Yoshito Kakinuma

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.

Fundamental Rhythm of Sympathetic Nerve Discharges in Animals with Total Artificial Hearts

To evaluate the effect of total artificial heart replacement on the autonomie nervous system, sympathetic neurograms were analyzed by power spectrum and coherence function. Two pneumatically driven, sac type ventricular assist devices were implanted as biventricular bypasses (BVB) in adult, mongrel dogs. After initiation of BVB pumping, the natural heart was electrically fibrillated to form a BVB TAH model. Renal sympathetic nerve activity (RSNA) was recorded using a bipolar electrode attached to the left renal sympathetic nerve. RSNA was amplified and integrated by use of an R-C integrator. Power spectra of the RSNA and values of squared coherence between the arterial pressure wave form and the RSNA were calculated by computer. In animals with total artificial hearts (TAHs), coherence at the cardiac rhythm frequency was decreased, and coherence at the TAH pumping rhythm frequency was increased. These results indicate that the arterial pulse wave observed in TAH animals contributed to the sympathetic neurogram.

Can the artificial heart make the circulation become fractal

In order to analyze the hemodynamic parameters in prosthetic circulation as an entity and not as decomposed parts, non linear mathematical analyzing techniques, including the fractal dimension analyzing theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted, as biventricular bypasses (BVB), in chronic animal experiments, using four healthy adult goats. For the comparison between the natural and prosthetic circulation in the same 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 with a personal computer system. Using the non-linear mathematical technique, the arterial blood pressure waveform was embedded into the return map as the beat-to-beat time series data and fractal dimension analysis were performed to analyze the reconstructed attractor. By the use of the Box counting method, fractal dimension analysis of the hemodynamics was performed. Return map of the hemodynamics during natural and artificial circulation showed fractal characteristics, and fractal dimension analysis of the arterial blood pressure revealed the fact that lower dimensional fractal dynamics were evident during prosthetic circulation. Fractal time series data is suggested to have robustness and error resistance, thus our results suggest that the circulatory regulatory system with an artificial heart may have these desired characteristics.

Estimation of the following Cardiac Output Using Sympathetic Tone and Hemodynamics for the Control of a Total Artificial Heart

A sympathetic neurogram is potentially useful for the development of a real time total artificial heart (TAH) control system. We used sympathetic tone and hemodynamic derivatives to estimate the following cardiac output in acute animal experiments using adult mongrel dogs. Moving averages of the mean left atrial pressure and mean aortic pressure were used as parameters of the preload and afterload, respectively. Renal sympathetic nerve activity (RSNA) was employed as a parameter of sympathetic tone. Equations for the following cardiac output were calculated using multiple linear regression analysis of the time series data. A significant correlation was observed between the estimated and following measured cardiac output. These results suggest the potential usefulness of the sympathetic neurogram for the real time TAH automatic control system.

Chaotic behavior of hemodynamics with ventricular assist system.

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.

Cardiac-related sympathetic nerve activity during circulation with only the left ventricular assist device.

Circulatory maintenance with a left ventricular assist device (LVAD) alone during cardiac arrest until heart transplantation has been evaluated. To assess the effect on the autonomic nervous system, the sympathetic neurogram was analyzed by power spectrum and coherence function. LVAD were inserted between the left atrium and the descending aorta in seven adult mongrel dogs and ventricular fibrillation was induced electrically. Renal sympathetic nerve activity (RSNA) was detected by bipolar electrodes attached to the left renal sympathetic nerve. Values of squared coherence between the arterial pulse wave and RSNA were calculated. Under the condition of circulatory maintenance with only LVAD, coherence at the cardiac rhythm frequency was decreased, and coherence at the LVAD pumping rhythm frequency was increased. These results indicate that the arterial pulse wave observed during maintenance of the circulation with only LVAD contributed to the sympathetic neurogram.

Mayer waves in dogs with total artificial heart.

To assess the effect of a total artificial heart (TAH) on the autonomic nervous system a power spectral analysis of the hemodynamics in a TAH animal was done by the maximum entropy method. Two pneumatically driven sac-type ventricular assist devices were implanted as total biventricular bypass (BVB) in adult mongrel dogs to compare the differences between natural heart and TAH. Once the BVB was pumping, the natural heart was electrically fibrillated to constitute the BVB-type TAH model. In the arterial pressure waveform in animals with TAH, respiratory waves were not changed (97.7±24.6%) though Mayer waves were significantly decreased (47.5 ± 22.6%) compared with the animal with a natural heart. These results suggest that prosthetic hemodynamics in the TAH animal affect fluctuations in the cardiovascular system.

An approach to single-beat estimation of E/sub max/ as an inverse problem

The present study has derived a new method for estimating the maximum value (E/sub max/) of the ventricular elastance (E(t)) without direct measurement of the ventricular volume (V(t)) by regarding the estimation process as an inverse problem. The method can estimate E/sub max/ in a single beat without any change in preload or afterload by measuring the ventricular pressure (P(t)) and outflow (i(t)) which is much easier to measure than V(t). This method is based on two assumptions that E(t) can be approximated by at+b and that V/sub ed/-V/sub 0/=I(t)+P(t)/E(t) holds for any t during the ejection period, where V/sub ed/ is the end-diastolic volume, I(t) is the integrated value of i(t) and V/sub 0/ is the volume axis intercept of the regression line of the end-systolic pressure-volume relation. In vivo experiments using two adult goats resulted in small mean equation error with respect to V/sub ed/-V/sub 0/ less than about 5% of the stroke volume of each heart beat. This implies that the proposed method is practical enough to monitor cardiac function in actual clinical settings.

Fractal Dimension Analysis of Chaos in Hemodynamics with Artificial Heart

To analyze the hemodynamic parameters in prosthetic circulation as a complete entity, not as a decomposed entity, non-linear mathematical techniques, including chaos and fractal theory, were utilized. Two pneumatically actuated ventricular assist devices were implanted as biventricular bypasses (BVB) in chronic animal experiments in four healthy adult goats. For the comparison between the natural and prosthetic circulation, the BVB type complete prosthetic circulation model with ventricular fibrillation was adopted. All hemodynamic parameters with natural circulation without BVB pumping and artificial circulation were recorded under awake conditions, and calculated with a computer system. By the use of a non-linear mathematical technique, arterial blood pressure waveform was embedded into the return map by the beat-to-beat variability, and fractal dimension analysis was performed to analyze the reconstructed attractor. By the use of the box-counting method, fractal dimension analysis of the hemodynamics was performed. The return map of the hemodynamics during natural and artificial circulation showed the characteristics of lower dimensional fractal. The fractal time series data were suggested to have robusticity and error resistance. Thus, our results suggest that the circulatory regulatory system with the artificial heart may have these desirable characteristics.

New Artificial Heart Control Method from the Neurophysiological Point of View

In order to determine optimal drive conditions for the total artificial heart (TAH) from the neurophysiological point of view, power spectral analysis of the hemodynamic parameters in animals chronically implanted with TAH was performed to analyze the rhythmical fluctuations that reflect the operation of cardiovascular regulatory systems. Two ventricular assist devices were implanted as total biventricular bypasses (BVB) in chronic animal experiments with adult goats. Natural hearts were then electrically fibril-lated to constitute the BVB type of TAH model for comparison of the circulation in animals with a natural heart and those with a TAH. Mayer waves and respiratory waves were clearly observed in the arterial pressure of the TAH animal, these fluctuations being significantly influenced by the TAH driving conditions. These results suggest that fluctuations in the hemodynamics of animals with TAH can provide information for TAH control systems.