AngioNet: a convolutional neural network for vessel segmentation in X-ray angiography.

Coronary Artery Disease (CAD) is commonly diagnosed using X-ray angiography, in which images are taken as radio-opaque dye is flushed through the coronary vessels to visualize the severity of vessel narrowing, or stenosis. Cardiologists typically use visual estimation to approximate the percent diameter reduction of the stenosis, and this directs therapies like stent placement. A fully automatic method to segment the vessels would eliminate potential subjectivity and provide a quantitative and systematic measurement of diameter reduction. Here, we have designed a convolutional neural network, AngioNet, for vessel segmentation in X-ray angiography images. The main innovation in this network is the introduction of an Angiographic Processing Network (APN) which significantly improves segmentation performance on multiple network backbones, with the best performance using Deeplabv3+ (Dice score 0.864, pixel accuracy 0.983, sensitivity 0.918, specificity 0.987). The purpose of the APN is to create an end-to-end pipeline for image pre-processing and segmentation, learning the best possible pre-processing filters to improve segmentation. We have also demonstrated the interchangeability of our network in measuring vessel diameter with Quantitative Coronary Angiography. Our results indicate that AngioNet is a powerful tool for automatic angiographic vessel segmentation that could facilitate systematic anatomical assessment of coronary stenosis in the clinical workflow.

Active training of physics-informed neural networks to aggregate and interpolate parametric solutions to the Navier-Stokes equations.

The goal of this work is to train a neural network which approximates solutions to the Navier-Stokes equations across a region of parameter space, in which the parameters define physical properties such as domain shape and boundary conditions. The contributions of this work are threefold:1.To demonstrate that neural networks can be efficient aggregators of whole families of parametric solutions to physical problems, trained using data created with traditional, trusted numerical methods such as finite elements. Advantages include extremely fast evaluation of pressure and velocity at any point in physical and parameter space (asymptotically, ∼3 µs/query), and data compression (the network requires 99% less storage space compared to its own training data).2.To demonstrate that the neural networks can accurately interpolate between finite element solutions in parameter space, allowing them to be instantly queried for pressure and velocity field solutions to problems for which traditional simulations have never been performed.3.To introduce an active learning algorithm, so that during training, a finite element solver can automatically be queried to obtain additional training data in locations where the neural network's predictions are in most need of improvement, thus autonomously acquiring and efficiently distributing training data throughout parameter space. In addition to the obvious utility of Item 2, above, we demonstrate an application of the network in rapid parameter sweeping, very precisely predicting the degree of narrowing in a tube which would result in a 50% increase in end-to-end pressure difference at a given flow rate. This capability could have applications in both medical diagnosis of arterial disease, and in computer-aided design.

CRIMSON: An open-source software framework for cardiovascular integrated modelling and simulation.

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.

A flexible framework for sequential estimation of model parameters in computational hemodynamics.

A major challenge in constructing three dimensional patient specific hemodynamic models is the calibration of model parameters to match patient data on flow, pressure, wall motion, etc. acquired in the clinic. Current workflows are manual and time-consuming. This work presents a flexible computational framework for model parameter estimation in cardiovascular flows that relies on the following fundamental contributions. (i) A Reduced-Order Unscented Kalman Filter (ROUKF) model for data assimilation for wall material and simple lumped parameter network (LPN) boundary condition model parameters. (ii) A constrained least squares augmentation (ROUKF-CLS) for more complex LPNs. (iii) A "Netlist" implementation, supporting easy filtering of parameters in such complex LPNs. The ROUKF algorithm is demonstrated using non-invasive patient-specific data on anatomy, flow and pressure from a healthy volunteer. The ROUKF-CLS algorithm is demonstrated using synthetic data on a coronary LPN. The methods described in this paper have been implemented as part of the CRIMSON hemodynamics software package.

Numerical considerations for advection-diffusion problems in cardiovascular hemodynamics.

Numerical simulations of cardiovascular mass transport pose significant challenges due to the wide range of Péclet numbers and backflow at Neumann boundaries. In this paper we present and discuss several numerical tools to address these challenges in the context of a stabilized finite element computational framework. To overcome numerical instabilities when backflow occurs at Neumann boundaries, we propose an approach based on the prescription of the total flux. In addition, we introduce a "consistent flux" outflow boundary condition and demonstrate its superior performance over the traditional zero diffusive flux boundary condition. Lastly, we discuss discontinuity capturing (DC) stabilization techniques to address the well-known oscillatory behavior of the solution near the concentration front in advection-dominated flows. We present numerical examples in both idealized and patient-specific geometries to demonstrate the efficacy of the proposed procedures. The three contributions discussed in this paper successfully address commonly found challenges when simulating mass transport processes in cardiovascular flows.

