Room 12, Brauer Hall
Mansoor A. Haider
Dept. of Mathematics & Biomathematics Graduate Program
North Carolina State University
and calibration of mathematical models for matrix accumulation and remodeling
in biological soft tissues
Many biological soft tissues exhibit interactions between passive (e.g. biophysical, biomechanical) mechanisms and active physiological responses that help maintain homeostasis, or influence alterations with aging and disease. In tissue engineering applications, such interactions often govern relationships between system design variables and functional outcomes. Model calibration can be challenging due to coupled interactions at diverse scales and constraints on collection of data measuring disease progression or functional properties of tissue constructs. Two mathematical modeling problems are presented in this context. The first problem addresses biosynthesis, transport and linking of extracellular matrix in cell-seeded scaffolds for cartilage tissue engineering applications. A mixture approach is employed to, inherently, capture effects of evolving porosity. A hybrid model is developed 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 wall constituents 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 and thickening increases blood pressure which, in turn, can induce further vessel wall remodeling. Yet, the manner in which these alterations occur is not well understood. Structural continuum mechanics models are presented that are tailored to incorporating PH-induced wall remodeling into 1D fluids network models of pulmonary cardiovascular dynamics. A two-layer Holzapfel-Gasser-Ogden (HGO)-type hyperelastic constitutive law for a nonlinear elastic tube is employed. This modeling approach is used to formulate nonlinear relations between blood pressure and vessel wall cross-sectional area that can capture 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.