Scipedia: 10th edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering (COUPLED PROBLEMS 2023)

Multiphysical modeling of soft-tissue stent interaction (Plenary Lecture)

Jesús Sánchez Pinedo — Thu, 16 Nov 2023 10:42:57 +0100

The efficacy of cardiological interventions, including the implantation of prostheses, is highly dependent on patient-specific immunohistology and can be enhanced with computational predictive tools. Therefore, an in silico replication of neointimal hyperplasia shall provide the necessary insights about the biochemical and cellular interactions within the vessel wall, and eventually address the risks of in-stent restenosis in a patient-specific manner. In this context, we set up a multiphysics framework considering key mediators of restenosis and couple them to a continuum mechanical vessel wall model. The governing set of coupled partial PDEs for the underlying mechanobiological system is solved via the finite element method and the results are compared to those obtained using a deep learning framework employing physics-informed neural networks (PINNs). Another interesting cardiological intervention-related problem is the maturation of tissue-engineered cardiovascular implants wherein the evolution of the collagen density affects the tissue’s mechanical behavior. The model we present allows us to predict the evolution of collagen density within textile-reinforced heart valves.

A coupled model for the formation of Atherosclerosis due to inflammation processes

Jesús Sánchez Pinedo — Thu, 16 Nov 2023 10:36:02 +0100

Atherosclerosis is a disease in blood vessels that often results in plaque formation and lumen narrowing. It is an inflammatory response of the tissue caused by disruptions in the vessel wall nourishment. Blood vessels are nourished by nutrients originating from the blood of the lumen. In medium-sized and larger vessels, nutrients are additionally provided from outside through a network of capillaries called vasa vasorum. It has recently been hypothesized [1] that the root of atherosclerotic diseases is the malfunction of the vasa vasorum. This, so called outside-in-theory, is supported by a recently developed numerical model [2] accounting for the inflammation initiation in the adventitial layer of the blood vessel. Building on the previous findings, this presentation proposes an extended material model for atherosclerosis formation that is based on the outside-in-theory. Beside the description of growth kinematics and nutrient diffusion, the roles of monocytes, macrophages, foam cells, smooth muscle cells and collagen are accounted for in a nonlinear continuum mechanics setting. Cells are activated due to a lack of vessel wall nourishment and proliferate, migrate, differentiate and synthesize collagen, leading to the formation of a plaque. Numerical studies show that the onset of atherosclerosis can qualitatively be reproduced. Thus, the in silico model backs the new theory.

Reduced-Order Models in Bayesian solvers for inverse problems

Jesús Sánchez Pinedo — Thu, 16 Nov 2023 10:33:31 +0100

Challenging inverse problems aim at identifying large sets of parameters using data from different sources and diverse accuracy. This is the case of data assimilation for geophysical crust dynamics, were the number of parameters to identify amounts to thousands. In this context, Bayesian inverse solvers combined with Markov-Chain Monte Carlo (MCMC) strategies are an affordable strategy, accounting for the uncertainty of the input data and quantifying also uncertainty of the output. Despite the efficiency of the MCMC approach, the direct problem has to be evaluated an extremely large number of times, many (after the burn-in phase) with the input parameters lying in a narrow range. This is the ideal situation for Reduced-Order Models (ROM): many repeated queries to the model corresponding to parameters lying in a limited manifold. Thus, we aim at applying ROM to large-dimensional parametric forward problems. In this case, it is important optimising the dimensionality reduction technique inherent to the ROM strategy. For instance, Proper Orthogonal Decomposition (POD) is associated with a linear Principal Component Analysis (PCA). PCA is linear in the sense that assumes the reduceddimension manifold to be Euclidean. We explore using kernel PCA (kPCA) to further reduce the dimension, thus devising a kPOD approach. Different options to select physically inspired kernels, based on the knowledge of the problem under consideration, are discussed. Moreover, the computational strategy to explore the feature space (the reduced-dimensional space) is also discussed.

Model Order Reduction in the Parametrized Multi-Scale and Coupled Setting

Jesús Sánchez Pinedo — Thu, 16 Nov 2023 10:29:32 +0100

A New Paradigm for Multiphysics Simulation: Its Initial Application to Fluid-Structure Interaction

Jesús Sánchez Pinedo — Thu, 16 Nov 2023 10:15:58 +0100

A new paradigm for simulating mulitipysics systems is presented with initial focus on FluidStructure Interaction (FSI). For each single-field governing equations adopting Lagrangian frame, a projection operator couples the coupled field without invoking interface Lagrange multipliers. For FSI problems where fluids are modeled by employing ALE kinematics, a physics-based interface equations are formulated as an independent set of third-field equations. This approach facilitates the connection of non-matching meshes and provides consistent dynamic equations of motion for the interface that can be integrated in parallel. The proposed simulation paradigm adopts stand-alone software modules for the fluid and the structure, which is coupled through a third interface system treating their interaction, which preserves the modularity of the singlediscipline software modules. The new FSI simulation paradigm is demonstrated as applied to several FSI benchmark examples, demonstrating its efficiency and accuracy. Extension of the proposed new multiphysics simulation paradigm to treat other multiplhysics problems are suggested.

Coupled problems in bio-inspired robotics

Jesús Sánchez Pinedo — Thu, 09 Nov 2023 11:48:39 +0100