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doi: 10.1097/MAT.0000000000000059
Adult Circulatory Support

Pulse-Pressure–Enhancing Controller for Better Physiologic Perfusion of Rotary Blood Pumps Based on Speed Modulation

Huang, Feng; Ruan, Xiaodong; Fu, Xin

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From The State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, China.

Disclosure: The authors have no conflicts of interest to report.

Reprint Requests: Xiaodong Ruan, PhD, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Zheda Road 38, Hangzhou, 310027, China. Email: xdruan@zju.edu.cn.

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Abstract

Sufficient pulsation is important for physiologic perfusion if adequate flow is to be guaranteed. A fuzzy control method for rotary blood pumps using active speed modulation is proposed in this article. It maintains the mean aortic pressure to provide sufficient perfusion while it simultaneously enhances the pulse pressure. The controller uses the indices extracted from the aortic pressure as feedback to determine the amplitude and offset of the rectangular speed modulation waveform, which is synchronous with the cardiac cycle. An additional algorithm is included to prevent regurgitation. The controller is tested both in a baroreflex-cardiovascular model and in a preliminary in vitro experiment. Simulation results demonstrate that the controller is able to increase the pulse pressure to approximately 20 mm Hg and at the same time maintains the mean pressure at 100 mm Hg, when heart failure occurs. It is also quite robust under various physiologic disturbances. Experimental results show that the speed modulation can be implemented in real pumps and that the controller is feasible in practice.

Rotary blood pumps (RBPs) have been widely used for treating end-stage heart failure during the past decades. They have gained great success in clinical use, given that most RBPs under in vivo trials show good performance and reliability. However, current RBPs usually work in a constant speed mode and are tuned manually to fit different physiologic demands. To make the pump more intelligent, a physiologic controller, which can optimize the perfusion of the blood pump, is highly demanded.

Recently, the physiologic control methods for blood pumps have gained more and more attention.1–4 Ohuchi et al.1 used predetermined cardiac output to get optimum rpm, meanwhile minimizing deleterious effects such as suction; some researchers controlled the pump in an attempt to maintain a constant pressure difference across the pump or between the pulmonary venous and the aorta.2,3 These methods mainly focused on providing sufficient flow for tissues and organs. However, adequate pump flow is not enough for enhanced perfusion, given that the natural human perfusion has pulsation, especially for a long-term assist device. Outcomes of animal experiments and clinical trials show that pulsatile perfusion is better in terms of less vital organ injury and systemic inflammation,5 and it has beneficial effects on vascular properties and microcirculation.6 Some current applications of RBPs are suitable if the natural heart contractility is sufficient enough to generate minimum physiologic pulsation and the continuous flow pump is at a low enough speed that it does not overly diminish pulsation. However, in advanced heart failure patients, in whom heart contractility is extremely small, and as a result, both mean pressure and pulse pressure are far from the normal range, there is a need to enhance the pulse pressure to optimize perfusion while the mean pressure is guaranteed. Although some control methods increase the aortic mean pressure to augment flow perfusion, almost none of them, to our knowledge, can enhance the pulse pressure. On the contrary, they make the pulsation even smaller because of the continuous flow pattern of an RBP. To avoid very small pulsations, some researchers limit the pump speed.7 However, this kind of pulsatile control method depends on the natural heart’s own pulsation, without any active external contribution by the pump. Therefore, the pulse pressure is insufficient when advanced heart failure occurs. Keeping in mind that pulse pressure is as important as the mean aortic pressure in optimizing perfusion, we aimed to enhance the pulse pressure by actively modulating pump speed while maintaining the normal mean pressure.

In this study, fuzzy logic control is adopted because of its ability to control complicated systems. The presented fuzzy controller attempts to maintain the mean aortic pressure to provide sufficient flow perfusion. Simultaneously, it enhances the pulse pressure to make the perfusion more natural on the premise of no regurgitation. The controller is first investigated by numerical simulations to see how it responds to heart failure and how robust it is under various physiologic disturbances. A preliminary in vitro experiment is implemented to further validate the fuzzy control method.

