Chalmers Conferences, 9th European Conference on Mathematical and Theoretical Biology

A multiscale analysis of tissue growth and nutrient transport in vitro
Reuben O'Dea

Last modified: 2014-03-28


The derivation of continuum models which represent underlying discrete or microscale phenomena is emerging as an important part of mathematical biology: integration between subcellular, cellular and tissue-level behaviour is crucial to understanding tissue growth and mechanics. For this reason, various multiscale (or homogenisation) techniques have been employed to derive continuum models directly from underlying microscale systems. Such methods have been widely used to study (e.g.) porous and poroelastic materials; however, a distinguishing feature of biological tissue is its ability continuously to remodel in response to local environmental cues. Here, a new macroscale description is derived, employing a multiple-scale homogenisation method to accommodate explicitly the influence of the underlying microscale tissue structure, and its evolution, on the macroscale dynamics. The model is broadly applicable to cell population growth within tissue engineering scaffolds, such as those employed in perfusion bioreactors. Illustrative numerical solutions are presented to indicate the influence of microscale growth on model dynamics; via the incorporation of micro CT data from an experimentally-relevant scaffold, the influence of scaffold geometry in determining flow dynamics and nutrient delivery to cells seeded in such structures is highlighted.


multiscale homogenisation; porous flow; tissue engineering