arXiv subjects

Tim Ricken

Publications and source records attributed to Tim Ricken.

11 recordsLinked to original sources

arXiv2026

Ultra-wideband MRE of the human liver and spleen for viscoelastic model identification in hepatic inflammation

Magnetic resonance elastography (MRE) is established for noninvasive assessment of liver fibrosis. Conventional abdominal MRE is typically limited to 40-60 Hz. Lower frequencies remain largely unexplored, particularly with regard to hepatic inflammation. We developed ultra-wideband MRE covering 5-80 Hz to investigate frequency-resolved viscoelastic dispersion of the liver and spleen and to identify biomechanical markers of hepatic inflammation. Following phantom validation, nine healthy volunteers and nine patients with inflammatory liver disease were examined at 12 frequencies. Spatiotemporal phase unwrapping and frequency-adaptive wavefield preprocessing enabled reconstruction of shear wave speed (SWS), penetration rate (PR), and loss angle ($\phi$). Six rheological models were evaluated. The largest inflammation-associated changes were observed at frequencies below 20 Hz: $\phi$ increased by 63% (p<0.001), PR decreased by 37% (p=0.003), and SWS increased by 8% (p=0.008), indicating predominantly dissipative, rather than stiffness-related, changes and a shift toward fluid-like behavior with minor stiffness changes in the lower frequency regime. The rheological springpot model with serial dashpot provided the best fit and revealed distinct dispersion functions for liver and spleen. In patients, springpot elastic modulus increased (101%, p=0.001), while viscosity and springpot power-law exponent decreased (52%, p=0.002 and 58%, p<0.001) suggesting a shift from soft-fluid to stiff-solid liver properties. Ultra-wideband MRE revealed that inflammatory liver disease is associated with property shifts toward stronger dissipation and fluid-like behavior at low frequencies while displaying solid-like behavior at higher frequencies. Ultra-low frequency MRE may provide a diagnostic window into inflammation-associated liver viscoelasticity without full rheological modeling.

physics.med-ph↗

arXiv2026

Architecture-agnostic Lipschitz-constant Bayesian header and its application to resolve semantically proximal classification errors with vision transformers

Label noise remains a critical bottleneck for the generalization of supervised deep learning models, particularly when errors are structured rather than random. Standard robust training methods often fail in the presence of such semantically proximal classification errors. This work presents an architecture-agnostic Lipschitz-constant Bayesian header that can be integrated into feature extractors such as vision transformers, yielding the bi-Lipschitz-constrained Bayesian Vision Transformer (LipB-ViT). In contrast to conventional Bayesian layers, our approach enforces spectral normalization on both the mean and log-variance of the variational weights, which promotes calibrated predictive uncertainty and mitigates noise amplification. We further propose a novel metric to jointly capture uncertainty and confidence across misclassification rates, as well as an adaptive arithmetic-mean fusion scheme that combines feature-space proximity with predictive uncertainty to detect corrupted labels outperforming the state of the art k-nearest neighbor based identification methods by more than 7% reaching a recall of more than 0.93 at 15% semantically misclassified labels. Although computational costs increase due to Monte Carlo sampling, the method offers plug-and-play compatibility with pre-trained backbones and consistent hyperparameters across domains, suggesting strong utility for high-stakes applications with variable annotation reliability. The stabilized confidence estimates serve as the foundation for an analysis pipeline that jointly assesses dataset quality and label noise, yielding a second novel metric for their combined quantification. Lastly, we systematically evaluate LipB-ViT under both structured (adversarial) and unstructured noise at inference time, demonstrating its robustness in realistic high-noise and attack scenarios. We compare its performance against baseline methods.

