Patent Publication Number: US-2023142152-A1

Title: System and method for deep-learning based estimation of coronary artery pressure drop

Description:
BACKGROUND 
     The subject matter disclosed herein relates to systems and methods for deep-learning-based estimation of coronary artery pressure drop. 
     Volumetric medical imaging technologies use a variety of techniques to gather three-dimensional information about the body. For example, a computed tomography (CT) imaging system measures the attenuation of X-ray beams passed through a patient from numerous angles. Based upon these measurements, a computer is able to reconstruct cross-sectional images of the portions of a patient&#39;s body responsible for the radiation attenuation. As will be appreciated by those skilled in the art, these images are based upon separate examination of a series of angularly-displaced measurements. It should be pointed out that a CT system produces data that represent the distribution of linear attenuation coefficients of the scanned object. The data are then reconstructed to produce an image that is typically displayed on a screen, and may be printed or reproduced on film. 
     For example, in the field of CT angiography (CTA), vasculature and other circulatory system structures may be imaged, typically by administration of a radio-opaque dye prior to imaging. Visualization of the CTA data typically is performed in a two-dimensional manner, i.e., slice-by-slice, or in a three-dimensional manner, i.e., volume visualization, which allows the data to be analyzed for vascular pathologies. For example, the data may be analyzed for aneurysms, vascular calcification, renal donor assessment, stent placement, vascular blockage, and vascular evaluation for sizing and/or runoff. Once a pathology is located, quantitative assessments of the pathology may be made of the on the original two-dimensional slices. 
     Atherosclerosis is a vascular disease in which cholesterol and other material accumulate along the inner lining of an artery forming atheromas or plaques. These plaque deposits, can over time, lead to a local narrowing of the blood vessel, often referred to as a stenosis. In the presence of a substantial stenosis, blood flow to the tissues downstream becomes severely restricted. Initially, severity of a stenosis was based purely on geometry, such as the percent reduction in lumen diameter. However, it was soon realized that anatomic significance of a stenosis did not always translate to functional significance. The concept of fractional flow reserve (FFR) was introduced to address this issue. It is defined as the ratio of pressure distal to the stenosis to the pressure proximal to it and measures the hemodynamic resistance of the stenosis relative to the resistance of the coronary microcirculation. Typically, FFR is measured at the time of invasive coronary angiography by inserting a tiny guide wire through a standard diagnostic catheter. A sensor at the tip of the wire measures pressure. Low values of FFR indicate a hemodynamically significant stenosis and clinical trials have demonstrated that intervention can be deferred when FFR&gt;0.8. 
     It is estimated that approximately 60 percent of invasive angiographies performed are diagnostic in nature and therefore unnecessary. Thus, the estimation of coronary FFR by combining computational fluid dynamics (CFD) modeling with CTA images has emerged as a non-invasive method for identifying ischemia-causing lesions. An accurate estimation of the FFR distribution along the coronary tree can be obtained with a three-dimensional (3D) CFD model of the large coronary epicardial arteries. However, the computation times can be large with this approach. Efforts to reduce computation times have involved utilizing a one-dimensional (1D) model. However, some of these 1D models involve several approximations and therefore FFR predictions may not be as accurate as a 3D model. For example, some of the empirical models utilized in the 1D model have been found to under predict the stenosis pressure drop when compared to 3D CFD. Thus, there is a need for approaches that can attain comparable accuracy to that obtained within 3D CFD while maintaining drastically lower computation times. 
     BRIEF DESCRIPTION 
     Certain embodiments commensurate in scope with the originally claimed subject matter are summarized below. These embodiments are not intended to limit the scope of the claimed subject matter, but rather these embodiments are intended only to provide a brief summary of possible embodiments. Indeed, the invention may encompass a variety of forms that may be similar to or different from the embodiments set forth below. 
