Patent Publication Number: US-2022230312-A1

Title: Systems and methods for processing electronic images to predict lesions

Description:
FIELD OF THE INVENTION 
     Various embodiments of the present disclosure relate generally to medical imaging and related methods. More specifically, particular embodiments of the present disclosure relate to systems and methods for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics. 
     BACKGROUND 
     Coronary artery disease (“CAD”) may produce coronary lesions, such as a stenosis (abnormal narrowing of a blood vessel), in the blood vessels providing blood to the heart. 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), positron emission tomography (PET), and coronary computed tomographic angiography (CCTA). 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). However, these noninvasive tests typically do not provide a direct assessment of coronary lesions or assess blood flow rates. 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. 
     However, both invasive and noninvasive tests for CAD are only useful in determining an amount of disease and/or risk of heart attack that has already been incurred. That is, tests for CAD are unable to predict future amounts of plaque build-up, stenosis, or other CAD that is likely to occur based on other known characteristics of an individual. Even though CAD is known to be associated with various risk factors, including smoking, diabetes, hypertension, and dietary habits, no techniques exist for predicting the onset of CAD. In addition, no techniques exist for predicting the type or location of plaque that is likely to develop in view of other known characteristics of an individual. 
     Consequently, the present disclosure describes new approaches for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics. 
     SUMMARY 
     Systems and methods are disclosed for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics. 
     According to one embodiment, a method is disclosed for predicting information relating to a coronary lesion. The method includes: acquiring, for each of a plurality of individuals, a geometric model, blood flow characteristics, and plaque information for at least part of the individual&#39;s vascular system; identifying, for each of a plurality of points in the geometric models, features predictive of the presence of plaque within the geometric models and blood flow characteristics of the plurality of individuals; training a machine learning algorithm based on the geometric models and blood flow characteristics for each of the plurality of individuals, and the predictive features; acquiring, for a patient, a geometric model and blood flow characteristics for at least part of the patient&#39;s vascular system; and executing the machine learning algorithm on the patient&#39;s geometric model and blood flow characteristics to determine, based on the predictive features, plaque information of the patient for at least one point in the patient&#39;s geometric model. 
     According to another embodiment, a system is disclosed for predicting information relating to a coronary lesion. The system includes a data storage device storing instructions for predicting information relating to a coronary lesion; and a processor configured to execute the instructions to perform a method including the steps of: acquiring, for each of a plurality of individuals, a geometric model, blood flow characteristics, and plaque information for at least part of the individual&#39;s vascular system; identifying, for each of a plurality of points in the geometric models, features predictive of the presence of plaque within the geometric models and blood flow characteristics of the plurality of individuals; training a machine learning algorithm based on the geometric models and blood flow characteristics for each of the plurality of individuals, and the predictive features; acquiring, for a patient, a geometric model and blood flow characteristics for at least part of the patient&#39;s vascular system; and executing the machine learning algorithm on the patient&#39;s geometric model and blood flow characteristics to determine, based on the predictive features, plaque information of the patient for at least one point in the patient&#39;s geometric model. 
     According to another embodiment, a non-transitory computer-readable medium is disclosed storing instructions that, when executed by a computer, cause the computer to perform a method for predicting information relating to a coronary lesion, the method including: acquiring, for each of a plurality of individuals, a geometric model, blood flow characteristics, and plaque information for at least part of the individual&#39;s vascular system; identifying, for each of a plurality of points in the geometric models, features predictive of the presence of plaque within the geometric models and blood flow characteristics of the plurality of individuals; training a machine learning algorithm based on the geometric models and blood flow characteristics for each of the plurality of individuals, and the predictive features; acquiring, for a patient, a geometric model and blood flow characteristics for at least part of the patient&#39;s vascular system; and executing the machine learning algorithm on the patient&#39;s geometric model and blood flow characteristics to determine, based on the predictive features, plaque information of the patient for at least one point in the patient&#39;s geometric model. 
     According to another embodiment, a computer-implemented method is disclosed for predicting information relating to a coronary lesion. One method includes acquiring, over a network, for a patient, a geometric model and blood flow characteristics for at least part of the patient&#39;s vascular system; and determining plaque information of the patient for at least one point in the patient&#39;s geometric model by executing on the patient&#39;s geometric model and blood flow characteristics, a machine learning algorithm trained based on plaque predictive features derived from geometric models, blood flow characteristics, and plaque information obtained for each of a plurality of individuals. 
     Additional objects and advantages of the disclosed embodiments will be set forth in part in the description that follows, and in part will be apparent from the description, or may be learned by practice of the disclosed embodiments. The objects and advantages of the disclosed embodiments will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. 
     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 disclosed embodiments, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate various exemplary embodiments and together with the description, serve to explain the principles of the disclosed embodiments. 
         FIG. 1  is a block diagram of an exemplary system and network for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 2  is a diagram of an exemplary three-dimensional mesh of a geometric model used in predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 3A  is a block diagram of an exemplary method of training a machine learning system for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics s, according to an exemplary embodiment of the present disclosure. 
         FIG. 3B  is a block diagram of an exemplary method of using a trained machine learning system for predicting the location, onset, and/or change of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 4A  is a block diagram of an exemplary method of training a machine learning system for predicting the location of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 4B  is a block diagram of an exemplary method of using a trained machine learning system for predicting the location of coronary lesions from factors such as vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 5A  is a block diagram of an exemplary method of training a machine learning system for predicting the onset and/or change (e.g., rate of growth/shrinkage) of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 5B  is a block diagram of an exemplary method of using a trained machine learning system for predicting the onset and/or change (e.g., rate of growth/shrinkage) of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. 
         FIG. 6  is a simplified block diagram of an exemplary computer system in which embodiments of the present disclosure may be implemented. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     Reference will now be made in detail to the exemplary embodiments of the disclosure, 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. 
     The present disclosure describes an approach for providing prognosis of coronary artery disease (“CAD”) and for predicting plaque growth/shrinkage based on patient-specific geometry and blood flow characteristics. Specifically, the present disclosure describes a system that receives patient information (e.g., 3D cardiac imaging, patient demographics, and history) and provides a patient-specific and location-specific risk score for the pathogenesis of CAD. Although the present disclosure is described with particular reference to coronary artery disease, the same systems and methods are applicable to creating a patient-specific prediction of lesion formation in other vascular systems beyond the coronary arteries. 
     More specifically, the present disclosure describes certain principles and embodiments for using patients&#39; cardiac imaging to: (1) derive a patient-specific geometric model of the coronary vessels; and (2) perform coronary flow simulation to extract hemodynamic characteristics, patient physiological information, and boundary conditions in order to predict the onset and location of coronary lesions. The present disclosure is not limited to a physics-based simulation of blood flow to predict the locations predisposed to plaque formation, but rather uses machine learning to predict the lesion location by incorporating various risk factors, including patient demographics and coronary geometry, as well as the results of patient-specific biophysical simulations (e.g., hemodynamic characteristics). If additional diagnostic test results are available, those results may also be used in the training and prediction. According to certain embodiments, the presently disclosed methods involve two phases: (1) a training phase in which the machine learning system is trained to predict one or more locations of coronary lesions, and (2) a production phase in which the machine learning system is used to produce one or more locations of coronary lesions. 