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METHODS

Model of the Cardiovascular and Baroreflex System

A model of the cardiovascular system is used to numerically evaluate the control method. It is modified from a previous study by Shi and Korakianitis8 to meet the requirements in the current application. The heart function is described with the pressure–volume relation using a variable elastance model, which is a gold standard in the simulation of ventricular function. It is widely used in numerical studies of the control strategy development of blood pumps7,9–11 and has proved itself in heart–pump interaction modeling. The time-varying elastance values are different between ventricles and atria in terms of their contractility. The general equation that describes the pressure and the volume of a heart chamber is as follows:

Equation (Uncited)
Equation (Uncited)
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The symbol * represents the four heart chambers, which are left ventricle (lv), right ventricle (rv), left atrium (la), and right atrium (ra).

Equation (Uncited)
Equation (Uncited)
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is the time-varying elastance, which is derived from the following:

Equation (Uncited)
Equation (Uncited)
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where

Equation (Uncited)
Equation (Uncited)
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and

Equation (Uncited)
Equation (Uncited)
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are the characteristic elastances of the four heart chambers, and

Equation (Uncited)
Equation (Uncited)
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is an activation function, which is the same for left and right ventricles, left and right atria, but different between ventricles and atria. The activation function is a piecewise function related to the contraction and the relaxation periods. The duration of systole is set to be linear with the cardiac cycle for different heart rates. More details about the heart model can be found in the literature.8

Lumped parameter models of the vascular network are adopted in this numerical study. The native circulation loop is divided into four parts: aortic sinus, aorta, small vessels including arterioles and capillaries, and veins, for both systemic and pulmonary circulations. Following the classical idea of electric–fluid analogue, an electric circuit is used to represent the whole circulation with characteristics of resistance, compliance, and inductance, which is shown in Figure 1. All the corresponding values of the physiologic parameters are listed in Table 1.

Table 1
Table 1
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Figure 1
Figure 1
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The heart valves regulate the flow directions by preventing backflow. They are described as the simplified diode-like model with little forward resistance (0.004 mm Hg·s/ml) but infinite inverse resistance.12

Speed modulation needs to synchronize with the heart rate. Because heart rate changes with different aortic pressures through the baroreflex system, it is necessary to introduce a model that establishes the relation between the aortic pressure and the heart rate. The baroreflex control system is modeled according to Ursino’s research.13 The heart period is regulated by both vagal and sympathetic activities. In this simulation, we adopt the same assumption from the study by Chen et al.14 that the heart rate remains constant within a cardiac cycle. More details about this baroreflex model can be found in the work of Ursino.13

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Model of a Rotary Blood Pump

The fuzzy controller does not work exclusively with a particular blood pump. In our simulations, we use an axial flow blood pump (Nimbus Medical, Rancho Cordova, CA) to test the controller. The pump is connected to the blood circulatory system by cannulations connecting to the left ventricular apex and aorta, as depicted in Figure 1. According to previous research by Choi et al.,15 an equation characterizing the hydraulic performance of the axial pump is shown below, with the pressure head (H), the flow rate (Q), and the rotary speed (ω) of the pump:

Equation (Uncited)
Equation (Uncited)
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where

Equation (Uncited)
Equation (Uncited)
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is the first derivative of the pump flow, and a0 = −0.296, a1 = −0.027, and a2 = 0.0000933 are the coefficients.

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Fuzzy Logical Controller Design

As previously mentioned, the objective of the controller is to maintain the mean aortic pressure and increase the pulse pressure to compensate for the failing heart. Two real-time indices, extracted from the aortic pressure waveform, are used as the controller’s inputs to control the mean pressure and the pulse pressure, respectively. The pump speed under the given settings is determined by the fuzzy logical inference system. The whole control diagram is shown in Figure 2.

Figure 2
Figure 2
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The control indices are the mean pressure index (MPI) and the pulse pressure index (PPI). The MPI is the direct current component obtained by passing the aortic pressure waveform through a low-pass filter with cutoff frequency at approximately 0.2 Hz. Similarly, the PPI is obtained from aortic pressure by a three-step signal processing shown in Figure 3A. Aortic pressure is first high-pass filtered at 0.5 Hz, then converted to an absolute value, and finally passed through a third-order Butterworth low-pass filter to obtain the PPI. The extraction method was tested by Choi et al.7 and proven to be suitable in representing pulse pressure. The PPI values under different pulsatile conditions are obtained by simulations of the cardiovascular system beforehand, without the left ventricular assist device (LVAD) connected. The normal range of the pulse pressure of adults is 20–50 mm Hg, with a PPI of approximately 6–14 correspondingly.

