arXiv subjects

Aaron L. Brown

Publications and source records attributed to Aaron L. Brown.

6 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

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↗

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↗

arXiv2023

A Data-Driven, Non-Linear, Parameterized Reduced Order Model of Metal 3D Printing

Directed energy deposition (DED) is a promising metal additive manufacturing technology capable of 3D printing metal parts with complex geometries at lower cost compared to traditional manufacturing. The technology is most effective when process parameters like laser scan speed and power are optimized for a particular geometry and alloy. To accelerate optimization, we apply a data-driven, parameterized, non-linear reduced-order model (ROM) called Gaussian Process Latent Space Dynamics Identification (GPLaSDI) to physics-based DED simulation data. With an appropriate choice of hyperparameters, GPLaSDI is an effective ROM for this application, with a worst-case error of about 8% and a speed-up of about 1,000,000x with respect to the corresponding physics-based data.

math.NA↗

arXiv2023

A Modular Framework for Implicit 3D-0D Coupling in Cardiac Mechanics

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.

math.NA↗