Unsupervised Denoising and Super-Resolution of Vascular Flow Data by Physics-Informed Machine Learning.

We present an unsupervised deep learning method to perform flow denoising and super-resolution without high-resolution labels. We demonstrate the ability of a single model to reconstruct three-dimensional stenosis and aneurysm flows, with varying geometries, orientations, and boundary conditions. Ground truth data was generated using computational fluid dynamics, and then corrupted with multiplicative Gaussian noise. Auto-encoders were used to compress the representations of the flow domain geometry and the (possibly noisy and low-resolution) flow field. These representations were used to condition a physics-informed neural network. A physics-based loss was implemented to train the model to recover lost information from the noisy input by transforming the flow to a solution of the Navier-Stokes equations. Our experiments achieved mean squared errors in the true flow reconstruction of O(1.0 × 10-4), and root mean squared residuals of O(1.0 × 10-2) for the momentum and continuity equations. Our method yielded correlation coefficients of 0.971 for the hidden pressure field and 0.82 for the derived wall shear stress field. By performing point-wise predictions of the flow, the model was able to robustly denoise and super-resolve the field to 20× the input resolution.

Automating Model Generation for Image-Based Cardiac Flow Simulation.

Computational fluid dynamics (CFD) modeling of left ventricle (LV) flow combined with patient medical imaging data has shown great potential in obtaining patient-specific hemodynamics information for functional assessment of the heart. A typical model construction pipeline usually starts with segmentation of the LV by manual delineation followed by mesh generation and registration techniques using separate software tools. However, such approaches usually require significant time and human efforts in the model generation process, limiting large-scale analysis. In this study, we propose an approach toward fully automating the model generation process for CFD simulation of LV flow to significantly reduce LV CFD model generation time. Our modeling framework leverages a novel combination of techniques including deep-learning based segmentation, geometry processing, and image registration to reliably reconstruct CFD-suitable LV models with little-to-no user intervention.1 We utilized an ensemble of two-dimensional (2D) convolutional neural networks (CNNs) for automatic segmentation of cardiac structures from three-dimensional (3D) patient images and our segmentation approach outperformed recent state-of-the-art segmentation techniques when evaluated on benchmark data containing both magnetic resonance (MR) and computed tomography(CT) cardiac scans. We demonstrate that through a combination of segmentation and geometry processing, we were able to robustly create CFD-suitable LV meshes from segmentations for 78 out of 80 test cases. Although the focus on this study is on image-to-mesh generation, we demonstrate the feasibility of this framework in supporting LV hemodynamics modeling by performing CFD simulations from two representative time-resolved patient-specific image datasets.

Integrated Image-Based Computational Fluid Dynamics Modeling Software as an Instructional Tool.

Computational modeling of cardiovascular flows is becoming increasingly important in a range of biomedical applications, and understanding the fundamentals of computational modeling is important for engineering students. In addition to their purpose as research tools, integrated image-based computational fluid dynamics (CFD) platforms can be used to teach the fundamental principles involved in computational modeling and generate interest in studying cardiovascular disease. We report the results of a study performed at five institutions designed to investigate the effectiveness of an integrated modeling platform as an instructional tool and describe "best practices" for using an integrated modeling platform in the classroom. Use of an integrated modeling platform as an instructional tool in nontraditional educational settings (workshops, study abroad programs, in outreach) is also discussed. Results of the study show statistically significant improvements in understanding after using the integrated modeling platform, suggesting such platforms can be effective tools for teaching fundamental cardiovascular computational modeling principles.

Construction of Analysis-Suitable Vascular Models Using Axis-Aligned Polycubes.