Computational analysis of renal artery flow characteristics by modeling aortoplasty and aortic bypass interventions for abdominal aortic coarctation.

OBJECTIVE: Suprarenal abdominal aortic coarctation (SAAC) alters flow and pressure patterns to the kidneys and is often associated with severe angiotensin-mediated hypertension refractory to drug therapy. SAAC is most often treated by a thoracoabdominal bypass (TAB) or patch aortoplasty (PA). It is currently unclear what effect these interventions have on renal flow and pressure waveforms. This study, using retrospective data from a patient with SAAC subjected to a TAB, undertook computational modeling to analyze aortorenal blood flow preoperatively as well as postoperatively after a variety of TAB and PA interventions. METHODS: Patient-specific anatomic models were constructed from preoperative computed tomography angiograms of a 9-year-old child with an isolated SAAC. Fluid-structure interaction (FSI) simulations of hemodynamics were performed to analyze preoperative renal flow and pressure waveforms. A parametric study was then performed to examine the hemodynamic impact of different bypass diameters and patch oversizing. RESULTS: Preoperative FSI results documented diastole-dominated renal perfusion with considerable high-frequency disturbances in blood flow and pressure. The postoperative TAB right and left kidney volumes increased by 58% and 79%, respectively, reflecting the increased renal artery blood flows calculated by the FSI analysis. Postoperative increases in systolic flow accompanied decreases in high-frequency disturbances, aortic pressure, and collateral flow after all surgical interventions. In general, lesser degrees of high-frequency disturbances followed PA interventions. High-frequency disturbances were eliminated with the 0% PA in contrast to the 30% and 50% PA oversizing and TAB interventions, in which these flow disturbances remained. CONCLUSIONS: Both TAB and PA dramatically improved renal artery flow and pressure waveforms, although disturbed renal waveforms remained in many of the surgical scenarios. Importantly, only the 0% PA oversizing scenario eliminated all high-frequency disturbances, resulting in nearly normal aortorenal blood flow. The study also establishes the relevance of patient-specific computational modeling in planning interventions for the midaortic syndrome.

Verification of the coupled-momentum method with Womersley's Deformable Wall analytical solution.

In this paper, we perform a verification study of the Coupled-Momentum Method (CMM), a 3D fluid-structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi-infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection-free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi-infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space-time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.

Cardiac remodelling following thoracic endovascular aortic repair for descending aortic aneurysms.

OBJECTIVES: Current endografts for thoracic endovascular aortic repair (TEVAR) are much stiffer than the aorta and have been shown to induce acute stiffening. In this study, we aimed to estimate the impact of TEVAR on left ventricular (LV) stroke work (SW) and mass using a non-invasive image-based workflow. METHODS: The University of Michigan database was searched for patients treated with TEVAR for descending aortic pathologies (2013-2016). Patients with available pre-TEVAR and post-TEVAR computed tomography angiography and echocardiography data were selected. LV SW was estimated via patient-specific fluid-structure interaction analyses. LV remodelling was quantified through morphological measurements using echocardiography and electrocardiographic-gated computed tomography angiography data. RESULTS: Eight subjects were included in this study, the mean age of the patients was 68 (73, 25) years, and 6 patients were women. All patients were prescribed antihypertensive drugs following TEVAR. The fluid-structure interaction simulations computed a 26% increase in LV SW post-TEVAR [0.94 (0.89, 0.34) J to 1.18 (1.11, 0.65) J, P = 0.012]. Morphological measurements revealed an increase in the LV mass index post-TEVAR of +26% in echocardiography [72 (73, 17) g/m2 to 91 (87, 26) g/m2, P = 0.017] and +15% in computed tomography angiography [52 (46, 29) g/m2 to 60 (57, 22) g/m2, P = 0.043]. The post- to pre-TEVAR LV mass index ratio was positively correlated with the post- to pre-TEVAR ratios of SW and the mean blood pressure (ρ = 0.690, P = 0.058 and ρ = 0.786, P = 0.021, respectively). CONCLUSIONS: TEVAR was associated with increased LV SW and mass during follow-up. Medical device manufacturers should develop more compliant devices to reduce the stiffness mismatch with the aorta. Additionally, intensive antihypertensive management is needed to control blood pressure post-TEVAR.