     In one embodiment, a computer-implemented method is provided. The method includes generating, via a processor, synthetic vessels. The method also includes performing, via the processor, three-dimensional (3D) computational fluid dynamics (CFD) on the synthetic vessels for different flow rates to generate 3D CFD data. The method further includes extracting, via the processor, 3D image patches from the synthetic vessels. The method even further includes obtaining, via the processor, pressure drops across the 3D image patches from the 3D CFD data. The method yet further includes training, via the processor, a deep neural network utilizing the 3D image patches, the pressure drops, and associated flow rates to generate a trained deep neural network. 
     In another embodiment, one or more non-transitory computer-readable media are provided. The computer-readable media encode one or more processor-executable routines. The one or more routines, when executed by a processor, cause acts to be performed. The acts include generating synthetic vessels. The acts also include performing three-dimensional (3D) CFD on the synthetic vessels for different flow rates to generate 3D CFD data. The acts further include extracting 3D image patches from the synthetic vessels. The acts even further include obtaining pressure drops across the 3D image patches from the 3D CFD data. The acts yet further include training a deep neural network utilizing the 3D image patches, the pressure drops, and associated flow rates to generate a trained deep neural network. 
     In a further embodiment, a processor-based system is provided. The processor-based system includes a memory encoding one or more processor-executable routines. The routines, when executed cause acts to be performed. The acts include generating synthetic vessels. The acts also include performing 3D CFD on the synthetic vessels for different flow rates to generate 3D CFD data. The acts further include extracting 3D image patches from the synthetic vessels. The acts even further include obtaining pressure drops across the 3D image patches from the 3D CFD data. The acts yet further include training a deep neural network utilizing the 3D image patches, the pressure drops, and associated flow rates to generate a trained deep neural network. The processor-based system also includes a processor configured to access and execute the one or more routines encoded by the memory. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other features, aspects, and advantages of the present subject matter will become better understood when the following detailed description is read with reference to the accompanying drawings in which like characters represent like parts throughout the drawings, wherein: 
         FIG.  1    is a schematic illustration of an embodiment of a computed tomography (CT) system configured to acquire CT images of a patient and process the images, in accordance with aspects of the present disclosure; 
         FIG.  2    is a flow chart of a method for training and utilizing a neural network for predicting a pressure drop (e.g., coronary artery pressure drop), in accordance with aspects of the present disclosure; 
         FIG.  3    is graphical representation of example of generated synthetic vessels, in accordance with aspects of the present disclosure; 
         FIG.  4    illustrates an example of a convolutional neural network architecture for predicting a pressure drop, in accordance with aspects of the present disclosure; 
         FIG.  5    illustrates an example of a multipath neural network having a long short-term memory (LSTM) cell for predicting a predicting a pressure drop, in accordance with aspects of the present disclosure; 
         FIG.  6    is a flow chart of a method for utilizing a trained neural network for predicting a pressure drop (e.g., coronary artery pressure drop), in accordance with aspects of the present disclosure; and 
         FIG.  7    is a schematic representation of a segmented vessel within a coronary tree with overlapping binary mask volumes and associated equations for determining pressure drop, in accordance with aspects for the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     One or more specific embodiments will be described below. In an effort to provide a concise description of these embodiments, not all features of an actual implementation are described in the specification. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business-related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. 
     When introducing elements of various embodiments of the present subject matter, the articles “a,” “an,” “the,” and “said” are intended to mean that there are one or more of the elements. The terms “comprising,” “including,” and “having” are intended to be inclusive and mean that there may be additional elements other than the listed elements. Furthermore, any numerical examples in the following discussion are intended to be non-limiting, and thus additional numerical values, ranges, and percentages are within the scope of the disclosed embodiments. 
     Some generalized information is provided to provide both general context for aspects of the present disclosure and to facilitate understanding and explanation of certain of the technical concepts described herein. 