Image-based modeling is an active and growing area of biomedical research that utilizes medical imaging to create patient-specific simulations of physiological function. Under this paradigm, anatomical structures are segmented from a volumetric image, creating a geometric model that serves as a computational domain for physics-based modeling. A common application is the segmentation of cardiovascular structures to numerically model blood flow or tissue mechanics. The segmentation of medical image data typically results in a discrete boundary representation (surface mesh) of the segmented structure. However, it is often desirable to have an analytic representation of the model, which facilitates systematic manipulation. For example, the model then becomes easier to union with a medical device, or the geometry can be virtually altered to test or optimize a surgery. Furthermore, to employ increasingly popular isogeometric analysis (IGA) methods, the parameterization must be analysis suitable. Converting a discrete surface model to an analysis-suitable model remains a challenge, especially for complex branched structures commonly encountered in cardiovascular modeling. To address this challenge, we present a framework to convert discrete surface models of vascular geometries derived from medical image data into analysis-suitable nonuniform rational B-splines (NURBS) representation. This is achieved by decomposing the vascular geometry into a polycube structure that can be used to form a globally valid parameterization. We provide several practical examples and demonstrate the accuracy of the methods by quantifying the fidelity of the parameterization with respect to the input geometry.

Reduced Order Models for Transstenotic Pressure Drop in the Coronary Arteries.

The efficacy of reduced order modeling for transstenotic pressure drop in the coronary arteries is presented. Coronary artery disease is a leading cause of death worldwide and the computation of pressure drop in the coronary arteries has become a standard for evaluating the functional significance of a coronary stenosis. Comprehensive models typically employ three-dimensional (3D) computational fluid dynamics (CFD) to simulate coronary blood flow in order to compute transstenotic pressure drop at the arterial stenosis. In this study, we evaluate the capability of different hydrodynamic models to compute transstenotic pressure drop. Models range from algebraic formulae to one-dimensional (1D), two-dimensional (2D), and 3D time-dependent CFD simulations. Although several algebraic pressure-drop formulae have been proposed in the literature, these models were found to exhibit wide variation in predictions. Nonetheless, we demonstrate an algebraic formula that provides consistent predictions with 3D CFD results for various changes in stenosis severity, morphology, location, and flow rate. The accounting of viscous dissipation and flow separation were found to be significant contributions to accurate reduce order modeling of transstenotic coronary hemodynamics.

A Re-Engineered Software Interface and Workflow for the Open-Source SimVascular Cardiovascular Modeling Package.

Patient-specific simulation plays an important role in cardiovascular disease research, diagnosis, surgical planning and medical device design, as well as education in cardiovascular biomechanics. simvascular is an open-source software package encompassing an entire cardiovascular modeling and simulation pipeline from image segmentation, three-dimensional (3D) solid modeling, and mesh generation, to patient-specific simulation and analysis. SimVascular is widely used for cardiovascular basic science and clinical research as well as education, following increased adoption by users and development of a GATEWAY web portal to facilitate educational access. Initial efforts of the project focused on replacing commercial packages with open-source alternatives and adding increased functionality for multiscale modeling, fluid-structure interaction (FSI), and solid modeling operations. In this paper, we introduce a major SimVascular (SV) release that includes a new graphical user interface (GUI) designed to improve user experience. Additional improvements include enhanced data/project management, interactive tools to facilitate user interaction, new boundary condition (BC) functionality, plug-in mechanism to increase modularity, a new 3D segmentation tool, and new computer-aided design (CAD)-based solid modeling capabilities. Here, we focus on major changes to the software platform and outline features added in this new release. We also briefly describe our recent experiences using SimVascular in the classroom for bioengineering education.

Numerical Investigation of Vasospasm Detection by Extracranial Blood Velocity Ratios.

