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.