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Simulations of coronary hemodynamics have improved non-invasive clinical risk stratification and treatment outcomes for coronary artery disease, compared to relying on anatomical imaging alone. However, simulations typically use empirical approaches to distribute total coronary flow amongst the arteries in the coronary tree. This ignores patient variability, the presence of disease, and other clinical factors. Further, uncertainty in the clinical data often remains unaccounted for in the modeling pipeline. We present an end-to-end uncertainty-aware pipeline to (1) personalize coronary flow simulations by incorporating branch-specific coronary flows as well as cardiac function; and (2) predict clinical and biomechanical quantities of interest with improved precision, while accounting for uncertainty in the clinical data. We assimilate patient-specific measurements of myocardial blood flow from CT myocardial perfusion imaging to estimate branch-specific coronary flows. We use adaptive Markov Chain Monte Carlo sampling to estimate the joint posterior distributions of model parameters with simulated noise in the clinical data. Additionally, we determine the posterior predictive distribution for relevant quantities of interest using a new approach combining multi-fidelity Monte Carlo estimation with non-linear, data-driven dimensionality reduction. Our framework recapitulates clinically measured cardiac function as well as branch-specific coronary flows under measurement uncertainty. We substantially shrink the confidence intervals for estimated quantities of interest compared to single-fidelity and state-of-the-art multi-fidelity Monte Carlo methods. This is especially true for quantities that showed limited correlation between the low- and high-fidelity model predictions. Moreover, the proposed estimators are significantly cheaper to compute for a specified confidence level or variance.

Scientific Machine Learning (ML) is gaining momentum as a cost-effective alternative to physics-based numerical solvers in many engineering applications. In fact, scientific ML is currently being used to build accurate and efficient surrogate models starting from high-fidelity numerical simulations, effectively encoding the parameterized temporal dynamics underlying Ordinary Differential Equations (ODEs), or even the spatio-temporal behavior underlying Partial Differential Equations (PDEs), in appropriately designed neural networks. We propose an extension of Latent Dynamics Networks (LDNets), namely Liquid Fourier LDNets (LFLDNets), to create parameterized space-time surrogate models for multiscale and multiphysics sets of highly nonlinear differential equations on complex geometries. LFLDNets employ a neurologically-inspired, sparse, liquid neural network for temporal dynamics, relaxing the requirement of a numerical solver for time advancement and leading to superior performance in terms of tunable parameters, accuracy, efficiency and learned trajectories with respect to neural ODEs based on feedforward fully-connected neural networks. Furthermore, in our implementation of LFLDNets, we use a Fourier embedding with a tunable kernel in the reconstruction network to learn high-frequency functions better and faster than using space coordinates directly as input. We challenge LFLDNets in the framework of computational cardiology and evaluate their capabilities on two 3-dimensional test cases arising from multiscale cardiac electrophysiology and cardiovascular hemodynamics. This paper illustrates the capability to run Artificial Intelligence-based numerical simulations on single or multiple GPUs in a matter of minutes and represents a significant step forward in the development of physics-informed digital twins.

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, plus a simultaneously learnt surrogate model with inputs on this manifold. The proposed dimensionality reduction framework can then be applied to perform outer loop many-query tasks, like sensitivity analysis and uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy, and highlight its advantages with respect to existing approaches in the literature.

Boundary condition (BC) calibration to assimilate clinical measurements is an essential step in any subject-specific simulation of cardiovascular fluid dynamics. Bayesian calibration approaches have successfully quantified the uncertainties inherent in identified parameters. Yet, routinely estimating the posterior distribution for all BC parameters in 3D simulations has been unattainable due to the infeasible computational demand. We propose an efficient method to identify Windkessel parameter posteriors using results from a single high-fidelity three-dimensional (3D) model evaluation. We only evaluate the 3D model once for an initial choice of BCs and use the result to create a highly accurate zero-dimensional (0D) surrogate. We then perform Sequential Monte Carlo (SMC) using the optimized 0D model to derive the high-dimensional Windkessel BC posterior distribution. We validate this approach in a publicly available dataset of N=72 subject-specific vascular models. We found that optimizing 0D models to match 3D data a priori lowered their median approximation error by nearly one order of magnitude. In a subset of models, we confirm that the optimized 0D models still generalize to a wide range of BCs. Finally, we present the high-dimensional Windkessel parameter posterior for different measured signal-to-noise ratios in a vascular model using SMC. We further validate that the 0D-derived posterior is a good approximation of the 3D posterior. The minimal computational demand of our method using a single 3D simulation, combined with the open-source nature of all software and data used in this work, will increase access and efficiency of Bayesian Windkessel calibration in cardiovascular fluid dynamics simulations.

