To further investigate the robustness of the controller, another computer simulation is performed. The desired HR is set to 80 bpm throughout entire process. The peripheral resistance in the model changes from 1.0 to 0.7 mm Hg/ml at 32 seconds for simulating the peripheral resistance under exercise. The simulation results are shown in Figure 7. It is seen that the settling time of HR (80 bpm) is 8 seconds without steady-state error when the peripheral resistance increases from 1.0 to 0.7 mm Hg/ml, and the amplitude of the blood flow increases correspondingly to ensure that the arterial pressure is constant.
In the cardiovascular pump models proposed by other groups, the HR is generally considered as a constant. It is not consistent with the clinical data. As the matter of fact, on one hand, the HR is affected by both pressure and CO. When the aortic pressure and CO is changed by the rVADs, the HR accordingly changed, owing to the HR is controlled by the hormonal and nervous system. On the other hand, the change of HR can adjust the CO and mean aortic pressure.14 Therefore, the HR should be considered as a state variable identical with aortic pressure and blood flow.
According to the Ref. 15, the HR responses to the change of arterial pressure by using the arterial baroreceptor. The baroreceptor is a pressure sensor located in the carotid sinus and arterial vessel, which converts pressure into afferent firing frequency. Then, the afferent firing frequency is translated into efferent signals by the nervous system: sympathetic firing frequency and vagal firing frequency. These efferent signals are the inputs of the regulation effectors, which change the HR. Therefore, the control strategy used here is to use the nervous system and baroreflex system to monitor the change of blood demand of patients for us. In response to the Refs. 16 and 17, it is seen that even if the patients suffered from the end-stage heart failure, the regulation system of HR also regulate the HR according to the change of arterial pressure. However, if the patients suffer from severe arrhythmia, the mechanism of HR regulation is abnormal18; the active of sympathetic nerves is different from the normal persons. Therefore, the control algorithm reported in this article is not fit for the patients who suffer from severe arrhythmia, and a HR analysis system should be added to the controller to decide whether the HR measured from patients is normal. If the HR cannot indicate the blood demand accurately, other algorithm will be adopted. This work will be investigated in the future.
The HR of the model is a nonlinear function of MAP according to the Ref. 15. The HR is considered as a sensor of MAP; consequently, the controller based on HR can regulate the MAP. For instance, in Figure 6, when the desired HR changes from 100 to 80 bpm at 32 seconds, the arterial pressure increases accordingly from 100 to 120 mm Hg. Because the desired HR of patients is different from each other, the increment of aortic pressure leads to the decrement of the HR. To maintain the actual HR tracking the desired one, the blood flow of the pump is increased by the controller. When the patients take exercises, the peripheral resistance of their aortic vessels will decrease to admit more blood flow into aorta.10 That is, when the blood flow demand of the circulatory system increases, the peripheral resistance of the aortic vessel will decrease. As shown in Figure 7, when the peripheral resistance decreases from 1.0 to 0.7 mm Hg/ml, the blood flow through the pump increases correspondingly to ensure that the arterial pressure is constant. That means the HR can indicate the blood demands of patients, and the fuzzy logic feedback controller can regulate the intraaorta pump to response to the demand of the circulatory system.
From Figure 1, it is seen that the coronary ostia locate at the inlet of the pump. That means the blood to the coronary vessel will be sucked by the pump, when the rotational speed of the pump is higher than the appropriate speed. To overcome this problem, coronary artery bypass will be operated to increase coronary perfusion. This will be investigated in the future.
From Figure 6, we find that the minimal value of the left ventricular pressure decreases, when the HR decreases. That means if the desired HR is not appropriate for the patients, the phenomenon of suction maybe occur. Therefore, a suction detection algorithm should be added in the controller to detect suction. Because the desired HR is different from each other, the algorithm can decide that whether the desired HR is appropriate for the patients is needed. This work is investigated by other person in our group.
