Motohisa Osaka

Background-Patients with a reduced nonlinear component of heart rate regulation have a poorer outcome. Methods and Results-We investigated whether a nonlinear correlation between renal sympathetic nerve activity (RSNA) and blood pressure or renal blood flow is reduced in conscious, spontaneously hypertensive rats (SHR) by comparing them with normotensive Wistar-Kyoto rats (WRY). We also determined the linearity and nonlinearity of the correlation in SHR who were givers an angiotensin 11 receptor blocker, candesartan, orally for 2 weeks. The RSNA value was higher in SHR than in WRY, and coherence peaks of transfer function were found at 0.05 and 0.80 Hz (ie, below respiratory- and cardiac-related fluctuations). The coherence (linearity) of the transfer function was significantly higher and gain was smaller in SHR than in WRY. Because mutual information values (linear and nonlinear correlation) were similar in both strains, we found the nonlinear correlation to be lower in SHR than in WRY. Time delay values calculated by the mutual information method demonstrated that RSNA preceded blood pressure and renal blood flow by 0,5 to 1.0 s. In SHR driven candesartan, the RSNA value was lower, and the linearity was lower and nonlinearity higher than SHR given vehicle. Conclusions-Linear correlation between RSNA and blood pressure or renal blood flow was higher in SHR than in WRY, whereas the nonlinear correlation was lower. Oral treatment with candesartan increased the nonlinearity and reduced the linearity in SHR. Increased RSNA and the renin-angiotensin system may be responsible for the lower nonlinearity and higher linearity in hypertension.

Atrial fibrillation (AF) is often described as a disorganized phenomenon, but many features that qualitatively suggest an underlying order have recently been reported. The present study aimed to disclose this underlying order of AF in a quantitative manner, using a new method of mutual information (MI), which is a measure for gauging the general correlation between 2 time series. Frequency analysis and the MI method were used to analyze 5 epicardial potentials on both atria during AF induced by vagal stimulation (Vs) in 15 dogs. Unipolar electrodes were placed on the right atrial appendage (Rap), the high right atrium (HRA), and the left atrial appendage (Lap). The other 2 electrodes were placed equidistantly between HRA and Rap (RAI-RA2). The power spectrum of AF had a discrete peak around 17 Hz during Vs. After Vs was stopped, the discrete peak shifted from 17 Hz to 7 Hz on all epicardial leads. Taking RA2 as a reference, MI was calculated between RA2 and each of the other electrodes. The MI values (0.066+/-0.005) were greater than 0.047 (the critical value for correlated data) even during Vs. The MI values increased significantly from the highly active process of AF during Vs to the less active one (0.126+/-0.006) before termination of AF. In addition, the MI values increased more at the electrodes close to RA2 (RAI and Rap) than at those far from it (HRA and Lap). These findings suggest that multiple wavelets, which are not random, progressively organize into a few major waves toward the termination of AF; therefore, AF is not a random phenomenon in this model.

To determine the attractor dimension of chaotic dynamics, the box-counting method has the difficulty in getting accurate estimates because the boxes are not weighted by their relative probabilities. We present a new method to minimize this difficulty. The local box-counting method can be quite effective in determining the attractor dimension of high-order chaos as well as low-order chaos.