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.

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.

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.

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.

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.

Cardiac Kinetic Energy and Viscous Dissipation Rate From Radial Flow Data.

Recent studies have correlated kinetic energy (KE) and viscous dissipation rate (VDR) in the left ventricle (LV) with heart health. These studies have relied on 4D-flow imaging or computational fluid dynamics modeling, which are able to measure, or compute, all 3 components (3C) of the blood flow velocity in 3 dimensional (3D) space. This richness of data is difficult to acquire clinically. Alternatively, color Doppler echocardiography (CDE) is more widespread clinically, but only measures a single radial component of velocity and typically only over a planar section. Because of this limitation, prior CDE-based studies have first reconstructed a second component of velocity in the measurement plane prior to evaluating VDR or KE. Herein, we propose 1C-based surrogates of KE and VDR that can be derived directly from the radial component of the flow velocity in the LV. Our results demonstrate that the proposed 1C-based surrogates of KE and VDR are generally as well-correlated with the true KE and VDR values as surrogates that use reconstructed 2C flow data. Moreover, the correlation of these 1C-based surrogates with the true values indicate that CDE (3D in particular) may be useful in evaluating these metrics in practice.

Multi-Centre, Multi-Vendor and Multi-Disease Cardiac Segmentation: The M&Ms Challenge.

The emergence of deep learning has considerably advanced the state-of-the-art in cardiac magnetic resonance (CMR) segmentation. Many techniques have been proposed over the last few years, bringing the accuracy of automated segmentation close to human performance. However, these models have been all too often trained and validated using cardiac imaging samples from single clinical centres or homogeneous imaging protocols. This has prevented the development and validation of models that are generalizable across different clinical centres, imaging conditions or scanner vendors. To promote further research and scientific benchmarking in the field of generalizable deep learning for cardiac segmentation, this paper presents the results of the Multi-Centre, Multi-Vendor and Multi-Disease Cardiac Segmentation (M&Ms) Challenge, which was recently organized as part of the MICCAI 2020 Conference. A total of 14 teams submitted different solutions to the problem, combining various baseline models, data augmentation strategies, and domain adaptation techniques. The obtained results indicate the importance of intensity-driven data augmentation, as well as the need for further research to improve generalizability towards unseen scanner vendors or new imaging protocols. Furthermore, we present a new resource of 375 heterogeneous CMR datasets acquired by using four different scanner vendors in six hospitals and three different countries (Spain, Canada and Germany), which we provide as open-access for the community to enable future research in the field.

A whole lung in silico model to estimate age dependent particle dosimetry.

Anatomical and physiological changes alter airflow characteristics and aerosol distribution in the developing lung. Correlation between age and aerosol dosimetry is needed, specifically because youth are more susceptible to medication side effects. In this study, we estimate aerosol dosages (particle diameters of 1, 3, and 5 [Formula: see text]m) in a 3 month-old infant, a 6 year-old child, and a 36 year-old adult by performing whole lung subject-specific particle simulations throughout respiration. For 3 [Formula: see text]m diameter particles we estimate total deposition as 88, 73, and [Formula: see text] and the conducting versus respiratory deposition ratios as 4.0, 0.5, and 0.4 for the infant, child, and adult, respectively. Due to their lower tidal volumes and functional residual capacities the deposited mass is smaller while the tissue concentrations are larger in the infant and child subjects, compared to the adult. Furthermore, we find that dose cannot be predicted by simply scaling by tidal volumes. These results highlight the need for additional clinical and computational studies that investigate the efficiency of treatment, while optimizing dosage levels in order to alleviate side effects, in youth.

Impact of BASILICA on the thrombogenicity potential of valve-in-valve implantations.

