arXiv subjects

Alison L. Marsden

Publications and source records attributed to Alison L. Marsden.

At least 19 recordsLinked to original sources

arXiv2026

svMultiPhysics: a finite element-based solver for cardiovascular simulations

Heart disease remains the leading cause of death in the United States, motivating extensive efforts to improve its diagnosis, treatment, and prevention. Over the past decade, computational modeling has emerged as a powerful tool to advance cardiovascular research by enabling detailed, patient-specific studies of cardiac physiology and pathology. svMultiPhysics is an open-source, parallel finite element solver written in C++ specifically designed for multiphysics cardiovascular problems. It provides a unified framework for simulating the partial differential equations that govern solid mechanics, fluid dynamics, diffusion, and cardiac electrophysiology. These equations can be solved independently or in a coupled fashion, allowing researchers to investigate interactions between physical processes in a modular yet integrated way. The solver's main strength lies in its ability to seamlessly couple multiple physics modules, enabling the study of complex, highly nonlinear systems. For example, svMultiPhysics can capture the interplay between cardiac electrophysiology, myocardial tissue mechanics, and blood flow dynamics, processes that are essential to understanding vascular and cardiac physiology and function in health and disease. Preliminary GPU-enabled simulations show up to approximately $30\times$ wall-clock speedup for selected linear solver configurations over CPU-based simulations. By offering a robust, extensible, and freely available platform, svMultiPhysics empowers researchers to explore multiphysics problems in cardiovascular science. As the primary 3D solver in the SimVascular open source project, it forms a key component of an end-to-end open source software ecosystem for image based patient specific modeling in the cardiovascular system. It is maintained and openly developed on GitHub, fostering transparency, reproducibility, and collaboration.

physics.flu-dyn↗

arXiv2026

Comparative analysis of resistive immersed surface and immersed boundary methods for aortic valve simulation

Numerical modeling of aortic valve dynamics is essential for understanding the complex fluid-structure interaction (FSI) governing valve biomechanics in health and disease. Immersed methods provide a flexible computational framework for simulating the large deformations of valve leaflets and associated blood flow without requiring body-fitted meshes. Among these approaches, the Resistive Immersed Surface (RIS) and Immersed Boundary (IB) methods are widely used. However, systematic comparative analysis of these methods for realistic aortic valve simulations has not been performed. In this work, we compare a prescribed-kinematics RIS workflow implemented in SimVascular's svMultiPhysics solver with a fully coupled IB workflow using IBAMR for trileaflet and bicuspid aortic valve configurations. The RIS method represents the valve as a surface with prescribed kinematics embedded in the fluid domain and introduces a penalty force that drives the surrounding fluid velocity toward the prescribed leaflet velocity. This formulation reduces modeling complexity and provides useful hemodynamic predictions when representative leaflet kinematics are available. In contrast, the IB method models the leaflets as elastic structures fully immersed in the fluid domain and resolves leaflet deformation through fully coupled two-way FSI. The study focuses on the extent to which RIS reproduces bulk hemodynamic features and transvalvular pressure gradients. Results show that the RIS method captures the large-scale flow structures and predicts the mean transvalvular pressure gradient with a relative error within 15% of the fully coupled IB simulation, improving to within 5% when inlet boundary conditions are matched, while reducing computational cost by approximately 60%.

physics.flu-dyn↗

arXiv2026

SDFStent: Real-time interactive virtual stenting via SDF deformation fields

Stenting is among the most common transcatheter interventions for congenital heart disease (CHD). Patient-specific computational fluid dynamics (CFD) simulations can predict hemodynamic outcomes of intervention scenarios but require post-operative vascular geometries that reflect stent-induced shape changes, which existing tools either model inadequately or require extensive time or manual effort to generate. We present SDFStent, a signed distance function (SDF) based mesh deformation method for virtual stenting that operates in real time, maintains mesh integrity, and preserves junction geometry. The stent is modeled as a pipe surface composed of piecewise-capsule SDFs joined by a smooth-minimum operator. Mesh vertices near the expanding SDF surface are displaced along the SDF gradient with a compactly supported fall-off function and an alpha blending mask. SDFStent was benchmarked against three existing approaches and validated on three tetralogy of Fallot (ToF) patients and three coarctation of the aorta (CoA) patients using rigid-wall steady-state CFD simulations against clinical catheterization measurements. Against a prescribed diameter of 6.0 mm, the method produced a mean stented diameter of 5.92 $\pm$ 0.08 mm in 1.5 s, over 100$\times$ faster than the best stenting-specific comparator. All output meshes were watertight and self-intersection-free. CFD-simulated post-operative pressure drops agreed with clinical measurements within 4 mmHg (mean error 2 mmHg). SDFStent produces simulation-ready post-stent models that match prescribed stent dimensions at interactive speeds, from pre-operative anatomy and catheterization data alone. The implementation is open-source and available in 3D Slicer. Its scriptable architecture enables automated generation of large synthetic cohorts for data-driven surrogate modeling.

