Variability and Fractal Analysis of Middle Cerebral Artery Blood Flow Velocity and Arterial Blood Pressure in Subarachnoid Hemorrhage

Abstract

Higher biologic systems operate far from equilibrium resulting in order, complexity, fluctuation of inherent parameters, and dissipation of energy. According to the decomplexification theory, disease is characterized by a loss of system complexity. We analyzed such complexity in patients after subarachnoid hemorrhage (SAH), by applying the standard technique of variability analysis and the novel method of fractal analysis to middle cerebral artery blood flow velocity (FV) and arterial blood pressure (ABP). In 31 SAH -patients, FV (using transcranial Doppler sonography) and direct ABP were measured. The standard deviations (s.d.) and coefficients of variation (CV=relative s.d.) for FV and ABP time series of length 2(10) secs were calculated as measures of variability. The spectral index beta(low) and the Hurst coefficient H(bdSWV) were analyzed as fractal measures. Outcome was assessed 1 year after SAH according to the Glasgow Outcome Scale (GOS). Both FV (beta(low)=2.2+/-0.4, mean+/-s.d.) and ABP (beta(low)=2.3+/-0.4) were classified as nonstationary (fractal Brownian motion) signals. FV showed significantly (P<0.05) higher variability (CV=7.2+/-2.5%) and Hurst coefficient (H(bdSWV)=0.26+/-0.13) as compared with ABP (CV=5.5+/-2.7%, H(bdSWV)=0.19+/-0.11). Better outcome (GOS) correlated significantly (P<0.05) with higher s.d. of FV (Spearman's r(s)=0.51, r(s)(2)=0.26) and ABP (r(s)=0.57, r(s)(2)=0.32), as well as with a higher Hurst coefficient of ABP (r(s)=0.46, r(s)(2)=0.21). Cerebral vasospasm reduced CV of FV, but left H(bdSWV) unchanged. FV and ABP fluctuated markedly despite homeostatic control. A reduced variability of FV and ABP might indicate a loss of complexity and was associated with a less favorable outcome. Therefore, the decomplexification theory of illness may apply to SAH.