Equilibrated fluid-solid-growth (FSGe) is a fast, open source, three-dimensional (3D) computational platform for simulating interactions between instantaneous hemodynamics and long-term vessel wall adaptation through mechanobiologically equilibrated growth and remodeling (G&R). Such models can capture evolving geometry, composition, and material properties in health and disease and following clinical interventions. In traditional G&R models, this feedback is modeled through highly simplified fluid solutions, neglecting local variations in blood pressure and wall shear stress (WSS). FSGe overcomes these inherent limitations by strongly coupling the 3D Navier-Stokes equations for blood flow with a 3D equilibrated constrained mixture model (CMMe) for vascular tissue G&R. CMMe allows one to predict long-term evolved mechanobiological equilibria from an original homeostatic state at a computational cost equivalent to that of a standard hyperelastic material model. In illustrative computational examples, we focus on the development of a stable aortic aneurysm in a mouse model to highlight key differences in growth patterns between FSGe and solid-only G&R models. We show that FSGe is especially important in blood vessels with asymmetric stimuli. Simulation results reveal greater local variation in fluid-derived WSS than in intramural stress (IMS). Thus, differences between FSGe and G&R models became more pronounced with the growing influence of WSS relative to pressure. Future applications in highly localized disease processes, such as for lesion formation in atherosclerosis, can now include spatial and temporal variations of WSS.

Reduced-order models (ROMs) allow for the simulation of blood flow in patient-specific vasculatures without the high computational cost and wait time associated with traditional computational fluid dynamics (CFD) models. Unfortunately, due to the simplifications made in their formulations, ROMs can suffer from significantly reduced accuracy. One common simplifying assumption is the continuity of static or total pressure over vascular junctions. In many cases, this assumption has been shown to introduce significant error. We propose a model to account for this pressure difference, with the ultimate goal of increasing the accuracy of cardiovascular ROMs. Our model successfully uses a structure common in existing ROMs in conjunction with machine-learning techniques to predict the pressure difference over a vascular bifurcation. We analyze the performance of our model on steady and transient flows, testing it on three bifurcation cohorts representing three different bifurcation geometric types. We also compare the efficacy of different machine-learning techniques and two different model modalities.

We study the problem of multifidelity uncertainty propagation for computationally expensive models. In particular, we consider the general setting where the high-fidelity and low-fidelity models have a dissimilar parameterization both in terms of number of random inputs and their probability distributions, which can be either known in closed form or provided through samples. We derive novel multifidelity Monte Carlo estimators which rely on a shared subspace between the high-fidelity and low-fidelity models where the parameters follow the same probability distribution, i.e., a standard Gaussian. We build the shared space employing normalizing flows to map different probability distributions into a common one, together with linear and nonlinear dimensionality reduction techniques, active subspaces and autoencoders, respectively, which capture the subspaces where the models vary the most. We then compose the existing low-fidelity model with these transformations and construct modified models with an increased correlation with the high-fidelity model, which therefore yield multifidelity Monte Carlo estimators with reduced variance. A series of numerical experiments illustrate the properties and advantages of our approaches.

The substantial computational cost of high-fidelity models in numerical hemodynamics has, so far, relegated their use mainly to offline treatment planning. New breakthroughs in data-driven architectures and optimization techniques for fast surrogate modeling provide an exciting opportunity to overcome these limitations, enabling the use of such technology for time-critical decisions. We discuss an application to the repair of multiple stenosis in peripheral pulmonary artery disease through either transcatheter pulmonary artery rehabilitation or surgery, where it is of interest to achieve desired pressures and flows at specific locations in the pulmonary artery tree, while minimizing the risk for the patient. Since different degrees of success can be achieved in practice during treatment, we formulate the problem in probability, and solve it through a sample-based approach. We propose a new offline-online pipeline for probabilsitic real-time treatment planning which combines offline assimilation of boundary conditions, model reduction, and training dataset generation with online estimation of marginal probabilities, possibly conditioned on the degree of augmentation observed in already repaired lesions. Moreover, we propose a new approach for the parametrization of arbitrarily shaped vascular repairs through iterative corrections of a zero-dimensional approximant. We demonstrate this pipeline for a diseased model of the pulmonary artery tree available through the Vascular Model Repository.

