Yambe T, Nanka S, Sonobe T, Naganuma S, Kobayashi S, Akiho H, Kakinuma Y, Mitsuoka M, Chiba S, Ohsawa N
Department of Medical Engineering and Cardiology, Tohoku University, Sendai, Japan.
Int J Artif Organs. 1995 Jan;18(1):17-21.
In order to analyze hemodynamic parameters during left ventricular assistance as an entity and not as decomposed parts, non-linear mathematical techniques were utilized. Pneumatically actuated ventricular assist systems (VAS) were implanted as left heart bypasses in acute animal experiments, using healthy adult mongrel dogs. By the use of the non-linear mathematical technique, the arterial blood pressure waveform (AP) was embedded into the four-dimensional phase space and projected into the three-dimensional phase space. The Lyapunov numerical method was used as an adjunct to the graphical analysis of the state space. The phase portrait of the attractor showed a complex structure; a three dimensional solid torus with a screw type structure as a part, suggesting deterministic chaos in the AP without left ventricular assistance. Positive lyapunov exponents confirmed the existence of chaos. During counterpulsation mode left ventricular assistance, the phase portrait of the attractor showed a more complex structure, and positive Lyapunov exponents suggested a greater dimensional deterministic chaos. However, non-structured patterns were seen in the phase space during internal mode VAS driving, suggesting the possibility of dissipative dynamics in the four dimensional phase space. These results suggest that the cardiovascular system with counterpulsation mode VAS driving is in a homeochaotic state, which is thought to be a flexible and intelligent control system. And there is greater dimensional complex dynamics in the circulatory regulatory system with VAD during internal mode assistance.
