Method for Modeling Residual Variance in Biomedical Signals Applied to Transcranial Doppler Ultrasonography Waveforms

Transcranial Doppler (TCD) ultrasonography measures pulsatile cerebral blood flow velocity in the arteries and veins of the head and neck. The velocity pulse waveform morphology has been shown to have physiological and diagnostic significance. However, the measured pulses may exhibit a high degree of variability that deteriorates the estimates of clinical parameters. This study characterizes the TCD residual variance that result in pulse variability. We retrospectively utilized the data from 82 subjects. A trained sonographer insonated the middle cerebral arteries using a 2MHz hand-held probe. We implemented a multi-stage algorithm to identify the TCD residuals in each scan: pulses were identified; outlier pulses were flagged and removed; the average pulse waveform was taken as the ensemble average of the accepted pulse waveforms; finally, the resampled average pulse waveforms subtracted from individual pulses were taken as the TCD residuals. For each scan, we reported the signal to noise ratio and parameterized models for residuals: their amplitude structure using probability density function models and their temporal structure using autoregressive models. The signal to noise ratio 90% range was [1.7, 18.2] dB. The estimated probability density functions were best characterized by a generalized normal distribution whose beta parameter was smaller than 2 in 93% of scans. The identified frequency structure showed the dynamics were low-pass in nature. Analysis of the TCD residuals is useful in the assessment of the signal quality. Moreover, our identified models can also be used to generate synthetic TCD signal that enables future realistic simulation studies.