Robust Parameters Identification of the Oxygen Kinetics by the Method of Nonlinear Least Squares

Abstract

The purpose of the work is identify the parameters that characterizes the curve of oxygen absorption rate of a person during controlled physical activity. The exercise load is constant and its intensity is classified as heavy or severe. The values of the oxygen absorption rate were measured experimentally through the process of pulmonary ventilation.
The oxygen absorption rate is modeled by sequential exponential functions. Each exponential is identified as a distinct physiological stage and represents the body’s response to increased energy metabolism. The dynamic response of pulmonary gas exchange reflects the integrated response of the ventilator, cardiovascular, and neuromuscular systems to the exercise challenge.
The characterization of the curve for each patient requires the identification of number of phases developed during the exercise and identification of the instants when the change of phases occurs. The parameter identification takes into account the uncertainties of the process. The identification is made by the nonlinear least squares method of Levenberg-Marquardt and stochastic descent. The curve of oxygen absorption rate can have three phases each one modeled by an exponential. The process is continuous and an robust optimization problem is solved to determine the instants of phase change.