Nonlinear analysis of blood flux in human vessels

Laser Doppler fluxmetry (LDF) is frequently used in research on microcircul ation 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 be haviour of the whole system. The fill factor is a tool for displaying the m ain properties of this attractor in two dimensions and for determining dive rse parameters for further analysis. A quantitative characterization of the system is possible by the distribution of correlation dimensions in the em bedding space. The singular value decomposition (SVD) can be used to displa y and characterize individual degrees of freedom. These methods were applie d to LDF time series from nine healthy controls and nine patients with Rayn aud's phenomenon due to connective tissue disease. The fill factor and the SVD indicate qualitatively that in the controls vas omotion 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 correlatio n dimensions were significantly higher in the patient group. Nonlinear analysis of LDF time series provides additional information which cannot be detected using conventional approaches.