Hemodynamic effects of various support modes of continuous flow LVADs on the cardiovascular system: A numerical study

Background

The CF-LVADs are now widely used clinically in patients with advanced, chronic cardiac failure. The clinical results are gratifying, even after long-term support. Hemodynamic changes after CF-LVADs implantation have been evaluated quite extensively. Left ventricular volume is significantly reduced [1]. The pulsatility of blood flow is reduced as the rotational speed of the pump is increased [2]. The systemic vascular impedance is significantly increased [3]. In addition, changes in the coronary flow and circulation have been demonstrated [4,5]. The coronary flow is reduced as the CF-LVADs support is increased. This might be the consequence of a drop in the left ventricular work itself due to left ventricular unloading and a drop in myocardial oxygen demand. The decreased myocardial oxygen demand may lead to a reactive increase in the coronary vascular resistance through the auto-regulatory system.

The support modes of CF-LVADs could significantly impact the hemodynamic changes and patient outcomes. Differences in the support mode might even account for the differences in results in the patients receiving an LVAD as a bridge to recovery.

Many support modes, achieving various aims, have been designed for CF-LVADs, including Heart Mate II, Jarvik 2000, Heart ware, and BJUT-II VAD. For instance, the constant speed mode, driving the CF-LVADs with a stable rotational speed in the whole process, was first proposed for clinical practice [6,7]. Under this mode, the rotational speed of CF-LVADs is considered as the input of the controller, and the actual speed of CF-LVADs is regulated by the constant speed mode to track the desired one. To achieve a controllable performance of arterial perfusion, the continuous flow mode has been proposed [8–10]. Under this mode, the blood flow rate is chosen as the control input and the support mode regulates CF-LVADs to achieve the desired blood flow rate. Finally, as clinical experience in CF-LVADs improved, the role of the pressure gradient between the left ventricle and ascending aorta has become a very important indicator of the cardiovascular system. Hence, several support modes, choosing this pressure head as the control variables, were designed [11,12]. The pressure head across CF-LVADs, in this mode, is controlled by the controller to track its desired value. However, the precise mechanism of the changes in the hemodynamics and perfusion due to the different support modes remains unclear.

The present work is focused on the study on a circulatory model of the hemodynamic changes in the cardiovascular system under different modes of left ventricular support. Three support modes – “constant speed”, “continuous flow”, and “constant pressure head” – were studied. Numerical studies have been conducted to evaluate the performances of these 3 support modes. The following indices have been computed on the model: the blood assist index (BAI), the left ventricular external work (LVEW), the energy of blood flow (EBF), the pulsatility index (PI), and the surplus hemodynamic energy (SHE). The abbreviations used are shown in Table 1.

Material and Methods

THE DESIGN OF VARIOUS SUPPORT MODES:

In this paper, 3 support modes, used widely in clinical practice, were designed to evaluate the hemodynamic changes. The first support mode, named “constant speed”, drives the CF-LVADs with a constant rotational speed during the whole cardiac cycle. The second control strategy, named “constant pressure head” [13], maintains a constant pressure across the CF-LVADs. For this support mode, the support level of CF-LVADs will be increased during the systolic period to achieve more blood perfusion. The support level is reduced during the diastolic phase to prevent suction. The third support mode, called “continuous flow”, is driving the CF-LVADs with a stable flow output of the CF-LVADs.

To compare the respective hemodynamic effects of the 3 different modes, an equivalent support level is necessary. Consequently, the blood assist index (BAI) [14] was used as the indicator of the support level. BAI reflects the energy distribution between the CF-LVADs and the native heart, which is a ratio of the power of CF-LVADs and total power of the cardiovascular system. The validity of this index has been demonstrated in previous publications [15]. In this study, the BAI value was increased from 20% to 90% to cover all types of LVAD support. The 20% BAI value represents the minimal support level and the 90% BAI value represents the maximal unloading of the left ventricle.

In this article, the control variables of the 3 support modes – the rotational speed for constant speed mode, the pressure head for constant pressure head mode, and the pump flow for continuous flow mode – were regulated to increase the BAI value from 20% to 90%.

