Growth curve analysis for cardio-pulmonary responses to physical exercise

Abstract

This dissertation investigates the fitting of growth curves to cardio-pulmonary responses on a treadmill. The practical application is based on two approaches in the growth curve literature, namely the Richards family of growth curves and the polynomial of Potthoff and Roy, and Rao and Khatri. The first part of this dissertation deals with the theoretical background to the two approaches. Derivations of the Richards family of growth curves are considered, distinguishing characteristics discussed, and the various estimation techniques employed in the fitting of these nonlinear growth curves. The different types of polynomials in the Potthoff and Roy model as well as the Raa-Khatri model are considered. The fitting of these growth curves as well as the hypothesis tests involved in choosing the correct degree of polynomial is also examined. The second part of this dissertation deals with the data taken from an exercise test examining cardia-pulmonary responses. The two approaches in the first part of the dissertation are used to fit the data to a specific function. The best fitting functions characterizing the data are chosen, and physiological interpretations of these results are provided. Experimental design difficulties are also discussed.