title: Estimation of expiratory time constants via fuzzy clustering.
abstract: OBJECTIVE
  In mechanically ventilated patients the expiratory time constant provides information about respiratory mechanics. In the present 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 constant behaviour during expiration can be assessed, instead of an average time constant. The time constants obtained with fuzzy clustering are compared to 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 (tau) 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 using a conventional method.
  
  
  RESULTS
  Fuzzy clustering revealed two patterns of expiratory time constant behaviour. In the patients with COPD an initial low time constant was found (mean tau1: 0.33 s, SD 0.21) followed by higher time constants; mean tau2: 2.00 s (SD 0.91s), mean tau3: 3.45 s (SD 1.44) and mean tau4: 5.47 s (SD 2.93). In the other patients only minor changes in time constants were found; mean tau1: 0.74 s (SD 0.30), mean tau2: 0.90 s (SD 0.23), mean tau3: 1.04 s (SD 0.42) and mean tau4: 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 time constants 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
authors.affiliation: Department of Pulmonary and Intensive Care Medicine, Erasmus Medical Centre Rotterdam, The Netherlands.
authors.forename: Marlies S
authors.initials: MS
authors.lastname: Lourens
authors.forename: Lejla
authors.initials: L
authors.lastname: Ali
authors.forename: Bart
authors.initials: B
authors.lastname: van den Berg
authors.forename: Anton F M
authors.initials: AF
authors.lastname: Verbraak
authors.forename: Jan M
authors.initials: JM
authors.lastname: Bogaard
authors.forename: Henk C
authors.initials: HC
authors.lastname: Hoogsteden
authors.forename: Robert
authors.initials: R
authors.lastname: Babuska
mesh_terms: D000328:Adult; D000368:Aged; D016000:Cluster Analysis; D005260:Female; D017143:Fuzzy Logic; D006801:Humans; D008297:Male; D008875:Middle Aged; D029424:Pulmonary Disease, Chronic Obstructive / Q000628:therapy; D012121:Respiration, Artificial; D015656:Respiratory Mechanics; D013997:Time Factors