Least squares estimation of respiratory system parameters

Abstract

In the estimation of physiological parameters, visual fitting of experimental data has the obvious drawback that a given “best-fit curve” is not equally satisfying to every observer. In this article an iterative, weighted nonlinear least squares method of parameter estimation is formulated. It provides a systematic procedure for the reduction of physiological data and obviates the need for visual fitting, which is subjective. The goodness of fit is evaluated in terms of a weighted least squares error criterion. This method is applied to estimate the parameters of a portion of the human respiratory control system. In particular, the subsystem examined is that relating tidal volume to alveolar CO 2 fraction. It is modeled by a transfer function that involves five parameters: two gain constants, two time constants, and a pure time delay; and is of the same form as that determined in an earlier study involving a visual fit. The estimation is based on sinusoidal steady-state magnitude and phase data for two human subjects. The details of the numerical procedure are discussed and possible extensions are indicated. The present method improves the goodness of fit by a factor of 3 to 4. Values of the parameters changed slightly, but not insignificantly compared with those previously