Fractal Analysis of the Cerebrovascular System Pathophysiology

The cerebrovascular system is characterized by parameters such as arterial blood pressure (ABP), cerebral perfusion pressure (CPP), and cerebral blood flow velocity (CBFV). These are regulated by interconnected feedback loops resulting in a fluctuating and complex time course. They exhibit fractal characteristics such as (statistical) self-similarity and scale invariance which could be quantified by fractal measures. These include the coefficient of variation, the Hurst coefficient H, or the spectral exponent α in the time domain, as well as the spectral index ß in the frequency domain. Prior to quantification, the time series has to be classified as either stationary or nonstationary, which determines the appropriate fractal analysis and measure for a given signal class. CBFV was characterized as a nonstationary (fractal Brownian motion) signal with spectral index ß between 2.0 and 2.3. In the high-frequency range (>0.15 Hz), CBFV variability is mainly determined by the periodic ABP variability induced by heartbeat and respiration. However, most of the spectral power of CBFV is contained in the low-frequency range (<0.15 Hz), where cerebral autoregulation acts as a low-pass filter and where the fractal properties are found. Cerebral vasospasm, which is a complication of subarachnoid hemorrhage (SAH), is associated with an increase in ß denoting a less complex time course. A reduced fractal dimension of the retinal microvasculature has been observed in neurodegenerative disease and in stroke. According to the decomplexification theory of illness, such a diminished complexity could be explained by a restriction or even dropout of feedback loops caused by disease.