THE COMBINED MODEL OF CARDIOVASCULAR SYSTEM AND CF-LVADS:

A mathematical model of the cardiovascular-pump system was use to evaluate the hemodynamic effects of the different support modes. Figure 1 shows the complete electric circuit analogy of the cardiovascular model in relation to the CF-LVADs. The model includes the left atrium, the active left ventricle, the CF-LVADs, and the peripheral circulation system. The active left ventricle in this model is mimicked by a time-varying elastance function: E(t)=1/C(t). In this work, the elastance function was defined as:

Where Emax and Emin denote the maximum and minimum values of E(t); and En(t) represents the normalized time-varying elastance function [15,16]:

Where tn=t/tmax and tmax=0.15*Tc+0.2; Tc represents the cardiac cycle interval (i.e., Tc=60/HR, where HR represents the heart rate of the native heart). In this work, the HR was fixed at 75 bpm. This model was compared to clinical data, and the results demonstrate that the model can accurately mimic the hemodynamic performance of the circulatory system [17]. The complete description and the parameters’ values (listed in Table 2) of the model were set as heart failure patient, as reported by Gu et al. [18].

According to previous research by our group, the mathematic model of CF-LVADs is described as a function of the flow rate, pressure head, and rotational speed of the pump, which is denoted by:

In which QPO represents the flow rate of the pump (L/min), PP is the pressure head of the pump (mmHg), ω is the rotational speed (R/s), and LP is the inertia of blood in intra-aorta pump. A detailed description of model of the BJUT-II VAD and its identification is reported in Chang [19]. Note that, although equation (3) is derived from BJUT-II VAD, it is confirmed to be appropriate for CF-LVADs placed between the left ventricular apex and the ascending aorta.

THE HEMODYNAMIC ANALYSIS:

The left ventricular external work (LVEW) as an index of cardiac recovery is defined to indicate the energy of native heart, denoted as:

in which ^ωLV represents LVEW, P_LV(t) is left ventricular pressure, Q_LV(t) is left ventricular flow, and T_c is cardiac cycle.

The input work of systemic circulation as an index of blood perfusion was defined to indicate the energy of circulatory system, denoted as:

in which ω_sys represents LVEW, P_sys(t) is the left ventricular pressure, Q_sys(t) is the left ventricular flow, and T_C denotes the cardiac cycle.

Kawahito [20] proposed use of PI to evaluate the pulsatility blood flow of VADs. Research findings indicate that the change of pulsating flow was exponential, with different levels of assist ratio, in an animal experiment. In this article, the pulsatility index (PI) [21] is used to estimate pulsatility of blood pressure. In this paper, it is defined as follows:

in which P_SB is the systolic blood pressure, P_DB represents the diastolic pressure, and MAP is the mean arterial pressure.

The energy-equivalent pressure (EEP) formula is defined as the ratio of the area beneath the hemodynamic power curve (fFPdt) to the area beneath the pump flow curve (fFdt) during each pulse cycle [22]. It represents the hemodynamic energy per unit volume of blood. It is calculated as follows:

in which F is the blood flow (in liters per minute) and P represents the arterial pressure (in mmHg). SHE is calculated in response to EEP and MAP as follows:

in which SHE represents the extra energy required for generation of pulsatile flow (PF) in terms of energy (not pressure) units and is thus a physiologically relevant measure of pulsatility because the generation of PF in the body is dependent on an energy gradient rather than a pressure gradient [23].

Results

The hemodynamic effects of the different support modes of the CF-LVADs were evaluated in numerical studies. The characteristics of the model before CF-LVADs support were simulated to validate the model. The clinical data and the results of simulation are listed in Table 3. In this table, the normal value is derived from the literature [18], and the clinical value was measured in clinical practice at Peking University third hospital. The results show that the proportional error of the systolic pressure (SBP) and the diastolic pressure (DBP) is 4.9% and 9%, respectively. The proportional error of end-diastolic volume (EDV) and end-systolic volume (ESV) was 13.4% and 3%, respectively. The proportional error of MAP was about 2.3%.

