An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix

Gianluca D'Antonio; Paul Macklin; Luigi Preziosi; Gianluca D'Antonio; Paul Macklin; Luigi Preziosi

doi:10.3934/mbe.2013.10.75

Mathematical Biosciences and Engineering

2013, Volume 10, Issue 1: 75-101. doi: 10.3934/mbe.2013.10.75

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An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix

1.
Politecnico di Torino, Torino, 10124
2.
Center for Applied Molecular Medicine, Keck School of Medicine, University of Southern California, Los Angeles, 90033, CA
3.
Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, 10124

Received: 01 March 2012 Accepted: 29 June 2018 Published: 01 December 2012
MSC : 65C20, 74B99, 74C99, 74D99, 92C05, 92C10, 74L15.

The basement membrane (BM) and extracellular matrix (ECM) play critical roles in developmental and cancer biology, and are of great interest in biomathematics. We introduce a model of mechanical cell-BM-ECM interactions that extends current (visco)elastic models (e.g. [8,16]), and connects to recent agent-based cell models (e.g. [2,3,20,26]). We model the BM as a linked series of Hookean springs, each with time-varying length, thickness, and spring constant. Each BM spring node exchanges adhesive and repulsive forces with the cell agents using potential functions. We model elastic BM-ECM interactions with analogous ECM springs. We introduce a new model of plastic BM and ECM reorganization in response to prolonged strains, and new constitutive relations that incorporate molecular-scale effects of plasticity into the spring constants. We find that varying the balance of BM and ECM elasticity alters the node spacing along cell boundaries, yielding a nonuniform BM thickness. Uneven node spacing generates stresses that are relieved by plasticity over long times. We find that elasto-viscoplastic cell shape response is critical to relieving uneven stresses in the BM. Our modeling advances and results highlight the importance of rigorously modeling of cell-BM-ECM interactions in clinically important conditions with significant membrane deformations and time-varying membrane properties, such as aneurysms and progression from in situ to invasive carcinoma.

Keywords:

Citation: Gianluca D'Antonio, Paul Macklin, Luigi Preziosi. An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix[J]. Mathematical Biosciences and Engineering, 2013, 10(1): 75-101. doi: 10.3934/mbe.2013.10.75

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Abstract

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