Chaotic Hemodynamics During Oscillated Blood Flow

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Abstract
A vibrating flow pump (VFP), which can generate oscillated blood flow (10–50 Hz/min), has been developed by our team for the artificial heart system. However, the flow pattern of this pump was different from that of the natural heart; therefore, it is important to analyze the effect of this oscillated blood flow on the circulatory regulatory system. To analyze the hemodynamics of high frequency oscillated blood flow as an entity, (not decomposed), nonlinear mathematical techniques were utilized. VFPs were implanted between the left atrium in animal experiments using adult goats. After the implantation procedure, the ascending aorta was clamped to constitute the complete left heart circulation with VFP. Using a nonlinear mathematical technique, an arterial blood pressure waveform was embedded into four–dimensional phase space and projected into three–dimensional phase space. The Lyapunov numerical method was used as an adjunct to graphic analysis of the state space. Phase portrait of the attractor showed a high dimension complex structure, suggesting deterministic chaos during natural circulation. However, phase portrait of the hemodynamics during oscillated blood flow showed a single circle with banding and a forbidden zone, similar to a limit–cycle attractor, suggesting a lower dimensional dynamic system. Positive Lyapunov exponent during oscillated blood flow suggests the existence of lower dimensional chaotic dynamics. These results suggest that the circulatory regulatory system during oscillated blood flow may be a lower dimensional homeochaotic state; thus, hemodynamic parameters must be carefully regulated when unexpected external stimuli are present.

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