     Deep-learning (DL) approaches discussed herein may be based on artificial neural networks, and may therefore encompass one or more of deep neural networks, fully connected networks, convolutional neural networks (CNNs), perceptrons, encoders-decoders, recurrent networks, wavelet filter banks, u-nets, generative adversarial networks (GANs), or other neural network architectures. The neural networks may include shortcuts, activations, batch-normalization layers, and/or other features. These techniques are referred to herein as deep-learning techniques, though this terminology may also be used specifically in reference to the use of deep neural networks, which is a neural network having a plurality of layers. 
     As discussed herein, deep-learning techniques (which may also be known as deep machine learning, hierarchical learning, or deep structured learning) are a branch of machine learning techniques that employ mathematical representations of data and artificial neural networks for learning and processing such representations. By way of example, deep-learning approaches may be characterized by their use of one or more algorithms to extract or model high-level abstractions of a type of data-of-interest. This may be accomplished using one or more processing layers, with each layer typically corresponding to a different level of abstraction and, therefore potentially employing or utilizing different aspects of the initial data or outputs of a preceding layer (i.e., a hierarchy or cascade of layers) as the target of the processes or algorithms of a given layer. In an image processing or reconstruction context, this may be characterized as different layers corresponding to the different feature levels or resolution in the data. In general, the processing from one representation space to the next-level representation space can be considered as one ‘stage’ of the process. Each stage of the process can be performed by separate neural networks or by different parts of one larger neural network. 
     The present disclosure provides systems and methods for predicting coronary artery pressure drop. The disclosed embodiments utilize deep neural networks to learn 3D CFD model predictions. In particular, a deep neural network is trained utilizing image patches (e.g., 3D image patches) extracted from synthetically generated vessels and the pressure drops occurring across these image patches (e.g., obtained from 3D CFD). The trained deep neural network is then used to predict the pressure drops across segmented image patches extracted from vessels in clinical image data (e.g., computed tomography angiography (CTA) data). The disclosed embodiments enable estimation of FFR with comparable accuracy to 3D CFD but with drastically lower computation times. Although described in the context of coronary artery disease, the methods provided are suitable for assessing the severity of vasculature narrowing anywhere in human anatomy, which may be due to atherosclerosis, other disease processes, general vasculature malformations, or the like. 
     With the foregoing discussion in mind,  FIG.  1    illustrates an embodiment of an imaging system  10  for acquiring and processing image data in accordance with aspects of the present disclosure. Although the following embodiments are discussed in terms of the computed tomography (CT) imaging system, the embodiments may also be utilized with other imaging systems (e.g., X-ray, PET, CT/PET, SPECT, nuclear CT, magnetic resonance imaging, etc.). In the illustrated embodiment, system  10  is a CT system designed to acquire X-ray projection data, to reconstruct the projection data into one or more tomographic images, and to process the image data for display and analysis. The CT imaging system  10  includes an X-ray source  12 . As discussed in detail herein, the source  12  may include one or more X-ray sources, such as an X-ray tube or solid-state emission structures. The X-ray source  12 , in accordance with present embodiments, is configured to emit an X-ray beam  20  at one or more energies. 
     In certain implementations, the source  12  may be positioned proximate to a collimator  22  used to define the size and shape of the one or more X-ray beams  20  that pass into a region in which a subject  24  (e.g., a patient) or object of interest is positioned. The subject  24  attenuates at least a portion of the X-rays. Resulting attenuated X-rays  26  impact a detector array  28  formed by a plurality of detector elements. Each detector element produces an electrical signal that represents the intensity of the X-ray beam incident at the position of the detector element when the beam strikes the detector  28 . Electrical signals are acquired and processed to generate one or more scan datasets or reconstructed images. 
     A system controller  30  commands operation of the imaging system  10  to execute examination and/or calibration protocols and to process the acquired data. With respect to the X-ray source  12 , the system controller  30  furnishes power, focal spot location, control signals and so forth, for the X-ray examination sequences. The detector  28  is coupled to the system controller  30 , which commands acquisition of the signals generated by the detector  28 . In addition, the system controller  30 , via a motor controller  36 , may control operation of a linear positioning subsystem  32  and/or a rotational subsystem  34  used to move components of the imaging system  10  and/or the subject  24 . The system controller  30  may include signal processing circuitry and associated memory circuitry. In such embodiments, the memory circuitry may store programs, routines, and/or encoded algorithms executed by the system controller  30  to operate the imaging system  10 , including the X-ray source  12 , and to process the data acquired by the detector  28  in accordance with the steps and processes discussed herein. In one embodiment, the system controller  30  may be implemented as all or part of a processor-based system such as a general-purpose or application-specific computer system. 