Figure 3
Figure 3
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The two control indices are regulated by two PI-type discrete fuzzy inference systems whose fuzzy variables are error (e) and error variety (e). For each index, it is first discretized and compared with the desired set point to obtain the error e(k), where k is the sample time. The error variety is then calculated by

Equation (Uncited)
Equation (Uncited)
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. According to e(k) and e(k) of the MPI, the output of the first fuzzy inference system is the difference of the middle rotary speed

Equation (Uncited)
Equation (Uncited)
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. The middle rotary speed at the next sample time is determined by:

Equation (Uncited)
Equation (Uncited)
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To provide additional pulsation with the blood pump, on the basis of the middle speed, the rotary speed is modulated according to the rectangular wave speed profile shown in Figure 3B during every cardiac cycle, maintaining pace with the heartbeat. The rectangular wave speed profile is characterized by the phase shift and the high pump speed period defined in Figure 3B. Unless explicitly specified, a 30% high pump speed period is used in this study. The phase shift is set to zero, which means high pump speed occurs during ventricular systole. This pump operation mode is called co-pulsation, which will mostly enhance the pulse pressure. In practice, the starting time of a cardiac cycle can be detected by the QRS complexes in the electrocardiogram (ECG) signal, which has been realized in Pirbodaghi’s experiment,16 and the previously measured heart period is used for determining the next speed modulation cycle. By this method, the frequency of the speed modulation is changed automatically. On the contrary, the offset amplitude from the middle pump speed is changing with the output of the second fuzzy inference system, for which e(k) and δe(k) of the PPI are the inputs. In conclusion, the instantaneous deviation from the middle rotary speed

Equation (Uncited)
Equation (Uncited)
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is as follows:

Equation (Uncited)
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where A(k) and δA(k + 1) are the offset amplitude for the current sample time and the amplitude change for the next sample time, respectively. T is the heart period, and u is fictitious time instead of the actual time, which is limited in the range of the heart period and set to zero at the beginning of each cardiac cycle. Lastly, the instantaneous rotary speed is determined as:

Equation (Uncited)
Equation (Uncited)
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In this design, triangular and trapezoidal membership functions are used (Figure 4), where “LN,” “N,” “Z,” “P,” and “LP,” representing “large negative,” “negative,” “zero,” “positive,” and “large positive,” respectively, are the linguistic labels. The rules for both fuzzy inference systems in the form of IF-THEN statements are listed in Table 2. Using the Mamdani fuzzy implication, the output fuzzy set is obtained and then transformed into a single numerical value

Table 2
Table 2
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Figure 4
Figure 4
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Equation (Uncited)
Equation (Uncited)
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or

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A through the popular centroid defuzzification method. All these stages are designed in the fuzzy toolbox of MATLAB (The MathWorks Inc., Natick, MA). More details about how a fuzzy inference system is developed can be found in the literature.17

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Regurgitation Prevention

Because of the pump speed variation, a low pump speed may occur in some physiologic circumstances, causing backflow in the blood pump, which is believed to be adverse to the ventricle. Therefore, a regurgitation prevention method is needed to restrict excessive speed change. To maximize the pulse pressure before regurgitation, the pump is expected to operate near the critical point just preventing regurgitation. To reach this target, considering the accuracy, the pump flow is recommended to be directly obtained to classify the pump states in this study. The minimum pump flow in each cardiac cycle is determined from the pump flow signal and used to switch between the fuzzy control method and the regurgitation prevention method in the next cardiac cycle. Two thresholds, 5 and 3 ml/s, are used to enable and disable the two methods: when the minimum flow is above 5 ml/s, the fuzzy control method to increase the pulse pressure is enabled; if the minimum flow is below 3 ml/s, the regurgitation prevention method is enabled, decreasing the pump speed variation amplitude to avoid backflow. Using this technique, the minimum pump flow will be kept in the transitional zone, 3 to 5 ml/s, providing the maximum pulse pressure while inhibiting regurgitation. A simple proportion control based on the error between the actual minimum pump flow and the 5 ml/s threshold is adopted as the regurgitation prevention method, with a 0.00025 proportion coefficient to provide satisfactory performance.