cs.CE↗

arXiv2026

Cardiac mechanics modeling: recent developments and current challenges

Patient-specific computational models of the heart are powerful tools for cardiovascular research and medicine, with demonstrated applications in treatment planning, device evaluation, and surgical decision-making. Yet constructing such models is inherently difficult, reflecting the extraordinary complexity of the heart itself. Numerous considerations are required, including reconstructing the anatomy from medical images, representing myocardial mesostructure, capturing material behavior, defining model geometry and boundary conditions, coupling multiple physics, and selecting numerical methods. Many of these choices involve a tradeoff between physiological fidelity and modeling complexity. In this review, we summarize recent advances and unresolved questions in each of these areas, with particular emphasis on cardiac tissue mechanics. We argue that clarifying which complexities are essential, and which can be safely simplified, will be key to enabling clinical translation of these models.

physics.med-ph↗

arXiv2026

Accelerated Patient-Specific Hemodynamic Simulations with Hybrid Physics-Based Neural Surrogates

Physics-based 0D reduced-order models provide computationally lightweight predictions of cardiovascular flows, resolving bulk hemodynamics in fractions of a second that would take days to solve using traditional 3D finite-element techniques. However, the accuracy of 0D models is limited as a result of the dramatic simplifications made in their derivations. In this work, we use 0D parameters learned from high-fidelity 3D data to improve 0D model accuracy without sacrificing its low computational cost or interpretability. We use the resistor-quadratic resistor-inductor (RRI) model to predict pressure drops over 0D vessels and bifurcations, where the resistances and inductance (0D parameters) are predicted from the bifurcation or vessel geometry using neural networks trained on high-fidelity 3D simulations. We validate the hybrid physics-based data-driven framework in three types of patient-specific vasculature - aortic, aortofemoral, and pulmonary anatomies. Use of learned 0D parameters reduces error by at least 50% compared to baseline 0D parameters across all anatomical cohorts. The improvements are especially marked for the more complex pulmonary anatomies, where 0D models with learned parameters reduced error from 30% to 7%. Exclusion of the quadratic resistor in the RRI model improved convergence compared to using the full RRI model. The resulting hybrid model presents a means of real-time (personal laptop runtime of <2 seconds for the most complex pulmonary anatomies), interpretable, and accurate cardiovascular flow modeling, enabling digital twins that support clinical decision-making as well as cardiovascular science and engineering research.

cs.CE↗

arXiv2026

FalconBC: Flow matching for Amortized inference of Latent-CONditioned physiologic Boundary Conditions

Boundary condition tuning is a fundamental step in patient-specific cardiovascular modeling. Despite an increase in offline training cost, recent methods in data-driven variational inference can efficiently estimate the joint posterior distribution of boundary conditions, with amortization of training efforts over clinical targets. However, even the most modern approaches fall short in two important scenarios: open-loop models with known mean flow and assumed waveform shapes, and anatomies affected by vascular lesions where segmentation influences the reachability of pressure or flow split targets. In both cases, boundary conditions cannot be tuned in isolation. We introduce a general amortized inference framework based on probabilistic flow that treats clinical targets, inflow features, and point cloud embeddings of patient-specific anatomies as either conditioning variables or quantities to be jointly estimated. We demonstrate the approach on two patient-specific models: an aorto-iliac bifurcation with varying stenosis locations and severity, and a coronary arterial tree.

cs.LG↗

arXiv2026

Simulations Predict Improved Valve Performance Without Direct Leaflet Intervention After Neonatal Truncus Arteriosus Repair

