimensional geometric model of the intracranial arteries may be generated from medical imaging data and combined with a morphometric model of a portion of the remaining intracranial arterial tree represented by perfusion segments or subvolumes (e.g., as described above in connection with  FIG.  40   ) to form an augmented model. The percentage of the total brain volume (or mass) downstream of a given, e.g. diseased, location in the augmented model may be calculated. Also, the percentage of the total cerebral blood flow at a given, e.g. diseased, location in the augmented model may be calculated. In addition, deficits noted in functional imaging studies (e.g., functional magnetic resonance imaging (fMRI)), perfusion CT or MRI, may then be traced to disease in the feeding vessels, anatomic variants, impaired autoregulatory mechanisms, hypotension, or other conditions, which may be useful for patients with ischemic stroke, syncope, orthostatic intolerance, trauma, or chronic neurologic disorders. 
     ii. Assessing Plaque Vulnerability 
     The computational analysis may also provide results that quantify patient-specific biomechanical forces acting on plaque that may build up in the patient&#39;s intracranial and extracranial arteries, e.g., carotid atherosclerotic plaque. The biomechanical forces may be caused by pulsatile pressure, flow, and neck motion. 
       FIG.  42    is a schematic diagram showing aspects of a method  1200  for providing various information relating to assessing plaque vulnerability, cerebral volume risk, and cerebral perfusion risk in a specific patient, according to an exemplary embodiment. The method  1200  may be implemented in the computer system described above, e.g., similar to the computer system used to implement one or more of the steps described above and shown in  FIG.  3   . The method  1200  may be performed using one or more inputs  1202 , and may include generating one or more models  1210  based on the inputs  1202 , performing one or more biomechanical analyses  1220  based on the one or more of the models  1210 , and providing various results based on the models  1210  and the biomechanical analyses  1220 . 
     The inputs  1202  may include medical imaging data  1203  of the patient&#39;s intracranial and extracranial arteries, e.g., the patient&#39;s aorta, carotid arteries (shown in  FIG.  37   ), vertebral arteries (shown in  FIG.  37   ), and brain, such as CCTA data (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The inputs  1202  may also include additional physiological data  1204  measured from the patient, such as the patient&#39;s brachial blood pressure, heart rate, and/or other measurements (e.g., obtained in a similar manner as described above in connection with step  100  of  FIG.  2   ). The additional physiological data  1204  may be obtained noninvasively. The inputs  1202  may be used to generate the models  1210  and/or perform the biomechanical analyses  1220  described below. 
     As noted above, one or more models  1210  may be generated based on the inputs  1202 . For example, the method  1200  may include generating a hemodynamic model  1212  including computed blood flow and pressure information at various locations throughout a three-dimensional geometric model of the patient&#39;s anatomy. The model of the patient&#39;s anatomy may be created using the medical imaging data  1203 , and, in an exemplary embodiment, the hemodynamic model  1212  may be a simulated blood pressure model, the simulated blood flow model, or other simulation produced after performing a computational analysis, e.g., as described above in connection with step  402  of  FIG.  3   . Solid mechanics models, including fluid structure interaction models, may be solved with the computational analysis with known numerical methods. Properties for the plaque and vessels may be modeled as linear or nonlinear, isotropic or anisotropic. The solution may provide stress and strain of the plaque and the interface between the plaque and the vessel. The steps for generating the hemodynamic model  1212  may be similar to the steps for generating the hemodynamic model  932  of  FIG.  35    described above. 
     The method  1200  may include performing a biomechanical analysis  1220  using the hemodynamic model  1212  by computing a pressure and shear stress acting on a plaque luminal surface due to hemodynamic forces at various physiological states, such as rest, varying levels of exercise or exertion, etc. (step  1222 ). The pressure and shear stress may be calculated based on information from the hemodynamic model  1212 , e.g., blood pressure and flow. Step  1222  may be similar to step  942  of  FIG.  35    described above. 
