arXiv subjects

Anna Hundertmark

Publications and source records attributed to Anna Hundertmark.

4 recordsLinked to original sources

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↗

arXiv2016

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↗