arXiv subjects

Marius Causemann

Publications and source records attributed to Marius Causemann.

3 recordsLinked to original sources

arXiv2025

Modeling and simulation of electrodiffusion in dense reconstructions of cerebral tissue

Excitable tissue is fundamental to brain function, yet its study is complicated by extreme morphological complexity and the physiological processes governing its dynamics. Consequently, detailed computational modeling of this tissue represents a formidable task, requiring both efficient numerical methods and robust implementations. Meanwhile, efficient and robust methods for image segmentation and meshing are needed to provide realistic geometries for which numerical solutions are tractable. Here, we present a computational framework that models electrodiffusion in excitable cerebral tissue, together with realistic geometries generated from electron microscopy data. To demonstrate a possible application of the framework, we simulate electrodiffusive dynamics in cerebral tissue during neuronal activity. Our results and findings highlight the numerical and computational challenges associated with modeling and simulation of electrodiffusion and other multiphysics in dense reconstructions of cerebral tissue.

physics.med-ph↗

arXiv2025

Parameter-robust preconditioners for a cell-by-cell poroelasticity model with interface coupling

This paper presents a scalable and robust solver for a cell-by-cell poroelasticity model, describing the mechanical interactions between brain cells embedded in extracellular space. Explicitly representing the complex cellular shapes, the proposed approach models both intracellular and extracellular spaces as distinct poroelastic media, separated by a permeable cell membrane which allows hydrostatic and osmotic pressure-driven fluid exchange. Based on a three-field (displacement, total pressure, and fluid pressure) formulation, the solver leverages the framework of norm-equivalent preconditioning and appropriately fitted norms to ensure robustness across all material parameters of the model. Scalability for large and complex geometries is achieved through efficient Algebraic Multigrid (AMG) approximations of the preconditioners' individual blocks. Furthermore, we accommodate diverse boundary conditions, including full Dirichlet boundary conditions for displacement, which we handle efficiently using the Sherman-Morrison-Woodbury formula. Our theoretical analysis is complemented by numerical experiments demonstrating the preconditioners' robustness and performance across various parameters relevant to realistic scenarios. A large scale example of cellular swelling on a dense reconstruction of the mouse visual cortex highlights the method's potential for investigating complex physiological processes such as cellular volume regulation in detailed biological structures.

math.NA↗

arXiv2024

Dense cell-by-cell systems of PDEs: approximation, spectral analysis, and preconditioning

In the present study, we consider the Extra-Membrane-Intra model (EMI) for the simulation of excitable tissues at the cellular level. We provide the (possibly large) system of partial differential equations (PDEs), equipped with ad hoc boundary conditions, relevant to model portions of excitable tissues, composed of several cells. In particular, we study two geometrical settings: computational cardiology and neuroscience. The Galerkin approximations to the considered system of PDEs lead to large linear systems of algebraic equations, where the coefficient matrices depend on the number $N$ of cells and the fineness parameters. We give a structural and spectral analysis of the related matrix-sequences with $N$ fixed and with fineness parameters tending to zero. Based on the theoretical results, we propose preconditioners and specific multilevel solvers. Numerical experiments are presented and critically discussed, showing that a monolithic multilevel solver is efficient and robust with respect to all the problem and discretization parameters. In particular, we include numerical results increasing the number of cells $N$, both for idealized geometries (with $N$ exceeding $10^5$) and for realistic, densely populated 3D tissue reconstruction.

math.NA↗