Estimation of expiratory time constants via fuzzy clustering

Objective. In mechanically ventilated patients the expiratorytime constant provides information about respiratory mechanics. In thepresent study a new method, fuzzy clustering, is proposed to determine expiratory time constants. Fuzzy clustering differs from other methods since it neither interferes with expiration nor presumes any functional relationship between the variables analysed. Furthermore, time constantbehaviour during expiration can be assessed, instead of an average timeconstant. The time constants obtained with fuzzy clustering are comparedto time constants conventionally calculated from the same expirations.
Methods. 20 mechanically ventilated patients, including 10 patients with COPD, were studied. The data of flow, volume and pressure were sampled. From these data, four local linear models were detected by fuzzy clustering. The time constants (τ) of the local linear models (clusters) were calculated by a least-squares technique. Time constant behaviour was analysed. Time constants obtained with fuzzy clustering were compared to time constants calculated from flow-volume curves usinga conventional method.
Results. Fuzzy clustering revealed twopatterns of expiratory time constant behaviour. In the patients with COPD an initial low time constant was found (mean τ 1: 0.33 s, SD0.21) followed by higher time constants; mean τ 2: 2.00 s (SD0.91s), mean τ 3: 3.45 s (SD 1.44) and mean τ 4: 5.47 s (SD2.93). In the other patients only minor changes in time constants werefound; mean τ 1: 0.74 s (SD 0.30), mean τ 2: 0.90 s (SD 0.23),mean τ 3: 1.04 s (SD 0.42) and mean τ 4: 1.74 s (SD 0.78). Both the pattern of expiratory time constants, as well as the time constants calculated from the separate clusters, were significantly different between the patients with and without COPD. Time constants obtained with fuzzy clustering for cluster 2, 3 and 4 correlated well with timeconstants obtained from the flow-volume curves.
Conclusions. In mechanically ventilated patients, expiratory time constant behaviour can be accurately assessed by fuzzy clustering. A good correlation was found between time constants obtained with fuzzy clustering and time constants obtained by conventional analysis. On the basis of the time constants obtained with fuzzy clustering, a clear distinction was made between patients with and without COPD.