     Referring now to the figures,  FIG. 1  depicts a block diagram of an exemplary system and network for predicting the location, onset, and/or change of coronary lesions from vessel geometry, physiology, and hemodynamics. Specifically,  FIG. 1  depicts a plurality of physician devices or systems  102  and third party provider devices or systems  104 , any of which may be connected to an electronic network  101 , such as the Internet, through one or more computers, servers, and/or handheld mobile devices. Physicians and/or third party providers associated with physician devices or systems  102  and/or third party provider devices or systems  104 , respectively, may create or otherwise obtain images of one or more patients&#39; cardiac and/or vascular systems. The physicians and/or third party providers may also obtain any combination of patient-specific information, such as age, medical history, blood pressure, blood viscosity, etc. Physicians and/or third party providers may transmit the cardiac/vascular images and/or patient-specific information to server systems  106  over the electronic network  101 . Server systems  106  may include storage devices for storing images and data received from physician devices or systems  102  and/or third party provider devices or systems  104 . Server systems  106  may also include processing devices for processing images and data stored in the storage devices. 
       FIG. 2  is a diagram of an exemplary three-dimensional mesh of a geometric model  200  used in predicting the location, onset, and/or change of coronary lesions from vessel geometry, according to an exemplary embodiment of the present disclosure. For example, as described above, a third party provider or physician may obtain patient-specific anatomical data of one or more patients. Patient-specific anatomical data may include 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. However, as-described above, patient-specific anatomical data may also or alternatively be obtained in relation to any portion of the patient&#39;s vasculature, including beyond the patient&#39;s heart. 
     Initially, a patient may be selected, e.g., 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. 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. 
     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 electronic network  101  of  FIG. 1 ). For example, the data may be transferred to server systems  106  or other computer system for performing computational analysis, e.g., the computational analysis described below with respect to  FIGS. 3-5B . In one exemplary embodiment, the patient-specific anatomical data may be transferred to server systems  106  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. 
     In one embodiment, server systems  106  may generate a three-dimensional solid model and/or three-dimensional mesh  200  based on the received patient-specific anatomical data. For example, server systems  106  may generate the three-dimensional model and/or mesh based on any of the techniques described in U.S. Pat. No. 8,315,812 by Taylor et al., which issued on Nov. 20, 2012, the entirety of which is hereby incorporated herein by reference. 
       FIG. 3A  is a block diagram of an exemplary method  300  for training a machine learning system, based on a plurality of patients&#39; blood flow characteristics and geometry, for predicting the location, onset, and/or change of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. Specifically, as shown in  FIG. 3A , method  300  may include obtaining patient imaging data (e.g., a geometric model) and physiologic and/or hemodynamic information  302  for a plurality of patients. Method  300  may include generating feature vectors  304  based on the plurality of patients&#39; imaging and physiologic and/or hemodynamic information. Method  300  further includes obtaining information about plaque  306  for the plurality of patients, and formatting the information about the plurality of patients&#39; plaque into the format that is desired of the output  308  of the learning system. Method  300  completes the training mode by inputting into a learning system  310  both the feature vectors  304  formed from the plurality of patients&#39; imaging data and physiologic and/or hemodynamic information, and the output  308  of the information about plaque for the plurality of patients. For example, as will be described in more detail below, any suitable type of machine learning system may process both the feature vectors  304  and outputs  308  to identify patterns and conclusions from that data, for later use in producing outputs of information about a particular user&#39;s plaque. 
       FIG. 3B  is a block diagram of an exemplary method  350  for using the trained machine learning system  310  for predicting, for a particular patient, the location, onset, and/or change of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. As shown in  FIG. 3B , method  350  may include obtaining patient imaging data (e.g., a geometric model) and physiologic and/or hemodynamic information  312  for a particular patient, for whom it is desired to predict plaque location, onset, and/or change based on the trained learning system  310 . Of course, method  350  may include obtaining the patient imaging data and physiologic and/or hemodynamic information for any number of patients for whom it is desired to predict plaque location, onset, and/or change based on the trained learning system. Method  350  may include generating a feature vector  314  for each of a plurality of points of the patient&#39;s geometric model, based on one or more elements of the received physiologic and/or hemodynamic information. Method  350  may then include operating the machine learning system  310  on the feature vectors generated for the patient to obtain an output  316  of the estimates of the presence or onset of plaque at each of a plurality of points in the patient&#39;s geometric model, and translating the output into useable information  318  about the location, onset, and/or change of plaque in the patient  318 . 
     Described below are exemplary embodiments for implementing a training mode method  300  and a production mode method  350  of machine learning for predicting the location, onset, and/or change of coronary lesions from vessel geometry, physiology, and hemodynamics, e.g. using server systems  106 , based on images and data received from physicians and/or third party providers over electronic network  101 . Specifically, the methods of  FIGS. 4A-5B  may be performed by server systems  106 , based on information received from physician devices or systems  102  and/or third party provider devices or systems  104  over electronic network  101 . 
       FIG. 4A  is a block diagram of an exemplary method  400  for training a machine learning system (e.g., a machine learning system  310  executed on server systems  106 ) for predicting the location of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. Specifically, method  400  may include, for one or more patients (step  402 ), obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  404 ), obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  406 ), and obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  408 ). 
     For example, the step of obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  404 ) may include obtaining a patient-specific model of the geometry for one or more of the patient&#39;s blood vessels, myocardium, aorta, valves, plaques, and/or chambers. In one embodiment, this geometry may be represented as a list of points in space (possibly with a list of neighbors for each point) in which the space can be mapped to spatial units between points (e.g., millimeters). In one embodiment, this model may be derived by performing a cardiac CT imaging of the patient in the end diastole phase of the cardiac cycle. This image then may be segmented manually or automatically to identify voxels belonging to the aorta and the lumen of the coronary arteries. Given a 3D image of coronary vasculature, any of the many available methods may be used for extracting a patient-specific model of cardiovascular geometry. Inaccuracies in the geometry extracted automatically may be corrected by a human observer who compares the extracted geometry with the images and makes corrections as needed. Once the voxels are identified, the geometric model can be derived (e.g., using marching cubes). 
     The step of obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  406 ) may include obtaining a list of one or more estimates of physiological or phenotypic parameters of the patient, such as blood pressure, blood viscosity, in vitro blood test results (e.g., LDL/Triglyceride cholesterol level), patient age, patient gender, the mass of the supplied tissue, etc. These parameters may be global (e.g., blood pressure) or local (e.g., estimated density of the vessel wall at a location). In one embodiment, the physiological or phenotypic parameters may include, blood pressure, hematocrit level, patient age, patient gender, myocardial mass (e.g., derived by segmenting the myocardium in the image, and calculating the volume in the image and using an estimated density of 1.05 g/mL to estimate the myocardial mass), general risk factors of coronary artery disease (e.g., smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history, etc.), and/or in vitro blood test results (e.g., LDL, Triglyceride cholesterol level). 
     The step of obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  408 ) may include obtaining a list of one or more estimates of biophysical hemodynamic characteristics from computational fluid dynamics analysis, such as wall-shear stress, oscillatory shear index, particle residence time, Reynolds number, Womersley number, local flow rate, and turbulent kinetic energy, etc. Specifically, the mean wall-shear stress, may be defined as 
     
