Mansoor Haider | Dept. of Mathematics & Biomathematics Graduate Program, North Carolina State University, Raleigh, NC, USA
Mathematical models for extracellular matrix regeneration and remodeling in biological soft tissues
Many biological soft tissues exhibit complex interactions between passive (biophysical, biomechanical) mechanisms, and active physiological responses. These interactions affect the ability of the tissue to remodel in order to maintain homeostasis, or govern alterations in tissue properties with aging and disease. In tissue engineering applications, such interactions also influence the relationship between system design parameters and functional outcomes. In this talk, I will discuss two mathematical modeling problems in this area. The first problem addresses biosynthesis and linking of articular cartilage extracellular matrix in cell-seeded scaffolds. A mixture approach is employed to, inherently, capture effects of evolving porosity in the tissue-engineered construct. We develop a hybrid model in which cells are represented, individually, as inclusions within a continuum reaction-diffusion model formulated on a representative domain. The second problem addresses structural remodeling of cardiovascular vessel walls in the presence of pulmonary hypertension (PH). As PH advances, the relative composition of key wall constituents (collagen, elastin, smooth muscle cells) becomes altered. The ensuing wall stiffening increases blood pressure which, in turn, can induce further vessel wall remodeling. Yet, the manner in which these alterations occur is not well understood. I will discuss structural continuum mechanics models that can incorporate PH-induced remodeling of the vessel wall into 1D fluid-structure models of pulmonary cardiovascular networks. A Holzapfel-Gasser-Ogden (HGO)-type hyperelastic constitutive law for combined bending, inflation, extension and torsion of a nonlinear elastic tube is employed. The model is used to formulate nonlinear relations between blood pressure and vessel wall cross-sectional area that reflect structural alterations with advancing PH. For both problems, model calibration and validation in the context of data from in vitro experiments will also be discussed.