PT  - JOURNAL ARTICLE
AU  - R. J. Murphy
AU  - P. R. Buenzli
AU  - R. E. Baker
AU  - M. J. Simpson
TI  - An individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation
AID  - 10.1101/485276
DP  - 2018 Jan 01
TA  - bioRxiv
PG  - 485276
4099  - http://biorxiv.org/content/early/2018/12/03/485276.short
4100  - http://biorxiv.org/content/early/2018/12/03/485276.full
AB  - Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. Applications of the model are discussed, including determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.