       
         
           
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     Method  400  may further include obtaining an indication of the presence or absence of plaque at one or more locations of the patient-specific geometric model (step  410 ). For example, in one embodiment, the location of calcified or non-calcified plaque may be determined using CT and/or other imaging modalities, including intravascular ultrasound, or optical coherence tomography. For example, the plaque may be detected in the three-dimensional image ( 200  of  FIG. 2 ) generated from patient-specific anatomical data. The plaque may be identified in a three-dimensional image or model as areas that are 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. The location of detected plaques may be parameterized by a distance from the ostium point (left main or right coronary ostium) to the projection of centroid of plaque coordinates onto the associated vessel centerline and an angular position of plaque with respect to myocardium (e.g., myocardial/pericardial side). The location of detected plaques may be also parameterized by start and end points of the projection of plaque coordinates onto the associated vessel centerline. If plaque exists at a location, method  400  may include obtaining a list of one or more measurements of coronary plaque composition, e.g., type, Hounsfield units (“HU”), etc., burden, shape (eccentric or concentric), and location. 
     Method  400  may further include, for each of a plurality of points in the patient-specific geometric model for which there is information about the presence or absence of plaque (step  412 ), creating a feature vector for the point (step  414 ) and associating the feature vector with the presence or absence of plaque at that point (step  416 ). In one embodiment, the step of creating a feature vector for the point may include creating a feature vector for that point that consists of a numerical description of the geometry and biophysical hemodynamic characteristics at that point, and estimates of physiological or phenotypic parameters of the patient. For example, a feature vector for attributes: distance to ostium, wall shear stress, local flow rate, Reynolds number, and centerline curvature, may be in the form of (50 mm, 70 dyne/cm 2 , 1500 mm 3 /sec, 400, 1 mm −1 ). Global physiological or phenotypic parameters may be used in the feature vector of all points, and local physiological or phenotypic parameters may change in the feature vector of different points. 
     In one embodiment, an exemplary feature vector generated in step  414  may include one or more of: (i) systolic and diastolic blood pressure, (ii) heart rate, (iii) blood properties including: plasma, red blood cells (erythrocytes), hematocrit, white blood cells (leukocytes) and platelets (thrombocytes), viscosity, yield stress, etc. (iv) patient age, gender, height, weight, etc., (v) lifestyle characteristics, e.g., presence or absence of current medications/drugs, (vi) general risk factors of CAD, such as smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history of CAD, etc., (vii) in vitro blood test results, such as LDL, Triglyceride cholesterol level, etc., (viii) coronary calcium score, (ix) amount of calcium in aorta and valve, (x) presence of aortic aneurysm, (xi) presence of valvular heart disease, (xii) presence of peripheral disease, (xiii) presence of dental disease, (xiv) epicardial fat volume, (xv) cardiac function (ejection fraction), (xvi) stress echocardiogram test results, (xvii) characteristics of the aortic geometry (e.g., cross-sectional area profile along the ascending and descending aorta, and surface area and volume of the aorta, (xviii) a SYNTAX score, as described in U.S. patent application Ser. No. 13/656,183, filed by Timothy A. Fonte et al. on Oct. 19, 2012, the entire disclosure of which is incorporated herein by reference, (xix) plaque burden of existing plaque, (xx) adverse plaque characteristics of existing plaque (e.g., presence of positive remodeling, presence of low attenuation plaque, presence of spotty calcification), (xxi) characteristics of the coronary branch geometry, (xxii) characteristics of coronary cross-sectional area, (xxiii) characteristics of coronary lumen intensity, e.g., intensity change along the centerline (slope of linearly-fitted intensity variation), (xxiv) characteristics of surface of coronary geometry, e.g., 3D surface curvature of geometry (Gaussian, maximum, minimum, mean), (xxv) characteristics of volume of coronary geometry, e.g., ratio of total coronary volume compared to myocardial volume, (xxvi) characteristics of coronary centerline, (xxvii) characteristics of coronary deformation, (xxviii) characteristics of existing plaque, and (xxix) characteristics of coronary hemodynamics derived from computational flow dynamics or invasive measurement. 
     In one embodiment, the characteristics of the coronary branch geometry may include one or more of: (1) total number of vessel bifurcations, and the number of upstream/downstream vessel bifurcations; (2) average, minimum, and maximum upstream/downstream cross-sectional areas; (3) distances (along the vessel centerline) to the centerline point of minimum and maximum upstream/downstream cross-sectional areas, (4) cross-sectional area of and distance (along the vessel centerline) to the nearest upstream/downstream vessel bifurcation, (5) cross-sectional area of and distance (along the vessel centerline) to the nearest coronary outlet and aortic inlet/outlet, (6) cross-sectional areas and distances (along the vessel centerline) to the downstream coronary outlets with the smallest/largest cross-sectional areas, and/or (7) upstream/downstream volumes of the coronary vessels. 
     In one embodiment, the characteristics of coronary cross-sectional area may include one or more of: (1) cross-sectional lumen area along the coronary centerline, (2) cross-sectional lumen area to the power of N (where N can be determined from various source of scaling laws such as Murray&#39;s law (N=1.5) and Uylings&#39; study (N=1.165˜1.5)), (3) a ratio of lumen cross-sectional area with respect to the main ostia (LM, RCA) (e.g., measure of cross-sectional area at the LM ostium, normalized cross-sectional area of the left coronary by LM ostium area, measure of cross-sectional area at the RCA ostium, normalized cross-sectional area of the right coronary by RCA ostium area), (4) ratio of lumen cross-sectional area with respect to the main ostia to the power of N (where N can be determined from various sources of scaling laws such as Murray&#39;s law (N=1.5) and Uyling&#39;s study (N=1.165˜1.5)), (5) degree of tapering in cross-sectional lumen area along the centerline (based on a sample centerline points within a certain interval (e.g., twice the diameter of the vessel) and computation of a slope of linearly-fitted cross-sectional area), (6) location of stenotic lesions (based on detecting minima of cross-sectional area curve (e.g., detecting locations, where first derivative of area curve is zero and second derivative is positive, and smoothing cross-sectional area profile to avoid detecting artifactual peaks), and computing distance (parametric arc length of centerline) from the main ostium, (7) length of stenotic lesions (computed based on the proximal and distal locations from the stenotic lesion, where cross-sectional area is recovered), (8) degree of stenotic lesions, by evaluating degree of stenosis based on reference values of smoothed cross-sectional area profile using Fourier smoothing or kernel regression, (9) location and number of lesions corresponding to 50%, 75%, 90% area reduction, (10) distance from stenotic lesion to the main ostia, and/or (11) irregularity (or circularity) of cross-sectional lumen boundary. 
     In one embodiment, the characteristics of coronary centerline may include: (1) curvature (bending) of coronary centerline, such as by computing Frenet curvature, based on 
     