BACKGROUND: Early diagnosis of vasospasm following subarachnoid hemorrhage can prevent cerebral ischemia and improve neurological outcomes. This study numerically evaluates the relevance of extracranial blood velocity indices to detect vasospasm. METHODS: A numerical model of cerebral blood flow was used to evaluate the hemodynamics associated with anterior and posterior vasospasm under normal and impaired cerebral autoregulation conditions. Extracranial blood velocities at the carotid and vertebral arteries and their ratios between ipsilateral and contralateral, anterior and posterior, and downstream and upstream arteries were monitored during vasospasm progression. RESULTS: For current clinical indices that track blood velocities at vasospastic arterial segments using transcranial Doppler (TCD), we observed that velocities increased initially and then decreased with vasospasm progression. This nonmonotonic behavior can lead to false-negative decisions in moderate to severe vasospasm. Alternatively, volumetric flow decreased monotonically at the affected arteries, leading to blood velocities upstream of the vasospastic artery also decreasing monotonically. Based on this principle, we demonstrate that velocity ratios between the carotid and vertebral arteries may better identify moderate to severe vasospasm and improve sensitivity and specificity of vasospasm detection. CONCLUSION: The velocity indices proposed in this study may enable new or improved noninvasive diagnosis of vasospasm using extracranial Doppler ultrasound. Compared to current clinical indices, the new indices may improve the handling of (1) scenarios of severe vasospasm or impaired cerebral autoregulation, (2) systemic changes in blood pressure and cardiac output, (3) vasospasm occurring in arteries distal to the cerebral circle region, and (4) cases with insufficient acoustic bone window for TCD. The results provide a concrete basis for future clinical evaluation of extracranial indices for vasospasm detection.

Characterizations and Correlations of Wall Shear Stress in Aneurysmal Flow.

Wall shear stress (WSS) is one of the most studied hemodynamic parameters, used in correlating blood flow to various diseases. The pulsatile nature of blood flow, along with the complex geometries of diseased arteries, produces complicated temporal and spatial WSS patterns. Moreover, WSS is a vector, which further complicates its quantification and interpretation. The goal of this study is to investigate WSS magnitude, angle, and vector changes in space and time in complex blood flow. Abdominal aortic aneurysm (AAA) was chosen as a setting to explore WSS quantification. Patient-specific computational fluid dynamics (CFD) simulations were performed in six AAAs. New WSS parameters are introduced, and the pointwise correlation among these, and more traditional WSS parameters, was explored. WSS magnitude had positive correlation with spatial/temporal gradients of WSS magnitude. This motivated the definition of relative WSS gradients. WSS vectorial gradients were highly correlated with magnitude gradients. A mix WSS spatial gradient and a mix WSS temporal gradient are proposed to equally account for variations in the WSS angle and magnitude in single measures. The important role that WSS plays in regulating near wall transport, and the high correlation among some of the WSS parameters motivates further attention in revisiting the traditional approaches used in WSS characterizations.

Computational Assessment of the Relation Between Embolism Source and Embolus Distribution to the Circle of Willis for Improved Understanding of Stroke Etiology.

Stroke caused by an embolism accounts for about a third of all stroke cases. Understanding the source and cause of the embolism is critical for diagnosis and long-term treatment of such stroke cases. The complex nature of the transport of an embolus within large arteries is a primary hindrance to a clear understanding of embolic stroke etiology. Recent advances in medical image-based computational hemodynamics modeling have rendered increasing utility to such techniques as a probe into the complex flow and transport phenomena in large arteries. In this work, we present a novel, patient-specific, computational framework for understanding embolic stroke etiology, by combining image-based hemodynamics with discrete particle dynamics and a sampling-based analysis. The framework allows us to explore the important question of how embolism source manifests itself in embolus distribution across the various major cerebral arteries. Our investigations illustrate prominent numerical evidence regarding (i) the size/inertia-dependent trends in embolus distribution to the brain; (ii) the relative distribution of cardiogenic versus aortogenic emboli among the anterior, middle, and posterior cerebral arteries; (iii) the left versus right brain preference in cardio-emboli and aortic-emboli transport; and (iv) the source-destination relationship for embolisms affecting the brain.

A Coupled Lumped-Parameter and Distributed Network Model for Cerebral Pulse-Wave Hemodynamics.