     The source  12  may be controlled by an X-ray controller  38  contained within the system controller  30 . The X-ray controller  38  may be configured to provide power and timing signals to the source  12 . The system controller  30  may include a data acquisition system (DAS)  40 . The DAS  40  receives data collected by readout electronics of the detector  28 , such as sampled analog signals from the detector  28 . The DAS  40  may then convert the data to digital signals for subsequent processing by a processor-based system, such as a computer  42 . In other embodiments, the detector  28  may convert the sampled analog signals to digital signals prior to transmission to the data acquisition system  40 . The computer may include processing circuitry  44  (e.g., image processing circuitry). The computer  42  may include or communicate with one or more non-transitory memory devices  46  that can store data processed by the computer  42 , data to be processed by the computer  42 , or instructions to be executed by a processor (e.g., processing circuitry  44 ) of the computer  42 . For example, the processing circuitry  44  of the computer  42  may execute one or more sets of instructions stored on the memory  46 , which may be a memory of the computer  42 , a memory of the processor, firmware, or a similar instantiation. In accordance with present embodiments, the memory  46  stores sets of instructions that, when executed by the processor, perform image processing methods as discussed herein. The memory  46  also stores one or more algorithms and/or neural networks  47  that may be utilized in estimating or predicting coronary artery pressure drop across segmented mage patches extracted from clinical data (e.g., imaging data) as described in greater detail below. 
     The computer  42  may also be adapted to control features enabled by the system controller  30  (i.e., scanning operations and data acquisition), such as in response to commands and scanning parameters provided by an operator via an operator workstation  48 . The system  10  may also include a display  50  coupled to the operator workstation  48  that allows the operator to view relevant system data, to observe reconstructed images, to control imaging, and so forth. Additionally, the system  10  may include a printer  52  coupled to the operator workstation  48  and configured to print images. The display  50  and the printer  52  may also be connected to the computer  42  directly or via the operator workstation  48 . Further, the operator workstation  48  may include or be coupled to a picture archiving and communications system (PACS)  54 . PACS  54  may be coupled to a remote system  56 , radiology department information system (RIS), hospital information system (HIS) or to an internal or external network, so that others at different locations can gain access to the image data. 
     Further, the computer  42  and operator workstation  48  may be coupled to other output devices, which may include standard or special-purpose computer monitors and associated processing circuitry. One or more operator workstations  40  may be further linked in the system for outputting system parameters, requesting examinations, viewing images, and so forth. In general, displays, printers, workstations, and similar devices supplied within the system may be local to the data acquisition components, or may be remote from these components, such as elsewhere within an institution or hospital, or in an entirely different location, linked to the image acquisition system via one or more configurable networks, such as the Internet, virtual private networks, and so forth. 
     While the preceding discussion has treated the various exemplary components of the imaging system  10  separately, these various components may be provided within a common platform or in interconnected platforms. For example, the computer  30 , memory  38 , and operator workstation  40  may be provided collectively as a general- or special-purpose computer or workstation configured to operate in accordance with the aspects of the present disclosure. In such embodiments, the general- or special-purpose computer may be provided as a separate component with respect to the data acquisition components of the system  10  or may be provided in a common platform with such components. Likewise, the system controller  30  may be provided as part of such a computer or workstation or as part of a separate system dedicated to image acquisition. 