cs.CV↗

arXiv2025

Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference

Accurately modeling and inferring solutions to time-dependent partial differential equations (PDEs) over extended horizons remains a core challenge in scientific machine learning. Traditional full rollout (FR) methods, which predict entire trajectories in one pass, often fail to capture the causal dependencies and generalize poorly outside the training time horizon. Autoregressive (AR) approaches, evolving the system step by step, suffer from error accumulation, limiting long-term accuracy. These shortcomings limit the long-term accuracy and reliability of both strategies. To address these issues, we introduce the Physics-Informed Time-Integrated Deep Operator Network (PITI-DeepONet), a dual-output architecture trained via physics-informed or hybrid physics- and data-driven objectives to ensure stable, accurate long-term evolution well beyond the training horizon. Instead of forecasting future states, the network learns the time-derivative operator from the current state, integrating it using classical time-stepping schemes to advance the solution in time. Additionally, the framework can leverage residual monitoring during inference to estimate prediction quality and detect when the system transitions outside the training domain. Applied to benchmark problems, PITI-DeepONet demonstrates enhanced accuracy and stability over extended inference time horizons when compared to traditional methods. Mean relative $\mathcal{L}_2$ errors reduced by 84\% (versus FR) and 79\% (versus AR) for 1D heat equation; by 87\% (versus FR) and 98\% (versus AR) for the 1D Burgers equation; by 42\% (versus FR) and 89\% (versus AR) for the 2D Allen-Cahn equation; and by 58\% (vs. FR) and 61\% (vs. AR) for the 1D Kuramoto-Sivashinsky equation. By moving beyond classic FR and AR schemes, PITI-DeepONet paves the way for more reliable, long-term integration of complex, time-dependent PDEs.

cs.LG↗

arXiv2025

Insights into experimental evaluation of the non-fourier heat transfer model in biological tissues

A comprehensive understanding of heat transfer mechanisms in biological tissues is essential for the advancement of thermal therapeutic techniques and the development of accurate bioheat transfer models. Conventional models often fail to capture the inherently complex thermal behavior of biological media, necessitating more sophisticated approaches for experimental validation and parameter extraction. In this study, the Two-Dimensional Three-Phase Lag (TPL) heat transfer model, implemented via the finite difference method (FDM), was employed to extract key phase lag parameters characterizing heat conduction in bovine skin tissue. Experimental measurements were obtained using a 450 nm laser source and two non-contact infrared sensors. The influence of four critical parameters was systematically investigated: heat flux phase lag ($\tau_{q}$), temperature gradient phase lag ($\tau_{\theta}$), thermal displacement coefficient ($k^*$), and thermal displacement phase lag ($\tau_{v}$). A carefully designed experimental protocol was used to assess each parameter independently. The results revealed that the extracted phase lag values were substantially lower than those previously reported in the literature. This highlights the importance of high-precision measurements and the need to isolate each parameter during analysis. These findings contribute to the refinement of bioheat transfer models and hold potential for improving the efficacy and safety of clinical thermal therapies.

physics.bio-ph↗

arXiv2025

Least-Squares Finite Element Methods for nonlinear problems: A unified framework

This paper presents a unified Least-Squares framework for solving nonlinear partial differential equations by recasting the governing system as a residual minimisation problem. A Least-Squares functional is formulated and the corresponding Gauss-Newton method derived, which approximates simultaneously primal and dual variables. We derive conditions under which the Least-Squares functional is coercive and continuous in an appropriate solution space, and establish convergence results while demonstrating that the functional serves as a reliable a posteriori error estimator. This inherent error estimation property is then exploited to drive adaptive mesh refinement across a variety of problems, including the stationary heat equation with either temperature-dependent or discontinuous conductivity, nonlinear elasticity based on the Saint-Venant Kirchhoff model and sea-ice dynamics.

math.NA↗

arXiv2025

Modelling Material Injection Into Porous Structures Under Non-isothermal Conditions

In this work, the Theory of Porous Media (TPM) is employed to model percutaneous vertebroplasty, a medical procedure in which acrylic cement is injected into cancellous vertebral bone. Previously, isothermal macroscale models have been derived to describe this material injection and the mechanical interactions which arise. However, the temperature of the injected cement is typically below the human body temperature, necessitating the extension of these models to the non-isothermal case. Following the modelling principles of the TPM and considering local thermal non-equilibrium conditions, our model introduces three energy balances as well as additional constitutive relations. If restricted to local thermal equilibrium conditions, our model equations are in agreement with other examples of TPM-based models. We observe that our model elicits physically reasonable behaviour in numerical simulations which employ parameter values and initial and boundary conditions relevant for our application. Noting that we neglect capillary effects, we claim our model to be thermodynamically consistent despite the employment of simplifying assumptions during its derivation, such as the Coleman and Noll procedure.

physics.flu-dyn↗

arXiv2024

Adaptive finite element methods based on flux and stress equilibration using FEniCSx

This contribution shows how a-posteriori error estimators based on equilibrated fluxes - H(div) functions fulfilling the underlying conservation law - can be implemented in FEniCSx. Therefore, dolfinx_eqlb is introduced, its algorithmic structure is described and classical benchmarks for adaptive solution procedures for the Poisson problem and linear elasticity are presented.

