arXiv subjects

Anna Hundertmark

Publications and source records attributed to Anna Hundertmark.

6 recordsLinked to original sources

arXiv2026

FSI modeling of case-specific nonlinear carotid artery mechanics and the role of outlet boundary conditions

Compliant arterial wall mechanics, contributing to the Windkessel effect in the carotid artery (CA), have significant impact on hemodynamic patterns and surface shear indicators for cardiovascular diseases, e.g. atherosclerosis. In this study, we extend the linear elastic Fluid-Structure Interaction (FSI) framework to account for nonlinear strain-dependent wall behavior. The model incorporates a Young's modulus generalized from tensile tests on silicone phantoms to capture the nonlinear stress-strain relation of arterial tissue. The final computational model, using a resistance-type boundary condition and in vitro measured stress-strain relation is validated against both, in vitro assessed silicon CA phantom as well as published clinical data on the flow splitting to the daughter branches in CA bifurcations. To better reflect physiological conditions, our model is subsequently extended to incorporate prestress of patient-specific geometries, and clinically measured stress-strain relations, followed by validation against clinical CA data. The present study demonstrates the feasibility of strain-dependent Young's (elastic) modulus as a means to enhance the capacity of the linear elastic framework to accurately represent the physiologically nonlinear mechanics of arterial walls, striking a balance between implementation effort and physiological fidelity. This approach yields realistic strains, volumetric inflation behavior and nonlinear pressure-volume relationships. Furthermore, the study reveals the importance of proper outlet boundary conditions and the shortcomings of resistance-type boundary condition in patient-specific modeling, leading to non-physiological pressure profiles and non-physiological temporal flow splitting.

math.AP↗

arXiv2026

On the compactness of artificial compressibility approximations of weak solutions for fluid problems in deforming domains

In this contribution, a fluid flow problem on a general deforming domain for a Newtonian fluid in two and three space dimensions with artificial compressibility approximation is studied. We prove an estimate on the integral equicontinuity in time of the weak solutions under suitable domain regularity assumptions, which is independent on the compressibility parameter and serves as an alternative compactness argument for the convergence of weak solution sequences for vanishing compressibility. The corresponding estimate is obtained by remapping the problem onto a fixed reference domain and using appropriate divergence-preserving testfunctions involving the difference of two solutions at different points in time, thus defined with respect to different domains/coordinates.

math.AP↗

arXiv2026

Parameter conditioned interpretable U-Net surrogate model for data-driven predictions of convection-diffusion-reaction processes

We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell plasticity. A finite-difference solver, implemented in C++, is developed using second-order spatial discretizations and a step-size controlled Runge-Kutta time integrator. A mesh refinement study confirms the second-order convergence for the spatial discretizations error. Based on simulated input-output pairs and corresponding parameterizations for the diffusion, advection, and reaction mechanisms, we train a parameter-conditioned U-Net surrogate to approximate the fixed-horizon solution map. The surrogate incorporates Feature-wise Linear Modulation (FiLM) for parameter conditioning, coordinate encoding to incorporate spatial location information, and residual blocks to enable multiscale representation learning in combination with the U-Nets skip connections. The trained model achieves low prediction error on held-out test data and provides favorable prediction times due to the GPU based parallelization. Generalization is analyzed using a factorial test dataset, separating initial conditions from parameter conditioning. The results reveal that approximation difficulty varies primarily with the conditioning vector (i.e., the induced PDE regime), rather than with the initial conditions.

cs.CE↗

arXiv2024

Instantaneous Visual Analysis of Blood Flow in Stenoses Using Morphological Similarity

The emergence of computational fluid dynamics (CFD) enabled the simulation of intricate transport processes, including flow in physiological structures, such as blood vessels. While these so-called hemodynamic simulations offer groundbreaking opportunities to solve problems at the clinical forefront, a successful translation of CFD to clinical decision-making is challenging. Hemodynamic simulations are intrinsically complex, time-consuming, and resource-intensive, which conflicts with the time-sensitive nature of clinical workflows and the fact that hospitals usually do not have the necessary resources or infrastructure to support CFD simulations. To address these transfer challenges, we propose a novel visualization system which enables instant flow exploration without performing on-site simulation. To gain insights into the viability of the approach, we focus on hemodynamic simulations of the carotid bifurcation, which is a highly relevant arterial subtree in stroke diagnostics and prevention. We created an initial database of 120 high-resolution carotid bifurcation flow models and developed a set of similarity metrics used to place a new carotid surface model into a neighborhood of simulated cases with the highest geometric similarity. The neighborhood can be immediately explored and the flow fields analyzed. We found that if the artery models are similar enough in the regions of interest, a new simulation leads to coinciding results, allowing the user to circumvent individual flow simulations. We conclude that similarity-based visual analysis is a promising approach toward the usability of CFD in medical practice.

physics.flu-dyn↗

arXiv2022

Longitudinal wall shear stress evaluation using centerline projection approach in the numerical simulations of the patient-based carotid artery

In this numerical study areas of the carotid bifurcation and of a distal stenosis in the internal carotid artery are closely observed to evaluate the patient's current risks of ischemic stroke. An indicator for the vessel wall defects is the stress the blood is exerting on the surrounding vessel tissue, expressed standardly by the amplitude of the wall shear stress vector (WSS) and its oscillatory shear index. In contrast, our orientation-based shear evaluation detects negative shear stresses corresponding with reversal flow appearing in low shear areas. In our investigations of longitudinal component of the wall shear vector, tangential vectors aligned longitudinally with the vessel are necessary. However, as a result of stenosed regions and imaging segmentation techniques from patients' CTA scans, the geometry model's mesh is non-smooth on its surface areas and the automatically generated tangential vector field is discontinuous and multi-directional, making an interpretation of the orientation-based risk indicators unreliable. We improve the evaluation of longitudinal shear stress by applying the projection of the vessel's center-line to the surface to construct smooth tangetial field aligned longitudinaly with the vessel. We validate our approach for the longitudinal WSS component and the corresponding oscillatory index by comparing them to results obtained using automatically generated tangents in both rigid and elastic vessel modeling as well as to amplitude based indicators. The major benefit of our WSS evaluation based on its longitudinal component for the cardiovascular risk assessment is the detection of negative WSS indicating persitent reversal flow. This is impossible in the case of the amplitude-based WSS.

math.AP↗

arXiv2018

On the convergence of fixed point iterations for the moving geometry in a fluid-structure interaction problem

In this paper a fluid-structure interaction problem for the incompressible Newtonian fluid is studied. We prove the convergence of an iterative process with respect to the computational domain geometry. In our previous works on numerical approximation of similar problems we refer this approach as the global iterative method. This iterative approach can be understood as a linearization of the so-called geometric nonlinearity of the underlying model. The proof of the convergence is based on the Banach fixed point argument, where the contractivity of the corresponding mapping is shown due to the continuous dependence of the weak solution on the given domain deformation. This estimate is obtained by remapping the problem onto a fixed domain and using appropriate divergence-free test functions involving the difference of two solutions.

math.AP↗