The physiological and clinical significance of nonlinear TCD waveform analysis in occlusive cerebrovascular disease.

In order to compare the results of nonlinear analysis of hemodynamically compromised and noncompromised cerebral circulations we measured consecutive transcranial Doppler (TCD) waveforms of fourteen patients with a unilateral or bilateral occlusion of the internal carotid artery. The cerebral vasomotor reactivity (VMR) to acetazolamide in both middle cerebral artery (MCA) territories was established by using TCD. Conventional TCD data and nonlinear TCD analysis of data were compared. Nonlinear analysis of the TCD time series suggested dynamical chaos based on the fractal dimension of the TCD curve and the positive Lyapunov exponents in the compromised and noncompromised MCA territories. In the areas with the compromised circulation the positive Lyapunov exponents were significantly lower compared to the noncompromised side and in some cases with a negative VMR, the Lyapunov exponent was almost zero. The latter is suggestive for periodic behavior of the impaired cerebral circulation instead of the dynamical chaos which is found under normal conditions. The TCD time series of a hemodynamic compromised cerebral territory not only shows phenomena related to a decreased perfusion pressure (such as a 'damped waveform') but also phenomena which are related to a more prominent periodicity. We speculate that conventional and nonlinear TCD analysis could be used to determine the VMR.

Dynamical chaos determines the variability of transcranial Doppler signals.

In order to estimate whether or not the variability of a timeseries of transcranial Doppler (TCD) waveforms is the result of a random or a deterministic process the following study was designed. From eight normal volunteers the middle cerebral artery blood flow velocities were measured for 50 sec and the maximum blood flow velocities (or waveforms) were analysed. From these waveforms socalled attractors were reconstructed and shown in a two dimensional phase portrait. The attractor of the TCD timeseries shows the entire range of states the cardiovascular system can display. The geometric structure of the attractor can be estimated by calculation of the correlation dimension D2. The correlation dimension D2 shows that the time evolution of the TCD timeseries is essentially nonperiodic and can be characterized by low dimensional chaos. It has been shown that the D2 value during hypocapnia has a significant higher value compared to the D2 values during normocapnia. The biological and clinical significance of these observations are outlined.

Non-linear dynamical analysis of multichannel EEG: clinical applications in dementia and Parkinson's disease.

The irregular, aperiodic character of the EEG is usually explained by a stochastic model. In this view the EEG is linearly filtered noise. According to chaos theory such irregular signals can also result from low dimensional deterministic chaos. In this case the underlying dynamics is nonlinear, and has only few effective degrees of freedom. In contrast, stochastic models are less efficient, because they require in principle infinite degrees of freedom. Chaotic dynamics in the EEG can be studied by calculating the correlation dimension (D2). Although it has become clear that D2 calculations alone cannot prove chaos, the D2 has potential value as an EEG diagnostic. In this study we investigated whether D2 could be used to discriminate EEGs from normal controls, demented patients and Parkinson patients. We have analyzed epochs (20 channels; 2.5 s) from 52 EEGs (20 controls; 15 patients with dementia; 17 patients with Parkinson's disease). Controls had a mean D2 of 6.5 (0.9); demented patients of 4.4 (1.5), and Parkinson patients of 5.3 (0.9). Both groups were significantly different from controls (p < 0.001). There was a significant positive correlation between D2 and relative power in the beta band (r = 0.81) and a significant negative correlation between D2 and power in the delta (r = -0.60) and theta band (r = -0.37). These results suggest the possible usefulness of multichannel D2 estimation in a clinical setting.