In order to develop an optimal automatic control algorithm of an artificial heart system for the creatures, investigation of the basic characteristics of the cardiovascular system may be important. The clinical significance of the chaotic dynamics had attracted attention, especially in the cardiovascular system, which had nonlinear dynamic behaviors [1,2]. Circulation system is a kind of "complex system" having many feedback circuits, so, it was very difficult to investigate the origin of chaos in the circulatory system.
In this study, we investigated the origin of chaos by the use of the methodology of the open loop analysis with an artificial heart, which did not have any fluctuation in their own pumping rhythm and contraction power, in the chronic animal experiments using healthy adult goats [3,4]. Firstly, we had investigated the hemodynamic time series data with the natural heart and an artificial heart circulation. For the comparison of the circulatory dynamics with a natural heart and an artificial heart, biventricular bypass type total artificial circulation model in which enables us the observation and comparison in the same animals, was adopted.
If the deterministic chaos was existed in the circulation with artificial heart, it might be originated from the dynamics of the peripheral vessel's property, because there was no fluctuations in the pumping rhythm and contractility of an artificial heart.
To search for the origin of chaos in circulation, we used the nonlinear mathematical methodologies including chaos and fractal theories [1,2]. By the use of these methodology, we had been searching for the origin of deterministic chaos in circulation, and consideration were added to the results and reported here.
Experimental goats used in this study was weighed from 60 to 70 kg with a mean of 65 kg. These goats were kept fasting for 2 days before the experiments. Three goats were anesthetized by halothane inhalation. After tracheal tube intubation by tracheotomy, they were placed on a respirator. Electrodes for electrocardiograph (ECG) were attached to the legs and later implanted in the pericardium. The left pleural cavity was opened by a left fourth rib resection. Arterial blood pressure was monitored continuously with catheters inserted into the aorta through the left internal mammalian artery. Central venous pressure (CVP) was measured by the fluid-filled catheter through the internal mammalian vein. For left artificial heart implantation, the intercostal arteries were separated to free the descending aorta. A polyvinyl chloride (PVC) out-flow cannula was sutured to the descending aorta. A PVC inflow cannula was inserted into the left atrium through the left atrial appendage. Both cannulae were connected to our TH-7B pneumatically driven sac-type blood pump by the built-in valve connectors. The PVC outflow and inflow cannulae were inserted into the pulmonary artery and the right atrium, respectively. Then, both cannulae were connected to the right pump. Pump output was measured by the electromagnetic flow meter attached to the outflow cannula.
The TH-7B pneumatically driven sac-type blood pumps were used in this experiment to constitute a biventricular bypass (BVB) type of artificial heart model (Fig. 1). The blood-contacting surface of the pump was coated with Cardiothane, and the outer casing of the pump is made of polycarbonate. Silicone ball valves were affixed to the inflow and outflow connectors. After the chest was closed, these pumps were placed paracorporeally on the chest wall, and then the goats were placed in a cage and extubated after waking. After the influence of the anesthesia was thought to be terminated (2-3 days after the operation), these goats received intravenous heparin (100 U/kg), and the control time series data were recorded without biventricular assist device driving. Data were recorded under awake conditions with the goats standing and in a preprandial condition. Time series data of the hemodynamic variablities were recorded with an ink-jet recorder and in magnetic tape after stabilization of the all hemodynamic derivatives without artificial heart driving (20-30 min after the biventricular assist devices were stopped). After the control data were recorded, bilateral ventricular assistance was started, and ventricular fibrillation was induced electrically. Confirming the stabilization of the hemodynamics with stable TAH drive conditions (20-30 min after stabilization of the hemodynamics), time series data of the hemodynamic variabilities were recorded. Driving conditions of the pump were manually operated both to maintain satisfactory pump output (80-100 ml/min/ kg) and to maintain the hemodynamic parameters within normal limits. Driving conditions of both pumps were fixed when the time series data of the hemodynamic parameters were recorded.