     Optionally, the method  1200  may also include generating a geometric analysis model for quantifying vessel deformation from four-dimensional imaging data, e.g., imaging data obtained at multiple phases of the cardiac cycle, such as the systolic and diastolic phases, in a similar manner as described above for the geometric analysis model  934  of  FIG.  35   . The method  1200  may also include performing a biomechanical analysis  1220  using the geometric analysis model by computing various deformation characteristics, such as longitudinal lengthening (elongation) or shortening, twisting (torsion), radial expansion or compression, and bending, etc., of the patient&#39;s intracranial and extracranial arteries and the plaque due to cardiac-induced pulsatile pressure, in a similar manner as described above for step  944  of  FIG.  35   . 
     The method  1200  may also include generating a plaque model  1214  for determining plaque composition and properties from the medical imaging data  1203 . For example, the plaque model  1214  may include information regarding density and other material properties of the plaque. 
     The method  1200  may also include generating a vessel wall model  1216  for computing information about the plaque, the vessel walls, and/or the interface between the plaque and the vessel walls. For example, the vessel wall model  1216  may include information regarding stress and strain, which may be calculated based on the plaque composition and properties included in the plaque model  1214  and the pressure and shear stress calculated in step  1220 . Optionally, stress and strain may also be calculated using calculated deformation characteristics, as described above. The steps for generating the plaque model  1214  and/or the vessel wall model  1216  may be similar to the steps for generating the plaque model  936  and/or the vessel wall model  938  of  FIG.  35    described above. 
     The method  1200  may include performing a biomechanical analysis  1220  using the vessel wall model  1216  by computing stress (e.g., acute or cumulative stress) on the plaque due to hemodynamic forces and neck movement-induced strain (step  1224 ). For example, the flow-induced force  904  ( FIG.  33   ) acting on the plaque may be computed. The stress or force on the plaque due to hemodynamic forces and neck movement-induced strain may be calculated based on information from the vessel wall model  1216 , e.g., stress and strain on the plaque. Step  1224  may be similar to step  946  of  FIG.  35    described above. 
     The method  1200  may include determining further information based on one or more of the models  1210  and one or more of the biomechanical analyses  1220  described above. 
     A plaque rupture vulnerability index may be calculated (step  1230 ). The plaque rupture vulnerability index may be calculated, e.g., based on hemodynamic stress, stress frequency, stress direction, and/or plaque strength or other properties. For example, a region surrounding a plaque of interest may be isolated from the three-dimensional model  1210  of the plaque, such as the plaque model  1214 . The strength of the plaque may be determined from the material properties provided in the plaque model  1214 . A hemodynamic and tissue stress on the plaque of interest, due to pulsatile pressure, flow, and neck motion, may be calculated under simulated baseline and exercise (or exertion) conditions by using the hemodynamic stresses and motion-induced strains previously computed in step  1224 . The vulnerability of the plaque may be assessed based on the ratio of plaque stress to plaque strength. Step  1230  may be similar to step  950  of  FIG.  35    described above. For example, the plaque rupture vulnerability index may be calculated for a plaque located in an extracranial artery for stroke assessment. 
     A cerebral volume risk index (CVRI) may also be calculated (step  1232 ). The CVRI may be defined as a percentage of the total brain volume affected by a plaque rupture or embolization and occlusion (closure or obstruction) of a vessel at a given location in the arterial tree. The CVRI may be calculated based on the portion of the brain supplied by the vessels downstream of the given plaque, which may take into account the size of the plaque with respect to the size of the downstream vessels and the probability that the plaque may flow into different vessels based on the three-dimensional hemodynamic solution. The CVRI may be assessed in diseased states, or before or after an intervention. Step  1232  may be similar to step  952  of  FIG.  35    described above. 
     The brain tissue may be modeled and divided into segments supplied by each vessel in the hemodynamic simulation (e.g., as described in connection with steps  1110  and  1112  of  FIG.  40   ). The geometric model may be modified to include a next generation of branches in the cerebral tree (e.g., as described in connection with step  1118  of  FIG.  40   ), and the brain tissue may be further segmented (e.g., as described in connection with step  1120  of  FIG.  40   ). Additional branches may be created in the subsegments, and the subsegments may be further segmented into smaller segments (e.g., as described in connection with step  1122  of  FIG.  40   ). Physiologic relationships, as previously described, may be used to relate the size of a vessel to a proportional amount of brain tissue supplied. 
