17 September 2020: Database Analysis
Effects of Pulsatile Frequency of Left Ventricular Assist Device (LVAD) on Coronary Perfusion: A Numerical Simulation StudyYuanfei Zhu1ABCE, Ming Yang1AEG*, Yan Zhang2BCF, Fan Meng1DEF, Tianyue Yang1AC, Zhiwei Fang1BF
Med Sci Monit 2020; 26:e925367
BACKGROUND: Left ventricular assist devices (LVADs) with counter-pulsation mode have been widely used to support left ventricular function and improve coronary circulation. However, the frequency characteristics of the coronary system have not been considered. The aim of this study was to investigate the effects of pulsatile frequency of LVADs on coronary perfusion.
MATERIAL AND METHODS: First, a lumped parameter (LP) model incorporating coronary circulation, systemic circulation, left heart, and LVAD was established to simulate the cardiovascular system. Then, the frequency characteristics of the coronary system were analyzed and the calculation results showed that the pulsatile frequency of the LVAD has a substantial effect on coronary blood flow. To verify the accuracy of the theoretical analysis, the hemodynamic effects of the LVAD on the coronary artery were compared under 4 support modes: co-pulsation mode, and counter-pulsation modes in synchronization ratios of 1: 1, 2: 1, and 3: 1.
RESULTS: We found that the coronary flow increased by 5% when the working mode changed from co-pulsation to counter-pulsation in a synchronization ratio of 1: 1, and by an additional 6% when the working mode changed from counter-pulsation in a synchronization ratio of 1: 1 to counter-pulsation in a synchronization ratio of 3: 1.
CONCLUSIONS: This work provides a useful method to increase coronary perfusion and may be beneficial for improving myocardial function in patients with end-stage heart failure, especially those with ischemic cardiomyopathy (ICM).
Keywords: Coronary Vessels, Heart-Assist Devices, Myocardial Reperfusion, Pulsatile Flow, Computer Simulation, Models, Cardiovascular, Ventricular Function, Left
The heart failure (HF) caused by ischemic cardiomyopathy (ICM) is common and is mainly related to insufficient coronary perfusion [1–4]. In recent years, continuous-flow left ventricular assist devices (CFLVADs) have been widely used in destination therapy for end-stage heart failure, with high reliability and durability [5–7]. However, several studies have shown decreased coronary flow under CFLVADs support [8,9]. The main reasons for decreased coronary perfusion are the decrease of left ventricular work and myocardial oxygen demand [9,10]. Moreover, under constant rotational speed, the mechanical characteristics of CFLVADs are also responsible for diminished coronary flow .
To increase coronary flow, Ando et al.  proposed a counter-pulsation mode for CFLVADs to improve myocardial perfusion. Lim et al.  also reported that the LVAD with counter-pulsation mode achieved better physiological coronary blood perfusion. Naito et al.  presented a rotational speed modulation system for CFLVADs to decrease the left ventricular (LV) load and increase coronary flow. However, under long-term support, CFLVADs may impair arterial contractility and myocardial microvascular structure, thus limiting coronary flow and causing myocardial ischemia [14,15]. Therefore, the flow profiles and pulsatility of LVADs still need to be optimized to improve destination therapy.
The cardiovascular system is a complicated impedance network [16,17]. The frequency characteristics of the cardiovascular system are closely related to blood perfusion. Wang et al.  reported that the arterial system had an optimal perfusion at its natural frequency. Gao et al.  showed that the heart beat generally matched the frequency characteristics of the arterial system, with low power consumption. Zhuang et al.  reported that when the pump speed was consistent with the resonance frequency of the arterial system, the perfusion of the arterial system was effectively improved. Rebholz et al.  analyzed the interaction between the high-frequency operating LVAD and the cardiovascular system to reduce the pump body size. However, in these studies, the coronary system was not included and the frequency characteristics of the coronary system were not investigated. Coronary flow is an important factor in determining cardiac function. However, the effects of pulsatile frequency of the LVAD on coronary perfusion have not been reported.
