Heart Rate Regulation: Modeling and Analysis

Abstract

Orthostatic stress tests, such as postural change from sitting to standing and head-up tilt, are common noninvasive procedures used to study short-term regulation of the cardiovascular system. The regulation involves a complex chain of reactions including regulation of heart rate, the topic of this dissertation. This dissertation focuses on developing and analyzing a mathematical model predicting heart rate regulation in response to changes in blood pressure during postural changes from sitting to standing and during head-up tilt. Two studies will be analyzed: 1) sit-to-stand versus head-up tilt and 2) healthy elderly versus elderly diabetic. Both studies are based on the same mathematical model predicting heart rate using a series of nonlinear delay differential equations with blood pressure as an input. The model is adapted to individuals by estimation of an optimal set of parameters and validated against clinical data.

Model complexity is a major obstacle to parameter estimation. Therefore, a focus of this research is on model reduction. In particular, our approach is to reduce the number of estimated parameters, but not at the expense of calibrating the model to data. We use a sensitivity analysis to rank the parameters from the most to least sensitive. The parameters that are insensitive are kept fixed during the parameter estimation procedure. In addition, we use subset selection to identify a subset of model parameters that are most identifiable. These modeling techniques allow us to identify a set of sensitive and identifiable parameters that could be estimated using nonlinear optimization procedures. The resulting model and parameter estimation techniques allow us to predict heart rate during sit-to-stand and head-up tilt. Using data from five healthy elderly subjects we are able to determine significant differences between the two groups of subjects. In the second study, a comparison of healthy elderly and subjects with diabetes during sit-to-stand reveals that the sympathetic response is delayed longer for subjects with diabetes than for healthy elderly subjects, and that vestibular, muscle sympathetic nerve, and central command response is more pronounced in healthy elderly subjects than in subjects with diabetes.