Mathematical assessment of variability in respiratory airflow patterns

Abstract

Mathematical approach was used to study and determine unsteady respiratory airflow dynamics for inspiratory and expiratory breathing cycles and to analyze pulmonary data under different levels of ventilatory conditions. The work involved acquiring and processing of respiratory airflow patterns from healthy subjects under varying levels of induced obstruction. A set of mathematical equations based on the Fourier series model were developed to describe the airflow patterns. Coefficients obtained from the Fourier series model were evaluated to obtain their ranges of values for different levels of ventilations. The goal to assess the airflow mechanics is approached by numerical modeling of the respiratory air- flow network. Graphical methods were used to evaluate the goodness of fit and their statistics including the SSE, R-Square, Adj R-Sqr and RMSE. Basic statistical analysis which includes the mean and standard deviation for the airflow signals was obtained. In order to study the variability of airflow limita- tions, different size mouthpieces were used.