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Simulation Conditions

Computer simulations were performed to demonstrate the performance of the control strategy in Simulink software (The MathWorks Inc.). To simulate the pathological condition of advanced left ventricle failure, the value of the maximum systolic elastance

Equation (Uncited)
Equation (Uncited)
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was set to 0.3 mm Hg/ml, much less than the normal level, which is approximately 2.0 mm Hg/ml. Other parameters were set according to Table 1. The controller was implemented 15 s after starting the simulation when the control indices were stable. The initial rotary speed of the pump before the controller started was set to 800 rad/s. The desired MPI was set as 100, which is the standard mean aortic pressure in an adult, while the PPI set point was 6, which reflects the minimum pulse pressure in a normal adult of approximately 20 mm Hg. The PPI was set to the minimum desired value because larger PPI meant greater speed variation amplitude, which would require more energy consumption. Moreover, to compare with the constant pump speed control, an additional independent simulation with MPI set to 100 and without PPI control was also implemented (Figure 5).

Figure 5
Figure 5
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Furthermore, to prove the robustness of the controller, series changes of the parameters that would vary in different movement states, including compliance,18 systemic resistance (Rsvr), and ventricular contractility, were performed. The control method was evaluated in two stages. First, step changes of the Rsvr, aortic compliance (Cao), and left ventricular contractility (Elv,s) were performed independently among their physiologic ranges, as shown in Figure 6G. Although step changes were not physiologic, they created the worse cases the controller may encounter. This test was used to assess the robustness of the controller under various physiologic disturbances. Second, the combinations of the linear changes of all three parameters over two 10 s periods were performed to simulate a rest-exercise-rest transition, which is shown in Figure 7E. The transition is very similar to an actual physiologic change process and investigates the response of the controller in practice.

Figure 6
Figure 6
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Figure 7
Figure 7
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Preliminary Experimental Validation

To further validate the proposed fuzzy control method, a preliminary in vitro experiment was also performed. The experimental rig is shown in Figure 8A. It contains a pressure sensor (CEMPX-2; Nokisens Inc., Kunshan, China) and a flow meter (T402; Transonic System, Ithaca, NY). The pressure sensor obtains the pump’s outlet pressure, which is regarded as the aortic pressure. A centrifugal blood pump designed by ourselves is used as the control object. The vascular resistance is reproduced by a throttle valve. The aortic pressure is acquired and sent to the computer through a data acquisition card (PCI-1712, Advantech, Taipei, Taiwan). The fuzzy controller is realized in LabVIEW software (National Instruments, Austin, TX).

Figure 8
Figure 8
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Results

Numerical Simulations

The effects of the pulse pressure–enhancing controller under the condition of heart failure are shown in Figure 5, which also includes the constant speed control results. Figure 5 shows the aortic pressure in several cardiac cycles. Both the pulse pressure–enhancing control and the constant speed control elevate the aortic pressure to a mean value of 100 mm Hg, which corresponds to a mean circulatory flow rate of approximately 100 ml/s. However, the constant speed control reduces the pulse pressure to an extremely low level, even much less than the heart failure condition without an LVAD. Compared with the constant speed control, it is clear that the pulse pressure is enhanced to approximately 20 mm Hg by the pulse pressure–enhancing control. Under this circumstance, the pump speed profile is rectangular wave, as shown in Figure 5B. It is noted here that the heart period is also changed by the baroreflex system because of the change of aortic pressure after controlling. In addition, the left ventricular pressure–volume (P-V) loops are displayed in Figure 5C. Either of the control methods can unload the failing left ventricle, but the constant speed control relieves the ventricle more. Stroke work under pulse-enhancing control is approximately 56.5% of that in the heart failure condition without an LVAD compared with a value of 26.4% under constant speed control.

The controller was tested under various physiologic disturbances, which were more rigorous than actual disturbances. Good results were yielded, which are depicted in Figure 6. It is clear that the controller could withstand these disturbances, thus showing good robustness. When Rsvr increases from 0.9 to 1.2 mm Hg·s/ml at time 100 s, MPI deviates from the set point but quickly stabilizes back to the desired value, while PPI decreases to approximately 5 and stays there because of regurgitation prevention, thus limiting the speed variation amplitude. After Rsvr returns to its initial value at 150 s and further decreases to 0.6 mm Hg·s/ml at 200 s, PPI increases to 6 again and then increases past 6 and remains unchanged at this level. Cao changes, from 2.0 to 2.5 mm Hg/ml and then to 1.5 ml/mm Hg during 300–450 s, affect PPI a lot while only having little influence on MPI. Elv,s changes in a similar way (among 0.6, 0.3, and 0.1 mm Hg/ml) from 500 s, and the controller still performs well. During all the simulation times, once the backflow is happening in the pump, the regurgitation prevention method takes effect and pulls the pump flow back to positive, as shown in Figure 6E. Figure 6F shows the heart period variation, which has a similar trend to MPI because of the baroreflex system.

