Fractal fluctuations in transcranial Doppler signals

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Abstract
Cerebral blood flow (CBF) velocity measured using transcranial Doppler ultrasonography (TCD) is not strictly constant, but has both a systematic and random component. This behavior may indicate that the axial blood flow in the middle cerebral artery is a chaotic process. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show by systematically aggregating the data that the correlation in the beat-to-beat CBF time series is a modulated inverse power law. This scaling of the CBF time series indicates the existence of long-time memory in the underlying control process. We argue herein that the control system has allometric properties that enable it to maintain a relatively constant brain perfusion.