Estimation of delay times in biological systems

The problem of delay time estimation in biological systems is addressed with the focus on practical applicability of methods. Four delay time estimators are described: a cross correlation method and three increasingly sophisticated interpretations of the phase spectrum, ranging from a pointwise interpretation of the phase spectrum in terms of a delay to a Hilbert transform method. The four methods are compared through simulation studies showing that, in general, the Hilbert transform method performs best. The methods are then used to estimate delay times in three physiological systems: vestibular stimulation, cerebral autoregulation, and human orthostatic tremor. In all three cases, the Hilbert transform method yields the best results, leading in some cases to physiologically more sensible interpretations of experiments than the other methods.