Estimation of time-varying respiratory mechanical parameters by recursive least squares

Continuous estimation of time-varying respiratory mechanical parameters is required to fully characterize the time course of bronchoconstriction. To achieve such estimation, we developed an estimator that uses the recursive linear least-squares algorithm to fit the equation Ptr = RV + EV + K to measurements of tracheal pressure (Ptr) and flow (V). The volume (V) is obtained by numerical integration of V. The estimator has a finite memory with length into the past at each point in time that varies inversely with the difference between the current measurement of Ptr and that predicted by the model, to allow the algorithm to track rapidly varying parameters (R, E, and K). V usually exhibits significant drift and must be corrected. Of the several correction methods investigated, subtraction of the recursively weighted average of V before integration to V was found to perform best. The estimator was tested on simulated noisy data where it successfully followed a fivefold increase in R and a twofold increase in E occurring over 10 s. Three dogs and two cats were anesthetized, paralyzed, tracheostomized, and challenged with a bolus of methacholine (approximately 13 mg/kg iv). Increases of 3- to 10-fold were observed in R and 2- to 3-fold in E, beginning within 10-40 s after the bolus injection. In some animals we found that the increase in E occurred more slowly than that in R, which the V signal suggested was due to dynamic hyperinflation of the lungs. These results demonstrate that our recursive estimator is able to track rapid changes in respiratory mechanical parameters during bronchoconstrictor challenge.