Figure 2 shows the relationship between the control variables of the 3 support modes and the BAI value. In this study, the control variables of 3 support modes, including the pressure head across CF-LVADs, flow rate of CF-LVADs, and the rotational speed of CF-LVADs, were increased to achieve the BAI value increasing from 20% to 90%. For the constant speed mode, the desired rotational speed of CF-LVADs is increased from 5880 RPM to 10 860 RPM. Similarly, the desired pressure head of CF-LVADs in constant pressure head mode is increased from 70 mmHg to 190 mmHg. The pump flow rate in the continuous flow mode increased from 1.9L/min to 10.5L/min.

Figure 3A shows the changes in the LVEW in the bypass model. Following the rise of BAI, the continuous flow has the minimum value of the LVEW. In the constant rotational speed mode and the constant pressure head mode, the LVEW is increased by 31% and 14%, respectively. In other words, the continuous flow control strategy may achieve higher ventricular unloading.

Figure 3B shows EBF in the bypass model. The 3 curves show the relationship between EBF and BAI in the bypass model. The constant rotational speed mode generates the highest energy of blood flow when compared to the continuous flow and the constant pressure head modes. EBF is improved by 21% and 15%, respectively. This suggests that the constant rotational speed mode has the best impact on the arterial perfusion.

Figure 4 represents the relationship between the pulsatility and the blood assist index. Before pump support,, PI was roughly 0.6. PI was reduced with the increase of BAI after support with bypass pump in the 3 support modes. The continuous flow mode curve shows that, PI was significant decreased and leveled off at 0 during more than 70% of BAI. Comparing the 3 support modes, the constant pressure head mode had the maximum value, suggesting that this mode had the best impact on the vascular function.

Figure 5 shows the changes in SHE of the 3 support modes along with the increase of BAI. SHE was negatively related to BAI in the 3 modes. Among the 3 support modes, the constant pressure head mode achieved the highest SHE value at the same BAI level. In contrast, the continuous flow support mode had the lowest SHE value at each BAI level. This means the constant pressure head mode has more benefit for restoring the pulsatility of blood pressure, compared with other 2 support modes.

Figure 6 shows the opening time of the aortic valves. In the simulated model, the aortic valves open when the ventricular pressure is higher than aortic pressure and close in the opposite situation. The aortic valves in the constant rotational speed mode and in the continuous flow support mode were closed at 40% and 70% BAI, respectively. This suggests that the continuous flow support mode may be optimal to protect the function of the native aortic valve.

Discussion

THE LIMITATIONS OF STUDY:

The interaction between support modes and right ventricular function is a very important issue for heart failure patients with CF-LVADs support. Many studies found that left ventricular unloading can affect the position of the ventricular septum [44], and further affect the right ventricular function [45,46]. For instance, if the left ventricular unloading level exceeds the normal range, the ventricular septum will be shifted to the left ventricle by the pressure gradient between left and right ventricles. This phenomenon will impair the right ventricular function. In the future, the mechanism of varied support modes on the left ventricular septum and right ventricular function will be studied.

These data, obtained in a simulation model, have to be confirmed by precise animal experimentation and the evaluation of the hemodynamic changes in the 3 different modes of function of a continuous flow CF-LVADs. They emphasize the need for precise study of hemodynamic and perfusion to optimize peripheral perfusion, and the possibility of left ventricular recovery and aortic valve preservation.

Conclusions

Three support modes of function of the CF-LVADs – the continuous flow mode, the constant rotational speed and the constant pressure head – were evaluated in a model using various parameters: the blood assist index (BAI), the left ventricular external work (LVEW), the energy of blood flow (EBF), pulsatility index (PI), and surplus hemodynamic energy (SHE). The numerical studies show that the various support modes can generate different hemodynamic effects on the cardiovascular system. The continuous flow appears to be most beneficial for protecting valve function. The constant rotational speed mode has the best performance in blood perfusion and ventricular unloading. Finally, the constant pressure head strategy can achieve the highest pulsatility of pressure, which may have benefit for keeping vascular functions.