       
         
           
             
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     where p is a coordinate of the centerline, and computing an inverse of the radius of a circumscribed circle along the centerline points, and (2) tortuosity (non-planarity) of coronary centerline, such as by computing Frenet torsion, based on 
     
       
         
           
             
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                       × 
                       
                         p 
                         ″ 
                       
                     
                     ) 
                   
                   · 
                   
                     
                       
                         p 
                         ′ 
                       
                       ′ 
                     
                     ′ 
                   
                 
                 
                   | 
                   
                     
                       p 
                       ′ 
                     
                     × 
                     
                       p 
                       ″ 
                     
                   
                   ⁢ 
                   
                     | 
                     2 
                   
                 
               
             
             , 
           
         
       
     
     where p is a coordinate of the centerline. 
     In one embodiment, calculation of the characteristics of coronary deformation may involve multi-phase CCTA (e.g., diastole and systole), including (1) distensibility of coronary artery over cardiac cycle, (2) bifurcation angle change over cardiac cycle, and/or (3) curvature change over cardiac cycle. In one embodiment, the characteristics of existing plaque may be calculated based on: (1) volume of plaque, (2) intensity of plaque, (3) type of plaque (calcified, non-calcified), (4) distance from the plaque location to ostium (LM or RCA), and (5) distance from the plaque location to the nearest downstream/upstream bifurcation. 
     In one embodiment, the characteristics of coronary hemodynamics may be derived from computational flow dynamics or invasive measurement. For example, pulsatile flow simulation may be performed to obtain transient characteristics of blood, by using a lumped parameter coronary vascular model for downstream vasculatures, inflow boundary condition with coupling a lumped parameter heart model and a closed loop model to describe the intramyocardial pressure variation resulting from the interactions between the heart and arterial system during cardiac cycle. For example, the calculation may include: measured FFR, coronary flow reserve, pressure distribution, FFRct, mean wall-shear stress, oscillatory shear index, particle residence time, turbulent kinetic energy, Reynolds number, Womersley number, and/or local flow rate. 
     Method  400  may then include associating the feature vector with the presence or absence of plaque at each point of the patient-specific geometric model (step  416 ). Method  400  may involve continuing to perform the above steps  412 ,  414 ,  416 , for each of a plurality of points in the patient-specific geometric model (step  418 ), and for each of any number of patients on which a machine learning algorithm may be based (step  420 ). Method  400  may then include training the machine learning algorithm to predict the probability of the presence of plaque at the points from the feature vectors at the points (step  422 ). Examples of machine learning algorithms suitable for performing this task may include support vector machines (SVMs), multi-layer perceptrons (MLPs), and/or multivariate regression (MVR) (e.g., weighted linear or logistic regression). 
     Method  400  may then include storing or otherwise saving the results of the machine learning algorithm (e.g., feature weights) to a digital representation, such as the memory or digital storage (e.g., hard drive, network drive) of a computational device, such as a computer, laptop, DSP, server, etc. of server systems  106  (step  424 ). 
       FIG. 4B  is a block diagram of an exemplary method  450  for using a machine learning system trained according to method  400  (e.g., a machine learning system  310  executed on server systems  106 ) for predicting, for a particular patient, the location of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. In one embodiment, method  450  may include, for one or more patients (step  452 ), obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  454 ), obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  456 ), and obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  458 ). 
     Specifically, the step of obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  454 ) may include obtaining a patient-specific model of the geometry for one or more of the patient&#39;s blood vessels, myocardium, aorta, valves, plaques, and/or chambers. In one embodiment, this geometry may be represented as a list of points in space (possibly with a list of neighbors for each point) in which the space can be mapped to spatial units between points (e.g., millimeters). In one embodiment, this model may be derived by performing a cardiac CT imaging of the patient in the end diastole phase of the cardiac cycle. This image then may be segmented manually or automatically to identify voxels belonging to the aorta and the lumen of the coronary arteries. Inaccuracies in the geometry extracted automatically may be corrected by a human observer who compares the extracted geometry with the images and makes corrections as needed. Once the voxels are identified, the geometric model can be derived (e.g., using marching cubes). 
     In one embodiment, the step of obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  456 ) may include obtaining a list of one or more estimates of physiological or phenotypic parameters of the patient, such as blood pressure, blood viscosity, in vitro blood test results (e.g., LDL/Triglyceride cholesterol level), patient age, patient gender, the mass of the supplied tissue, etc. These parameters may be global (e.g., blood pressure) or local (e.g., estimated density of the vessel wall at a location). In one embodiment, the physiological or phenotypic parameters may include, blood pressure, hematocrit level, patient age, patient gender, myocardial mass (e.g., derived by segmenting the myocardium in the image, and calculating the volume in the image and using an estimated density of 1.05 g/mL to estimate the myocardial mass), general risk factors of coronary artery disease (e.g., smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history, etc.), and/or in vitro blood test results (e.g., LDL, Triglyceride cholesterol level). 
     In one embodiment, the step of obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  458 ) may include obtaining a list of one or more estimates of biophysical hemodynamic characteristics from computational fluid dynamics analysis, such as wall-shear stress, oscillatory shear index, particle residence time, Reynolds number, Womersley number, local flow rate, and turbulent kinetic energy, etc. Specifically, the mean wall-shear stress, may be defined as 
     
       
         
           
             
               | 
               
                 
                   1 
                   
                     
                       T 
                       1 
                     
                     - 
                     
                       T 
                       0 
                     
                   
                 
                 ⁢ 
                 
                   
                     ∫ 
                     
                       T 
                       0 
                     
                     
                       T 
                       1 
                     
                   
                   ⁢ 
                   
                     
                       
                         t 
                         s 
                       
                       → 
                     
                     ⁢ 
                     d 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     t 
                   
                 
               
               | 
               
                 · 
                 
                   
                     t 
                     s 
                   
                   → 
                 
               
             
             , 
           
         
       
     
     which may be the wall shear stress vector defined as the in-plane component of the surface traction vector. The oscillatory shear index (OSI), may be defined as 
     
       
         
           
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   1 
                   - 
                   
                     
                       | 
                       
                         
                           1 
                           
                             
                               T 
                               1 
                             
                             - 
                             
                               T 
                               0 
                             
                           
                         
                         ⁢ 
                         
                           
                             ∫ 
                             
                               T 
                               0 
                             
                             
                               T 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 t 
                                 s 
                               
                               → 
                             
                             ⁢ 
                             d 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             t 
                           
                         
                       
                       | 
                     
                     
                       
                         
                           1 
                           
                             
                               T 
                               1 
                             
                             - 
                             
                               T 
                               0 
                             
                           
                         
