Until recently, heart failure (HF) is the leading cause of mortality and morbidity all over the world. Although nowadays heart transplantation is the mainly accepted therapy for the treatment of severe cases, the limited availability of heart donors and the increasing number of patients diagnosed with HF has led to the development of left ventricular assist devices (LVADs) as a bridge to transplantation, recovery, or destination therapy.1,2 Over the past few decades, a large number of LVADs, including pulsatile-flow LVADs (PF-LVADs) and continuous-flow LVADs (CF-LVADs), have been developed and applied clinically.3
The pump rate of LVADs support has a significant implication on the cardiovascular system. For instance, Lukic and Weiss4 studied the effect of pump rate and filling of the pulsatile LVAD on the degree of hemolysis and found out that the hemolysis was affected by the pump rate. Noor et al.5 investigated the relationship between pump speed and exercise capacity. In their research, it is shown that the patients with lower residual left ventricular (LV) function are more sensitive to pump speed reduction. Clinically, PF-LVADs are mainly operated at constant pulsatile rates synchronizing to the natural cardiac cycle or running at fixed pump rates determined by a specialist, depending on the physiologic needs of the patient. Although CF-LVADs have widely gained clinical acceptance within the medical community due to the advantages of smaller pump size and improved mechanical reliability, the constant rotational speed has led to reduced arterial pulsatility and limited reduction over cardiac workload, which reduces reverse remodeling in LV.6 Furthermore, the effects of diminished pulsatility with CF-LVADs on end-organ function might be the cause for the vascular malformations, the higher rate of gastrointestinal bleeding events, and aortic valve insufficiency.7–10 To partially resolve these problems, the pump speeds of CF-LVADs have been modulated synchronizing to the natural cardiac cycle when a reliable synchronous triggering source is available.11–14 The most common method to realize synchronization is to use the R-wave detection of the electrocardiogram.15 However, in contrast to these studies with a reliable synchronous reference, there are few reports related to selecting a suitable pump rate of LVAD in the cases of HF patients associated with arrhythmia.16
Because the pulsatile flows generated by the native heart and LVAD exist in the compliant aorta as the form of pressure and flow waves, there are strong coupling effects between LVAD and cardiovascular system. In fact, pulsatile-flow output from the heart is essential for power transmission, reducing dissipation of energy in the artery.17,18 Significant efforts have been performed in the past few decades to elucidate the interaction between the heart’s pumping characteristics (heart rate [HR]) and wave dynamics of the arterial system.19–21 Lin Wang et al.22 reported that the cardiovascular system has its natural frequencies and found out that when the heart beats at a frequency near the fundamental natural frequency of the arterial system, the heart will have an optimal perfusion for the blood pressure and flow rate; other researches focus on the interaction between the cardiovascular system and LVAD. For instance, Vollkron et al.23 used a numerical model of the cardiovascular system to investigate the interaction between a continuous-flow pump and the cardiovascular system; Lim et al.24 performed animal experimental measurements on their numerical model to optimize heart-pump interaction model under varying conditions, such as pump speed and systematic vascular resistance (SVR). However, all these interactions are based on the excitation or synchronization to the natural cardiac cycle, and they cannot be used to the LVAD support without a cardiac triggering source.
Arterial systems are blood-filled elastic vessels so that they have resonance phenomena in hemodynamics.25 Also, the HR can be adjusted by the blood of body’s demands based on the baroreflex system and nervous system.26 Although the mechanism of the HR regulation is very complex, the HR represents the signal of the blood demand to some degree. This suggests that the HR normally matches the frequency-domain characteristics of the arterial system. Hence, the blood circulation of human body can be maintained by the native heart with low power consumption. In this study, a method combining the pump rate with HR and the resonant characteristics of the arterial system is investigated for selecting the pump rate of LVAD, especially when there is no reliable synchronous reference. Also, the experiments on a mock circulatory system (MCS) have been conducted to evaluate the hemodynamic effects of LVAD with a different pump rate on cardiovascular system. In addition, the hemodynamic performance indices were quantified by using total input work (TIW) of systemic circulation and energy equivalent pressure (EEP) calculated from hemodynamic waveform measurements.
