Applied Mathematics Colloquium – Mansoor Haider, North Carolina State University

Title: Local identifiability analysis approaches for mathematical modeling of biological soft tissues

Speaker: Mansoor Haider, Department of Mathematics, North Carolina State University

Abstract: The accurate estimation, interpretation, and elimination of parameters in mathematical models depends on the structure of the model with respect to its parameters and the responses for which data is available. For many models of biological systems, data is available for only a limited number of responses, compared to the overall size of the model. This leads to non-identifiability of model parameters; these parameters cannot be uniquely estimated from the data or are noninfluential in affecting a particular model response. Techniques for local sensitivity-based identifiability analysis will be presented for a variety of models of biological soft tissues. These techniques are based on a decomposition of the sensitivity matrix. Approaches will be illustrated in the context of three applications: (i) reaction kinetics for enzyme-mediated polymerization of fibrinogen into insoluble fibrin matrix in a wound healing system, (ii) a biomechanical model of arterial wall deformation in pulmonary hypertension, and (iii) a PBPK (compartmental) model for antibody concentrations in brain tissue. The tailoring of techniques for local identifiability analysis will be discussed for each model, including approaches in the presence or absence of data.