Slight exercise in a heart failure patient was simulated by linearly changing the Rsvr (decreased linearly by 0.3 mm Hg·s/ml), Cao (increased linearly by 0.3 ml/mm Hg), and

Equation (Uncited)
Equation (Uncited)
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(increased linearly by 0.3 mm Hg/ml) simultaneously. Figure 7 shows the responses to this physical activity. The controller still performs well during the transition from rest to exercise and back to rest. When in exercise, left ventricular pressure (LVP) decreases to low levels because more blood is pumped out to meet the metabolic demand. The pump flow shown in Figure 7D indicates that regurgitation is less likely to take place during exercise.

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Preliminary Experiment

Figure 8B shows the results of the preliminary experiment. Similar to the numerical simulation, the controller reaches the set points very well. The mean pressure of the pump’s outlet is kept at 100 mm Hg to provide a mean flow of approximately 5 L/min, and the pump alone generates a pulse pressure of approximately 20 mm Hg. The experiment demonstrates that the dynamic characteristic of a general blood pump is sufficient to track a speed modulation in one cardiac cycle. The controller is feasible in practical use. More experiments on a mock circulatory system or in animal trials need to be implemented to further validate the controller.

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Discussion

The controller proposed in this study is successful in enhancing the pulse pressure compared with the constant speed controller, but at the cost of less unloading of the ventricle. We can see this from the P-V loops in Figure 5. However, because excessive unloading of the left ventricle might lead to cardiac disuse atrophy,19 it is reasonable and acceptable to use 56.5% of the stroke work during no-LVAD-assisting heart failure for unloading. On the contrary, as shown in Figure 6B, PPI stays in the range 6–14 in some cases, as expected, which is due to the particular setting of the zero error membership function in Figure 4B. In this manner, the controller will not decrease the pulse pressure if the ventricle recovers and increases pulsation, unless the pulse pressure becomes more than 50 mm Hg as a result of other diseases such as arteriosclerosis.

Another notable aspect is that the LVP may decrease low values when the

Equation (Uncited)
Equation (Uncited)
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reduces, as shown in Figure 6C during 200–250 s. A similar situation occurs when a patient is doing exercise (Figure 7), mainly because of the reduction in resistance. If the

Equation (Uncited)
Equation (Uncited)
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decreases to abnormal levels because of drugs or over exercise, a suction event might happen. Thus, suction detection is needed. The pump flow signal acquired for regurgitation prevention can also be used to develop a suction detection system.20 It is worth noting that suction under this control method is a little different from traditional constant speed control. Suction occurs intermittently because of speed variation and only for a short time in every cardiac cycle. The effect of this phenomenon on the heart is not clear and needs to be further investigated.

There are two necessary signals in this study, the aortic pressure used to extract the indices and the pump flow used to prevent regurgitation. They can either be obtained by sensors implanted in the blood pump or estimated noninvasively using intrinsic pump parameters, such as current, voltage, and speed.9,10,21 However, it is more accurate to use sensors than estimation. Therefore, sensor is a better choice, especially during short-term transition therapy. Estimation might be better for long-term use. Take pressure sensors for example, although some of the long-term implantable pressure sensors are already available,22,23 reliability must be improved. Sensor drift influences MPI more than PPI. Baseline drift has almost no effect on PPI. However, if sensors are picked for long-term use, it is still necessary to perform regular calibration in a medical center.