Resonant Frequency in the Systemic Circulation
There are many physiologic models to describe the hemodynamics of the systemic circulation.23 To survey the resonant frequency of the systemic circulation, it is needed to choose a model that is easy to be used in the frequency-domain analysis. Among them, the Windkessel model has been the most widely used to analyze vascular characteristics or facilitate the application of identification techniques.27 An electrical analog of four-element Windkessel model (W4S) is illustrated in Figure 1, in which an inertial term LC is connected in parallel with the resistant term RC.28 In this W4S model, the models parameters are RC, LC, CS, and RS, respectively, accounting for the aortic characteristic resistance, the inertia of blood mass, total arterial compliance, and total peripheral resistance. In addition, QA and PA represent the aortic flow and pressure, respectively. QL denotes flow through LC, while PS represents pressure over CS.
The W4S model consists of two dynamic elements. As a consequence, the state vector needs two state variables to describe the dynamics, which defines as follows:
. So the state equations for the W4S model can be derived from Kirchhoff’s voltage and current law, written as follows
in which QL is equal to QA in the W4S model.
To calculate the resonant frequency of systemic circulation, the state Equation 1 needs to be converted to the input impedance equation of vascular system denoting as the frequency response.29 The input impedance equation Z(jω) is defined by
where j is an imaginary unit, ω represents the angular frequency, and a1, a2, b1, b2 are the coefficients, given by the expressions as follows:
Then, the magnitude of input impedance equation is expressed by
So, the resonant frequency of systemic circulation is obtained from the inflection point with calculating derivative of the magnitude of the input impedance equation, solved as
Here, it assumes that the resonant frequency of systemic circulation is the real positive value. Hence, the solution of the equation is expressed as follows:
where the unit of f is Hz.
Configuration of the Mock Circulatory System
It is widely used to test and validate the artificial cardiovascular devices in vitro experiments based on an MCS.30,31 In this experiment, the LVAD was attached to an MCS, simulating the interaction between the LVAD and the cardiovascular system, as shown in Figure 2. The MCS is mainly composed of the pneumatically driven mock left ventricle and the systemic circulation. The left ventricle is mimicked by a hemiellipsoidal container, which is divided by a flexible silicone diaphragm into an air chamber and a water chamber. Two check valves are placed at the inlet and outlet of the water chamber, simulating the mitral and aortic valves, respectively. The mock aorta is a silicone rubber tube with a specified length. The arterial compliance is simulated by the use of Windkessel chamber, designed by an airtight tank securing some of compressed air above the fluid level. The amount of the sealed air is adjusted by the air control valve on the top of the tank, and therefore, it achieves the desired value of arterial compliance. To reproduce the total peripheral resistance, a tunable ball valve located downstream of the arterial compliance chamber is used. The left atrium is simulated by an open tank, where the specified height of fluid level provides the mean left atrial pressure for the mock left ventricle.
The dashed area shown in Figure 2 represents the cam-type electric motor-driven LVAD (CT-LVAD), which is a pulsatile LVAD with maximum stroke volume equal to 55 ml, and Figure 3 illustrates a draft of the internal principal components of the CT-LVAD.32–35 The CT-LVAD has the mechanism that converts the rotational motion of the electric motor with the cam into the reciprocating motion of a follower, which is connected to a pusher plate. When the follower restricted by a vertical guide moves up and down along a cam groove, thus exerting a driven force on the pusher plate, the blood chamber is alternately compressed and expanded by the pusher plate. A couple of mechanical valves are mounted on the inlet and outlet of the chamber to control the unidirectional flow.
The aortic flow signal P2 is obtained with an ultrasonic flowmeter (MA-16PAU; Transonic Inc., Ithaca, NY), and the pressure signals are measured by pressure transducer P1 and P3. In the beginning of experiment, the pressure and flow transducers were calibrated to ensure measurement accuracy. In addition, all the hemodynamic waveform data were filtered by a low-pass filter with cutoff 40 Hz and recorded by a PowerLab 8/30 data acquisition device (ADInstruments, Sydney, Australia), sampling rate at 4,000 Hz per channel, and then automatically stored in the LabChart 7 (ADInstruments).
