A Mathematical Model of HIF-1 Regulated Cellular Energy Metabolism - Bocharov, Gennady; Jäger, Willi; Knoch, Jonas; Neuss-Radu, Maria; Thiel, Manfred (Vietnam Journal of Mathematics, 2020)
In this study, we formulated a mathematical model of hypoxia-inducible factor 1 (HIF-1)mediated regulation of cellular energy metabolism describing the reprogramming of cellmetabolic processes from oxidative phosphorylation to glycolysis under reduced oxygenlevels. The model considers the dynamics of fifteen biochemical species and the protonconcentration with the underlying reaction processes localized in three intracellular com-partments, i.e. the cytoplasm, mitochondrion and nucleus. More than sixty parameters ofthe model were calibrated using both the published data and the system steady-state basedidentification procedure. The model was validated by generating predictions which could becompared to empirical observations. The model behaviors representing the cell metabolismswitching over in response to transitioning from a normoxic to hypoxic environment areconsistent with the current views of the role of HIF-1 in hypoxi
Keywords: Cellular energy metabolism; Oxidative phosphorylation; Glycolysis; Mathematical model; Regulation; Hypoxia-inducible factor 1

GLOBAL WELL-POSEDNESS AND NUMERICAL JUSTIFICATION OF AN EFFECTIVE MICRO-MACRO MODEL FOR REACTIVE TRANSPORT IN ELASTIC PERFORATED MEDIA - Knoch, Jonas; Gahn, Markus; Neuss-Radu, Maria (Multiscale Modeling & Simulation, 2025)
In this paper, we investigate an effective model for reactive transport in elastically deformable perforated media. This model was derived by formal asymptotic expansions in [J. Knoch, M. Gahn, M. Neuss-Radu, and N. Neuβ, Transp. Porous Media, 147 (2023), pp. 93-123], starting from a microscopic model consisting of a linear elasticity problem on a fixed domain, i.e., in the Lagrangian framework, and a problem for reactive transport on the current deformed domain, i.e., in the Eulerian framework. The effective model is of micro-macro type and features strong nonlinear couplings. Here, we prove global existence in time and uniqueness for the effective micro-macro model under a smallness assumption for the data of the macroscopic elasticity subproblem. Moreover, we show numerically the convergence of microscopic solutions towards the solution of the effective model when the scale parameter ε > 0 becomes smaller and smaller, and also compute the approximation error. The numerical justification of the formally derived effective micro-macro model is particularly important, as rigorous analytical convergence proofs or error estimates are not available so far. Finally, we compare the effective micro-macro model with alternative, simpler effective descriptions of transport in elastic perforated media.
CRIS-Team Scopus Importer:2025-03-14
Keywords: finite element method; global existence and uniqueness; perforated elastic medium; reactive transport; two-scale expansion

Multi-Scale Modeling and Simulation of Transport Processes in an Elastically Deformable Perforated Medium - Knoch, Jonas; Gahn, Markus; Neuss-Radu, Maria; Neuß, Nicolas (Transport in Porous Media, 2023)
In this paper, we derive an effective model for transport processes in periodically perforated elastic media, taking into account, e.g., cyclic elastic deformations as they occur in lung tissue due to respiratory movement. The underlying microscopic problem couples the deformation of the domain with a diffusion process within a mixed Lagrangian/Eulerian formulation. After a transformation of the diffusion problem onto the fixed domain, we use the formal method of two-scale asymptotic expansion to derive the upscaled model, which is nonlinearly coupled through effective coefficients. The effective model is implemented and validated using an application-inspired model problem. Numerical solutions for both, cell problems and macroscopic equations, are investigated and interpreted. We use simulations to qualitatively determine the effect of the deformation on the transport process.
CRIS-Team Scopus Importer:2023-01-20
Keywords: Diffusive transport; Evolving microstructure; Finite-element methods; Perforated elastic medium; Two-scale expansion