Modeling and Parameter Subset Selection for Fibrin Polymerization Kinetics with Applications to Wound Healing

Bayesian inference informed by parameter subset selection for a minimal PBPK brain model

Physiologically based pharmacokinetic (PBPK) models use a mechanistic approach to delineate the processes of the absorption, distribution, metabolism and excretion of biological substances in various species. These models generally comprise coupled systems of ordinary differential equations involving multiple states and a moderate to a large number of parameters. Such models contain compartments corresponding to various organs or tissues in the body. Before employing the models for treatment, the quantification of uncertainties for the parameters, based on a priori information or data for a specific response, is necessary. This requires the determination of identifiable parameters, which are uniquely determined by data, and uncertainty analysis based on frequentist or Bayesian inference. We introduce a strategy to integrate parameter subset selection, based on identifiability analysis, with Bayesian inference. This approach further refines the subset of identifiable parameters, quantifies parameter and response uncertainties, enhances model prediction and reduces computational cost.This article is part of the theme issue 'Uncertainty quantification for healthcare and biological systems (Part 1)'.

Application and reduction of a nonlinear hyperelastic wall model capturing ex vivo relationships between fluid pressure, area, and wall thickness in normal and hypertensive murine left pulmonary arteries

Pulmonary hypertension is a cardiovascular disorder manifested by elevated mean arterial blood pressure (>20 mmHg) together with vessel wall stiffening and thickening due to alterations in collagen, elastin, and smooth muscle cells. Hypoxia-induced (type 3) pulmonary hypertension can be studied in animals exposed to a low oxygen environment for prolonged time periods leading to biomechanical alterations in vessel wall structure. This study introduces a novel approach to formulating a reduced order nonlinear elastic structural wall model for a large pulmonary artery. The model relating blood pressure and area is calibrated using ex vivo measurements of vessel diameter and wall thickness changes, under controlled pressure conditions, in left pulmonary arteries isolated from control and hypertensive mice. A two-layer, hyperelastic, and anisotropic model incorporating residual stresses is formulated using the Holzapfel-Gasser-Ogden model. Complex relations predicting vessel area and wall thickness with increasing blood pressure are derived and calibrated using the data. Sensitivity analysis, parameter estimation, subset selection, and physical plausibility arguments are used to systematically reduce the 16-parameter model to one in which a much smaller subset of identifiable parameters is estimated via solution of an inverse problem. Our final reduced one layer model includes a single set of three elastic moduli. Estimated ranges of these parameters demonstrate that nonlinear stiffening is dominated by elastin in the control animals and by collagen in the hypertensive animals. The pressure-area relation developed in this novel manner has potential impact on one-dimensional fluids network models of vessel wall remodeling in the presence of cardiovascular disease.