Figure 6 shows the statuses of HR, blood flow, and arterial pressure. It is seen that, from 0 to 2 seconds, the HR is up to 150 bpm, because the rotational speed of the pump is very low (approximate to 0 rpm). Also, the blood flow and arterial pressure in this period represent the situation of the heart failure without supported. The mean flow rate in this period is approximately 2 L/min, and the MAP is approximately 60 mm Hg, which are consistent with the clinical data proposed by literatures. From 2 to 8 seconds, because of the increase of rotational speed of the pump regulated by the controller, the mean flow rate and MAP increase significantly. When the HR has tracked the desired HR (after 8 seconds), the mean flow rate and MAP increases to 5.5 L/min and 100 mm Hg, respectively. It is seen that the controller based on HR can regulate the pump according to the blood demands of patients and maintain the arterial pressure and blood flow in a normal range.
The theoretical source of the physiological control by maintaining HR is from the fact that the natural regulatory mechanism of the body is able to effectively represent the physiological demands. Unfortunately, when the regulatory mechanism does not perform normally, such as hypertension, there is a decrease in the performance of the HR control algorithm if the control algorithm is based on the mathematic model of the cardiovascular pump system, because the relationship between the HR and mean aortic pressure has changed. In this case, Equation 10 has to be modified to adapt to the status of patients. However, the fuzzy logic feedback control does not directly use the model of the system, and it is insensitive to the change of cardiovascular pump system. Hence, the fuzzy logic feedback control is an appropriate control algorithm for the intraaorta pump controller.
The fuzzy logic controller monitors the error of the HR to regulate the gain of the system. The rotational speed is actually controlled by the feedback controller. The structure of the controller used in this work has advantages. On one hand, the fuzzy logic feedback control is a combination of fuzzy logic supervisory and classical feedback control. The feedback control algorithm can always achieve good performance.19 However, because the cardiovascular pump model is a complex nonlinear model with much internal uncertainty and external disturbance, it is difficult to obtain an appropriate gain of the feedback for all status of the model. To overcome this problem, the fuzzy logic supervisory has been derived into this control strategy to adjusted gain of the feedback control intelligently. The fuzzy logic supervisory does not use the mathematical model but the knowledge and experience to adjust the gain; hence, the fuzzy logic controller has more robustness than other control algorithms based on model. Despite the accuracy and dynamic characters, which are shortages of the fuzzy logic control,11 from Figures 6 and 7, we note that when the desired HR decrease from 100 to 80 bpm, or the peripheral resistance decreases from 1.0 to 0.7 mm Hg/ml, the controller can maintain the actual HR tracking the desired one without steady-state error, that means the fuzzy logic feedback control obtains the predominance of feedback control and fuzzy logic control. On the other hand, because the cardiovascular pump system is a complex nonlinear system, for a single-objective control algorithm, it is difficult to achieve good performance for all situation of the system.3 The fuzzy logic supervisory algorithm provides a method to solve this problem by being determined by the experience and a priori knowledge of the designers, and it is easy to be modified to a multiobjective control algorithm, which maybe include such hemodynamic parameters as HR, mean flow rate, pulsatile of the pressure waveform, and blood flow waveform.
The mathematical model of the cardiovascular pump system has been established. For the reason that the HR could reflect the status of the hemodynamic of the system, the HR in the model is designed as a variable that is a nonlinear function of MAP. The fuzzy logic feedback controller of the intraaorta pump is designed, in which HR is considered as the controlled variable. The aim of the controller is to maintain the actual HR tracking the desired one. Couples of simulations are performed to verify the robustness and the dynamic characters of the controller. The simulation results demonstrate that the settling time of the controller is <10 seconds without steady-state error.
Supported partly by the National Natural Science Foundation of China (Grant No. 11072012), the Furtherance Program of 10 Beijing University of Technology on Strengthening Talents Education (31500054R5001), and the National Academic Working Group-Talents Training Program (01500054R8001).
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