FITTING CURVES TO HUMAN RESPIRATORY DATA

Records of gas flow during breathing are cyclical, with the cycles var ying in duration. The shape of these cycles may change with the intens ity of respiratory stimulation or the development of respiratory disea se, but currently research is hampered by the lack of a fully satisfac tory technique for determining the shape of a typical cycle. The appro ach adopted here is to replace the time series by a 'phase diagram', p lotting the time integral of flow against flow itself. Principal curve s are then fitted. These are curves 'through the middle of the data' w hich were introduced by Hastie and Stuetzle. The shapes of these curve s are compared, either directly or after reconstructing an average cyc le corresponding to each fitted curve. This has the advantage that the shape of the waveform is separated from the amplitude, and from the d uration of the breath. A disadvantage is that periods of zero flow are lost, and the reconstructed average cycle may show irregularities at points near zero flow as a result. In practice, the methodology showed clear differences in shape between the protocols, gave reasonable ave rage cycles and ordered the waveform shapes according to the hardness of breathing induced by the protocols.