Deterministic chaos in the hemodynamics of an artificial heart

To analyze the hemodynamic parameters during prosthetic circulation as an entity, non linear mathematical techniques were used. To compare natural and prosthetic circulation, two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses in chronic animal experiments using adult goats to consitute the biventricular bypass complete prosthetic circulation model with ventricular fibrillation. After implantation, these goats were placed in a cage and extubated after waking. All hemodynamic parameters with the natural circulation without biventricular bypass pumping, and the artificial circulation with biventricular bypass pumping under ventricular fibrillation were recorded under awake conditions. By the use of a non linear mathematical technique, the arterial blood pressure waveform was embedded into a four dimensional phase space and projected into three dimensional phase space. The Lyapunov numeric method is used as an adjunct to the graphic analysis of the state space. A phase portrait of the attractor showed a high dimension complex structure, with three dimensional solid torus suggesting deterministic chaos during natural circulation. However, a simple attractor, such as a limit cycle attractor, was observed during artificial circulation. Positive Lyapunov exponents during artificial circulation suggest the lower dimensional chaotic system. Thus, hemodynamic parameters during prosthetic circulation must be carefully controlled when unexpected stimuli are fed from outside.