- Open Access
Effects on the pulmonary hemodynamics and gas exchange with a speed modulated right ventricular assist rotary blood pump: a numerical study
© The Author(s) 2018
- Received: 17 March 2018
- Accepted: 11 October 2018
- Published: 20 October 2018
Rotary blood pumps (RBPs) are the newest generation of ventricular assist devices. Although their continuous flow characteristics have been accepted widely, more and more research has focused on the pulsatile modulation of RBPs in an attempt to provide better perfusion. In this study, we investigated the effects of an axial RBP serving as the right ventricular assist device on pulmonary hemodynamics and gas exchange using a numerical method with a complete cardiovascular model along with airway mechanics and a gas exchange model. The RBP runs in both constant speed and synchronized pulsatile modes using speed modulation. Hemodynamics and airway O2 and CO2 partial pressures were obtained under normal physiological conditions, and right ventricle failure conditions with or without RBP. Our results showed that the pulsatile mode of the RBP could support right ventricular assist to restore most hemodynamics. Using speed modulation, both pulmonary arterial pressure and flow pulsatility were increased, while there was only very little effect on alveolar O2 and CO2 partial pressures. This study could provide basic insight into the influence of pulmonary hemodynamics and gas exchange with speed modulated right ventricular assist RBPs, which is concerned when designing their pulsatile control methods.
- Speed modulation
- Pulmonary gas exchange
- Rotary blood pump
- Right ventricular assist
Rotary blood pumps (RBPs) have become the most popular ventricular assist device (VAD) due to their numerous advantages [1, 2]. Among the existing RBPs, most are designed to assist the left ventricle because it is subjected to a heavy systemic circulatory load and is more likely to fail than the right side. However, there are still some scenarios in which a right ventricular assist device (RVAD) is required, such as severe right ventricular failure after implantation of a left ventricular assist device (LVAD) . Some studies have focused on the development of RVADs, in particular, in which two up-to-date prototypes are RBPs .
Throughout the extensive usage of RBPs, other than the constant speed operation mode, the idea to develop pulsing control methods to make RBPs “beat” more like the natural heart has been put forward [4–9]. The physiological effects of pulsatile versus continuous blood flow have been studied extensively [10–12]. It has been demonstrated that pulsatile flow would not only unload the heart better, but would also not induce the typical “stiffening” of peripheral arteries typically found in a continuous flow state . Besides, pulsatile perfusion has the advantages of causing less vital organ injury and systemic inflammation .
Up to now, almost all of the pulsatile operation methods have focused on RBPs used as LVADs. Along with the development of specific RBPs used as RVADs, the same issue also arises if to make them pulsatile. Taking the benefits of the pulsatile perfusion mentioned before into account, and considering the fact that even in the pulmonary vein the flow pulsatility is still much obvious , it is desirable to design pulsatile control methods for right ventricular assist RBPs.
Before the control method design, it is necessary to investigate the physiological effect with pulsatile operation of right ventricular assist RBPs. With different purposes, there are several methods that could be used. To investigate a specific part of the cardiovascular system or three-dimensional structures of blood vessels, CFD is thought to be a good tool and adopted by many researchers [14–16]. Apart from CFD, some researchers newly introduced state-space approaches when studying the artery wall [17–19]. These are all effective methods to investigate the effect of pulsatile flow in cardiovascular system. However, when regarding the whole circulation system and two-dimensional hemodynamics, a simple system model could be effective and computational saving, and will be adopted in this study .
Generally, the pulsatile operation is realized by rotary speed modulation synchronized with the heartbeat. For LVADs, researchers usually only consider the resultant hemodynamic effects. However, for pulmonary circulatory assist another factor could also be taken into account. There is a unique important function of the pulmonary circulation that it is where oxygen (O2) and carbon dioxide (CO2) gas exchange take place between the blood in the lungs and the atmosphere. Hence, besides hemodynamics, we are going to also include the effect investigation of pulmonary gas exchange when implementing the pulsatile modulation operation for a right ventricular assist RBP.
In this study, we investigated the effects of a right ventricular assist RBP running in both constant and synchronized pulsatile mode on pulmonary hemodynamics and O2 and CO2 gas exchange using a numerical method. In addition to the complete lumped parameter cardiovascular model, which includes both systemic and pulmonary circulation, models for airway mechanics and gas exchange for O2 and CO2 between the lung and the atmosphere were also obtained. Using an RBP model in various speed patterns to assist the failing right ventricle, hemodynamics and airway O2 and CO2 partial pressures were obtained, revealing the effects of these speed modulations.