The cerebral circulation is unique in its ability to maintain blood flow to the brain under widely varying physiologic conditions. Incorporating this autoregulatory response is necessary for cerebral blood flow (CBF) modeling, as well as investigations into pathological conditions. We discuss a one-dimensional (1D) nonlinear model of blood flow in the cerebral arteries coupled to autoregulatory lumped-parameter (LP) networks. The LP networks incorporate intracranial pressure (ICP), cerebrospinal fluid (CSF), and cortical collateral blood flow models. The overall model is used to evaluate changes in CBF due to occlusions in the middle cerebral artery (MCA) and common carotid artery (CCA). Velocity waveforms at the CCA and internal carotid artery (ICA) were examined prior and post MCA occlusion. Evident waveform changes due to the occlusion were observed, providing insight into cerebral vasospasm monitoring by morphological changes of the velocity or pressure waveforms. The role of modeling of collateral blood flows through cortical pathways and communicating arteries was also studied. When the MCA was occluded, the cortical collateral flow had an important compensatory role, whereas the communicating arteries in the circle of Willis (CoW) became more important when the CCA was occluded. To validate the model, simulations were conducted to reproduce a clinical test to assess dynamic autoregulatory function, and results demonstrated agreement with published measurements.

Mechanical platelet activation potential in abdominal aortic aneurysms.

Intraluminal thrombus (ILT) in abdominal aortic aneurysms (AAA) has potential implications to aneurysm growth and rupture risk; yet, the mechanisms underlying its development remain poorly understood. Some researchers have proposed that ILT development may be driven by biomechanical platelet activation within the AAA, followed by adhesion in regions of low wall shear stress. Studies have investigated wall shear stress levels within AAA, but platelet activation potential (AP) has not been quantified. In this study, patient-specific computational fluid dynamic (CFD) models were used to analyze stress-induced AP within AAA under rest and exercise flow conditions. The analysis was conducted using Lagrangian particle-based and Eulerian continuum-based approaches, and the results were compared. Results indicated that biomechanical platelet activation is unlikely to play a significant role for the conditions considered. No consistent trend was observed in comparing rest and exercise conditions, but the functional dependence of AP on stress magnitude and exposure time can have a large impact on absolute levels of anticipated platelet AP. The Lagrangian method obtained higher peak AP values, although this difference was limited to a small percentage of particles that falls below reported levels of physiologic background platelet activation.

A longitudinal comparison of hemodynamics and intraluminal thrombus deposition in abdominal aortic aneurysms.

Abdominal aortic aneurysm (AAA) is often accompanied by in traluminal thrombus (ILT), which complicates AAA progression and risk of rupture. Patient-specific computational fluid dynamics modeling of 10 small human AAA was performed to investigate relations between hemodynamics and ILT progression. The patients were imaged using magnetic resonance twice in a 2- to 3-yr interval. Wall content data were obtained by a planar T1-weighted fast spin echo black-blood scan, which enabled quantification of thrombus thickness at midaneurysm location during baseline and followup. Computational simulations with patient-specific geometry and boundary conditions were performed to quantify the hemodynamic parameters of time-averaged wall shear stress (TAWSS), oscillatory shear index (OSI), and mean exposure time at baseline. Spatially resolved quantifications of the change in ILT thickness were compared with the different hemodynamic parameters. Regions of low OSI had the strongest correlation with ILT growth and demonstrated a statistically significant correlation coefficient. Prominent regions of high OSI (>0.4) and low TAWSS (<1 dyn/cm(2)) did not appear to coincide with locations of thrombus deposition.

Size-dependent predilections of cardiogenic embolic transport.

While it is intuitively clear that aortic anatomy and embolus size could be important determinants for cardiogenic embolic stroke risk and stroke location, few data exist confirming or characterizing this hypothesis. The objective of this study is to use medical imaging and computational modeling to better understand if aortic anatomy and embolus size influence predilections for cardiogenic embolic transport and right vs. left hemisphere propensity. Anatomically accurate models of the human aorta and branch arteries to the head were reconstructed from computed tomography (CT) angiography of 10 patients. Blood flow was modeled by the Navier-Stokes equations using a well-validated flow solver with physiologic inflow and boundary conditions. Embolic particulate was released from the aortic root and tracked through the common carotid and vertebral arteries for a range of particle sizes. Cardiogenic emboli reaching the carotid and vertebral arteries appeared to have a strong size-destination relationship that varied markedly from expectations based on blood distribution. Observed trends were robust to modeling parameters. A patient's aortic anatomy appeared to significantly influence the probability a cardiogenic particle becomes embolic to the head. Right hemisphere propensity appeared dominant for cardiogenic emboli, which has been confirmed clinically. The predilections discovered through this modeling could represent an important mechanism underlying cardiogenic embolic stroke etiology.