Subclinical leaflet thrombosis is becoming a major concern in valve-in-valve procedures, whereby a transcatheter aortic valve device is deployed inside a failed bioprosthetic surgical valve. Blood flow stagnation and prolonged residence times in the neo-sinuses have been suggested as possible explanations for leaflet thrombosis. The BASILICA technique, which was originally developed to treat coronary flow obstruction, has also been proposed as an alternative to reduce the risk of thrombus formation. The aim of this study is to understand the impact of BASILICA on the valve-in-valve thrombogenicity using computational fluid dynamics simulations. To this end, two Eulerian and two Lagrangian approaches were employed to estimate near-wall stagnation measures in eight valve-in-valve models. The models included an intact or lacerated Sorin Mitroflow surgical valve, and either a SAPIEN or Evolut transcatheter aortic valve device. The Lagrangian approaches predicted a high number of particles and vortices concentration in the proximal areas of the neo-sinuses, while the Eulerian approaches did so in the distal areas. As a consequence, this study demonstrated that Lagrangian approaches are better predictors of subclinical leaflet thrombosis, since they match experimental and clinical findings. Additionally, the SAPIEN valve possess a higher risk for developing leaflet thrombosis, and two lacerations are shown to provide the best results in terms of development of vortices and accumulation of particles within the neo-sinuses. This study highlights the potential of computational modeling in aiding clinicians in their decision-making in valve-in-valve and BASILICA procedures.

Computational investigation of blood flow and flow-mediated transport in arterial thrombus neighborhood.

A pathologically formed blood clot or thrombus is central to major cardiovascular diseases like heart attack and stroke. Detailed quantitative evaluation of flow and flow-mediated transport processes in the thrombus neighborhood within large artery hemodynamics is crucial for understanding disease progression and assessing treatment efficacy. This, however, remains a challenging task owing to the complexity of pulsatile viscous flow interactions with arbitrary shape and heterogeneous microstructure of realistic thrombi. Here, we address this challenge by conducting a systematic parametric simulation-based study on characterizing unsteady hemodynamics and flow-mediated transport in the neighborhood of an arterial thrombus. We use a hybrid particle-continuum-based finite element approach to handle arbitrary thrombus shape and microstructural variations. Results from a cohort of 50 different unsteady flow scenarios are presented, including unsteady vortical structures, pressure gradient across the thrombus boundary, finite time Lyapunov exponents, and dynamic coherent structures that organize advective transport. We clearly illustrate the combined influence of three key parameters-thrombus shape, microstructure, and extent of wall disease-in terms of: (a) determining hemodynamic features in the thrombus neighborhood and (b) governing the balance between advection, permeation, and diffusion to regulate transport processes in the thrombus neighborhood.

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.

Novel measurement tool and model for aberrant urinary stream in 3D printed urethras derived from human tissue.

BACKGROUND: An estimated 10% of male adults have split or dribbled stream leading to poor hygiene, embarrassment, and inconvenience. There is no current metric that measures male stream deviation. OBJECTIVE: To develop a novel method to measure spray in normal and abnormal anatomical conformations. DESIGN, SETTING, AND PARTICIPANTS: We developed a novel platform to reliably describe spray. We used cadaveric tissues and 3D Printed models to study the impact of meatal shape on the urinary stream. Cadaveric penile tissue and 3D printed models were affixed to a fluid pump and used to simulate micturition. Dye captured on fabric allowed for spray detection. OUTCOME MEASUREMENTS AND STATISTICAL ANALYSIS: Spray pattern area, deviation from normal location, and flowrates were recorded. Computational fluid dynamic models were created to study fluid vorticity. RESULTS AND LIMITATIONS: Obstructions at the penile tip worsened spray dynamics and reduced flow. Ventral meatotomy improved flowrate (p<0.05) and reduced spray (p<0.05) compared to tips obstructed ventrally, dorsally or in the fossa navicularis. 3D models do not fully reproduce parameters of their parent cadaver material. The average flowrate from 3D model was 10ml/sec less than that of the penis from which it was derived (p = 0.03). Nonetheless, as in cadavers, increasing obstruction in 3D models leads to the same pattern of reduced flowrate and worse spray. Dynamic modeling revealed increasing distal obstruction was correlated to higher relative vorticity observed at the urethral tip. CONCLUSIONS: We developed a robust method to measure urine spray in a research setting. Dynamic 3D printed models hold promise as a methodology to study common pathologies in the urethra and corrective surgeries on the urine stream that would not be feasible in patients. These novel methods require further validation, but offer promise as a research and clinical tool.

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.

A Distributed Lumped Parameter Model of Blood Flow.