Evaluation of Hemodynamic Performance
To evaluate the hemodynamic effect of LVAD with a different pump rate on the systemic circulation, the TIW and EEP are calculated and analyzed in MATLAB (MathWorks, Natick, MA). The TIW as an important index of systemic perfusion is calculated by the integration of the product of the arterial pressure Psys (t) (mm Hg) and blood flow Qsys (t) (L/min) over a cardiac cycle, denoted as,
where THR is the cardiac cycle.
According to a previous work,36 the hemodynamic energies generated by the pulsatile pressure and flow waveforms can be quantified with the EEP. The EEP expressed in mm Hg is the ratio of the integrated hemodynamic power curve to the integrated aortic flow during each cardiac cycle, which represents the hemodynamic energy per unit volume of fluid pumped, and is equivalent to unit of pressure. It is defined by the following formula37,38:
in which AF(t) is the instantaneous arterial flow, whose unit is L/min, AP(t) represents the instantaneous arterial pressure, whose unit is mm Hg, and THR denotes the cardiac cycle.
To determine the initial experimental conditions with native left ventricle, baseline hemodynamic measurements are performed. The pneumatically driven mock left ventricular pressure, vascular resistance, and compliance are adjusted initially to reproduce mean arterial pressures and cardiac outputs of a failing ventricle. After producing baseline conditions, the mock left ventricular pressure, vascular resistance, and compliance are fixed. Normally, the W4S parameters can be identified by relying on the real-time measurements of physiologic blood pressure and flow rate.28 Here, the two groups of the model parameters and their physiologic meanings in our MCS are listed in the Table 1.28,39 A mixture of glycerin (40%) and water (60%) is used as the fluid medium and blood analog solution.40 In the first group, all the four test conditions are reproduced by using four HRs, which are set at 55, 60, 66, and 70 beats per minute (bpm), respectively. In the second group, the test conditions are conducted by using seven HRs, which are set at 55, 60, 65, 70, 75, 80, and 85 bpm, respectively. Also, the preload is set as approximately 10 mm Hg, and the afterload is set as approximately 60–90 mm Hg in these experiments. The hemodynamic waveforms generated by the native left ventricle are illustrated in Figures 4 and 5, in which the mean flow and pressure are maintained at approximately 1.4 L/min and 46 mm Hg, respectively. In each test condition, the aortic pressure, aortic flow, and driving current of LVAD are recorded simultaneously for the different pump rates of LVAD. Finally, the performance with the different pump rates of LVAD is analyzed by the variations in TIW and EEP, respectively.
Theoretical Resonant Frequency of the Arterial System
According to the coefficients (a1, a2, b1, b2) of Equation 7, they are mainly determined by the W4S parameters (RC, LC, CS, RS). And the W4S parameters listed in the Table 1 are used to calculate the solution of Equation 7 in this study. From the results, the two groups of resonant frequencies of the mock systemic circulation are approximately equal to 1.5 and 1.62 Hz, respectively. In other words, the impedances of the systemic circulation are minimized at the 90 and 97 bpm. The theoretical resonant frequencies are within the normal HR of human body.
Experimental Results Only Contributed by LVAD
Initially, the pneumatic driving controller in Figure 2 is shutdown, and the mock left ventricle does not work. As a consequence, the results of TIW and EEP in the first group are only contributed by LVAD, as illustrated in Figure 6. Figure 6A shows that TIW increases from 0.33 to 0.67 W as pump rates increase from 51 to 79 bpm. As shown in Figure 6B, the similar variation pattern is also found in the EEP, increasing from 76 to 120 mm Hg with the increasing pump rates. Also, the variation patterns of TIW and EEP in the second groups are found when the pump rate increases from 45 to 90 bpm, as shown in Figure 7.