Optimization of a Y-graft design for improved hepatic flow distribution in the fontan circulation.

Single ventricle heart defects are among the most serious congenital heart diseases, and are uniformly fatal if left untreated. Typically, a three-staged surgical course, consisting of the Norwood, Glenn, and Fontan surgeries is performed, after which the superior vena cava (SVC) and inferior vena cava (IVC) are directly connected to the pulmonary arteries (PA). In an attempt to improve hemodynamic performance and hepatic flow distribution (HFD) of Fontan patients, a novel Y-shaped graft has recently been proposed to replace the traditional tube-shaped extracardiac grafts. Previous studies have demonstrated that the Y-graft is a promising design with the potential to reduce energy loss and improve HFD. However these studies also found suboptimal Y-graft performance in some patient models. The goal of this work is to determine whether performance can be improved in these models through further design optimization. Geometric and hemodynamic factors that influence the HFD have not been sufficiently investigated in previous work, particularly for the Y-graft. In this work, we couple Lagrangian particle tracking to an optimal design framework to study the effects of boundary conditions and geometry on HFD. Specifically, we investigate the potential of using a Y-graft design with unequal branch diameters to improve hepatic distribution under a highly uneven RPA/LPA flow split. As expected, the resulting optimal Y-graft geometry largely depends on the pulmonary flow split for a particular patient. The unequal branch design is demonstrated to be unnecessary under most conditions, as it is possible to achieve the same or better performance with equal-sized branches. Two patient-specific examples show that optimization-derived Y-grafts effectively improve the HFD, compared to initial nonoptimized designs using equal branch diameters. An instance of constrained optimization shows that energy efficiency slightly increases with increasing branch size for the Y-graft, but that a smaller branch size is preferred when a proximal anastomosis is needed to achieve optimal HFD.

Variability of computational fluid dynamics solutions for pressure and flow in a giant aneurysm: the ASME 2012 Summer Bioengineering Conference CFD Challenge.

Stimulated by a recent controversy regarding pressure drops predicted in a giant aneurysm with a proximal stenosis, the present study sought to assess variability in the prediction of pressures and flow by a wide variety of research groups. In phase I, lumen geometry, flow rates, and fluid properties were specified, leaving each research group to choose their solver, discretization, and solution strategies. Variability was assessed by having each group interpolate their results onto a standardized mesh and centerline. For phase II, a physical model of the geometry was constructed, from which pressure and flow rates were measured. Groups repeated their simulations using a geometry reconstructed from a micro-computed tomography (CT) scan of the physical model with the measured flow rates and fluid properties. Phase I results from 25 groups demonstrated remarkable consistency in the pressure patterns, with the majority predicting peak systolic pressure drops within 8% of each other. Aneurysm sac flow patterns were more variable with only a few groups reporting peak systolic flow instabilities owing to their use of high temporal resolutions. Variability for phase II was comparable, and the median predicted pressure drops were within a few millimeters of mercury of the measured values but only after accounting for submillimeter errors in the reconstruction of the life-sized flow model from micro-CT. In summary, pressure can be predicted with consistency by CFD across a wide range of solvers and solution strategies, but this may not hold true for specific flow patterns or derived quantities. Future challenges are needed and should focus on hemodynamic quantities thought to be of clinical interest.

Learning Whole Heart Mesh Generation From Patient Images for Computational Simulations.

Patient-specific cardiac modeling combines geometries of the heart derived from medical images and biophysical simulations to predict various aspects of cardiac function. However, generating simulation-suitable models of the heart from patient image data often requires complicated procedures and significant human effort. We present a fast and automated deep-learning method to construct simulation-suitable models of the heart from medical images. The approach constructs meshes from 3D patient images by learning to deform a small set of deformation handles on a whole heart template. For both 3D CT and MR data, this method achieves promising accuracy for whole heart reconstruction, consistently outperforming prior methods in constructing simulation-suitable meshes of the heart. When evaluated on time-series CT data, this method produced more anatomically and temporally consistent geometries than prior methods, and was able to produce geometries that better satisfy modeling requirements for cardiac flow simulations. Our source code and pretrained networks are available at https://github.com/fkong7/HeartDeformNets.