       FIG.  2    is a flow chart of a method  58  for training and utilizing a neural network for predicting a pressure drop (e.g., coronary artery pressure drop). Some or all of the steps of the method  58  may be performed by the computer  42 , operator workstation  48 , and/or a remote computing device. One or more steps of the illustrated method  58  may performed in a different order from the order depicted in  FIG.  2    and/or simultaneously. The method  58  includes generating synthetic vessels (e.g., synthetic blood vessels) (block  60 ). In certain embodiments, a mathematical model (e.g., Lindenmayer system) may be utilized to generate the synthetic vessels. The process of synthetic vessel generation can be broken down into two steps: the vessel centerline generation and extraction of the vessel boundary for each slice. The vessel centerline generation involves the generation of a 3D random noise field, which is smoothed and thresholded with two kernels of different scales. The sum of these results is further smoothed and tapered in the axial direction. The center of mass is computed for each slice and then scaled and smoothed in the axial direction. Next, a series of stenosis locations are randomly positioned, and each is associated with a set of random parameters, including skew, depth, length, eccentricity, shape factor, and other parameters. Based on these parameters, the nominal centerline position and the nominal radius are smoothly modified in the areas of stenosis. The vessel boundary extraction involves evaluating the sum of a parabolic function and a modified noise field at each slice. The parabolic function is offset and scaled so that (in the absence of noise) it would take on a positive value at all points that are within the nominal radius of the nominal centerline position. Adding the noise field provides distortion to this boundary and can either increase or decrease the cross-sectional area moderately. The noise field intensity may be modulated by a factor of 2 in the axial direction, with higher noise near the middle of the vessel in order to provide a range of distortion levels. The slope of the parabola may be adjusted based on the nominal radius to ensure the sensitivity of the boundary to the noise field is not strongly dependent on the nominal radius. A surface mesh is generated from the boundaries extracted from each slice and the cross-sectional coordinates of the mesh are smoothed by convolving each point with its mesh neighborhood. The generated synthetic vessels lack branches. Examples of generated synthetic vessels  62  are shown in  FIG.  3   . 
     Returning to the method  58 , the method  58  includes performing 3D CFD modeling using the generated synthetic vessels for different flow rates (e.g., volume flow rates) (block  64 ). The different flow rates are applied to each synthetic vessel. Blood is assumed to an incompressible, Newtonian fluid in the proposed process and the equations governing its motion are the incompressible Navier-Stokes equations. A commercial solver is used to solve these equations. At the inlet of each synthetic vessel, a randomly chosen flow rate between 0 and 400 milliliters/minute is imposed. The vessel walls are assumed to be rigid and no-slip and no-flow-through boundary conditions are imposed there. Zero pressure boundary conditions are imposed at the vessel exit. For each vessel, CFD calculations are performed for seven different randomly chosen flows (e.g., flow rates). The convergence of the CFD calculations is judged based on how much the residual at each iteration has dropped from their initial values and only the converged cases are post-processed to obtain the pressure drops. 
     The method  58  also includes extracting 3D image patches from the generated synthetic vessels to generate training data (block  66 ). In certain embodiments, 3D image patches are extracted at regular intervals from the synthetic vessels. In certain embodiments, the 3D patches are overlapping. In certain embodiments, the 3D image patches may be extracted randomly. The axial patch dimension (e.g., axial distance) is chosen to be much smaller than the vessel length while the dimensions in the other two directions are chosen large enough to encompass the largest synthetic vessel cross section. In certain embodiments, the axial patch dimension is the same for each 3D image patch. 
     The method  58  further includes obtaining pressure drops across the 3D image patches from the 3D CFD data obtained above (block  68 ). For each of these 3D image patches, a total pressure drop across an entire axial length of the patch or a portion of the axial patch length is determined from the 3D CFD calculation. By extracting the pressure drop over only a portion of the axial patch length as opposed to the whole length, the influence of upstream and downstream patch geometric features on the pressure drop can be incorporated into a deep neural network. Instead of extracting a single total pressure drop over the entire axial patch length, in certain embodiments, multiple pressure drops over portions of the axial patch length are extracted. 
