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 signicant membrane deformations and time-varying membrane properties, such as aneurysms and progression from in situ to invasive carcinoma.
|Titolo:||An agent-based model for elasto-plastic mechanical interactions between cells, basement membrane and extracellular matrix|
|Data di pubblicazione:||2013|
|Digital Object Identifier (DOI):||10.3934/mbe.2013.10.75|
|Appare nelle tipologie:||1.1 Articolo in rivista|