Congenital heart disease (CHD) encompasses a spectrum of cardiovascular structural abnormalities, often requiring customized treatment plans for individual patients. Computational modeling and analysis of these unique cardiac anatomies can improve diagnosis and treatment planning and may ultimately lead to improved outcomes. Deep learning (DL) methods have demonstrated the potential to enable efficient treatment planning by automating cardiac segmentation and mesh construction for patients with normal cardiac anatomies. However, CHDs are often rare, making it challenging to acquire sufficiently large patient cohorts for training such DL models. Generative modeling of cardiac anatomies has the potential to fill this gap via the generation of virtual cohorts; however, prior approaches were largely designed for normal anatomies and cannot readily capture the significant topological variations seen in CHD patients. Therefore, we propose a type- and shape-disentangled generative approach suitable to capture the wide spectrum of cardiac anatomies observed in different CHD types and synthesize differently shaped cardiac anatomies that preserve the unique topology for specific CHD types. Our DL approach represents generic whole heart anatomies with CHD type-specific abnormalities implicitly using signed distance fields (SDF) based on CHD type diagnosis, which conveniently captures divergent anatomical variations across different types and represents meaningful intermediate CHD states. To capture the shape-specific variations, we then learn invertible deformations to morph the learned CHD type-specific anatomies and reconstruct patient-specific shapes. Our approach has the potential to augment the image-segmentation pairs for rarer CHD types for cardiac segmentation and generate cohorts of CHD cardiac meshes for computational simulation.

In numerical simulations of cardiac mechanics, coupling the heart to a model of the circulatory system is essential for capturing physiological cardiac behavior. A popular and efficient technique is to use an electrical circuit analogy, known as a lumped parameter network or zero-dimensional (0D) fluid model, to represent blood flow throughout the cardiovascular system. Due to the strong physical interaction between the heart and the blood circulation, developing accurate and efficient numerical coupling methods remains an active area of research. In this work, we present a modular framework for implicitly coupling three-dimensional (3D) finite element simulations of cardiac mechanics to 0D models of blood circulation. The framework is modular in that the circulation model can be modified independently of the 3D finite element solver, and vice versa. The numerical scheme builds upon a previous work that combines 3D blood flow models with 0D circulation models (3D fluid - 0D fluid). Here, we extend it to couple 3D cardiac tissue mechanics models with 0D circulation models (3D structure - 0D fluid), showing that both mathematical problems can be solved within a unified coupling scheme. The effectiveness, temporal convergence, and computational cost of the algorithm are assessed through multiple examples relevant to the cardiovascular modeling community. Importantly, in an idealized left ventricle example, we show that the coupled model yields physiological pressure-volume loops and naturally recapitulates the isovolumic contraction and relaxation phases of the cardiac cycle without any additional numerical techniques. Furthermore, we provide a new derivation of the scheme inspired by the Approximate Newton Method of Chan (1985), explaining how the proposed numerical scheme combines the stability of monolithic approaches with the modularity and flexibility of partitioned approaches.

Objective: Severe congenital aortic valve pathology in the growing patient remains a challenging clinical scenario. Bicuspidization of the diseased aortic valve has proven to be a promising repair technique with acceptable durability. However, most understanding of the procedure is empirical and retrospective. This work seeks to design the optimal gross morphology associated with surgical bicuspidization with simulations, based on the hypothesis that modifications to the free edge length cause or relieve stenosis. Methods: Model bicuspid valves were constructed with varying free edge lengths and gross morphology. Fluid-structure interaction simulations were conducted in a single patient-specific model geometry. The models were evaluated for primary targets of stenosis and regurgitation. Secondary targets were assessed and included qualitative hemodynamics, geometric height, effective height, orifice area and prolapse. Results: Stenosis decreased with increasing free edge length and was pronounced with free edge length less than or equal to 1.3 times the annular diameter d. With free edge length 1.5d or greater, no stenosis occurred. All models were free of regurgitation. Substantial prolapse occurred with free edge length greater than or equal to 1.7d. Conclusions: Free edge length greater than or equal to 1.5d was required to avoid aortic stenosis in simulations. Cases with free edge length greater than or equal to 1.7d showed excessive prolapse and other changes in gross morphology. Cases with free edge length 1.5-1.6d have a total free edge length approximately equal to the annular circumference and appeared optimal. These effects should be studied in vitro and in animal studies.