                         ⁢ 
                         
                           ∫ 
                           
                             T 
                             0 
                           
                           
                             T 
                             1 
                           
                         
                       
                       | 
                       
                         
                           t 
                           s 
                         
                         → 
                       
                       | 
                       
                         d 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         t 
                       
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
     which may be a measure of the uni-directionality of shear stress. The particle residence time may be a measure of the time it takes blood to be flushed from a specified fluid domain. The turbulent kinetic energy (TKE) may be a measure of the intensity of turbulence associated with eddies in turbulent flow, and may be characterized by measured root-mean-square velocity fluctuation, and may be normalized by kinetic energy. The Reynolds number may be defined as 
     
       
         
           
             
               ρ 
               ⁢ 
               U 
               ⁢ 
               D 
             
             μ 
           
         
       
     
     where (ρ: density of blood, U: average flow velocity, D: vessel diameter, μ: dynamic viscosity). The Womersley number may be defined as 
     
       
         
           
             
               D 
               2 
             
             ⁢ 
             
               
                 ϖρ 
                 μ 
               
             
           
         
       
     
     where ( ω : angular frequency, equal to 
     
       
         
           
             
               
                 1 
                 
                   cardiac cycle length 
                 
               
               ) 
             
             . 
           
         
       
     
     Method  450  may include, for every point in the patient-specific geometric model of the patient (step  460 ), creating for that point a feature vector comprising a numerical description of the geometry and biophysical hemodynamic characteristic at that point, and estimates of physiological or phenotypic parameters of the patient (step  462 ). Global physiological or phenotypic parameters may be used in the feature vector of one or more points, and local physiological or phenotypic parameters may change in the feature vector of different points. Method  450  may involve continuing to perform the above steps  460 ,  462 , for each of a plurality of points in the patient-specific geometric model (step  464 ). 
     Method  450  may then include producing estimates of the probability of the presence or absence of plaque at each point in the patient-specific geometric model based on the stored machine learning results (stored at B,  FIG. 4A ) (step  468 ). Specifically, method  450  may use the saved results of the machine learning algorithm  310  produced in the training mode of method  400  (e.g., feature weights) to produce estimates of the probability of the presence of plaque at each point in the patient-specific geometric model (e.g., by generating plaque estimates as a function of the feature vector at each point). These estimates may be produced using the same machine learning algorithm technique used in the training mode (e.g., the SVM, MLP, MVR technique). In one embodiment, the estimates may be a probability of the existence of plaque at each point of a geometric model. If there is no existing plaque at a point, the method may include generating an estimated probability of the onset of plaque (e.g., lipid-rich, non-calcified plaque). If plaque does exist at a point, the method may include generating an estimated probability of progression of the identified plaque to a different stage (e.g., fibrotic or calcified), and the amount or shape of such progression. In one embodiment, the estimates may be a probability of a shape, type, composition, size, growth, and/or shrinkage of plaque at any given location or combination of locations. For example, in one embodiment, (in the absence of longitudinal training data) the progression of plaque may be predicted by determining that the patient appears that they should have disease characteristic X based on the patient&#39;s population, despite actually having characteristic Y. Therefore, the estimate may include a prediction that the patient will progress from state X to state Y, which may include assumptions and/or predictions about plaque growth, shrinkage, change of type, change of composition, change of shape, etc.). Method  450  may then include saving the estimates of the probability of the presence or absence of plaque (step  470 ), such as to the memory or digital storage (e.g., hard drive, network drive) of a computational device, such as a computer, laptop, DSP, server, etc., of server systems  106 , and communicating these patient-specific and location-specific predicted probabilities of lesion formation to a health care provider, such as over electronic network  101 . 
       FIG. 5A  is a block diagram of an exemplary method  500  for training a machine learning system (e.g., a machine learning system  310  executed on server systems  106 ) for predicting the onset or change (e.g., growth and/or shrinkage), of coronary lesions over time, such as by using longitudinal data (i.e., corresponding data taken from the same patients at different points in time) of vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. Specifically, method  500  may include, for one or more patients (step  502 ), obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  504 ), obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  506 ), and obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  508 ). 
     For example, the step of obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  504 ) may include obtaining a patient-specific model of the geometry for one or more of the patient&#39;s blood vessels, myocardium, aorta, valves, plaques, and/or chambers. In one embodiment, this geometry may be represented as a list of points in space (possibly with a list of neighbors for each point) in which the space can be mapped to spatial units between points (e.g., millimeters). In one embodiment, this model may be derived by performing a cardiac CT imaging of the patient in the end diastole phase of the cardiac cycle. This image then may be segmented manually or automatically to identify voxels belonging to the aorta and the lumen of the coronary arteries. Inaccuracies in the geometry extracted automatically may be corrected by a human observer who compares the extracted geometry with the images and makes corrections as needed. Once the voxels are identified, the geometric model can be derived (e.g., using marching cubes). 
     The step of obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  506 ) may include obtaining a list of one or more estimates of physiological or phenotypic parameters of the patient, such as blood pressure, blood viscosity, in vitro blood test results (e.g., LDL/Triglyceride cholesterol level), patient age, patient gender, the mass of the supplied tissue, etc. These parameters may be global (e.g., blood pressure) or local (e.g., estimated density of the vessel wall at a location). In one embodiment, the physiological or phenotypic parameters may include, blood pressure, hematocrit level, patient age, patient gender, myocardial mass (e.g., derived by segmenting the myocardium in the image, and calculating the volume in the image and using an estimated density of 1.05 g/mL to estimate the myocardial mass), general risk factors of coronary artery disease (e.g., smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history, etc.), and/or in vitro blood test results (e.g., LDL, Triglyceride cholesterol level). 
     The step of obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  508 ) may include obtaining a list of one or more estimates of biophysical hemodynamic characteristics from computational fluid dynamics analysis, such as wall-shear stress, oscillatory shear index, particle residence time, Reynolds number, Womersley number, local flow rate, and turbulent kinetic energy, etc. Specifically, the mean wall-shear stress, may be defined as 
     
       
         
           
             | 
             
               
                 1 
                 
                   
                     T 
                     1 
                   
                   - 
                   
                     T 
                     0 
                   
                 
               
               ⁢ 
               
                 
                   ∫ 
                   
                     T 
                     0 
                   
                   
                     T 
                     1 
                   
                 
                 ⁢ 
                 
                   
                     
                       t 
                       s 
                     
                     -&gt; 
                   
                   ⁢ 
                   dt 
                 
               
             
             | 
             . 
           