In this study, the rectangular wave is adopted to modulate the pump speed because it increases the pulse pressure most compared with other basic waveforms such as a sine signal.24 The phase shift and high pump speed period defined in Figure 3B affect pulsation enhancement, which is depicted in Figure 9,A and B. The results are obtained when the pump works under maximum speed variation amplitude that prevents regurgitation. From Figure 9A, we can see that the pulse pressure is enhanced the most when the phase shift is zero, which fits our objective. If other considerations, such as a specific ventricular unloading are included, more investigations are required to find the optimal phase shift. The pulse pressure has an inverse relation with the high pump speed period, as shown in Figure 9B. This is because a shorter high pump speed period means that the mean pump speed must increase under the same desired mean aortic pressure, which can increase the maximum speed variation amplitude before regurgitation. However, too short of a high pump speed period is not achievable in practice because of the limited pump response. Similarly, a higher desired mean aortic pressure also increases the mean pump speed and thus leads to a higher pulse pressure the controller can generate before regurgitation, as shown in Figure 9C. Therefore, an appropriate increase in the MPI set point is desirable because it makes the controller easier to achieve the minimum pulse pressure of 20 mm Hg.

Figure 9
Figure 9
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Theoretically, a permanent magnet motor is rapid enough to let the pump accelerate and decelerate during every single cardiac cycle because its mechanical and electrical time constants are much less than the heart period.25 Moreover, within the power limitation, high speed accuracy can be achieved with feedback control of the motor. As a result, the speed output of the controller is able to be realized in a real blood pump, which has been demonstrated by the preliminary experiment and some other experiments.11,16

Pulsatile control of continuous flow blood pumps is a new topic and attracts more and more attention worldwide. More investigations support the point that pulsatile perfusion is better.5,26 In continuous flow blood pump therapy, current clinical investigations also suggest some negative effects such as arteriovenous malformations and bleeding events related to diminished pulse pressure,27 implying it will be beneficial to control pulsation of RBPs even for short-term transition therapy. Unlike other pulsatile control strategies using the inherent pulsatility in the native ventricle,7,11 the controller proposed by us actively regulates the pump speed to produce extra pulsation. The controller may also work well in advanced heart failure patients whose hearts cannot generate enough pulsation. Except for pulsation, sufficient perfusion is achieved by maintaining the mean aortic pressure at 100 mm Hg. Furthermore, compared with the previous investigations that focus on the physiologic effects of typical fixed speed modulations,16,24 the speed modulation in our study is autocontrolled to fit various physiologic conditions. It is noted that this control needs ECG signal to synchronize the pump with the natural heart. If arrhythmia exists or the heart is totally removed, a modulation waveform with a fixed cycle may be used instead. Another two concerns of speed modulation are whether there will be increased wear to the bearings and additional shear stress to the blood. It is likely to have increased wear, but the extent of the increase is not explicit and needs further investigations. Fortunately, the latest generation of blood pumps is usually suspended without contact bearings, so there is no need to worry about such a problem. As for shear stress, a previous group has demonstrated that there was no excessive hemolysis due to the speed alternation.28 However, more investigations are needed to support the conclusion.

Fuzzy control is believed to be superior in control applications in which the mathematic model of the cardiovascular system is limited and uncertain. Other fuzzy control studies of blood pumps have also shown advantages.29,30 The controller can be easily transplanted between multiple patients with different kinds of blood pumps. Both the simulation with the cardiovascular system and the preliminary experiment in vitro demonstrated the performance of this fuzzy controller, as shown in the results.

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Conclusions

A novel approach to control an RBP in advanced heart failure patients has been proposed in this article. It can provide additional pulsation while maintaining the mean aortic pressure. The pulse pressure is enhanced to a normal physiologic minimum value of 20 mm Hg by means of continuous regulation of the pump speed according to a modulating signal, which is synchronous with the cardiac cycle. The mean aortic pressure of 100 mm Hg is also achieved to provide sufficient flow. Perfusion will benefit from the adequate flow and enhanced pulsation. Fuzzy logical inference is used in this research, and it is very simple and easy to be applied in the field of blood pump control. Numerical simulations under various physiologic disturbances have been performed to demonstrate the effectiveness and robustness of the algorithm, and satisfying results are delivered. A preliminary in vitro experiment has also been implemented to prove the feasibility of the controller in practice. Future tests on a mock circulatory system or even in vivo experiments are needed to further verify the reliability of the control strategy.

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Acknowledgments

The authors are grateful to National Natural Science Foundation of China (Grant No. 51275461), the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51221004), and Zhejiang Provincial Natural Science Foundation of China (Grant No. Z1110189).

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physiologic control; fuzzy logic; pulse pressure; rotary blood pump; ventricular assist device

Copyright © 2014 by the American Society for Artificial Internal Organs

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