Truncus arteriosus (TA) is a rare and severe congenital heart disease. Quadricuspid valve morphology occurs in 25% of all TA patients and is linked to regurgitation and increased risk of re-operation. It remains unclear how hemodynamic changes after TA repair alter valve performance. This study simulated pre- and postoperative conditions in a neonatal TA patient to investigate valve performance without direct intervention. We hypothesize that valve performance before and after truncal repair can be predicted in-silico, matching in-vivo imaging and identifying mechanisms how hemodynamic changes after repair will reduce valve regurgitation without direct intervention. Pre- and postoperative CT images of a neonatal patient with quadricuspid valve were segmented. Free edge length and geometric height from the patient's echocardiogram were used to model the valve. For the preoperative condition, ventricular pressures were set equal modeling an unrestricted ventricular septal defect. Systemic and pulmonary resistances were tuned based on the patient's Qp:Qs ratio. For the postoperative condition, boundary conditions were modified to mimic patient-specific hemodynamics after TA repair. The preoperative simulation confirmed mild valve regurgitation seen in-vivo. Interaction between asymmetric flow and surrounding vessel resulted in asymmetric opening and closing. Poor central coaptation led to a central regurgitant jet toward the septum. Altered postoperative hemodynamics improved coaptation and eliminated regurgitation, as seen in-vivo. This modeling approach reproduced in-vivo pre- and postoperative valve performance and identified mechanisms improving coaptation after TA repair. TA repair led to elimination of regurgitation due to enhanced central coaptation. Thus, altered postoperative hemodynamic conditions after TA repair may improve valve performance without direct leaflet intervention.

q-bio.TO↗

arXiv2025

On the performance of multi-fidelity and reduced-dimensional neural emulators for inference of physiological boundary conditions

Solving inverse problems in cardiovascular modeling is particularly challenging due to the high computational cost of running high-fidelity simulations. In this work, we focus on Bayesian parameter estimation and explore different methods to reduce the computational cost of sampling from the posterior distribution by leveraging low-fidelity approximations. A common approach is to construct a surrogate model for the high-fidelity simulation itself. Another is to build a surrogate for the discrepancy between high- and low-fidelity models. This discrepancy, which is often easier to approximate, is modeled with either a fully connected neural network or a nonlinear dimensionality reduction technique that enables surrogate construction in a lower-dimensional space. A third possible approach is to treat the discrepancy between the high-fidelity and surrogate models as random noise and estimate its distribution using normalizing flows. This allows us to incorporate the approximation error into the Bayesian inverse problem by modifying the likelihood function. We validate five different methods which are variations of the above on analytical test cases by comparing them to posterior distributions derived solely from high-fidelity models, assessing both accuracy and computational cost. Finally, we demonstrate our approaches on two cardiovascular examples of increasing complexity: a lumped-parameter Windkessel model and a patient-specific three-dimensional anatomy.

stat.ML↗

arXiv2025

Neural active manifolds: nonlinear dimensionality reduction for uncertainty quantification

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, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity 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.

math.NA↗

arXiv2025

Data-Driven Bifurcation Handling in Physics-Based Reduced-Order Vascular Hemodynamic Models

Three-dimensional (3D) finite-element simulations of cardiovascular flows provide high-fidelity predictions to support cardiovascular medicine, but their high computational cost limits clinical practicality. Reduced-order models (ROMs) offer computationally efficient alternatives but suffer reduced accuracy, particularly at vessel bifurcations where complex flow physics are inadequately captured by standard Poiseuille flow assumptions. We present an enhanced numerical framework that integrates machine learning-predicted bifurcation coefficients into zero-dimensional (0D) hemodynamic ROMs to improve accuracy while maintaining computational efficiency. We develop a resistor-resistor-inductor (RRI) model that uses neural networks to predict pressure-flow relationships from bifurcation geometry, incorporating linear and quadratic resistances along with inductive effects. The method employs non-dimensionalization to reduce training data requirements and apriori flow split prediction for improved bifurcation characterization. We incorporate the RRI model into a 0D model using an optimization-based solution strategy. We validate the approach in isolated bifurcations and vascular trees, across Reynolds numbers from 0 to 5,500, defining ROM accuracy by comparison to 3D finite element simulation. Results demonstrate substantial accuracy improvements: averaged across all trees and Reynolds numbers, the RRI method reduces inlet pressure errors from 54 mmHg (45%) for standard 0D models to 25 mmHg (17%), while a simplified resistor-inductor (RI) variant achieves 31 mmHg (26%) error. The enhanced 0D models show particular effectiveness at high Reynolds numbers and in extensive vascular networks. This hybrid numerical approach enables accurate, real-time hemodynamic modeling for clinical decision support, uncertainty quantification, and digital twins in cardiovascular biomedical engineering.

