modeling in physiology Breath - to - breath relationships between respiratory cycle variables in humans at fixed end - tidal PCO 2 and PO 2

Busso, Thierry, Pei-Ji Liang, and Peter A. Robbins. Breath-to-breath relationships between respiratory cycle variables in humans at fixed end-tidal PCO2 and PO2. J. Appl. Physiol. 81(5): 2287–2296, 1996.—This study examined the statistical properties of breath-to-breath variations in the inspiratory and expiratory volumes and times during rest and light exercise. Sixty data sets were analyzed. Initial data and residuals after fitting time-series models were examined for 1) sustained periodicities with use of spectral analysis, 2) temporal changes in signal power with use of evolutionary spectral analysis, and 3) autoand cross correlations with use of a portmanteau test. The major findings were as follows: 1) no sustained periodic components were detected; 2) temporal changes in signal power were normally present, but these did not affect significantly the results from time-series modeling; 3) for all variables, a simple autoregressive moving average (ARMA) AR1MA1 model generally described the autocorrelation; 4) considerable cross correlation remained between residuals from the AR1MA1 model; 5) relationships between variables could be described by using a multivariate timeseries model; 6) residual fluctuations in end-tidal PCO2 had little influence; and 7) responses were broadly similar between rest and exercise, although some quantitative differences were found. The multivariate model provides a description of the structure of the interrelationships between cycle variables in a quantitative and a qualitative form.