Nonlinear analysis of blood flux in human vessels.

Laser Doppler fluxmetry (LDF) is frequently used in research on microcirculation of blood. Usually LDF time series are analysed by conventional linear methods, mainly Fourier analysis. These methods may not be optimal for the investigation of nonlinear effects of vasomotion, heartbeat or vessels. Nonlinear methods are based on a reconstruction of the system trajectory in an embedding space describing not only the measured time series but the behaviour of the whole system. The fill factor is a tool for displaying the main properties of this attractor in two dimensions and for determining diverse parameters for further analysis. A quantitative characterization of the system is possible by the distribution of correlation dimensions in the embedding space. The singular value decomposition (SVD) can be used to display and characterize individual degrees of freedom. These methods were applied to LDF time series from nine healthy controls and nine patients with Raynaud's phenomenon due to connective tissue disease. The fill factor and the SVD indicate qualitatively that in the controls vasomotion and heartbeat are the main influences on blood flow and act fairly independently of each other. In the patients there was a mixture of strong but irregular degrees of freedom. The mean and the maximal local correlation dimensions were significantly higher in the patient group. Nonlinear analysis of LDF time series provides additional information which cannot be detected using conventional approaches.