Patient-specific modeling of right coronary circulation vulnerability post-liver transplant in Alagille's syndrome.

OBJECTIVES: Cardiac output (CO) response to dobutamine can identify Alagille's syndrome (ALGS) patients at higher risk of cardiovascular complications during liver transplantation. We propose a novel patient-specific computational methodology to estimate the coronary autoregulatory responses during different hemodynamic conditions, including those experienced in a post-reperfusion syndrome (PRS), to aid cardiac risk-assessment. MATERIAL AND METHODS: Data (pressure, flow, strain and ventricular volumes) from a 6-year-old ALGS patient undergoing catheter/dobutamine stress MRI (DSMRI) were used to parameterize a closed-loop coupled-multidomain (3D-0D) approach consisting of image-derived vascular models of pulmonary and systemic circulations and a series of 0D-lumped parameter networks (LPN) of the heart chambers and the distal arterial and venous circulations. A coronary microcirculation control model (CMCM) was designed to adjust the coronary resistance to match coronary blood flow (and thus oxygen delivery) with MVO2 requirements during Rest, Stress and a virtual PRS condition. RESULTS: In all three simulated conditions, diastolic dominated right coronary artery (RCA) flow was observed, due to high right ventricle (RV) afterload. Despite a measured 45% increase in CO, impaired coronary flow reserve (CFR) (~1.4) at Stress was estimated by the CMCM. During modeled PRS, a marked vasodilatory response was insufficient to match RV myocardial oxygen requirements. Such exhaustion of the RCA autoregulatory response was not anticipated by the DSMRI study. CONCLUSION: Impaired CFR undetected by DSMRI resulted in predicted myocardial ischemia in a computational model of PRS. This computational framework may identify ALGS patients at higher risk of complications during liver transplantation due to impaired coronary microvascular responses.

A computational analysis of different endograft designs for Zone 0 aortic arch repair.

OBJECTIVES: Aortic arch repair remains a major surgical challenge. Multiple manufacturers are developing branched endografts for Zone 0 endovascular repair, extending the armamentarium for minimally invasive treatment of aortic arch pathologies. We hypothesize that the design of the Zone 0 endograft has a significant impact on the postoperative haemodynamic performance, particularly in the cervical arteries. The goal of our study was to compare the postoperative haemodynamic performance of different Zone 0 endograft designs. METHODS: Patient-specific, clinically validated, computational fluid dynamics simulations were performed in a 71-year-old woman with a 6.5-cm saccular aortic arch aneurysm. Additionally, 4 endovascular repair scenarios using different endograft designs were created. Haemodynamic performance was evaluated by calculation of postoperative changes in blood flow and platelet activation potential (PLAP) in the cervical arteries. RESULTS: Preoperative cervical blood flow and mean PLAP were 1080 ml/min and 151.75, respectively. Cervical blood flow decreased and PLAP increased following endovascular repair in all scenarios. Endografts with 2 antegrade inner branches performed better compared to single-branch endografts. Scenario 3 performed the worst with a decrease in the total cervical blood flow of 4.8%, a decrease in the left hemisphere flow of 6.7% and an increase in the mean PLAP of 74.3%. CONCLUSIONS: Endograft design has a significant impact on haemodynamic performance following Zone 0 endovascular repair, potentially affecting cerebral blood flow during follow-up. Our results demonstrate the use of computational modelling for virtual testing of therapeutic interventions and underline the need to monitor the long-term outcomes in this cohort of patients.

Reproducing Patient-Specific Hemodynamics in the Blalock-Taussig Circulation Using a Flexible Multi-Domain Simulation Framework: Applications for Optimal Shunt Design.

For babies born with hypoplastic left heart syndrome, several open-heart surgeries are required. During Stage I, a Norwood procedure is performed to construct an appropriate circulation to both the systemic and the pulmonary arteries. The pulmonary arteries receive flow from the systemic circulation, often using a Blalock-Taussig (BT) shunt between the innominate artery and the right pulmonary artery. This procedure causes significantly disturbed flow in the pulmonary arteries. In this study, we use computational hemodynamic simulations to demonstrate its capacity for examining the properties of the flow through and near the BT shunt. Initially, we construct a computational model which produces blood flow and pressure measurements matching the clinical magnetic resonance imaging (MRI) and catheterization data. Achieving this required us to determine the level of BT shunt occlusion; because the occlusion is below the MRI resolution, this information is difficult to recover without the aid of computational simulations. We determined that the shunt had undergone an effective diameter reduction of 22% since the time of surgery. Using the resulting geometric model, we show that we can computationally reproduce the clinical data. We, then, replace the BT shunt with a hypothetical alternative shunt design with a flare at the distal end. Investigation of the impact of the shunt design reveals that the flare can increase pulmonary pressure by as much as 7% and flow by as much as 9% in the main pulmonary branches, which may be beneficial to the pulmonary circulation.