     The method  58  still further includes utilizing the 3D image patches and associated pressure drops and flow rates to train a deep neural network (block  70 ). The structure of the deep neural network is described in greater detail below. For each of the 3D image patches, a binary mask is generated using a CT simulation tool. The binary mask and volume flow (e.g., volume flow rate) through the vessel are provided as inputs to the deep-learning network. The output from the deep neural network is the pressure drop across the whole axial length or a portion of the axial length of the 3D image patch with the corresponding label data being the 3D CFD determined value. In certain other embodiments, the output from the deep neural network is multiple pressure drops over portions of the axial patch length. Since a large portion of the synthetic vessel is healthy and a stenosis only occurs occasionally, most of the 3D image patches extracted by the above approach will be in the healthy section. As a result, a considerable number of the patch pressure drops will be small. Indeed, if one were to plot a histogram of the training data pressure drops, a highly imbalanced distribution may be seen with a large fraction of the 3D image patches having pressure drops between approximately 0 to 1 mm Hg and very few patches with pressure drops between approximately 49 to 50 mm Hg corresponding to high degrees of vessel stenosis. Due to this imbalance the training loss will be skewed towards patches with pressure drops in the range of approximately 0 to 1 mm Hg. To avoid this issue, augmentation of patches outside the 0 to 1 mm Hg range may be performed. The augmentations may be done by rotating the 3D image patch as well as by in-plane translations. These transformations do not affect the patch pressure drop. Further, an unlimited number of synthetic vessels could be generated, while increasing the percentage of highly stenosed vessels in the training data for the deep neural network. 
     The method  58  yet further includes applying the trained deep neural network to vessels (e.g., blood vessels) in a clinical image (e.g., CTA image data) to predict a pressure drop (e.g. coronary artery pressure drop) for least a portion of at least one vessel in the clinical image (block  72 ). The utilization of the trained deep neural network is described in greater detail below. 
     Different types of network architecture may be utilized for the deep neural network described herein.  FIG.  4    illustrates an example of a convolutional neural network (CNN) architecture  74  for predicting a pressure drop. The CNN  74  may include convolutional layers  76  alternating with max pooling layers  78  followed by dense layers  80  with neurons used. When training the network, a binary mask image  82  corresponding to a 3D geometric patch extracted from a synthetic vessel is provided as input to the convolutional layers  76 . After feature extraction, the features are merged with the input flow rate  84  and provided as input to the dense network  86 . An output  88  from the dense network  86  is the predicted pressure drop from the patch with the CFD obtained pressure drop as the label data. In certain embodiments, the output  88  from the dense network  86  will be more than one number corresponding to multiple pressure drops predicted over portions of the axial patch length. The loss function minimized during training in the CNN architecture  74  is the mean square error between the predicted pressure drop and the CFD obtained pressure drop. 
     In certain embodiments, other loss function formulations may be utilized. One such example is a physics informed neural network (PINN) where the loss function is the residual in the equations governing the physics of the problem. For the particular problem disclosed here within the governing equations are the incompressible Navier-Stokes equations and the loss function would include the residuals in the mass and momentum conservation equations when using PINNs. The loss function would also include residuals in the imposed boundary conditions. In addition, the loss function may also include the error between the predicted pressure drop and the CFD obtained pressure drop. The network architecture for the PINN would be similar to the one depicted in  FIG.  4   . Similarly, the inputs to the network would be the binary mask and the flow rate. In addition, randomly chosen co-ordinate positions within the interior and boundaries of the 3D geometric patch would also be provided as inputs to the network. The output from the network would be the velocities and pressures at the randomly chosen co-ordinate positions. From the predicted pressures, the pressure drop within the patch may be determined. The predicted flow may also be used to determine quantities such as wall shear stress within the patch. 