cs.CE↗

arXiv2025

Simulation-Based Design of Bicuspidization of the Aortic Valve

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 billow. Results: Stenosis decreased with increasing free edge length and was pronounced with free edge length $\leq$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 billow occurred with free edge length $\geq$1.7d. Conclusions: Free edge length $\geq$1.5d was required to avoid aortic stenosis in simulations. Cases with free edge length $\geq$1.7d showed excessive billow 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.

q-bio.TO↗

arXiv2025

A Fluid-Structure Interaction Model of the Zebrafish Aortic Valve

The zebrafish is a valuable model organism for studying cardiac development and diseases due to its many shared aspects of genetics and anatomy with humans and ease of experimental manipulations. Computational fluid-structure interaction (FSI) simulations are an efficient and highly controllable means to study the function of cardiac valves in development and diseases. Due to their small scales, little is known about the mechanical properties of zebrafish cardiac valves, limiting existing computational studies of zebrafish valves and their interaction with blood. To circumvent these limitations, we took a largely first-principles approach called design-based elasticity that allows us to derive valve geometry, fiber orientation and material properties. In FSI simulations of an adult zebrafish aortic valve, these models produce realistic flow rates when driven by physiological pressures and demonstrate the spatiotemporal dynamics of valvular mechanical properties. These models can be used for future studies of zebrafish cardiac hemodynamics, development, and disease.

q-bio.TO↗

arXiv2025

Deformable registration and generative modelling of aortic anatomies by auto-decoders and neural ODEs

This work introduces AD-SVFD, a deep learning model for the deformable registration of vascular shapes to a pre-defined reference and for the generation of synthetic anatomies. AD-SVFD operates by representing each geometry as a weighted point cloud and models ambient space deformations as solutions at unit time of ODEs, whose time-independent right-hand sides are expressed through artificial neural networks. The model parameters are optimized by minimizing the Chamfer Distance between the deformed and reference point clouds, while backward integration of the ODE defines the inverse transformation. A distinctive feature of AD-SVFD is its auto-decoder structure, that enables generalization across shape cohorts and favors efficient weight sharing. In particular, each anatomy is associated with a low-dimensional code that acts as a self-conditioning field and that is jointly optimized with the network parameters during training. At inference, only the latent codes are fine-tuned, substantially reducing computational overheads. Furthermore, the use of implicit shape representations enables generative applications: new anatomies can be synthesized by suitably sampling from the latent space and applying the corresponding inverse transformations to the reference geometry. Numerical experiments, conducted on healthy aortic anatomies, showcase the high-quality results of AD-SVFD, which yields extremely accurate approximations at competitive computational costs.

cs.CV↗

arXiv2025

Optimal patient allocation for echocardiographic assessments

Scheduling echocardiographic exams in a hospital presents significant challenges due to non-deterministic factors (e.g., patient no-shows, patient arrival times, diverse exam durations, etc.) and asymmetric resource constraints between fetal and non-fetal patient streams. To address these challenges, we first conducted extensive pre-processing on one week of operational data from the Echo Laboratory at Stanford University's Lucile Packard Children's Hospital, to estimate patient no-show probabilities and derive empirical distributions of arrival times and exam durations. Based on these inputs, we developed a discrete-event stochastic simulation model using SimPy, and integrate it with the open source Gymnasium Python library. As a baseline for policy optimization, we developed a comparative framework to evaluate on-the-fly versus reservation-based allocation strategies, in which different proportions of resources are reserved in advance. Considering a hospital configuration with a 1:6 ratio of fetal to non-fetal rooms and a 4:2 ratio of fetal to non-fetal sonographers, we show that on-the-fly allocation generally yields better performance, more effectively adapting to patient variability and resource constraints. Building on this foundation, we apply reinforcement learning (RL) to derive an approximated optimal dynamic allocation policy. This RL-based policy is benchmarked against the best-performing rule-based strategies, allowing us to quantify their differences and provide actionable insights for improving echo lab efficiency through intelligent, data-driven resource management.

cs.LG↗

arXiv2024

Personalized and uncertainty-aware coronary hemodynamics simulations: From Bayesian estimation to improved multi-fidelity uncertainty quantification

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.

physics.flu-dyn↗

arXiv2024

Liquid Fourier Latent Dynamics Networks for fast GPU-based numerical simulations in computational cardiology

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.

cs.LG↗

arXiv2024

FSGe: A fast and strongly-coupled 3D fluid-solid-growth interaction method

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.

cs.CE↗

arXiv2024

Bayesian Windkessel calibration using optimized 0D surrogate models

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.

cs.CE↗