Computational Fluid Dynamics and Aortic Thrombus Formation Following Thoracic Endovascular Aortic Repair.

BACKGROUND: We present the possible utility of computational fluid dynamics in the assessment of thrombus formation and virtual surgical planning illustrated in a patient with aortic thrombus in a kinked ascending aortic graft following thoracic endovascular aortic repair. METHODS: A patient-specific three-dimensional model was built from computed tomography. Additionally, we modeled 3 virtual aortic interventions to assess their effect on thrombosis potential: (1) open surgical repair, (2) conformable endografting, and (3) single-branched endografting. Flow waveforms were extracted from echocardiography and used for the simulations. We used the computational index termed platelet activation potential (PLAP) representing accumulated shear rates of fluid particles within a fluid domain to assess thrombosis potential. RESULTS: The baseline model revealed high PLAP in the entire arch (119.8 ± 42.5), with significantly larger PLAP at the thrombus location (125.4 ± 41.2, p < 0.001). Surgical repair showed a 37% PLAP reduction at the thrombus location (78.6 ± 25.3, p < 0.001) and a 24% reduction in the arch (91.6 ± 28.9, p < 0.001). Single-branched endografting reduced PLAP in the thrombus region by 20% (99.7 ± 24.6, p < 0.001) and by 14% in the arch (103.8 ± 26.1, p < 0.001), whereas a more conformable endograft did not have a profound effect, resulting in a modest 4% PLAP increase (130.6 ± 43.7, p < 0.001) in the thrombus region relative to the baseline case. CONCLUSIONS: Regions of high PLAP were associated with aortic thrombus. Aortic repair resolved pathologic flow patterns, reducing PLAP. Branched endografting also relieved complex flow patterns reducing PLAP. Computational fluid dynamics may assist in the prediction of aortic thrombus formation in hemodynamically complex cases and help guide repair strategies.

A mathematical model of coronary blood flow control: simulation of patient-specific three-dimensional hemodynamics during exercise.

This work presents a mathematical model of the metabolic feedback and adrenergic feedforward control of coronary blood flow that occur during variations in the cardiac workload. It is based on the physiological observations that coronary blood flow closely follows myocardial oxygen demand, that myocardial oxygen debts are repaid, and that control oscillations occur when the system is perturbed and so are phenomenological in nature. Using clinical data, we demonstrate that the model can provide patient-specific estimates of coronary blood flow changes between rest and exercise, requiring only the patient's heart rate and peak aortic pressure as input. The model can be used in zero-dimensional lumped parameter network studies or as a boundary condition for three-dimensional multidomain Navier-Stokes blood flow simulations. For the first time, this model provides feedback control of the coronary vascular resistance, which can be used to enhance the physiological accuracy of any hemodynamic simulation, which includes both a heart model and coronary arteries. This has particular relevance to patient-specific simulation for which heart rate and aortic pressure recordings are available. In addition to providing a simulation tool, under our assumptions, the derivation of our model shows that ß-feedforward control of the coronary microvascular resistance is a mathematical necessity and that the metabolic feedback control must be dependent on two error signals: the historical myocardial oxygen debt, and the instantaneous myocardial oxygen deficit.

Chaste: an open source C++ library for computational physiology and biology.

Chaste - Cancer, Heart And Soft Tissue Environment - is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high-performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cell-based simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to 're-invent the wheel' with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular test-driven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at http://www.cs.ox.ac.uk/chaste, together with details of a mailing list and links to documentation and tutorials.

Efficient simulation of cardiac electrical propagation using high order finite elements.

We present an application of high order hierarchical finite elements for the efficient approximation of solutions to the cardiac monodomain problem. We detail the hurdles which must be overcome in order to achieve theoretically-optimal errors in the approximations generated, including the choice of method for approximating the solution to the cardiac cell model component. We place our work on a solid theoretical foundation and show that it can greatly improve the accuracy in the approximation which can be achieved in a given amount of processor time. Our results demonstrate superior accuracy over linear finite elements at a cheaper computational cost and thus indicate the potential indispensability of our approach for large-scale cardiac simulation.