University of Heidelberg, Applied Analysis Seminar
Thu 01.07.2021
13:30, posted in Applied Analysis
Dr. Mariya Ptashnyk (Heriot-Watt University, Edinburgh)
Multiscale modelling and analysis of transport processes in biological tissues
Online via Zoom

In the first part of the talk, we will consider oxygen transport in a biological tissue.
We shall focus on the two-layer tissue architecture in the context of abdominal tissue flaps that are commonly used for reconstructive surgery. We will consider the arterial and venous microstructure within the tissue and apply two-scale convergence and unfolding operator methods to derive macroscopic equations, which involve different unit cell geometries in the two distinct tissue layers (skin layer and fat tissue) to account for different arterial branching patterns.

In the second part of the talk, we shall consider multiscale analysis and simulations for a coupled system of nonlinear bulk-surface partial differential equations modelling the dynamics of signalling molecules in the inter- and intra-cellular spaces and of cell membrane receptors.

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