Deconvolution of the vestibular evoked myogenic potential using the power spectrum of the electromyogram

BACKGROUND: The vestibular evoked myogenic potential (VEMP) can be modelled reasonably well by convolving two functions: one representing an average motor unit action potential (MUAP), the other representing the temporal modulation of the MUAP rate (rate modulation). It is the latter which contains the information of interest, and so it would be desirable to be able to estimate this function from a combination of the VEMP with some other data. As the VEMP is simply a stimulus-triggered average of the electromyogram (EMG), a supplementary, easily accessible source of information is the EMG power spectrum, which can be shown to be roughly proportional to the squared modulus of the Fourier transform of the MUAP. But no phase information is available for the MUAP so that a straightforward deconvolution is not possible. METHODS: To get around the problem of incomplete information, the rate modulation is described by a thoughtfully chosen function with just a few adjustable parameters. The convolution model is then used to make predictions as to the energy spectral density of the VEMP, and the parameters are optimized using a cost function that quantifies the difference between model prediction and data. RESULTS: The workability of the proposed approach is demonstrated by analysing Monte Carlo simulated data and exemplary data from patients who underwent VEMP testing as part of a clinical evaluation of their dizziness symptoms. CONCLUSIONS: The approach is suited, for example, to estimate the duration of the inhibition causing the VEMP or to disentangle a VEMP consisting of more than one component.