A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation. (26th July 2019)

• Record Type: Journal Article
• Authors: Murphy, R. J.; Buenzli, P. R.; Baker, R. E.; Simpson, M. J.
• Is Part Of: Proceedings. Volume 475:Number 2227(2019)
• Publication Date: 2019-07-26
• Subjects: cell-based model -- partial differential equation -- continuum-limit -- multi-scale -- discrete model; Physical sciences -- Periodicals; Engineering -- Periodicals; Mathematics -- Periodicals; 500
• DOI: 10.1098/rspa.2018.0838
• Languages: English
• ISSNs: 1364-5021

Abstract

Abstract : 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. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.