In this study we investigated the effects of pulsatile frequency of the LVAD on coronary perfusion. Firstly, we established a lumped parameter (LP) model of the cardiovascular system and analyzed the effects of coronary system frequency characteristics on blood perfusion. Then, the effectiveness of the established cardiovascular model was verified by comparing the present results with those of a previous study. Finally, the hemodynamic effects of the LVAD on the coronary artery were compared under 4 support modes: co-pulsation mode, and counter-pulsation modes in synchronization ratios of 1: 1, 2: 1, and 3: 1.
Material and Methods
MODEL OF CARDIOVASCULAR SYSTEM:
The cardiovascular system is modeled using a LP electric network, which includes 3 parts: left heart, systemic circulation, and coronary circulation. To analyze the frequency characteristics of the coronary system, the coronary circulation model was constructed from 3 main components: the coronary artery, the arteriolar resistance, and the myocardial vessels [24,25], as shown in Figure 1B. The coronary flow originates from the aorta root and flows into the vein . The arteriolar resistance RAR is mainly responsible for hyperemia and baseline conditions. Because ventricular pressure acts upon intramyocardial (IMC) vessels, the IMC pressure is represented by an external pressure element (PIMC in Figure 1). The variable intramyocardial resistance RMA depends on PIMC and is modeled as RMA=0.9PIMC, PIMC=PLV , where PLV represents left ventricular pressure.
The left heart was modeled as a chamber pump with 2 valves that control the direction of ventricular blood flow. The ventricle was simulated with a commonly used time-varying elastance model [23,27], and the atrial compliance was characterized by a capacitor of electric analog . The function CLV (t) of ventricle compliance was adapted from a previous model . The function CLV (t)=1/E(t) can be calculated as:
The systemic circulation was modeled by the aorta and the typical four-element Windkessel model (W4S) , as shown in Figure 1C. The aorta compliance is represented by CA. In the W4S model, the model parameters are RA, LA, CS, and RS, which represent the aortic resistance, the aortic blood inertia, total arterial compliance, and total peripheral resistance, respectively. The parameters of the cardiovascular model were adapted from previous studies [22–29], as summarized in Table 1.
MODEL OF LVAD:
The LVAD model was established based on previous research [12,30]. The prototype of the LVAD is a pulsatile pneumatic ventricular assist device (the Hybrid Ventricular Assist Device; Korea Artificial Organ Center, Seoul, Korea) . As shown in Figure 1A, the LVAD model consists of a flow generator (QLVAD), a blood cavity (CLVAD), and 2 valves (Di and Do). The flow profiles of the proposed pump model are simulated directly as sinusoidal waves for simplification, as the sinusoidal-wave-flow profiles parameterized with the stroke volume, the pulsatile frequency, and the phase shift . The phase shift ϕ was introduced to represent the time delay between the start of the native cardiac cycle and the middle of the pump systole. The starting point of the cardiac cycle was defined as the middle of native heart systole. As shown in Figure 2, the phase shift ϕ was simulated as 50%, 25%, and 16.6% to characterize the counter-pulsation mode with the synchronization ratio of 1: 1, 2: 1, and 3: 1, respectively. To ensure comparable results for various operation modes, the stroke volume of the LVAD was further manually adjusted to keep mean aortic pressure and LVAD flow constant .
FREQUENCY CHARACTERISTICS OF THE CORONARY SYSTEM:
The main factors affecting the coronary blood flow are blood pressure within the aortic root and vascular resistance. Generally, the coronary blood flow is about 250 ml/min and predominantly occurs during diastole . Hence, the frequency characteristics of the coronary system were analyzed during diastole in our model. The diastolic ventricle pressure is very small and is close to zero. Therefore, the IMC pressure (PIMC) and intramyocardial resistance (RMA) can be ignored in the diastole. The relationship between the input impedance Z(jω) and frequency f can be expressed as:
The magnitude of input impedance can be obtained by the above equations, as shown in Figure 3, showing that the magnitude of input impedance initially decreases and then increases with increasing frequency. The magnitude of impedance reaches the smallest value near 20 Hz, which is the smallest impedance frequency point. Further, the coronary impedance seriously restricts the coronary flow. Hence, the pulsatile frequency of LVAD can have a substantial influence on the coronary flow.