Experimental Results Contributed by Both the Mock Left Ventricle and LVAD
Next, the pneumatic driving controller in Figure 2 is turned on, and both the mock left ventricle and the LVAD contribute to the results of TIW and EEP. Figure 8 illustrated the TIW of the systemic circulation at four HRs based on the first group’s parameters. From Figure 8, it is shown that the maximum values of TIW obtained at 55, 60, 66, and 70 bpm are 0.57, 0.66, 0.81, and 0.82 W, respectively. So, it means that the maximum values of TIW are obtained when the pump rate is equal to mock ventricle rate. Importantly, when the pump rate of LVAD is greater than the mock ventricle rate, the overall trend of TIW will gradually increase, with increasing pump rate of LVAD (Figure 8A), while the overall trend of TIW (Figure 8, B and D) is first decreased, where the minimum value is reached at a pump rate of 63 and 73 bpm, and then continues to increase when the pump rate of LVAD is greater than 63 and 73 bpm, respectively. Furthermore, the trend of TIW (Figure 8C) is first decreased from 66 to 68 bpm, where the value is minimal, then increased until 70 bpm, which is a local maximum point, then decreased until 71 bpm, and then increased until 76 bpm.
Similarly, the EEP is calculated for four HR conditions, as shown in Figure 9. As clearly seen in Figure 9, it is indicated that the maximum values of EEP are also obtained when the pump rate of LVAD is equal to the mock ventricle rate and that are 108, 119, 131, and 136 mm Hg, respectively. Also, when the pump rate of LVAD is greater than the mock ventricle rate, the overall values of EEP will gradually increase with increasing pump rate of LVAD (Figure 9A), while the EEP (Figure 9, B and D) is first decreased, where the minimum value is obtained at a pump rate of 63 and 73 bpm, and then continues to increase when the pump rate of LVAD is greater than 63 and 73 bpm, respectively. Meanwhile, the trend of EEP (Figure 9C) is first increased until 70 bpm, where the local maximum value is achieved, then decreased until 71 bpm, which is a local minimum point, then increased until 76 bpm. Although the TIW and EEP (Figure 8C and 9C) are fluctuating, the overall trends are also increasing when the pump rate of LVAD is close to the calculated resonant frequency.
The TIW and EEP of the systemic circulation for the second group’s parameters are shown in Figures 10 and 11. And it is found that the maximum values of TIW and EEP are also obtained when the pump rate is equal to mock ventricle rate. In particular, when the pump rate of LVAD is greater than the mock ventricle rate, the overall trend of TIW and EEP tend to be relatively large.
In the current study, the TIW represents the total input energy of blood that is injected into the aorta with both LVAD and mock left ventricle supporting. In other words, the larger the TIW value is, the more energy of blood can be injected into the arterial system. According to the previous study,41 the hemodynamic energy is the essential reason for keeping the blood circulation, and it is regarded as the best metrics to evaluate the capacity of blood perfusion relative to the use of pressure or flow. Both PF-LVADs and speed modulated CF-LVADs can be configured at a rate independent of the native HR (asynchronous) or equal to native HR (synchronous), with the latter requiring an synchronous triggering source, such as R-wave detection.42–45 No matter the ejection time delay of CT-LVAD with respect to the cardiac cycle may be set at a certain phase between zero (co-pulsation) and half a cardiac cycle (counter-pulsation), the TIW achieves its maximum value in Figure 8 when the pump rate is equal to the mock left ventricle rate. This agrees with the previous research,46 where the authors concluded that when the rotational speed of the CF-LVADs was synchronized to the heart beat, the arterial perfusion was improved. Similarly, Heredero et al.47 reported that the synchronized mode of LVAD operation might satisfy the blood demand. As shown in Figure 9, the EEP exhibits similar pattern, which is consistent with the previous research.48 In short, it is demonstrated that LVAD operating at a synchronous mode with HR is beneficial to augment the input energy of the arterial system.