         
       
     
     {right arrow over (t s )}, which may be the wall shear stress vector defined as the in-plane component of the surface traction vector. The oscillatory shear index (OSI), may be defined as 
     
       
         
           
             
               
                 1 
                 2 
               
               ⁢ 
               
                 ( 
                 
                   1 
                   - 
                   
                     
                       | 
                       
                         
                           1 
                           
                             
                               T 
                               1 
                             
                             - 
                             
                               T 
                               0 
                             
                           
                         
                         ⁢ 
                         
                           
                             ∫ 
                             
                               T 
                               0 
                             
                             
                               T 
                               1 
                             
                           
                           ⁢ 
                           
                             
                               
                                 t 
                                 s 
                               
                               ¯ 
                             
                             ⁢ 
                             dt 
                           
                         
                       
                       | 
                     
                     
                       
                         1 
                         
                           
                             T 
                             1 
                           
                           - 
                           
                             T 
                             0 
                           
                         
                       
                       ⁢ 
                       
                         
                           ∫ 
                           
                             T 
                             0 
                           
                           
                             T 
                             1 
                           
                         
                         ⁢ 
                         
                           
                              
                             
                               
                                 t 
                                 s 
                               
                               -&gt; 
                             
                              
                           
                           ⁢ 
                           dt 
                         
                       
                     
                   
                 
                 ) 
               
             
             , 
           
         
       
     
     which may be a measure of the uni-directionality of shear stress. The particle residence time may be a measure of the time it takes blood to be flushed from a specified fluid domain. The turbulent kinetic energy (TKE) may be a measure of the intensity of turbulence associated with eddies in turbulent flow, and may be characterized by measured root-mean-square velocity fluctuation, and may be normalized by kinetic energy. The Reynolds number may be defined as 
     
       
         
           
             
               ρ 
               ⁢ 
               U 
               ⁢ 
               D 
             
             μ 
           
         
       
     
     where (ρ: density of blood, U: average flow velocity, D: vessel diameter, μ: dynamic viscosity). The Womersley number may be defined as 
     
       
         
           
             
               D 
               2 
             
             ⁢ 
             
               
                 ϖρ 
                 μ 
               
             
           
         
       
     
     where  ω : angular frequency, equal to 
     
       
         
           
             
               
                 1 
                 
                   cardiac cycle length 
                 
               
               ) 
             
             . 
           
         
       
     
     Method  500  may further include obtaining an indication of the growth, shrinkage, or onset of plaque at one or more locations of the patient-specific geometric model (step  510 ). For example, in one embodiment, the location of plaque may be determined using CT and/or other imaging modalities, including intravascular ultrasound, or optical coherence tomography. If plaque exists at a location, method  500  may include obtaining a list of one or more measurements of coronary plaque composition, burden and location. 
     In order to synchronize geometry obtained from patients over time, it may be desirable to determine point correspondence between multiple time variant scans of each individual. In other words, it may be desirable to learn the vessel characteristics in a location at the earlier time point that are correlated with the progression of disease in the same location at the later time point, such as by using a database of pairs of images of the same patient at two different time points. Given the image of a new patient, training data of local disease progression may then be used to predict the change in disease at each location. Accordingly, in one embodiment, step  510  may further include: (i) determining a mapping of a coronary centerline from an initial scan to a follow-up scan; and (ii) determining a mapping of extracted plaques using curvilinear coordinates defined along the centerline. In one embodiment, the coronary centerline mapping may be determined by (i) extracting centerlines of major epicardial coronary arteries (e.g., left descending coronary artery, circumlex artery, right coronary artery) and branch vessels (e.g, diagonal, marginal, etc) for each scan; (ii) using bifurcating points as fiducial landmarks to determine common material points between the scans; and (iii) for points between bifurcations, using linear interpolation or cross-sectional area profile (e.g., value, slope) of coronary vessels to identify correspondence. In one embodiment, the mapping of extracted plaques may be determined by: (i) extracting plaque from each scan; (ii) parameterizing the location of plaque voxels by curvilinear coordinate system for each associated centerline (r, θ, s); and determining correspondence of plaque voxels in each curvilinear coordinate system. In one embodiment, the curvilinear coordinate system may be defined where: 
     r=distance from plaque voxel to the associated centerline (projection of plaque); 
     s=distance from ostium point (Left main or right coronary) to the projection of plaque voxel onto associated centerline; and 
     θ=angular position with respect to reference parallel path to centerline. 
     Method  500  may further include, for each of a plurality of points in the patient-specific geometric model for which there is information about the growth, shrinkage, or onset of plaque (step  512 ), creating a feature vector for the point (step  514 ) and associating the feature vector with the growth, shrinkage, or onset of plaque at that point (step  516 ). In one embodiment, the step of creating a feature vector for the point may include creating a feature vector for that point that consists of a numerical description of the geometry and biophysical hemodynamic characteristics at that point, and estimates of physiological or phenotypic parameters of the patient. For example, a feature vector for attributes: hematocrit, plaque burden, plaque Hounsfield unit, distance to ostium, wall shear stress, flow, Reynolds number, and centerline curvature may be in the form of: (45%, 20 mm 3 , 130 HU, 60.5 mm, 70 dyne/cm 2 , 1500 mm 3 /sec, 400, 1 mm −1 ). Global physiological or phenotypic parameters may be used in the feature vector of all points, and local physiological or phenotypic parameters may change in the feature vector of different points. 
     In one embodiment, an exemplary feature vector generated in step  514  may include one or more of: (i) systolic and diastolic blood pressure, (ii) heart rate, (iii) blood properties including: plasma, red blood cells (erythrocytes), hematocrit, white blood cells (leukocytes) and platelets (thrombocytes), viscosity, yield stress, etc. (iv) patient age, gender, height, weight, etc., (v) lifestyle characteristics, e.g., presence or absence of current medications/drugs, (vi) general risk factors of CAD, such as smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history of CAD, etc., (vii) in vitro blood test results, such as LDL, Triglyceride cholesterol level, etc., (viii) coronary calcium score, (ix) amount of calcium in aorta and valve, (x) presence of aortic aneurysm, (xi) presence of valvular heart disease, (xii) presence of peripheral disease, (xiii) presence of dental disease, (xiv) epicardial fat volume, (xv) cardiac function (ejection fraction), (xvi) stress echocardiogram test results, (xvii) characteristics of the aortic geometry (e.g., cross-sectional area profile along the ascending and descending aorta, and Surface area and volume of the aorta, (xviii) a SYNTAX score, as described above, (xix) plaque burden of existing plaque, (xx) adverse plaque characteristics of existing plaque (e.g., presence of positive remodeling, presence of low attenuation plaque, presence of spotty calcification), (xxi) characteristics of the coronary branch geometry, (xxii) characteristics of coronary cross-sectional area, (xxiii) characteristics of coronary lumen intensity, e.g., intensity change along the centerline (slope of linearly-fitted intensity variation), (xxiv) characteristics of surface of coronary geometry, e.g., 3D surface curvature of geometry (Gaussian, maximum, minimum, mean), (xxv) characteristics of volume of coronary geometry, e.g., ratio of total coronary volume compared to myocardial volume, (xxvi) characteristics of coronary centerline, (xxvii) characteristics of coronary deformation, (xxviii) characteristics of existing plaque, and/or (xxix) characteristics of coronary hemodynamics derived from computational flow dynamics or invasive measurement. 
     In one embodiment, the characteristics of the coronary branch geometry may include one or more of: (1) total number of vessel bifurcations, and the number of upstream/downstream vessel bifurcations; (2) average, minimum, and maximum upstream/downstream cross-sectional areas; (3) distances (along the vessel centerline) to the centerline point of minimum and maximum upstream/downstream cross-sectional areas, (4) cross-sectional area of and distance (along the vessel centerline) to the nearest upstream/downstream vessel bifurcation, (5) cross-sectional area of and distance (along the vessel centerline) to the nearest coronary outlet and aortic inlet/outlet, (6) cross-sectional areas and distances (along the vessel centerline) to the downstream coronary outlets with the smallest/largest cross-sectional areas, and/or (7) upstream/downstream volumes of the coronary vessels. 
     In one embodiment, the characteristics of coronary cross-sectional area may include one or more of: (1) cross-sectional lumen area along the coronary centerline, (2) cross-sectional lumen area to the power of N (where N can be determined from various source of scaling laws such as Murray&#39;s law (N=1.5) and Uylings&#39; study (N=1.165˜1.5)), (3) a ratio of lumen cross-sectional area with respect to the main ostia (LM, RCA) (e.g., measure of cross-sectional area at the LM ostium, normalized cross-sectional area of the left coronary by LM ostium area, measure of cross-sectional area at the RCA ostium, normalized cross-sectional area of the right coronary by RCA ostium area, (4) ratio of lumen cross-sectional area with respect to the main ostia to the power of N (where power can be determined from various source of scaling laws such as Murray&#39;s law (N=1.5) and Uylings&#39; study (N=1.165˜1.5)), (5) degree of tapering in cross-sectional lumen area along the centerline (based on a sample centerline points within a certain interval (e.g., twice the diameter of the vessel) and compute a slope of linearly-fitted cross-sectional area), (6) location of stenotic lesions (based on detecting minima of cross-sectional area curve (e.g., detecting locations, where first derivative of area curve is zero and second derivative is positive, and smoothing cross-sectional area profile to avoid detecting artifactual peaks), and computing distance (parametric arc length of centerline) from the main ostium, (7) length of stenotic lesions (computed based on the proximal and distal locations from the stenotic lesion, where cross-sectional area is recovered, (8) degree of stenotic lesions, by evaluating degree of stenosis based on reference values of smoothed cross-sectional area profile using Fourier smoothing or kernel regression, (9) location and number of lesions corresponding to 50%, 75%, 90% area reduction, (10) distance from stenotic lesion to the main ostia, and/or (11) irregularity (or circularity) of cross-sectional lumen boundary. 
     In one embodiment, the characteristics of coronary centerline may include: (1) curvature (bending) of coronary centerline, such as by computing Frenet curvature, based on 
     
