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 determineexpiratory time constants. Fuzzy clustering differs from other methodssince it neither interferes with expiration nor presumes any functionalrelationship 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 10patients with COPD, were studied. The data of flow, volume and pressurewere sampled. From these data, four local linear models were detected byfuzzy clustering. The time constants (τ) of the local linear models(clusters) were calculated by a least-squares technique. Time constantbehaviour was analysed. Time constants obtained with fuzzy clusteringwere 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 withCOPD 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). Boththe pattern of expiratory time constants, as well as the time constantscalculated from the separate clusters, were significantly differentbetween the patients with and without COPD. Time constants obtained withfuzzy clustering for cluster 2, 3 and 4 correlated well with timeconstants obtained from the flow-volume curves. Conclusions.Inmechanically ventilated patients, expiratory time constant behaviour canbe accurately assessed by fuzzy clustering. A good correlation was foundbetween time constants obtained with fuzzy clustering and time constantsobtained by conventional analysis. On the basis of the time constantsobtained with fuzzy clustering, a clear distinction was made betweenpatients with and without COPD.