Overview

Physiological systems usually consist of several components that may occur on different length scales, different time scales and be governed by different types of physics. Thus to capture this type of complex behaviour using computational models these components must be coupled. This coupling typically produces interesting and challenging computational issues such as maintenance of stability; and the accurate representation of all underlying mechanisms at different scales in the coupled model.

These issues and ideas are developed in this course using the example of the heart, probably the most advanced example of a coupled multi-physics model.

Synopsis

1. Introduction to mathematical models describing the fundemental function of the heart: electrical conduction; biochemical reactions; soft tissue deformation; and fluid flow. Simple techniques for the numerical solution of the governing equations for each component.
2. Outline of coupled approaches. Example demonstrating the dangers of naive coupling of the numerical techniques described earlier in the course. Derivation of stable numerical schemes for coupled problems in cardiac physiology. Implementation of coupled multi-physics models.
3. Error analysis for coupled problems occurring on different length and time scales. Effect of using different computational meshes for different components of the whole model.

Prerequisites

Prerequisites for this course are the B1 course on Finite Element Methods for Partial Differential Equations.