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Sensor-Based Physiologic Control Strategy for Biventricular Support with Rotary Blood Pumps

Wang, Yu*; Koenig, Steven, C.†,‡; Wu, Zhongjun; Slaughter, Mark, S.; Giridharan, Guruprasad, A.

doi: 10.1097/MAT.0000000000000671
Biomedical Engineering
Free

Rotary biventricular assist devices (BiVAD) are becoming a clinically accepted treatment option for end-stage biventricular failure. To improve BiVAD efficacy and safety, we propose a control algorithm to achieve the clinical objectives of maintaining left-right–sided balance, restoring physiologic flows, and preventing ventricular suction. The control algorithm consists of two proportional-integral (PI) controllers for left and right ventricular assist devices (LVAD and RVAD) to maintain differential pump pressure across LVAD (ΔPL) and RVAD (ΔPR) to provide left-right balance and physiologic flow. To prevent ventricular suction, LVAD and RVAD pump speed differentials (ΔRPML, ΔRPMR) were maintained above user-defined thresholds. Efficacy and robustness of the proposed algorithm were tested in silico for axial and centrifugal flow BiVAD using 1) normal and excessive ΔPL and/or ΔPR setpoints, 2) rapid threefold increase in pulmonary vascular or vena caval resistances, 3) transient responses from exercise to rest, and 4) ventricular fibrillation. The study successfully demonstrated that the proposed BiVAD algorithm achieved the clinical objectives but required pressure sensors to continuously measure ΔPL and ΔPR. The proposed control algorithm is device independent, should not require any modifications to the pump or inflow/outflow cannulae/grafts, and may be directly applied to current rotary blood pumps for biventricular support.

From the *Department of Biomedical Engineering, Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian, Liaoning, China

Department of Bioengineering, Cardiovascular Innovation Institute, University of Louisville, Louisville, KY

Department of Cardiovascular and Thoracic Surgery, Cardiovascular Innovation Institute, University of Louisville, Louisville, KY.

Submitted for consideration September 2016; accepted for publication in revised form July 2017.

Supported, in part, by NIH R15 Grant (1R15HL115556–01A1) and the University of Louisville Cardiac Implant Science Endowment.

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

Correspondence: Guruprasad A. Giridharan, Department of Bioengineering, Cardiovascular Innovation Institute, Room 407, 302 East Muhammad Ali Blvd, University of Louisville, Louisville, KY 40202. Email: gagiri01@louisville.edu.

Rotary biventricular assist devices (BiVAD) have become a therapeutic option for patients with end-stage biventricular failure refractory to pharmacologic treatment.1–3 Continuous flow ventricular assist devices are preferred over pulsatile flow devices for biventricular mechanical circulatory support (MCS) due to their smaller size that reduced surgical trauma, higher durability, and energy efficiency.4 However, rotary BiVAD have lower preload sensitivity compared with the native heart5,6 and are devoid of inherent biological control mechanisms (Frank-Starling and baroreceptor responses). The inherent biological control mechanisms regulate cardiac output and maintain the balance between systemic and pulmonary flows, which may be disproportionate due to coronary and bronchial shunt circulation.7–9 Thus, rotary BiVAD are susceptible to imbalances between systemic and pulmonary (left-right side) flows and improper adaptation to cardiac demand. Clinically, the RVAD is manually set at a lower pump speed to balance flows and the outflow cannulae have been tapered to avoid overpumping.10 However, these approaches require close monitoring to prevent left-right imbalances.

A rotary BiVAD must meet the patient’s cardiac demand during varying levels of physical activity to avoid hypoperfusion of end-organs and for patient quality of life. However, the low preload and high afterload sensitivity of rotary BiVADs5,6 may cause inaccurate adaptation of the pump flow to meet the cardiac demand.11,12 This is more pronounced with mechanical pulmonary circulatory support since the native right ventricle (RV) is more afterload sensitive than the left ventricle (LV).12,13 Control strategies for maintaining the target flow rate during biventricular support with a pair of rotary flow pumps have been proposed14 such as those for the Baylor Gyro BiVAD (Houston, TX)15 and a combination of CorAide LVAD and DexAide RVAD (Cleveland Clinic, Cleveland, OH).16 Although these methods can effectively balance left-right pump flow rates, maintaining fixed flow rates cannot consistently provide sufficient flow over a wide range of physical activity conditions. A passive control system for rotary BiVADs has also been proposed, but this approach has several limitations including the algorithm being specific to a single device17 and hypersensitivity to outlet/arterial pressure and afterload.18,19 A passive control algorithm that was proposed prevented suction, but physiological responses have not been demonstrated with this algorithm.20 An active control algorithm was proposed for BiVAD support that minimized suction events but did not prevent suction.21 A combination of active and passive control systems for BiVAD was proposed and successfully tested in vivo, but this approach required modifications to the device design and incorporation of a compliant inflow/outflow cannula.22

