In Reply:

—We thank Dr. Rampil for bringing up the matter of experiment design. Although in some circumstances system identification using a single fixed-size step change input may indeed suffer from the limitations described, our approach is very close to optimal. In our study, 1we applied one or more steps in and out of end-tidal anesthetic concentration of variable duration depending on the observed dynamics of the bispectral index (BIS; see fig. 3).

When there is no information available on applicable model structures, a pseudorandom binary sequence can be a useful test signal, but the choice of length and switching interval need to be guided by step–response data. 2However, when information on applicable model structures is available, it can be used to design more optimal test signals. 2,3 

With the anesthetic literature in mind, it is reasonable to assume a nonlinear relation between effect-site concentration and electroencephalographic (EEG) effect parameter and that there is a lag between end-tidal concentration and effect that is mainly determined by the blood–brain tissue partition coefficient. The nonlinear relation can be identified from step–response data because the effect-site concentration does not change in a stepwise fashion.

For the proposed model and the estimated population parameters, and taking into account the experimental conditions, we constructed a posteriori  an optimal binary sequence by maximizing the determinant of the information matrix. 3The information gained by using the optimal input signal (which deviated only minimally from step inputs) instead of the optimal single-step signal is negligible in the light of interindividual variability and the fact that step durations depended on the occurrence of near steady states in measured bispectral index (BIS) values. It is of interest to note that for a nonlinear model of the ventilatory controller consisting of a slow and a fast compartment, Bellville et al.  4found that step changes provided the most information on the values of the model parameters.

Olofsen E, Dahan A: The dynamic relationship between end-tidal sevoflurane and isoflurane concentrations and bispectral index and spectral edge frequency of the electroencephalogram. A NESTHESIOLOGY 1999; 90:1345–53
Godfrey K: Introduction to perturbation signals for time-domain system identification, Perturbation signals for system identification. Edited by Godfrey K. New York, Prentice Hall, 1993, pp 1–59
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Bellville JW, Ward DS, Wiberg D. Respiratory system. Modelling and Identification, Systems and Control Encyclopedia: Theory, Technology, Applications. Edited by Singh HG. Oxford, Pergamon Press, 1988, pp 4055–62