math.NA↗

arXiv2024

Separable DeepONet: Breaking the Curse of Dimensionality in Physics-Informed Machine Learning

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the absence of labeled datasets, we utilize the PDE residual loss to learn the physical system, an approach known as physics-informed DeepONet. This method faces significant computational challenges, primarily due to the curse of dimensionality, as the computational cost increases exponentially with finer discretization. In this paper, we introduce the Separable DeepONet framework to address these challenges and improve scalability for high-dimensional PDEs. Our approach involves a factorization technique where sub-networks handle individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix. By using forward-mode automatic differentiation, we further optimize the computational cost related to the Jacobian matrix. As a result, our modifications lead to a linear scaling of computational cost with discretization density, making Separable DeepONet suitable for high-dimensional PDEs. We validate the effectiveness of the separable architecture through three benchmark PDE models: the viscous Burgers equation, Biot's consolidation theory, and a parametrized heat equation. In all cases, our proposed framework achieves comparable or improved accuracy while significantly reducing computational time compared to conventional DeepONet. These results demonstrate the potential of Separable DeepONet in efficiently solving complex, high-dimensional PDEs, advancing the field of physics-informed machine learning.

cs.LG↗

arXiv2023

Rheological Analysis and Evaluation of Measurement Techniques for the Curing Polymethylmethacrylate Bone Cement in Vertebroplasty

Vertebroplasty is a minimally invasive surgical procedure used to treat vertebral fractures, which conventionally involves injecting polymethylmethacrylate (PMMA) bone cement into the fractured vertebra. A common risk associated with vertebroplasty is cement leaking out of the vertebra during the injection, which may occur due to a lack of understanding of the bone cement's complex flow behavior. Therefore, experiments to quantify the cement's flow properties are necessary for understanding and proper handling of the bone cement. In this study, we aimed to characterize the behavior of the PMMA bone cement in its curing stages to obtain parameters that govern the flow behavior during the injection. We used rotational and oscillatory rheometry for our measurements, as well as a custom-made injector setup that replicated a typical vertebroplasty setting. Our results showed that the complex viscoelastic behavior of the bone cement is significantly affected by deformations and temperature. We found that the results from rotational tests, often used for characterizing the bone cement, are susceptible to measurement artifacts caused by wall slip and "ridge"-like formations in the test sample. We also found the Cox-Merz rule to be conditionally valid, which affects the use of oscillatory tests to obtain shear-thinning characteristics for the bone cement. Our findings identify important differences in the measured flow behavior of PMMA bone cement when assessed by different rheological methods, understanding which is crucial for its risk-free usage in downstream medical applications.

cond-mat.soft↗

arXiv2022

A continuum mechanical porous media model for vertebroplasty: Numerical simulations and experimental validation

The outcome of vertebroplasty is hard to predict due to its dependence on complex factors like bone cement and marrow rheologies. Cement leakage could occur if the procedure is done incorrectly, potentially causing adverse complications. A reliable simulation could predict the patient-specific outcome preoperatively and avoid the risk of cement leakage. Therefore, the aim of this work was to introduce a computationally feasible and experimentally validated model for simulating vertebroplasty. The developed model is a multiphase continuum-mechanical macro-scale model based on the Theory of Porous Media. The related governing equations were discretized using a combined Finite Element - Finite Volume approach by the so-called Box discretization. Three different rheological upscaling methods were used to compare and determine the most suitable approach for this application. For validation, a benchmark experiment was set up and simulated using the model. The influence of bone marrow and parameters like permeability, porosity, etc., was investigated to study the effect of varying conditions on vertebroplasty. The presented model could realistically simulate the injection of bone cement in porous materials when used with the correct rheological upscaling models, of which the semi-analytical averaging of the viscosity gave the best results. The marrow viscosity is identified as the crucial reference to categorize bone cements as high- or low- viscosity in the context of vertebroplasty. It is confirmed that a cement with higher viscosity than the marrow ensures stable development of the injection and a proper cement interdigitation inside the vertebra.

physics.flu-dyn↗

arXiv2020

Least Squares Finite Element Method for Hepatic Sinusoidal Blood Flow

The simulation of complex biological systems such as the description of blood flow in organs requires a lot of computational power as well as a detailed description of the organ physiology. We present a novel Least-Squares discretization method for the simulation of sinusoidal blood flow in liver lobules using a porous medium approach for the liver tissue. The scaling of the different Least-Squares terms leads to a robust algorithm and the inherent error estimator provides an efficient refinement strategy.

math.NA↗