The lower preload sensitivity of the rotary BiVAD makes it prone to suction events,11,23 potentially causing myocardial damage, pump flow stoppage, ventricular collapse, or trigger ventricular arrhythmias that may result in adverse events or death. Previously developed LVAD control algorithms for physiologic control and suction may not be directly applicable for RVAD as the RV is more susceptible to suction compared with the LV, as the RV wall is approximately 3 times thinner than LV wall.24,25 To overcome this limitation, several control algorithms for BiVAD/total artificial heart (TAH) support have been proposed in the literature. A conductance and arterial pressure method (1/R control) was proposed with the undulation pump TAH.26,27 However, suction still occurred due to an unexpected excursion of the control algorithm. A control algorithm with pulse wave modulation (PWM) mode for TAH was reported, but it was only successful in detecting suction after its onset, which is less desirable to preventing suction.28 An outflow control for avoiding atrial suction in a continuous flow TAH was reported, but oscillations, long settling times, and an inability to avoid RV suction were observed.29 Clinically, LVAD, which are designed to pump against a high pressure gradient, are implanted in the RV, which may result in overpumping and/or cause suction events. Clinically, outflow cannulae have been clamped to augment the pressure head to pump against a higher afterload and reduce the likelihood of suction.10 Further, a compliant inflow cannula that collapses before the onset of ventricular suction has been designed.9 However, the narrowing of the inflow or outflow cannulae can augment shear stresses and increase blood trauma while simultaneously creating areas of blood stagnation that may promote thrombosis.

Balancing left-right side flow rates while simultaneously maintaining physiological flows and avoiding ventricular suction during BiVAD support with rotary pumps remains a significant clinical concern and challenge. To overcome the limitations of current approaches, we propose a BiVAD control algorithm for use with axial or centrifugal rotary blood pumps, and test the efficacy and robustness of the proposed algorithm in an established computational model of the human circulatory system.

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Methods

Model of the Circulatory System

A lumped parameter model of the human circulatory system with heart failure (HF) was used to test the proposed BiVAD algorithm in silico. The parameters of the computer simulation model for rest and exercise conditions have been published previously, and the computer simulation model has been previously validated and used to develop algorithms for different MCS devices including physiological control, flow modulation, and fault detection.30–34 In this study, the human circulatory system was divided into 13 elements: nine blocks including LV, RV, pulmonary artery, pulmonary arterial and venous circulation, systemic circulation, coronary circulation, vena cava, and aorta, and four heart valves. In each block, the blood volume is characterized by a differential equation as a function of volume (V), pressure (P), compliance (C), and resistance (R), which is an expression for the material balance for the block given by:

where dVn/dt is the rate of change of volume in block n, Fin is the blood flow rate into the block, and Fout is the blood flow rate out of the block. LV and RV were characterized by time varying compliances, while the coronary vasculature block had time-varying resistive and compliance elements. The remaining blocks had constant resistance and compliance. The axial flow (AF) or centrifugal flow (CF) VAD were integrated into the circulatory system model as parallel flow paths from LV to the aorta block (LVAD) and from RV to the pulmonary artery block (RVAD).

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Models of the AF and CF VAD

The dynamic mathematical model of the AF LVAD and RVAD used in this study were previously described by the following equations34–36:

where J is the inertia of the rotor, ω is the rotor speed in rad/s, KB is the back EMF constant, I is the amplitude of the phase current, B is the damping coefficient, a0 and a1 are correlation constants, Fp is VAD generated flow rate, ω is the pump rotational speed, ΔPPL or ΔPR) is the pressure head across the pump, and b0, b1, and b2 are experimental constants.

A parameter-based dynamic CF LVAD and RVAD model proposed by Kitamura et al.37 is described by the following equations:

where ϕ is the total inertance of the inlet and outlet cannulas, J1 is the inertia of the rotor, K1 is the torque constant of the DC motor, I is the pump current, TR is the kinetic friction coefficient, ωfull is the rotor speed at full support, and c1, c2, c3, c4, and K2 are experimental constants. The values of experimental constants for AF and CF VAD have been previously published.34–38

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BiVAD Control Algorithm

The control objectives for the proposed BiVAD algorithm were to provide left-right balance and physiologic flow by maintaining the target pressure heads across LVAD and RVAD (ΔPL, ΔPR) close to the reference average pressure differences (ΔPrL, ΔPrR). The pump speed differentials for LVAD (ΔRPML) and RVAD (ΔRPMR) were maintained above user-defined thresholds (ΔRPMrL, ΔRPMrR) to prevent LV and RV suction. These control objectives implemented with a gain-scheduled, PI controller in both LVAD and RVAD by manipulating the motor currents for LVAD (IL) and RVAD (IR) based on the following control equations:

where ΔRPML and ΔRPMR are measured RPM for LVAD and RVAD, and ΔPL and ΔPR are measured pressure differentials across LVAD and RVAD, respectively. LKP1, LKP2, τ1, RKP1, RKP2, and τ2 are user-defined gain scheduled controller coefficients. The schematic of the control algorithm is shown in Figure 1. Controller tuning was performed and optimized offline for each device. The controller tuning parameters are unique and dependent upon the dynamic response characteristics of the device. The gain-scheduled, PI controller coefficients were tuned apriori using a direct numerical search approach30 to maximize the speed of response and minimize overshoot and were maintained at same values for all test conditions. The proposed BiVAD control algorithm was derived from the SPPC LVAD control algorithm.34 The proposed control algorithm will fail if ventricular fibrillation occurs, as fibrillation reduces both the pump speed differentials and pump flows significantly. To prevent this, the controller was programmed to maintain ΔPL at 60 mm Hg and ΔPR at 17 mm Hg (Figure 1) when pump speed differentials were close to zero for more than 5 seconds.