     An alternative network architecture would be using two or more patches  90  in a multipath network  92  along with an LSTM cell  94  as depicted in  FIG.  5   . The hypothesis here is, given the 3D geometry and flow in two or more consecutive patches  90  (considered as time points in the LSTM cell  94 ), the pressure drop can be computed for the downstream patch  90 . The network architecture is similar to  FIG.  4    except two or more separate paths  96  would exist for the convolution chain of each patch  90 . Finally, the convolution output for each patch  90  will be concatenated as timepoints for input to the LSTM cell  94  with pressure drop as output  98  of the network  92 . This is a case where the LSTM cell  94  is used for regression analysis, where given some observed variables (e.g., 3D geometry and flow) for certain time steps (number of patches  90 ), the target variable (pressure drop) value is predicted. 
       FIG.  6    is a flow chart of a method  100  for utilizing a trained neural network for predicting a pressure drop (e.g., coronary artery pressure drop). Some or all of the steps of the method  100  may be performed by computer  42 , operator workstation  48 , and/or a remote computing device. One or more steps of the illustrated method  100  may performed in a different order from the order depicted in  FIG.  6    and/or simultaneously. The training of the deep neural network described above is done entirely using synthetic vessels without any branches. However, in reality, there are branches in clinical vessels. To apply the trained network to these vessels, the following method  100  is utilized. The method  100  includes obtaining or receiving clinical images (e.g., 3D CTA images) with vessels (block  102 ). The method  100  also includes generating straightened-out images for each coronary tree path within respective clinical images (block  104 ). Vessel centerlines are determined along the coronary tree. Then, for each coronary tree path (a path here is defined as starting from the left or right coronary ostia and ending at a terminal point in the tree), the image normal to the vessel centerline is determined. This helps to transform each coronary tree path and the surrounding image from physical space to a straightened-out space. 
     The method  100  further includes extracting segmented 3D image patches (block  106 ). A deep-learning algorithm, a traditional segmentation algorithm (e.g., level-set segmentation), active contour model, atlas, or a combination thereof is utilized to segment the vessels that include each straightened-out coronary path. The method  100  even further includes, for each vessel segment within a straightened-out coronary path, determining overlapping binary mask volumes that make up each segment (block  108 ). 
     The method  100  still further includes predicting (or estimating) one or more pressure drops across each segmented binary mask volume (block  110 ). For each binary mask volume, the trained deep neural network (as described above) is run for multiple flow rates and a pressure drop (Δp) versus flow rate (Q) curve of the form Δp=AQ+BQ 2  is constructed. Constructing such a curve avoids having to call the deep neural network multiple times during hyperemia flow optimization and helps reduce overall run time. Since a given vessel segment may belong to multiple coronary paths, the A and B coefficients are averaged over the respective paths. The averaged coefficients are then used to determine the pressure drop through the coronary tree under both rest and hyperemia. 
       FIG.  7    illustrates a schematic representation of a segmented vessel within a coronary tree  112  and associated equations  114  for determining pressure drop as discussed in the method  100 . The depicted segmented coronary tree  112  in  FIG.  7    includes multiple straightened-out coronary paths  116 ,  118 ,  120 . The coronary tree  112  also includes two branch points  121 ,  122  between the different coronary paths  116 ,  118 ,  120 . Branch point  121  is common to the coronary paths  116 ,  118 . Branch point  122  is common to the coronary paths  118 ,  120 . 
     For a vessel segment  124  (belonging to coronary paths  118 ,  120 ) extending between the branch points  121 ,  122 , a first region  126  includes binary mask volumes (represented by boxes  128 ,  130 ,  132  with labels m 1 , m 2 , and m 3 , respectively) and a second region  134  includes binary mask volumes (represented by boxes  136 ,  138 ,  140  with labels m 1 , m 2 , and m 3 , respectively). Binary mask volumes in region  126  overlap with binary mask volumes in region  134 . For example, binary mask volume  128  overlaps with binary mask volume  136 , binary mask volume  130  overlaps with binary mask volumes  136  and  138 , binary mask volume  132  overlaps with binary mask volumes  138  and  140 . 