However, since the high pulsatile frequency requires more reliable and accurate control of the LVAD, the smallest impedance frequency is difficult to realize in clinical applications. Therefore, our study mainly investigated the effects of increased pulsatile frequency on coronary flow. In addition, when the pulsatile frequency increases by 2 Hz, the magnitude of coronary impedance decreases by about 4%. In other words, the coronary blood flow can increase by about 4% (10 ml/min) when the pulsatile frequency is 3 Hz.
To further evaluate the effectiveness of coronary perfusion, the total input work (TIW)  and energy equivalent pressure (EEP) [32,33] were introduced. The TIW is an important index of hemodynamic power and is calculated as:
The simulated pressure and flow waveforms of the cardiovascular system are shown in Figure 4 and the key hemodynamic results for simulated normal and severe HF conditions are summarized in Table 2. In normal conditions, the peak systolic pressure of LV was about 125 mmHg and the cardiac output was approximately 5.4 L/min. However, the peak systolic pressure of LV declined to 83 mmHg and the cardiac output was about 3.5 L/min in the HF condition. We also found that the coronary flow of the HF condition had a 33% decrease compared with the normal condition, which was approximately consistent with previous reports .
HEMODYNAMIC EFFECTS UNDER VARIOUS PULSATILE FREQUENCIES OF LVAD:
Four different operation modes of LVAD were simulated: co-pulsation mode, counter-pulsation mode, and counter-pulsation modes in synchronization ratios of 2: 1 and 3: 1. The hemodynamic waveforms of the various operation modes are shown in Figure 5. The cardiac cycle starting point was set to the start of systole. To compare the effects of pulsatile frequency of LVAD on coronary perfusion, the LVAD flow was set as 5.4 L/min and the mean aortic pressure was maintained at 100 mmHg in all operation modes of LVAD. The arterial pressure exceeded the peak LV pressure, as shown in Figure 5D, 5G, and 5J, respectively. Therefore, the aortic valve was not open and the native cardiac output did not generate any flow in the counter-pulsation modes. We also found that the peak LV pressure gradually decreased with increasing pulsatile frequency, which suggests that elevated pulsatile frequency can result in lower LV pressure.
The changes in the aortic flow for various LVAD operation modes are shown in Figure 5B, 5E, 5H, and 5K, respectively. With the increase of pulsatile frequency, several similar peaks were formed in the aortic flow. Similarly, the number of coronary flow wave peaks was consistent with frequency, as shown in Figure 5C, 5F, 5I, and 5L, respectively. The simulation results are summarized in Table 3, showing that the pump stroke volume in a synchronization ratio of 3: 1 declined to 35.8% of that in the synchronization ratio of 1: 1. Therefore, this result suggests that the pump volume may be reduced with increasing pulsatile frequency.
Coronary perfusion was effectively improved with increasing pulsatile frequency because the magnitude of coronary impedance decreases with increasing pulsatile frequency, as shown in Table 3 and Figure 6. Under the same mean aortic pressure, the mean coronary flow was enhanced. The EEP of the coronary artery was almost constant under LVAD support, which can be attributed to unchanged mean aortic pressure. The TIW of the coronary artery under the HF condition was 0.0228 J/s, which is only 44% of that under the normal condition. However, under LVAD support, the maximum TIW of coronary artery increased to 0.0583 J/s. Moreover, the TIW of the coronary artery had the same trend as the coronary flow under various pulsatile frequencies. These results indicate that increasing LVAD pulsatile frequency can effectively improve coronary perfusion by reducing the coronary impedance. As shown in Figure 7, the coronary flow increased with increasing mean aortic pressure in the counter-pulsation mode with a synchronization ratio of 3: 1. Therefore, normal aortic pressure is also crucial for coronary perfusion.