Distributed lumped parameter modeling of blood flow in compliant vessels.

We extend our previous distributed lumped parameter (DLP) modeling approach to take into account blood vessel wall deformability. This is achieved by adding a compliance term for each vascular segment based on 1D NS equations. The results of the proposed method are compared against 1D Navier-Stokes and 3D fluid-structure interaction (FSI) modeling in idealized and patient-specific models. We show that 1D Navier-Stokes blood flow modeling can be highly inaccurate in predicting flow and pressure dynamics in diseased cases, while in comparison the DLP approach produces consistently accurate flow and pressure waveforms as compared to 3D FSI modeling. The relative accuracy and computational efficiency of the proposed DLP approach offer the possibility to replace or augment 1D or 3D modeling to study hemodynamics in a variety of applications.

Interpolating log-determinant and trace of the powers of matrix A + t B.

We develop heuristic interpolation methods for the functions t ↦ log det A + t B and t ↦ trace ( A + t B ) p where the matrices A and B are Hermitian and positive (semi) definite and p and t are real variables. These functions are featured in many applications in statistics, machine learning, and computational physics. The presented interpolation functions are based on the modification of sharp bounds for these functions. We demonstrate the accuracy and performance of the proposed method with numerical examples, namely, the marginal maximum likelihood estimation for Gaussian process regression and the estimation of the regularization parameter of ridge regression with the generalized cross-validation method.

Machine Learning for Cardiovascular Biomechanics Modeling: Challenges and Beyond.

Recent progress in machine learning (ML), together with advanced computational power, have provided new research opportunities in cardiovascular modeling. While classifying patient outcomes and medical image segmentation with ML have already shown significant promising results, ML for the prediction of biomechanics such as blood flow or tissue dynamics is in its infancy. This perspective article discusses some of the challenges in using ML for replacing well-established physics-based models in cardiovascular biomechanics. Specifically, we discuss the large landscape of input features in 3D patient-specific modeling as well as the high-dimensional output space of field variables that vary in space and time. We argue that the end purpose of such ML models needs to be clearly defined and the tradeoff between the loss in accuracy and the gained speedup carefully interpreted in the context of translational modeling. We also discuss several exciting venues where ML could be strategically used to augment traditional physics-based modeling in cardiovascular biomechanics. In these applications, ML is not replacing physics-based modeling, but providing opportunities to solve ill-defined problems, improve measurement data quality, enable a solution to computationally expensive problems, and interpret complex spatiotemporal data by extracting hidden patterns. In summary, we suggest a strategic integration of ML in cardiovascular biomechanics modeling where the ML model is not the end goal but rather a tool to facilitate enhanced modeling.

Reconstructing vascular homeostasis by growth-based prestretch and optimal fiber deposition.

Computational modeling of cardiovascular biomechanics should generally start from a homeostatic state. This is particularly relevant for image-based modeling, where the reference configuration is the loaded in vivo state obtained from imaging. This state includes residual stress of the vascular constituents, as well as anisotropy from the spatially varying orientation of collagen and smooth muscle fibers. Estimation of the residual stress and fiber orientation fields is a formidable challenge in realistic applications. To help address this challenge, we herein develop a growth based Algorithm to recover a residual stress distribution in vascular domains such that the stress state in the loaded configuration is equal to a prescribed homeostatic stress distribution at physiologic pressure. A stress-driven fiber deposition process is included in the framework, which defines the distribution of the fiber alignments in the vascular homeostatic state based on a minimization procedure. Numerical simulations are conducted to test this two-stage homeostasis generation algorithm in both idealized and non-idealized geometries, yielding results that agree favorably with prior numerical and experimental data.