Correlation dimension analysis of the artificial circulation

Abstract

Artificial circulation has been analyzed by decomposing it into parts. However, the sum of the decomposed parts is not equal to the whole system, especially in nonlinear dynamic systems such as biological systems. To evaluate prosthetic circulation as an entity, not as decomposed parts, nonlinear mathematical analytic techniques, including fractal dimension analyzing theory, were used. Two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses (BVB) in chronic animal experiments using four healthy adult goats. For comparison between natural and prosthetic circulation in the same experimental animals, the BVB-type complete prosthetic circulation model with ventricular fibrillation was adopted. All hemodynamic parameters with natural and prosthetic circulation were recorded under awake conditions and calculated by a personal computer system. By the use of nonlinear mathematical techniques, time-series data of the hemodynamics were embedded into the phase space, and correlation dimension analysis was performed to evaluate the reconstructed attractor. Our results suggest that the correlation dimension of the arterial blood pressure does not linearly increase according to the increase of the embedding dimension, even during artificial circulation, suggesting those are the fractal time series data. Dimensional analysis of the hemodynamics revealed that lower dimensional fractal dynamics were observed during prosthetic circulation. Fractal time series data are suggested to have robustness and error resistance. Thus, our results suggest that the circulatory regulatory system with the artificial heart may have these desirable characteristics.