Piecewise nonlinear mixed-effects models for modeling cardiac function and assessing treatment effects

Mixed-effects model is an efficient tool for analyzing longitudinal data. The random effects in a mixed-effects model can be used to capture the correlations among repeated measurements within a subject. Mixed effects model can be used to describe individual response profile as well as population response profile. In this manuscript, we apply mixed-effects models to the repeated measurements of cardiac function variables including heart rate, coronary flow, and left ventricle developed pressure (LVDP) in the isolated, Langendorff-perfused hearts of glutathione s-transferase P1/P2 (GSTP) gene knockout and wild-type mice. Cardiac function was measured before and during ischemia/reperfusion injury in these hearts. To describe the dynamics of each cardiac function variable during the entire experiment, we developed piecewise nonlinear mixed-effects models and a change point nonlinear mixed effect model. These models can be used to examine how cardiac function variables were altered by ischemia/reperfusion-induced injury and to compare the cardiac function variable between genetically engineered (null or transgenic) mice and wild-type mice. Hypothesis tests were constructed to evaluate the impact of deletion of GSTP gene for different cardiac function variables. These findings provide a new application for mixed-effects models in physiological and pharmacological studies of the isolated Langendorff-perfused heart.