The cardiovascular system model used in this study has some limitations, similar to other zero-dimensional LP models. Some researchers have shown that pulsatile flow is directly related to endothelial production of nitric oxide, which can increase bradykinin-dependent vascular relaxation and decrease vascular oxidative stress [41,42]. Therefore, the corresponding nervous and hormonal regulation system should be considered in clinical applications. In addition, some peripheral organs, such as pulmonary and kidney tissue, should also be considered. The aortic valve is assumed to be closed during the cardiac cycle, which may result in aortic insufficiency . Therefore, the LVAD operating mode still needs to be improved to protect the aortic valve in clinical applications. Moreover, further in vivo experiments are needed to evaluate the effects of LVAD pulsatile frequency on coronary perfusion.
We investigated the effects of pulsatile frequency of LVAD on coronary perfusion. First, we simulated the cardiovascular system using the LP model, which incorporates left heart, LVAD, coronary circulation, and systemic circulation. Then, the effects of pulsatile frequency on the coronary impedance were analyzed. The present theoretical analysis suggests that increased pulsatile frequency can effectively decrease the coronary impedance when the pulsatile frequency is not higher than the resonance frequency. Therefore, the 4 different operation modes of LVAD (co-pulsation and counter-pulsation modes in synchronization ratio of 1: 1, 2: 1, and 3: 1) were simulated to compare the hemodynamic effects. The simulation results show that the counter-pulsation mode with high pulsatile frequency not only effectively improves the coronary flow, but also helps unload the LV. Although the pulsatile LVAD was used in the study, changing the pulsatile frequency of CFLVADs by the speed control algorithms to improve myocardial function in patients with ICM appears to be promising.
FiguresFigure 1. Circuit diagram of the cardiovascular system model. (A) Cardiovascular system and left ventricular assist device (LVAD), (B) Coronary circulation, (C) Systemic circulation. R – vascular resistance; C – vascular compliance; L – blood inertia; D – valve; P – pressure; Q – blood flow; LV – left ventricle; LA – left atrium; CA – coronary artery; A – aorta; S – total peripheral artery; MiV – mitral valve; AoV – aortic valve; AR – arteriolar resistance; IMC – intramyocardial vessels; RM1, RMA, RM2 and RMP – the myocardial resistances. Figure 2. Flow waveforms of the LVAD in the co-pulsation mode and the counter-pulsation modes. The negative flows represent the pump’s diastole and positive flows represent the pump’s systole. Figure 3. Frequency characteristics of the coronary system. Figure 4. Simulated pressure waveforms (A) and flow waveforms (B) in the cardiovascular system. PA – aortic pressure; PLV – left ventricular pressure; QA – aortic flow; QCA – coronary artery flow. Figure 5. Simulated hemodynamic waveforms in the cardiovascular model with 4 different operation modes. (A–C) co-pulsation mode; (D–F) counter-pulsation mode; (G–I) counter-pulsation mode in a synchronization ratio of 2: 1; (J–L) counter-pulsation mode in a synchronization ratio of 3: 1. Figure 6. Coronary perfusion in the normal, HF, co-pulsation mode, and counter-pulsation mode in synchronization ratios of 1: 1, 2: 1, and 3: 1. Figure 7. The effects of aortic pressure on coronary perfusion in counter-pulsation mode with a synchronization ratio of 3: 1.
TablesTable 1. Parameter values of the lumped parameter model. Table 2. Key hemodynamic results for simulated normal and severe HF conditions (normal and HF-III, respectively). Table 3. Simulated hemodynamic responses of the normal, severe HF, and HF with different modes of LVAD support (TIW – total input work; EEP – energy equivalent pressure).
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