Our ability to produce human-scale bio-manufactured organs is critically limited by the need for vascularization and perfusion. For tissues of variable size and shape, including arbitrarily complex geometries, designing and printing vasculature capable of adequate perfusion has posed a major hurdle. Here, we introduce a model-driven design pipeline combining accelerated optimization methods for fast synthetic vascular tree generation and computational hemodynamics models. We demonstrate rapid generation, simulation, and 3D printing of synthetic vasculature in complex geometries, from small tissue constructs to organ scale networks. We introduce key algorithmic advances that all together accelerate synthetic vascular generation by more than 230-fold compared to standard methods and enable their use in arbitrarily complex shapes through localized implicit functions. Furthermore, we provide techniques for joining vascular trees into watertight networks suitable for hemodynamic CFD and 3D fabrication. We demonstrate that organ-scale vascular network models can be generated in silico within minutes and can be used to perfuse engineered and anatomic models including a bioreactor, annulus, bi-ventricular heart, and gyrus. We further show that this flexible pipeline can be applied to two common modes of bioprinting with free-form reversible embedding of suspended hydrogels and writing into soft matter. Our synthetic vascular tree generation pipeline enables rapid, scalable vascular model generation and fluid analysis for bio-manufactured tissues necessary for future scale up and production., Comment: 58 pages (19 main and 39 supplement pages), 4 main figures, 9 supplement figures

We introduce Branched Latent Neural Maps (BLNMs) to learn finite dimensional input-output maps encoding complex physical processes. A BLNM is defined by a simple and compact feedforward partially-connected neural network that structurally disentangles inputs with different intrinsic roles, such as the time variable from model parameters of a differential equation, while transferring them into a generic field of interest. BLNMs leverage latent outputs to enhance the learned dynamics and break the curse of dimensionality by showing excellent generalization properties with small training datasets and short training times on a single processor. Indeed, their generalization error remains comparable regardless of the adopted discretization during the testing phase. Moreover, the partial connections significantly reduce the number of tunable parameters. We show the capabilities of BLNMs in a challenging test case involving electrophysiology simulations in a biventricular cardiac model of a pediatric patient with hypoplastic left heart syndrome. The model includes a 1D Purkinje network for fast conduction and a 3D heart-torso geometry. Specifically, we trained BLNMs on 150 in silico generated 12-lead electrocardiograms (ECGs) while spanning 7 model parameters, covering cell-scale and organ-level. Although the 12-lead ECGs manifest very fast dynamics with sharp gradients, after automatic hyperparameter tuning the optimal BLNM, trained in less than 3 hours on a single CPU, retains just 7 hidden layers and 19 neurons per layer. The resulting mean square error is on the order of $10^{-4}$ on a test dataset comprised of 50 electrophysiology simulations. In the online phase, the BLNM allows for 5000x faster real-time simulations of cardiac electrophysiology on a single core standard computer and can be used to solve inverse problems via global optimization in a few seconds of computational time.

We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains., Comment: 36 pages, 11 figures

Understanding the complex interplay between morphologic and hemodynamic features in aortic dissection is critical for risk stratification and for the development of individualized therapy. This work evaluates the effects of entry and exit tear size on the hemodynamics in type B aortic dissection by comparing fluid-structure interaction (FSI) simulations with in vitro 4D-flow magnetic resonance imaging (MRI). A baseline patient-specific 3D-printed model and two variants with modified tear size (smaller entry tear, smaller exit tear) were embedded into a flow- and pressure-controlled setup to perform MRI as well as 12-point catheter-based pressure measurements. The same models defined the wall and fluid domains for FSI simulations, for which boundary conditions were matched with measured data. Results showed exceptionally well matched complex flow patterns between 4D-flow MRI and FSI simulations. Compared to the baseline model, false lumen flow volume decreased with either a smaller entry tear (-17.8 and -18.5 %, for FSI simulation and 4D-flow MRI, respectively) or smaller exit tear (-16.0 and -17.3 %). True to false lumen pressure difference (initially 11.0 and 7.9 mmHg, for FSI simulation and catheter-based pressure measurements, respectively) increased with a smaller entry tear (28.9 and 14.6 mmHg), and became negative with a smaller exit tear (-20.6 and -13.2 mmHg). This work establishes quantitative and qualitative effects of entry or exit tear size on hemodynamics in aortic dissection, with particularly notable impact observed on FL pressurization. FSI simulations demonstrate acceptable qualitative and quantitative agreement with flow imaging, supporting its deployment in clinical studies., Comment: Judith Zimmermann and Kathrin B\"aumler contributed equally

Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience reduced accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 2% and 3% for pressure and flow rate, respectively, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models, while maintaining high efficiency at inference time.

