Nonlinear mathematical analysis of the hemodynamic parameters during left ventricular assistance with oscillated blood flow

For the development of a totally implantable ventricular assist system (VAS), we have been developing the vibrating flow pump (VFP), which can generate oscillated blood flow with a relatively high frequency (10-50 Hz) for a totally implantable system. In this study, effects of left ventricular assistance with this unique oscillated blood flow were analyzed by nonlinear mathematics for evaluation as the entire circulatory regulatory system, not as a separate part of the system. Left heart bypasses using VFPs from the left atriums to the descending aortas were performed in chronic animal experiments using healthy adult goats. Electrocardiogram (ECG), arterial blood pressure, VFP pump flow, and flow of the descending aorta data taken while the goats were awake were recorded in the data recorder and analyzed in the personal computer system through the AD convertor. Using nonlinear mathematics, time series data were embedded into the phase space, and the Lyapunov numerical method, fractal dimension analysis, and power spectrum analysis were performed to evaluate the nonlinear dynamics. During left ventricular assistance with the VFP, Mayer wave fluctuations were decreased in the power spectrum, the fractal dimension of the hemodynamics was significantly decreased, and peripheral vascular resistance was significantly decreased. These results suggest that nonlinear dynamics, which mediate the cardiovascular dynamics, may be affected during LV bypass with oscillated flow. Decreased power of the Mayer wave in the spectrum caused the limit cycle attractor of the hemodynamics and decreased the peripheral resistance. Decreased sympathetic discharges may be the origin of the decreased Mayer wave and fractal dimension. These nonlinear dynamical analyses may be useful to design the optimal VAS control.