The five-elements model was applied to both the systemic and pulmonary arterial systems as parts of the cardiovascular mathematic model. It can reproduce the main arterial characteristics over the entire frequency range of interest . The systemic and pulmonary venous systems are both characterized by resistance and compliance.
Airway and lung mechanics model
Gas exchange model
Model of the right ventricular assist RBP
The RBP serving as the right ventricular assistance is connected to the blood circulatory system via cannulation from the right ventricle to the pulmonary artery (Fig. 1). There is a worldwide lack of existing RBPs with hydraulic characteristics designed especially for right ventricle assisting; therefore, there is no ready-to-use model of a right RBP. Here we used the method proposed by Krabatsch et al. , which enables the use of an already available LVAD for right ventricular assistance. The main problem of using an LVAD as an RVAD is the excessive flowrate against the much lower pulmonary resistance compared with the systemic resistance, even at the lowest rotary speed. The key point of the proposed method was to add an additional resistance in series with the left ventricular assist RBP in order to decrease the flow delivered into the pulmonary circulation.
All of the models were programmed using Simulink/Matlab software (The MathWorks Inc., Natick, MA, USA). The first-order spatial derivative in the gas exchange model was approximated by using a four-point upwind biased formula , after which all the equations of the models were ODEs that can be implemented in Simulink. The Runge–Kutta solver and a 10−3 s fixed step were chosen in the simulation.
First, simulations without the RVAD were carried out for modeling validation in both normal and right heart failure conditions. Basic hemodynamics and airway gaseous partial pressures were obtained. The right heart failure condition was achieved by setting the right ventricular contractility to 10% of the normal value and the heart rate to 90 bpm. Then the RBP was connected in parallel to the failing right ventricle. Constant rotary speed and sinusoidal modulated speeds were compared. The mean value of the sinusoidal speed profile was the same as the constant speed, which was set to 9000 rpm. The amplitudes of the sine speed profiles were set to 1000, 2000, and 3000 rpm, respectively. The sinusoidal modulated speed was synchronized with the heartbeat, meaning that the pump was running in copulsation mode. During all the simulations, the breathing and gas exchange were always considered normal.
Normally, the right ventricular pressure (RVP), which ranges from 0 to 29 mmHg, and the pulmonary arterial pressure (PAP), which ranges from 10 to 29 mmHg, are consistent with physiological values. During right ventricle failure, RVP and PAP fluctuate within a narrow range, and the waveforms becomes disordered (Fig. 6a), as does the pulmonary arterial flowrate (PAF) waveform measured at the node Rpvr. It is worth noting that the flow pulsatile in the pulmonary circulation is much larger than in the systemic circulation, and both decrease significantly during right heart failure. Another point worth noting is the change in heart period from 60 to 90 bpm between the two figures, which is in accordance with the settings.
Airway gaseous partial pressure
Effects of speed modulation
In this study, the axial blood pump serving as a RVAD during right ventricular failure was run in constant speed mode and sinusoidal modulated speed mode with three different amplitudes. As mentioned previously, the offset of the sinusoidal speed is the same as the constant speed value, which was 9000 rpm in our simulation.
In systemic hemodynamics, the speed modulation of the right RBP has very little effect. As can be seen from Fig. 9c, d, the systemic pressure and flow waveforms with different RBP speed profiles (including constant speed) almost overlap. Although all of the running modes could undertake the right ventricular assisting task, a different influence was found in the pulmonary circulation between them. Along with increasing the sinusoidal modulation amplitude (the amplitude of the constant speed could be regarded as zero), PAP and PAF become more pulsatile (Fig. 9a, b); however, these were still much weaker than the pulsatility in the normal physiological conditions (Fig. 5).
Many studies have focused on the pulsatile speed modulation of RBPs as LVADs, whereas there have been few reports on RVADs. Flow pulsation in the pulmonary circulation is remarkable (Fig. 5b). Previous reports have shown the peak flow velocity in pulmonary vein is 52.1 ± 16.4 cm/s , and the average pulmonary vein ostium diameter can reach 20 mm , which corresponds to a peak volume flow of about 164 ± 51 mL/s. In the present study, the peak flow results agreed with previous studies, side demonstrating the effectiveness of the numerical model. Besides blood transportation, another important function of the pulmonary circulation is gas exchange. Therefore, this study aimed to investigate the effects on both hemodynamics and gas exchange when a right ventricular assist RBP runs in pulsatile mode.