After the recording, all time series data were analyzed in the personal computer system (PC9801BA) by the off line analysis. By the use of the AD converter, time series of the hemodynamic parameters were input into the computer system. And then, quantification and the statistical handling were performed. By the use of the nonlinear mathematical methodology, chaotic dynamics and fractal theory analysis were performed. Time series data were embedded into the phase space by the use of the methodology of Takens et al. For the quantitative analysis, Lyapunov exponents of the reconstructed attractors were calculated by the methodology of the algorithm of the Wolf, et al.
By the use of the biventricular bypass type total artificial circulation animal model, comparison of the natural heart circulation and artificial heart circulation were realized in the same creatures. For the evaluation of the nonlinear dynamics in this experimental creature, we had used the reconstruction of the strange attractor in the phase space, the Lyapunov exponents analysis, Correlation dimension analysis and Fractal dimension analysis of the return map.
During artificial heart circulation, natural heart was fibrillated by the electrical stimulation, and systemic and pulmonary circulation were maintained with biventricular assist pump. Ventricular assist devices used in this experiment were designed for human clinical use and pneumatically driven by the driving console outside of the body of the experimental animals. During the recording of the time series data of an artificial heart circulation, driving condition of this artificial heart was fixed, thus, there was no fluctuations in their own driving rhythm and contraction power. So we could observe the circulation without fluctuations of the natural heart beat. And of course, artificial heart was stopped to drive during the observation of the natural heart circulation.
Figure 1 showed the photograph of an experimental goat with biventricular assist type total artificial circulation model. Two pneumatically actuated sac type blood pumps were shown in this photograph. Upper side pump was left heart bypass pump. Blood was received from left atrium and pumped to the descending aorta. And lower one was the right heart bypass pump. Blood was received from right atrium and pumped into the pulmonary artery. All hemodynamic parameters were recorded in the magnetic tape data recorder and off line analysis were performed through the AD converter. Reconstructed attractors of the arterial blood pressure during natural heart beat embedded into the four dimensional phase space and projected into the three dimensional phase space was shown in figure 2. Before we reconstruct this attractor, two dimensional reconstruction and three dimensional reconstruction was also checked and found that more than three dimension may be desirable.
Strange attractor may be shown in the figure. Basic cycle in this attractor of arterial blood pressure was, of course, coincident with cardiac cycle. Rhythmical fluctuations like respiratory fluctuations and Mayer wave were seen in the time series data and may be shown as the band-width of this attractor. Chaotic systems characteristically exhibit sensitive dependence upon initial conditions [1-4]. To evaluate this character, we calculated the Lyapunov exponents from the reconstructed attractor. Lyapunov exponents were the quantitative measure of the rate of separation of the attractors in the phase space. In this study, we calculated the Lyapunov exponents by the use of Wolf method [5,6]. As we shown an example in figure 3, it converges in a value of plus, suggesting sensitive dependence on initial conditions suggesting the existence of deterministic chaos.
Chaotic dynamics were shown by the various investigators in hemodynamic parameters in creatures. Our result in this study supports these reports, too. Of course, it is the next issue that is interesting here.
The results were shown in fig.4 and fig.5. Fig.4 showed an example of a reconstructed attractor of the arterial blood pressure during artificial heart circulation embedded into four dimensional phase space and projected into the three dimensional phase space. Banding may be suggest the fluctuations in hemodynamic parameters and having fractal structures, suggesting the existence of the deterministic chaos. Lyapunov exponents of the reconstructed attractor of the arterial blood pressure during artificial heart circulation embedded into four dimensional phase space were shown in fig.5. The results suggest that lower dimensional chaotic dynamics may be shown compared with that during natural heart beat.
This may be considered as an interesting result. There was chaos, in circulation without natural heart. It must affect the baroreceptor in arterial wall, and this information were communicated to the central nervous system. Brain regulating sinus nodes, must be respond to this input. And make chaos, too. If another information is added in this stage, larger dimensional chaos may be generated like figure 2 and 3. Of course, other probability is thought about. The natural heart beat is regulated by not only central nervous system, but also another regulatory system like hormonal factors, preload, afterload and so on. If another information were added to the chaotic dynamics in an artificial heart circulation, it may make a larger dimensional chaotic dynamics in circulation. It is very interesting and it is a result understood with this experiment for the first time. In the next step, we want to consider the central nervous system, which is , of course, mediating the circulation.