Mathematical Biosciences and Engineering (MBE)

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

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

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Gianluca D'Antonio - Politecnico di Torino, Torino, 10124, Italy (email)
Paul Macklin - Center for Applied Molecular Medicine, Keck School of Medicine, University of Southern California, Los Angeles, 90033, CA, United States (email)
Luigi Preziosi - Dipartimento di Scienze Matematiche, Politecnico di Torino, Torino, 10124, Italy (email)

Abstract: 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:  Agent-based model, basement membrane, extracellular matrix, biomechanics, elasto-plasticity.
Mathematics Subject Classification:  65C20, 74B99, 74C99, 74D99, 92C05, 92C10, 74L15.

Received: March 2012;      Accepted: July 2012;      Available Online: December 2012.