     Potential paths for a ruptured plaque to follow may be determined. The hemodynamic solution may be used to determine a percent chance that a plaque fragment or embolus may flow into different downstream vessels. 
     The size of the ruptured plaque may be compared with the size of the downstream vessels to determine where the plaque may eventually create an impediment to flow. This information may be combined with the vulnerability index to provide a probability map of the volume of the brain tissue that may potentially be affected by the ruptured plaque. The CVRI may be assigned to each potential affected segment. 
     A cerebral perfusion risk index (CPRI) may also be calculated (step  1234 ). The CPRI may be defined as a percentage of the total cerebral blood flow affected by a plaque rupture and occlusion of a vessel at a given location in the arterial tree. The CPRI indicates a potential loss of perfusion to the brain tissue segments, rather than the volume affected as indicated by the CVRI. For example, the effect of a rupture or embolization of a carotid artery plaque may vary depending on the geometry of the patient&#39;s circle of Willis (shown in  FIG.  37   ) and may yield different CVRI and CPRI values due to these differences in anatomy. The perfusion rate to each segment of the brain tissue may be calculated, and the loss of perfusion may be calculated based on the vulnerability index, the hemodynamic solution, and the sizes of the plaque and vessels. The CPRI may be assessed in diseased states, or before or after an intervention. Step  1234  may be similar to step  954  of  FIG.  35    described above. 
     As a result, biomechanical forces acting on carotid atherosclerotic plaques resulting from pulsatile pressure, pulsatile blood flow, and/or optionally neck motion may be assessed. The total stress that the plaque experiences resulting from the pulsatile pressure, pulsatile blood flow, and/or optionally neck motion may be quantified. The solution may take into account multiple sources of patient-specific hemodynamic stress acting on the plaque or on the interface between the plaque and the vessel wall. Also, plaque strength may be estimated based on medical imaging data, and indices relating to plaque vulnerability, cerebral volume risk, and cerebral perfusion risk may be quantified. 
     By determining anatomic and physiologic data for extracranial and intracranial arteries as described below, changes in blood flow at the arterial or organ level for a specific patient at various physical conditions may be predicted. Further, other information may be provided, such as a risk of transient ischemic attack, ischemic stroke, or aneurysm rupture, forces acting on atherosclerotic plaques or aneurysms, a predicted impact of medical interventional or surgical therapies on intracranial or extracranial blood flow, pressure, wall stress, or brain perfusion. Blood flow, pressure, and wall stress in the intracranial or extracranial arteries, and total and regional brain perfusion may be quantified and the functional significance of disease may be determined. 
     In addition to quantifying blood flow in the three-dimensional geometric model constructed from imaging data (e.g., as described above in step  1212 ), the model may be modified to simulate the effect of progression or regression of disease or medical, percutaneous, or surgical interventions. In an exemplary embodiment, the progression of atherosclerosis may be modeled by iterating the solution over time, e.g., by solving for shear stress or particle residence time and adapting the geometric model to progress atherosclerotic plaque development based on hemodynamic factors and/or patient-specific biochemical measurements. Furthermore, the effect of changes in blood flow, heart rate, blood pressure, and other physiologic variables on extracranial and/or intracranial artery blood flow or cerebral perfusion may be modeled through changes in the boundary conditions and used to calculate the cumulative effects of these variables over time. 
     Any aspect set forth in any embodiment may be used with any other embodiment set forth herein. Every device and apparatus set forth herein may be used in any suitable medical procedure, may be advanced through any suitable body lumen and body cavity, and may be used for imaging any suitable body portion. 
     It will be apparent to those skilled in the art that various modifications and variations can be made in the disclosed systems and processes without departing from the scope of the disclosure. Other embodiments will be apparent to those skilled in the art from consideration of the specification and practice of the disclosure disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the disclosure being indicated by the following claims.