We propose a distributed lumped parameter (DLP) modeling framework to efficiently compute blood flow and pressure in vascular domains. This is achieved by developing analytical expressions describing expected energy losses along vascular segments, including from viscous dissipation, unsteadiness, flow separation, vessel curvature and vessel bifurcations. We apply this methodology to solve for unsteady blood flow and pressure in a variety of complex 3D image-based vascular geometries, which are typically approached using computational fluid dynamics (CFD) simulations. The proposed DLP framework demonstrated consistent agreement with CFD simulations in terms of flow rate and pressure distribution, with mean errors less than 7% over a broad range of hemodynamic conditions and vascular geometries. The computational cost of the DLP framework is orders of magnitude lower than the computational cost of CFD, which opens new possibilities for hemodynamics modeling in timely decision support scenarios, and a multitude of applications of imaged-based modeling that require ensembles of numerical simulations.

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.

Numerical models for assessing the risk of leaflet thrombosis post-transcatheter aortic valve-in-valve implantation.

Leaflet thrombosis has been suggested as the reason for the reduced leaflet motion in cases of hypoattenuated leaflet thickening of bioprosthetic aortic valves. This work aimed to estimate the risk of leaflet thrombosis in two post-valve-in-valve (ViV) configurations, using five different numerical approaches. Realistic ViV configurations were calculated by modelling the deployments of the latest version of transcatheter aortic valve devices (Medtronic Evolut PRO, Edwards SAPIEN 3) in the surgical Sorin Mitroflow. Computational fluid dynamics simulations of blood flow followed the dry models. Lagrangian and Eulerian measures of near-wall stagnation were implemented by particle and concentration tracking, respectively, to estimate the thrombogenicity and to predict the risk locations. Most of the numerical approaches indicate a higher leaflet thrombosis risk in the Edwards SAPIEN 3 device because of its intra-annular implantation. The Eulerian approaches estimated high-risk locations in agreement with the wall sheer stress (WSS) separation points. On the other hand, the Lagrangian approaches predicted high-risk locations at the proximal regions of the leaflets matching the low WSS magnitude regions of both transcatheter aortic valve implantation models and reported clinical and experimental data. The proposed methods can help optimizing future designs of transcatheter aortic valves with minimal thrombotic risks.

Automated reduction of blood coagulation models.

Mathematical modeling of thrombosis typically involves modeling the coagulation cascade. Models of coagulation generally involve the reaction kinetics for dozens of proteins. The resulting system of equations is difficult to parameterize, and its numerical solution is challenging when coupled to blood flow or other physics important to clotting. Prior research suggests that essential aspects of coagulation may be reproduced by simpler models. This evidence motivates a systematic approach to model reduction. We herein introduce an automated framework to generate reduced-order models of blood coagulation. The framework consists of nested optimizations, where an outer optimization selects the optimal species for the reduced-order model and an inner optimization selects the optimal reaction rates for the new coagulation network. The framework was tested on an established 34-species coagulation model to rigorously consider what level of model fidelity is necessary to capture essential coagulation dynamics. The results indicate that a nine-species reduced-order model is sufficient to reproduce the thrombin dynamics of the benchmark 34-species model for a range of tissue factor concentrations, including those not included in the optimization process. Further model reduction begins to compromise the ability to capture the thrombin generation process. The framework proposed herein enables automated development of reduced-order models of coagulation that maintain essential dynamics used to model thrombosis.

Data-Augmented Modeling of Intracranial Pressure.

Precise management of patients with cerebral diseases often requires intracranial pressure (ICP) monitoring, which is highly invasive and requires a specialized ICU setting. The ability to noninvasively estimate ICP is highly compelling as an alternative to, or screening for, invasive ICP measurement. Most existing approaches for noninvasive ICP estimation aim to build a regression function that maps noninvasive measurements to an ICP estimate using statistical learning techniques. These data-based approaches have met limited success, likely because the amount of training data needed is onerous for this complex applications. In this work, we discuss an alternative strategy that aims to better utilize noninvasive measurement data by leveraging mechanistic understanding of physiology. Specifically, we developed a Bayesian framework that combines a multiscale model of intracranial physiology with noninvasive measurements of cerebral blood flow using transcranial Doppler. Virtual experiments with synthetic data are conducted to verify and analyze the proposed framework. A preliminary clinical application study on two patients is also performed in which we demonstrate the ability of this method to improve ICP prediction.

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.