       
         
           
             
               κ 
               = 
               
                 
                   | 
                   
                     
                       p 
                       ′ 
                     
                     × 
                     
                       p 
                       ″ 
                     
                   
                   | 
                 
                 
                   
                      
                     
                       
                         p 
                         ′ 
                       
                       × 
                       
                         p 
                         ″ 
                       
                     
                      
                   
                   2 
                 
               
             
             , 
           
         
       
     
     where p is a coordinate of the centerline, and computing an inverse of the radius of a circumscribed circle along the centerline points, and/or (2) tortuosity (non-planarity) of coronary centerline, such as by computing Frenet torsion, based on 
     
       
         
           
             
               τ 
               = 
               
                 
                   
                     ( 
                     
                       
                         p 
                         ′ 
                       
                       × 
                       
                         p 
                         ″ 
                       
                     
                     ) 
                   
                   · 
                   
                     p 
                     ′′′ 
                   
                 
                 
                   | 
                   
                     
                       p 
                       ′ 
                     
                     × 
                     
                       p 
                       ″ 
                     
                   
                   ⁢ 
                   
                     | 
                     2 
                   
                 
               
             
             , 
           
         
       
     
     where p is a coordinate of the centerline. 
     In one embodiment, calculation of the characteristics of coronary deformation may involve multi-phase CCTA (e.g., diastole and systole), including (1) distensibility of coronary artery over cardiac cycle, (2) bifurcation angle change over cardiac cycle, and/or (3) curvature change over cardiac cycle. In one embodiment, the characteristics of existing plaque may be calculated based on: (1) volume of plaque, (2) intensity of plaque, (3) type of plaque (calcified, non-calcified), (4) distance from the plaque location to ostium (LM or RCA), and/or (5) distance from the plaque location to the nearest downstream/upstream bifurcation. 
     In one embodiment, the characteristics of coronary hemodynamics may be derived from computational flow dynamics or invasive measurement. For example, pulsatile flow simulation may be performed to obtain transient characteristics of blood, by using a lumped parameter coronary vascular model for downstream vasculatures, inflow boundary condition with coupling a lumped parameter heart model and a closed loop model to describe the intramyocardial pressure variation resulting from the interactions between the heart and arterial system during cardiac cycle. For example, the calculation may include one or more of: measured FFR, coronary flow reserve, pressure distribution, FFRct, mean wall-shear stress, oscillatory shear index, particle residence time, turbulent kinetic energy, Reynolds number, Womersley number, and/or local flow rate. 
     Method  500  may then include associating the feature vector with the growth, shrinkage, or onset of plaque at each point of the patient-specific geometric model (step  516 ). Method  500  may involve continuing to perform the above steps  512 ,  514 ,  516 , for each of a plurality of points in the patient-specific geometric model (step  518 ), and for each of any number of patients for which a machine learning algorithm may be based (step  520 ). Method  500  may also involve continuing to perform the above steps  512 ,  514 ,  516 , for each of a plurality of points in the patient-specific geometric model, and for each of any number of patients for which a machine learning algorithm may be based, across any additional time period or periods useful for generating information about the growth, shrinkage, or onset of plaque (i.e., the change and/or rate of change of plaque at each point of the model) (step  522 ). 
     Method  500  may then include training a machine learning algorithm to predict the probability of amounts of growth, shrinkage, or onset of plaque at the points from the feature vectors at the points (step  524 ). Examples of machine learning algorithms suitable for performing this task may include support vector machines (SVMs), multi-layer perceptrons (MLPs), and/or multivariate regression (MVR) (e.g., weighted linear or logistic regression). In one embodiment, if training data causes the machine learning algorithm to predict a lower amount (e.g., size or extent) of plaque than what is detected, then the machine learning algorithm may be interpreted as predicting plaque shrinkage; if training data causes the machine learning algorithm to predict a higher amount (e.g., size or extent) of plaque than what is detected, then the machine learning algorithm may be interpreted as predicting plaque growth. 
     Method  500  may then include storing or otherwise saving the results of the machine learning algorithm (e.g., feature weights) to a digital representation, such as the memory or digital storage (e.g., hard drive, network drive) of a computational device, such as a computer, laptop, DSP, server, etc. of server systems  106  (step  526 ). 
       FIG. 5B  is a block diagram of an exemplary method of using the machine learning system (e.g., machine learning system  310  executed on server systems  106 ) for predicting, for a particular patient, the rate of onset, growth/shrinkage, of coronary lesions from vessel geometry, physiology, and hemodynamics, according to an exemplary embodiment of the present disclosure. In one embodiment, method  550  may include, for one or more patients (step  552 ), obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  554 ), obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  556 ), and obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  558 ). 
     Specifically, the step of obtaining a patient-specific geometric model of a portion of the patient&#39;s vasculature (step  554 ) may include obtaining a patient-specific model of the geometry for one or more of the patient&#39;s blood vessels, myocardium, aorta, valves, plaques, and/or chambers. In one embodiment, this geometry may be represented as a list of points in space (possibly with a list of neighbors for each point) in which the space can be mapped to spatial units between points (e.g., millimeters). In one embodiment, this model may be derived by performing a cardiac CT imaging of the patient in the end diastole phase of the cardiac cycle. This image then may be segmented manually or automatically to identify voxels belonging to the aorta and the lumen of the coronary arteries. Inaccuracies in the geometry extracted automatically may be corrected by a human observer who compares the extracted geometry with the images and makes corrections as needed. Once the voxels are identified, the geometric model can be derived (e.g., using marching cubes). 
     In one embodiment, the step of obtaining one or more estimates of physiological or phenotypic parameters of the patient (step  556 ) may include obtaining a list of one or more estimates of physiological or phenotypic parameters of the patient, such as blood pressure, blood viscosity, in vitro blood test results (e.g., LDL/Triglyceride cholesterol level), patient age, patient gender, the mass of the supplied tissue, etc. These parameters may be global (e.g., blood pressure) or local (e.g., estimated density of the vessel wall at a location). In one embodiment, the physiological or phenotypic parameters may include, blood pressure, hematocrit level, patient age, patient gender, myocardial mass (e.g., derived by segmenting the myocardium in the image, and calculating the volume in the image and using an estimated density of 1.05 g/mL to estimate the myocardial mass), general risk factors of coronary artery disease (e.g., smoking, diabetes, hypertension, abdominal obesity, dietary habits, family history, etc.), and/or in vitro blood test results (e.g., LDL, Triglyceride cholesterol level). 
     In one embodiment, the step of obtaining one or more estimates of biophysical hemodynamic characteristics of the patient (step  558 ) may include obtaining a list of one or more estimates of biophysical hemodynamic characteristics from computational fluid dynamics analysis, such as wall-shear stress, oscillatory shear index, particle residence time, Reynolds number, Womersley number, local flow rate, and turbulent kinetic energy, etc. Specifically, the mean wall-shear stress, may be defined as 
     