We propose svMorph, a framework for interactive virtual sculpting of patient-specific vascular anatomic models. Our framework includes three tools for the creation of tortuosity, aneurysms, and stenoses in tubular vascular geometries. These shape edits are performed via geometric operations on the surface mesh and vessel centerline curves of the input model. The tortuosity tool also uses the physics-based Oriented Particles method, coupled with linear blend skinning, to achieve smooth, elastic-like deformations. Our tools can be applied separately or in combination to produce simulation-suitable morphed models. They are also compatible with popular vascular modeling software, such as SimVascular. To illustrate our tools, we morph several image-based, patient-specific models to create a range of shape changes and simulate the resulting hemodynamics via three-dimensional, computational fluid dynamics. We also demonstrate the ability to quickly estimate the hemodynamic effects of the shape changes via automated generation of associated zero-dimensional lumped-parameter models.

In our recent work, we introduced the reduced unified continuum formulation for vascular fluid-structure interaction (FSI) and demonstrated enhanced solver accuracy, scalability, and performance compared to conventional approaches. We further verified the formulation against Womersley's deformable wall theory. In this study, we assessed its performance in a compliant patient-specific aortic model by leveraging 3D printing, 2D magnetic resonance imaging (MRI), and 4D-flow MRI to extract high-resolution anatomical and hemodynamic information from an in vitro flow circuit. To accurately reflect experimental conditions, we additionally enabled in-plane vascular motion at each inlet and outlet, and implemented viscoelastic external tissue support and vascular tissue prestressing. Validation of our formulation is achieved through close quantitative agreement in pressures, lumen area changes, pulse wave velocity, and early systolic velocities, as well as qualitative agreement in late systolic flow structures. Our validated suite of FSI techniques can be used to investigate vascular disease initiation, progression, and treatment at a computational cost on the same order as that of rigid-walled simulations. This study is the first to validate a cardiovascular FSI formulation against an in vitro flow circuit involving a compliant vascular phantom of complex patient-specific anatomy.

We recently demonstrated the reduction of the unified continuum and variational multiscale formulation to a computationally efficient fluid-structure interaction (FSI) formulation via three sound modeling assumptions pertaining to the vascular wall. Similar to the coupled momentum method introduced by Figueroa et al., the resulting semi-discrete formulation yields a monolithically coupled FSI system posed in an Eulerian frame of reference with only a minor modification of the fluid boundary integral. To achieve uniform second-order temporal accuracy and user-controlled high-frequency algorithmic damping, we adopt the generalized-$\alpha$ method for uniform temporal discretization of the entire coupled system. In conjunction with a fully consistent, segregated predictor multi-corrector algorithm preserving the block structure of the incompressible Navier-Stokes equations in the implicit solver's associated linear system, a three-level nested block preconditioner is adopted for improved representation of the Schur complement. In this work, we apply our reduced unified continuum formulation to an appropriately prestressed patient-specific abdominal aortic aneurysm and investigate the effects of varying spatial distributions of wall properties on hemodynamic and vascular wall quantities of interest., Comment: arXiv admin note: substantial text overlap with arXiv:2110.08391

Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N=72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers.

The immersed boundary (IB) method is a mathematical framework for fluid-structure interaction problems (FSI) that was originally developed to simulate flows around heart valves. Direct comparison of FSI simulations around heart valves against experimental data is challenging, however, due to the difficulty of performing robust and effective simulations, the complications of modeling a specific physical experiment, and the need to acquire experimental data that is directly comparable to simulation data. Such comparators are a necessary precursor for further formal validation studies of FSI simulations involving heart valves. In this work, we performed physical experiments of flow through a pulmonary valve in an in vitro pulse duplicator, and measured the corresponding velocity field using 4D flow MRI (4-dimensional flow magnetic resonance imaging). We constructed a computer model of this pulmonary artery setup, including modeling valve geometry and material properties via a technique called design-based elasticity, and simulated flow through it with the IB method. The simulated flow fields showed excellent qualitative agreement with experiments, excellent agreement on integral metrics, and reasonable relative error in the entire flow domain and on slices of interest. These results illustrate how to construct a computational model of a physical experiment for use as a comparator., Comment: Ann Biomed Eng (2023)