The basic hemodynamics under normal and right ventricle failure conditions generated by the numerical model fit the physiological and pathological results well, demonstrating the effectiveness of the used model. Then sinusoidal speed modulations with different amplitudes under right ventricle failure condition are implemented, revealing that with a sufficient mean rotary speed the hemodynamics could recover back to normal and meanwhile enhance the pulsatility of the pulmonary circulation. The airway gaseous partial pressures also return to normal with the help of the RVAD. Enlarging the modulation amplitude will influence alveolar PO2 and PCO2 inversely, decreasing PO2 and increasing PCO2. However, this influence is slight and not as obvious as the hemodynamic effect. Considering the change in mean flowrate (Fig. 9b), this influence might be caused from this mean flow difference. This finding is consistent with a recent report claiming that pulsatile blood flow has only a small to no effect on the gas exchange performance in an oxygenator . Therefore, it implies pulsatile operation using speed modulation would not influence the gas exchange much while could improve the hemodynamics (including pulsatility) enormously. More experimental validations could be carried out further with a breath sensor and a wearable sensor system [29, 30].
As O2 diffusion across the alveolar–capillary membrane decreases, alveolar PO2 rises during right ventricle failure (Fig. 8). This is due to the low flowrate in the lung, meaning that oxygen diffusing into the blood cannot be taken away immediately. The total flux of O2 across the alveolar–capillary membrane decreasing from about 3.5 to nearly 1.7 mL/s could also support this. Lower O2 diffusion would mean lower O2 partial pressure in the arterial blood after gas exchange, in line with the actual situation in which a patient with right heart failure would have low blood O2 partial pressure. Breathing function was regarded as normal during the simulations, whereas generally, heart failure is accompanied by abnormal breathing, such as faster breath frequency. Further models describing the relationship between heart failure and respiratory function are required to improve the numerical simulation.
Another limitation of this study is that it does not include tissue O2 consumption and CO2 generation model. The initial O2 and CO2 partial pressures from the venous blood are set as constant values according to the study by Lu et al. . Introducing a tissue O2 and CO2 exchange model to construct a whole closed-loop cardiovascular–pulmonary tissue model would extend the capability of the numerical study. More physiological conditions, such exercise, can be simulated and it would be beneficial to designing control algorithms of RBPs in use.
The speed modulation method of the RBP adopted in this study was limited to sinusoidal modulation. Only amplitude varied, while the modulation frequency was set at a constant heart rate. Besides, the RBP was run in copulsation mode to enhance the pulsation, and no other modes, such as counterpulsation mode was implemented in this study. To give a more comprehensive understanding of speed modulation of continuous flow RVAD, investigations using more rotary speed modulated waveforms, such as square wave, and more modulation modes, such as counterpulsation mode, and even asynchronous modulation with different heartbeats, could be carried out in the future.
In this study, we investigated the effects of a right ventricular assist RBP running in both constant and synchronized pulsatile modes on the pulmonary hemodynamics and gas exchange using a numerical method. Basic hemodynamics and airway O2 and CO2 partial pressures in both normal physiological conditions and during right ventricle failure were obtained. Results showed that the pulsatile run mode of the assist pump was able to recover most hemodynamics to normal levels during right ventricular failure, and that speed modulation could obviously increase the flow and pressure pulsatility in the pulmonary circulation while with only little effect on the pulmonary gas exchange. This study could provide basic insight of the influence of speed modulation of a right ventricular assist RBP when designing pulsatile control algorithms for them.
FH proposed the method and established the model in this research, and was a major contributor in writing the manuscript. ZG analyzed the results and was a minor contributor in writing the manuscript. YF provided the numerical implementation of the model. XR overviewed the research and provided some discussions. All authors read and approved the final manuscript.
This work is supported by National Natural Science Foundation of China (Grant No. 51505455) and funded by Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (No. GZKF-201713).
The authors declare that they have no competing interests.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Consent for publication
This work is supported by National Natural Science Foundation of China (Grant No. 51505455) and funded by Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (No. GZKF-201713).
Ethics approval and consent to participate
This work is supported by National Natural Science Foundation of China (Grant No. 51505455) and Open Foundation of the State Key Laboratory of Fluid Power and Mechatronic Systems (No. GZKF-201713).
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