Temporal heterogeneity of the blood flow velocity at the middle cerebral artery in the normal human characterized by fractal analysis

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Abstract
The objective of this study is to characterize the temporal fluctuation of the axial blood flow velocity (BFV) at the middle cerebral artery (MCA). Biological observables such as BFV present complex oscillations. The irregularity of physiological systems may be assessed by fractal analysis by computing the fractal dimension (D gamma) and the corresponding temporal correlation (r gamma). The BFV at the MCA was registered with transcranial Doppler ultrasonography (TCD) in four adult volunteers. As fractal processes are assumed to have no absolute time scale, two time scales were compared. The digitized signal was averaged respectively at 1-s intervals and for each heart beat. D gamma and r gamma were determined using relative dispersion analysis. The results were D gamma = 1.24 +/- 0.09 and r gamma = 0.45 +/- 0.19 (mean +/- SD) for the 1-s based time scale and D(r) = 1.17 +/- 0.09 and r gamma = 0.57 +/- 0.20 for the heart-beat scale. We conclude that the temporal heterogeneity of the BFV at the MCA in the normal human has fractal properties. Fractal analysis of TCD data may become useful in clinical diagnosis because loss of complexity in physiological systems has been linked to senescence or disease conditions. Wide variations of the so called normal values of BFV measured by TCD have been reported. The physiological BFV fluctuations may explain, in part, the variability of values recorded during routine TCD diagnostic examinations. Our observations may also be of value for understanding the interaction of the vascular endothelium and the blood flow stream (shear stress).