We recently derived the unified continuum and variational multiscale formulation for fluid-structure interaction (FSI) using the Gibbs free energy. Restricting our attention to vascular FSI, we now reduce this arbitrary Lagrangian-Eulerian (ALE) formulation by adopting three assumptions for the vascular wall. The resulting reduced unified continuum formulation achieves monolithic FSI coupling in the Eulerian frame through a simple modification of the fluid boundary integral. While ostensibly similar to the semi-discrete formulation of the coupled momentum method, its underlying derivation does not rely on an assumption of a fictitious body force in the elastodynamics sub-problem and therefore represents a direct simplification of the ALE method. Uniform temporal discretization is performed via the generalized-$\alpha$ scheme. In contrast to the predominant approach yielding only first-order accuracy for pressure, we collocate both pressure and velocity at the intermediate time step to achieve uniform second-order temporal accuracy. In conjunction with quadratic tetrahedral elements, our methodology offers higher-order temporal and spatial accuracy for quantities of clinical interest. Furthermore, without loss of consistency, a segregated predictor multi-corrector algorithm is developed to preserve the same block structure as for the incompressible Navier-Stokes equations in the implicit solver's associated linear system. Block preconditioning of a monolithically coupled FSI system is therefore made possible for the first time. Compared to alternative preconditioners, our three-level nested block preconditioner, which improves representation of the Schur complement, demonstrates robust performance over a wide range of physical parameters. We present verification against Womersley's deformable wall theory and additionally develop practical modeling techniques for clinical applications.

Bicuspid aortic valve is the most common congenital heart defect, affecting 1-2% of the global population. Patients with bicuspid valves frequently develop dilation and aneurysms of the ascending aorta. Both hemodynamic and genetic factors are believed to contribute to dilation, yet the precise mechanism underlying this progression remains under debate. Controlled comparisons of hemodynamics in patients with different forms of bicuspid valve disease are challenging because of confounding factors, and simulations offer the opportunity for direct and systematic comparisons. Using fluid-structure interaction simulations, we simulate flows through multiple aortic valve models in a patient-specific geometry. The aortic geometry is based on a healthy patient with no known aortic or valvular disease, which allows us to isolate the hemodynamic consequences of changes to the valve alone. Four fully-passive, elastic model valves are studied: a tricuspid valve and bicuspid valves with fusion of the left- and right-, right- and non-, and non- and left-coronary cusps. The resulting tricuspid flow is relatively uniform, with little secondary or reverse flow, and little to no pressure gradient across the valve. The bicuspid cases show localized jets of forward flow, excess streamwise momentum, elevated secondary and reverse flow, and clinically significant levels of stenosis. Localized high flow rates correspond to locations of dilation observed in patients, with the location related to which valve cusps are fused. Thus, the simulations support the hypothesis that chronic exposure to high local flow contributes to localized dilation and aneurysm formation.

The analysis of quantitative hemodynamics and luminal pressure may add valuable information to aid treatment strategies and prognosis for aortic dissections. This work directly compared in vitro 4D-flow magnetic resonance imaging (MRI), catheter-based pressure measurements, and computational fluid dynamics that integrated fluid-structure interaction (CFD FSI). Experimental data was acquired with a compliant 3D-printed model of a type-B aortic dissection (TBAD) that was embedded into a physiologically tuned flow circuit. In vitro flow and pressure information were used to tune the CFD FSI Windkessel boundary conditions. Results showed very good overall agreement of complex flow patterns, true to false lumen flow splits, and pressure distribution. This work demonstrates feasibility of a tunable experimental setup that integrates a patient-specific compliant model and provides a test bed for exploring critical imaging and modeling parameters that ultimately may improve the prognosis for patients with aortic dissections., Comment: 12 pages, 7 figures, in press

In this article, we review the mathematical modeling for the vascular system.

Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determine whether a simulation has yet reached that periodic state. In this work, we propose use of the asymptotic error measure to quantify the difference between simulation results and their ideal periodic state using lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patient-specific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.