No matter the mock left ventricle operates at 55, 60, 66, and 70 bpm, both patterns of TIW and EEP exhibits two peaks as shown in Figures 8 and 9. The first peaks appear when the pump rate is equal to the mock left ventricle rate. The second peaks appear when the pump rate of LVAD is close to the theoretical resonant frequency 90 bpm of the arterial system. That is, the overall trend of TIW and EEP continues to increase with increasing pump rate of LVAD when the pump rate of LVAD is greater than the mock left ventricle rate for each test condition. So it is suggested that the arterial system may be acting like a resonant system that exhibits a resonant response. These results are in agreement with the previous theoretical study,49 which has shown that the hemodynamic energy in delivering the blood from the left ventricle to arterial system was optimized when the pump rate of LVAD was close to the dominant frequency of the arterial system. Also, with periodic forced blood flow generated by the mock LV and LVAD, the forced vibration will occur in the arterial system.18 Therefore, if the frequency between the mock left ventricle and LVAD is not equal, the amplitude of blood pressure or flow rate will fluctuate. This may be the reason for the TIW and EEP to keep rising and falling with the change of pump rate, as shown in Figures 8 and 9. Furthermore, the two groups of the model parameters represent the different vascular state, and the patterns as shown in the Figures 10 and 11 are consistent with the Figures 8 and 9 when the pump rate is equal to the mock left ventricle rate, while others are less fluctuating when the pump rate is greater than the mock left ventricle rate. It is shown that the resonant behavior of the arterial system is affected by both the vascular state and the pump rate.
The current research clearly shows that the hemodynamic effect of the arterial system can be affected by variations in the pump rate of LVAD relative to the native HR. As a result, it may be applied to select a suitable pump rate of LVAD. For example, at the beginning of LVAD accessing the human body, the majority of the commercial PF-LVADs or CF-LVADs are mainly operated at a constant pump rate or run at a fixed speed modulation when patient’s HF remains serious. With the myocardial function gradually recovering, however, if the LVAD is still operating at the fixed pump rate or constant pump speed modulation, it may not be able to achieve the appropriate or better supporting effects due to the variation of the arterial system natural frequency. So, care must be considered to ensure that the pump rate of LVAD is suitable for the body’s demand of cardiac output. In particular, if arrhythmia exists or the failing heart is totally removed, there is no method to provide a reliable synchronous triggering source for the LVAD.44 In these cases, it is suggested that the natural frequency of the arterial system can be selected as a pump rate of LVAD, which makes LVAD achieve better supporting effects. In other words, we can take a measure to identify and track the natural frequency of the arterial system in real time, and then the pump rate can also be adjusted to match the physiologic demand in real time. This study will be continued in future research.
The output performance of CT-LVAD is not perfect since it is a prototype pulsatile LVAD developed in our laboratory. Particularly, because the pneumatic driving controller contains the pneumatic components such as the pneumatic solenoid valve, the maximum response time of the pneumatic driving system is limited, which the maximum HR of the mock left ventricle reaches to approximately 85 bpm. So, the pump rate of CT-LVAD reaches to 89 bpm without testing a higher pump rate. In addition, despite the effects of CT-LVAD support with different pump rates investigated, the hemodynamic effects of different phase shifts on the arterial system have not been considered yet. To select a suitable pump rate of LVAD is a very important issue for HF patients with LVAD support. However, the experimental data are obtained in an MCS, in which the performance of the MCS is representative of clinical observations from a purely hydrodynamic viewpoint. Obviously, it is not able to replace in vivo models and is incapable of replicating all expected clinical responses. It is, therefore, needed to be confirmed by animal experimentation to evaluate the performance of these studies in the subsequent research too. Despite these limitations, the experimental findings of this research may provide valuable approach to evaluate the performance with different pumping rate of LVAD support.
In this article, the hemodynamic effects of different LVAD pump rates on the cardiovascular system have been investigated. A prototype pulsatile LVAD connecting to an MCS is used to evaluate the hemodynamic effects of different LVAD pump rates on the cardiovascular system. It demonstrates that the change of pumping rates of LVAD has a significant influence on the perfusion of cardiovascular system due to the resonance characteristics of the arterial system. The results may be helpful to select the suitable pump rate of LVAD for HF patients at different stages of the use of LVAD in contrast to a fixed cycle or a constant pump rate. To validate in vivo experiments, further researches are needed.
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Keywords:Copyright © 2016 by the American Society for Artificial Internal Organs
heart failure; pump rate selection; left ventricular assist device; resonant frequency; mock circulatory system