Properties of rectified averaging of an evoked-type signal: theory and application to the vestibular-evoked myogenic potential.

The properties of rectified averages were investigated using the VEMP (vestibular-evoked myogenic potential) as an example of an evoked-type response. Recordings were made of surface EMG from the sternocleidomastoid (SCM) muscles of six volunteers, unstimulated, at different levels of tonic activation and then in response to clicks of different intensities. The stochastic properties of the surface EMG recorded were shown to be well modelled using a zero mean normal distribution with a standard deviation equivalent to the mean RMS (root mean squared) value (mean residual error variance 0.87%). Assuming a normal distribution, equations were derived for the expected value of both the rectified and RMS average with the addition of constant waveforms of different sizes. A simulation using recorded EMG and added sine waves of different amplitudes demonstrated that the equations predicted the rectified averages accurately. It also confirmed the importance of the relative amplitude of the added signal in determining whether it was detected using rectified averages. The same equations were then applied to actual data consisting of VEMPs of different relative amplitudes recorded from the volunteers. Whilst the signal-to-noise ratio (measured by corrected amplitude) was a major determinant of the nature of the rectified average, consistent deviations were detected between the predicted and actual rectified averages. Deviations from predicted values indicated that the VEMP did not behave simply like a constant signal added to tonic background EMG. A more complicated model, which included temporal jitter as well as inhibition of background EMG during the VEMP, was required to fit the physiological recordings. Rectified averages are sensitive to physiological properties, which are not apparent when using unrectified averages alone. Awareness of the properties of rectified averages should improve their interpretation.