arXiv subjects

Martin R. Pfaller

Publications and source records attributed to Martin R. Pfaller.

18 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↗

arXiv2025

Influence of coronary plaque morphology on local mechanical states and associated in-stent restenosis

In-stent restenosis (ISR) after percutaneous coronary intervention is a multi-factorial process. Specific morphological lesion characteristics were observed to contribute to the occurrence of ISR. Local mechanical factors, such as stresses and strains, are known to influence tissue adaptation after stent implantation. However, the influence of morphological features on those local mechanical states and, hence, on the occurrence of ISR remains understudied. This work explores how local mechanical quantities relate to ISR by evaluating the stress distributions in the artery wall during and after stent implantation for morphology-informed lesion examples. We perform computational simulations of the stenting procedure with physics-based patient-specific coronary artery models. Different morphologies are assessed using the spatial plaque composition information from high-resolution coronary computed tomography angiography data. In the sample cases, elevated local tensile stresses were consistently found at sites corresponding to ISR. We found that specific morphological characteristics like circumferential or asymmetric block calcifications result in higher stresses in the surrounding tissue. These findings show that for the observed connection between plaque morphology and ISR, the local mechanical state may represent a relevant link. This study provides a mechanistic, illustrative insight for the examined cases. Future work with larger cohorts and systematic follow-up can establish statistically robust associations.

cs.CE↗

arXiv2024

Patient-specific coronary angioplasty simulations -- a mixed-dimensional finite element modeling approach

Coronary angioplasty with stent implantation is the most frequently used interventional treatment for coronary artery disease. However, reocclusion within the stent, referred to as in-stent restenosis, occurs in up to 10% of lesions. It is widely accepted that mechanical loads on the vessel wall strongly affect adaptive and maladaptive mechanisms. Yet, the role of procedural and lesion-specific influence on restenosis risk remains understudied. Computational modeling of the stenting procedure can provide new mechanistic insights, such as local stresses, that play a significant role in tissue growth and remodeling. Previous simulation studies often featured simplified artery and stent geometries and cannot be applied to real-world examples. Realistic simulations were computationally expensive since they featured fully resolved stenting device models. The aim of this work is to develop and present a mixed-dimensional formulation to simulate the patient-specific stenting procedure with a reduced-dimensional beam model for the stent and 3D models for the artery. In addition to presenting the numerical approach, we apply it to realistic cases to study the intervention's mechanical effect on the artery and correlate the findings with potential high-risk locations for in-stent restenosis. We found that high artery wall stresses develop during the coronary intervention in severely stenosed areas and at the stent boundaries. Herewith, we lay the groundwork for further studies towards preventing in-stent restenosis after coronary angioplasty.

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↗

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

Adaptive integration of history variables in constrained mixture models for organ-scale growth and remodeling

In the last decades, many computational models have been developed to predict soft tissue growth and remodeling (G&R). The constrained mixture theory describes fundamental mechanobiological processes in soft tissue G&R and has been widely adopted in cardiovascular models of G&R. However, even after two decades of work, large organ-scale models are rare, mainly due to high computational costs (model evaluation and memory consumption), especially in long-range simulations. We propose two strategies to adaptively integrate history variables in constrained mixture models to enable large organ-scale simulations of G&R. Both strategies exploit that the influence of deposited tissue on the current mixture decreases over time through degradation. One strategy is independent of external loading, allowing the estimation of the computational resources ahead of the simulation. The other adapts the history snapshots based on the local mechanobiological environment so that the additional integration errors can be controlled and kept negligibly small, even in G&R scenarios with severe perturbations. We analyze the adaptively integrated constrained mixture model on a tissue patch for a parameter study and show the performance under different G&R scenarios. To confirm that adaptive strategies enable large organ-scale examples, we show simulations of different hypertension conditions with a real-world example of a biventricular heart discretized with a finite element mesh. In our example, adaptive integrations sped up simulations by a factor of three and reduced memory requirements to one-sixth. The reduction of the computational costs gets even more pronounced for simulations over longer periods. Adaptive integration of the history variables allows studying more finely resolved models and longer G&R periods while computational costs are drastically reduced and largely constant in time.

q-bio.TO↗

arXiv2024

Hybrid Physics-Based and Data-Driven Modeling of Vascular Bifurcation Pressure Differences

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.

cs.CE↗

arXiv2023

A Probabilistic Neural Twin for Treatment Planning in Peripheral Pulmonary Artery Stenosis

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.

physics.med-ph↗

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↗

arXiv2023

A Fluid-Solid-Growth Solver for Cardiovascular Modeling

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.

cs.CE↗

arXiv2023

A homogenized constrained mixture model of cardiac growth and remodeling: Analyzing mechanobiological stability and reversal

Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extra cellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.

q-bio.TO↗

arXiv2023

Learning Reduced-Order Models for Cardiovascular Simulations with Graph Neural Networks

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.

cs.LG↗

arXiv2022

svMorph: Interactive geometry-editing tools for virtual patient-specific vascular anatomies

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.

physics.med-ph↗

arXiv2022

Automated generation of 0D and 1D reduced-order models of patient-specific blood flow

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.

cs.CE↗

arXiv2021

On the periodicity of cardiovascular fluid dynamics simulations

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.

cs.CE↗

arXiv2018

Automatic Mapping of Atrial Fiber Orientations for Patient-Specific Modeling of Cardiac Electromechanics using Image-Registration

Knowledge of appropriate local fiber architecture is necessary to simulate patient-specific electromechanics in the human heart. However, it is not yet possible to reliably measure in-vivo fiber directions, especially in human atria. Thus, we present a method which defines the fiber architecture in arbitrarily shaped atria using image registration and reorientation methods based on atlas atria with fibers predefined from detailed histological observations. Thereby, it is possible to generate detailed fiber families in every new patient-specific geometry in an automated, time-efficient process. We demonstrate the good performance of the image registration and fiber definition on ten differently shaped human atria. Additionally, we show that characteristics of the electrophysiological activation pattern which appear in the atlas atria also appear in the patients' atria. We arrive at analogous conclusions for coupled electro-mechano-hemodynamical computations.

physics.med-ph↗

arXiv2018

Parametric model order reduction and its application to inverse analysis of large nonlinear coupled cardiac problems

Predictive high-fidelity finite element simulations of human cardiac mechanics co\-mmon\-ly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90\% of the computation time is spent solving linear systems of equations. We propose a novel approach to reduce only the structural dimension of the monolithically coupled structure-windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. To incorporate changes in the parameter set into our reduced order model, we provide a comparison of subspace interpolation methods. We further show how projection-based model order reduction can be easily integrated into a gradient-based optimization and demonstrate its performance in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.

cs.CE↗

arXiv2018

The importance of the pericardium for cardiac biomechanics: From physiology to computational modeling

The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and frictionless sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simulation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respect to atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial-myocardial interaction can correctly predict the pumping mechanisms of the heart as previously assessed in clinical studies. Utilizing a pericardial model can not only provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial-myocardial interaction which cannot be assessed in clinical measurements yet.

cs.CE↗