       
         
           
             
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     Method  550  may include, for every point in the patient-specific geometric model (step  560 ), creating for that point a feature vector comprising a numerical description of the geometry and biophysical hemodynamic characteristic at that point, and estimates of physiological or phenotypic parameters of the patient. Global physiological or phenotypic parameters can be used in the feature vector of all points and local physiological or phenotypic parameters can change in the feature vector of different points. Method  550  may involve continuing to perform the above steps  560 ,  562 , for each of a plurality of points in the patient-specific geometric model (step  564 ). 
     Method  550  may then include producing estimates of the probability and/or rate of the growth, shrinkage, or onset of plaque at each point in the patient-specific geometric model based on the stored machine learning results (stored at B,  FIG. 5A ) (step  566 ). Specifically, method  550  may use the saved results of the machine learning algorithm produced in the training mode of method  500  (e.g., feature weights) to produce estimates of the probability of growth, shrinkage, or onset (e.g., rates of growth/shrinkage) of plaque at each point in the patient-specific geometric model (e.g., by generating plaque estimates as a function of the feature vector at each point). These estimates may be produced using the same machine learning algorithm technique used in the training mode (e.g., the SVM, MLP, MVR technique). Method  550  may then include saving the estimates of the probability of the growth, shrinkage, or onset of plaque (step  568 ), such as to the memory or digital storage (e.g., hard drive, network drive) of a computational device, such as a computer, laptop, DSP, server, etc., of server systems  106 , and communicating these patient-specific and location-specific predicted probabilities of lesion formation to a health care provider. 
       FIG. 6  is a simplified block diagram of an exemplary computer system  600  in which embodiments of the present disclosure may be implemented, for example as any of the physician devices or servers  102 , third party devices or servers  104 , and server systems  106 . A platform for a server  600 , for example, may include a data communication interface for packet data communication  660 . The platform may also include a central processing unit (CPU)  620 , in the form of one or more processors, for executing program instructions. The platform typically includes an internal communication bus  610 , program storage and data storage for various data files to be processed and/or communicated by the platform such as ROM  630  and RAM  640 , although the server  600  often receives programming and data via a communications network (not shown). The hardware elements, operating systems and programming languages of such equipment are conventional in nature, and it is presumed that those skilled in the art are adequately familiar therewith. The server  600  also may include input and output ports  650  to connect with input and output devices such as keyboards, mice, touchscreens, monitors, displays, etc. Of course, the various server functions may be implemented in a distributed fashion on a number of similar platforms, to distribute the processing load. Alternatively, the servers may be implemented by appropriate programming of one computer hardware platform. 
     As described above, the computer system  600  may include any type or combination of computing systems, such as handheld devices, personal computers, servers, clustered computing machines, and/or cloud computing systems. In one embodiment, the computer system  600  may be an assembly of hardware, including a memory, a central processing unit (“CPU”), and/or optionally a user interface. The memory may include any type of RAM or ROM embodied in a physical storage medium, such as magnetic storage including floppy disk, hard disk, or magnetic tape; semiconductor storage such as solid state disk (SSD) or flash memory; optical disc storage; or magneto-optical disc storage. The CPU may include one or more processors for processing data according to instructions stored in the memory. The functions of the processor may be provided by a single dedicated processor or by a plurality of processors. Moreover, the processor may include, without limitation, digital signal processor (DSP) hardware, or any other hardware capable of executing software. The user interface may include any type or combination of input/output devices, such as a display monitor, touchpad, touchscreen, microphone, camera, keyboard, and/or mouse. 
     Program aspects of the technology may be thought of as “products” or “articles of manufacture” typically in the form of executable code and/or associated data that is carried on or embodied in a type of machine readable medium. “Storage” type media include any or all of the tangible memory of the computers, processors or the like, or associated modules thereof, such as various semiconductor memories, tape drives, disk drives and the like, which may provide non-transitory storage at any time for the software programming. All or portions of the software may at times be communicated through the Internet or various other telecommunication networks. Such communications, for example, may enable loading of the software from one computer or processor into another, for example, from a management server or host computer of the mobile communication network into the computer platform of a server and/or from a server to the mobile device. Thus, another type of media that may bear the software elements includes optical, electrical and electromagnetic waves, such as used across physical interfaces between local devices, through wired and optical landline networks and over various air-links. The physical elements that carry such waves, such as wired or wireless links, optical links or the like, also may be considered as media bearing the software. As used herein, unless restricted to non-transitory, tangible “storage” media, terms, such as computer or machine “readable medium” refer to any medium that participates in providing instructions to a processor for execution. 
     Other embodiments of the disclosure will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.