Nonlinear parameters estimation from sequential short time data series.

Procedures of nonlinear parameter estimation require large samples of data. In stationary physiological situations, usually short time series are available. The method of dynamics-dependent windowing and data aggregation procedure are proposed. This technique was tested on chaotic signal generated by Lorenz model and applied to investigate beat-to-beat control of the cardiovascular system in 10 healthy volunteers. Nonivasively recorded blood pressure, respiratory activity and blood oxygen saturation were digitized and saved for further off-line analysis. The experimental procedure consisted of 10 min control--C, 20 voluntary apneas 1 min each-A, interapnea 20 periods of 1 min spontaneous breathing--B, and 10 min free-breathing recovery--R. Respiration signal served as a reference for apnea and interapnea free-breathing identification period. Correlation dimension-CD, according to Grassberger and Procaccia, and recurrence plot strategy, according to Webber and Zbilut, were applied to check dynamical properties of the signals. Results of numerical experiment on Lorenz model, original and transformed by segmentation and aggregation, support our assumption of similarity of their dynamics. Error in CD and recurrence parameters estimation strongly depended on segment length and was about 5% for 600 to 1,200 data points. However, even for segments of 75 to 100 samples, it did not exceed 10% for all, but one, periodic testing signal. Segmentation and aggregation applied to interbeat interval (IBI) and total peripheral resistance (TPR) data showed that CD and recurrence variables estimated separately for apneic and interapneic period and those calculated for mixed (apneic and interapneic) intervals were different. Average CD and recurrence parameters of IBI and TPR for 10 subjects during apnea and interapnea intervals were significantly different than during control and recovery. The lowest CD (mean +/- S.D.) of 6.38 +/- 0.4, 5.62 +/- 0.2 and %recurrence 10.35 +/- 0.8, 6.62 +/- 0.6 (highest ratio 4.95 +/- 0.2, 5.13 +/- 0.3) were observed in apnea for IBI and TPR, respectively. Low values of the estimates computed for mixed periods may suggest the influence of slowly varying, quasiperiodic driving force due to experimental procedure regime. Signal dynamics-dependent windowing and data aggregation regardless of the sequence of data could be a practical solution for nonlinear analysis of very short repeatable time series.