An analytical model of the vestibular evoked myogenic potential

The vestibular evoked myogenic potential (VEMP) can be modeled (scaling factors aside) as a convolution of the motor unit action potential (MUAP) of a representative motor unit, h(t), with the temporal modulation of the MUAP rate of all contributing motor units, r(t). Accordingly, the variance modulation associated with the VEMP can be modeled as a convolution of r(t) with the square of h(t). To get a deeper theoretical understanding of the VEMP phenomenon, a specific realization of this general model is investigated here. Both r(t) and h(t) were derived from a Gaussian probability density function (in the latter case taking the first derivative). The resulting model turned out to be simple enough to be evaluated analytically in the time and in the frequency domain, while still being realistic enough to account for the basic aspects of the VEMP generation. Perhaps the most significant conclusion of this study is that, in the case of noisy data, it may be difficult to falsify the hypothesis of a rate modulation of infinitesimal duration. Thus, certain aspects of the data (particularly the peak amplitudes) can be interpreted using a short-modulation approximation rather than the general model. The importance of this realization arises from the fact that the approximation offers an exceptionally simple and convenient way for a model-based interpretation of experimental data, whereas any attempt to use the general model for that purpose would result in an ill-posed inverse problem that is far from easy to solve.