     Normalized length l 1  represents the non-overlapping length between binary mask volume  128  and binary mask volume  136  (i.e., how far binary mask volume  128  extends beyond binary mask volume  136 ). Normalized length l 2  represents the overlapping length between binary mask volume  128  and binary mask volume  136 . Normalized length l 3  represents the overlapping length between binary mask volume  130  and binary mask volume  136 . Normalized length l 4  represents the overlapping length between binary mask volume  130  and binary mask volume  138 . Normalized length l 5  represents the overlapping length between binary mask volume  132  and binary mask volume  138 . Normalized length l 6  represents the overlapping length between binary mask volume  132  and binary mask volume  140 . Normalized length l 7  represents the non-overlapping length between mask volume  140  and binary mask volume  132  (i.e., how far binary mask volume  140  extends beyond binary mask volume  132 ). Pressure drops Δp 1 , Δp 2 , Δp 3 , Δp 4 , Δp 5 , Δp 6 , and Δp 7  occur across normalized lengths l 1 , l 2 , l 3 , l 4 , l 5 , l 6 , and l 7 , respectively. 
     The equations  114  are for calculating the pressure drops Δp 1 , Δp 2 , Δp 3 , Δp 4 , Δp 5 , Δp 6 , and Δp 7  across normalized lengths (axial lengths) l 1 , l 2 , l 3 , l 4 , l 5 , l 6 , and l 7 , respectively. In the equation  114  for Δp 1 , the coefficients A 1  and B 1  are derived from the binary mask volume  128  by running the trained deep neural network for multiple flow rates. In the equation  114  for Δp 2 , the coefficients A 1  and B 1  on the left side are derived from the binary mask volume  128  and the coefficients A 1  and B 1  on the right side are derived from the binary mask volume  136 . In the equation  114  for Δp 3 , the coefficients A 2  and B 2  on the left side are derived from the binary mask volume  130  and the coefficients A 1  and B 1  on the right side are derived from the binary mask volume  136 . In the equation  114  for Δp 4 , the coefficients A 2  and B 2  on the left side are derived from the binary mask volume  130  and the coefficients A 2  and B 2  on the right side are derived from the binary mask volume  138 . In the equation  114  for Δp 5 , the coefficients A 3  and B 3  on the left side are derived from the binary mask volume  132  and the coefficients A 2  and B 2  on the right side are derived from the binary mask volume  138 . In the equation  114  for Δp 6 , the coefficients A 3  and B 3  on the left side are derived from the binary mask volume  132  and the coefficients A 3  and B 3  on the right side are derived from the binary mask volume  140 . In the equation  114  for Δp 7 , the coefficients A 3  and B 3  are derived from the binary mask volume  140 . 
     Technical effects of the disclosed subject matter include providing systems and methods for predicting coronary artery pressure drop. The disclosed embodiments utilize deep neural networks to learn 3D CFD model predictions. In particular, a deep neural network is trained utilizing image patches (e.g., 3D image patches) extracted from synthetically generated vessels and the pressure drops across these image patches (e.g., obtained from 3D CFD). The trained deep neural network is then used to predict the pressure drops across segmented image patches extracted from vessels in clinical image data (e.g., computed tomography angiography (CTA) data). The disclosed embodiments enable estimation of FFR with comparable accuracy to 3D CFD but with drastically lower computation times. 
     The techniques presented and claimed herein are referenced and applied to material objects and concrete examples of a practical nature that demonstrably improve the present technical field and, as such, are not abstract, intangible or purely theoretical. Further, if any claims appended to the end of this specification contain one or more elements designated as “means for [perform]ing [a function] . . . ” or “step for [perform]ing [a function] . . . ”, it is intended that such elements are to be interpreted under 35 U.S.C. 112(f). However, for any claims containing elements designated in any other manner, it is intended that such elements are not to be interpreted under 35 U.S.C. 112(f). 
     This written description uses examples to disclose the present subject matter, including the best mode, and also to enable any person skilled in the art to practice the subject matter, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the subject matter is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they have structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal languages of the claims.