Figure 1

Figure 1

In this computer simulation, we simulated a normal heart during rest and exercise test conditions to evaluate cardiac output and cardiac demand. Next, we simulated HF with BiVAD support using different control strategies and compared to total output with pump support to that of the cardiac output of a healthy heart during exercise to compare the performance of the controllers. Efficacy and robustness of the BiVAD control algorithm was tested in silico under rest and exercise conditions for 1) regular ΔPL and ΔPR setpoints of 110 and 20 mm Hg, 2) excessive ΔPL and/or ΔPR setpoints of 130 and 25 mm Hg, 3) a rapid threefold increase in pulmonary vascular resistance (PVR) or vena caval resistance (VCR) in 20 seconds for 1) through 2), 4) step transition from exercise to rest, and 5) sudden onset of ventricular fibrillation. The simulated heart rates were 80 beats per minute (bpm) for rest and 120 bpm for exercise conditions. Initial LVAD and RVAD flow rates and RPM were zero. At time t = 0, with initial pump speeds of zero, LVAD and RVAD support were implemented with the reference pressure head (ΔPrL = 82 mm Hg or 110 mm Hg or 130 mm Hg for AF and CF LVAD and ΔPr = 13 mm Hg or 20 mm Hg or 25 mm Hg for AF and CF RVAD) and reference differential pump speed (ΔRPMrL = 1375 RPM for AF LVAD, ΔRPMrL = 640 RPM for CF LVAD, ΔRPMrR = 575 RPM for AF RVAD, ΔRPMrR = 510 RPM for CF RVAD) setpoints. The actual ΔRPML and ΔRPMR were calculated as the difference between the maximum and minimum RPM values during the preceding 1-second time window, regardless of the simulated native heart rate. The parameters for the gain scheduled controller (LKP1, LKP2, τ1, RKP1, RKP2, and τ2) were unchanged during all test conditions for each type of BiVAD, and the simulation was continued for 1,200 seconds. The performance of the BiVAD algorithm was compared with the performance of maintaining constant ΔPL and ΔPR and maintaining a constant LVAD and RVAD RPM.

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Data Analysis

The hemodynamic parameter values and BiVAD parameters were calculated on a beat-to-beat basis using m-files developed in Matlab (MathWorks, Natick, MA). The parameters calculated included the left and right sided total output (cardiac output + pump flow rate), left and right ventricular systolic, end diastolic, peak, and minimum pressures and volumes, aortic and pulmonary systolic, diastolic and mean pressures, and aortic, pulmonary artery, LVAD, and RVAD flow rates for all experimental conditions. Suction was defined to have occurred when the instantaneous ventricular pressure value was 1 mm Hg or lower34 and ventricular pressures between 1–2 mm Hg was defined as “approaching suction.”

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Results

Physiological Control

The axial and centrifugal BiVAD flow rates were significantly augmented from baseline HF cardiac output values. Higher ΔPL and ΔPR setpoints increased BiVAD flow rates, but this increase was limited with the BiVAD control algorithm to avoid suction compared with the constant ΔP control algorithm. BiVAD, constant ΔP, and constant RPM control algorithms augmented BiVAD flow rates during the exercise test condition. However, the BiVAD control algorithm produced pump flow rates that best matched the cardiac demand, defined as the cardiac output of the normal heart during exercise condition. The BiVAD control algorithm successfully diminished LVAD flow in response to augmentation in PVR (reduced preload for LVAD) and RVAD flow rates with augmentation VCR (reduced preload for RVAD). The BiVAD control algorithm simultaneously reduced LVAD and RVAD flow rates when transitioning from exercise to rest (Tables 1–4).

Table 1

Table 1

Table 2

Table 2

Table 3

Table 3

Table 4

Table 4

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Suction Prevention

With the constant ΔP control, a rapid increase in PVR or VCR resulted in either constant suction (Figure 2 A–D, I—L; Figure 3 A–D, I—L; Figure 4 A–D, I—L; Tables 1 and 2) or approaching suction (Tables 1 and 2), as indicated by low ventricular pressures and volumes. In contrast, LV and RV suction were prevented with the BiVAD control algorithm during a rapid increase in PVR (Figure 2 E–H, M–P; Figure 3 E–H, M–P; Figure 4 E–H, M–P) even with elevated ΔPL and ΔPR setpoints. A temporary transient reduction in left ventricular pressures and volumes occurred with both AF and CF BiVAD with the onset of a rapid increase in PVR (initiated at t = 330 seconds), while the values of right ventricular pressures and volumes were temporarily lowered during a rapid increase in VCR even with the BiVAD control algorithm, but did not cause suction. The BiVAD control algorithm provided a greater safety margin for suction with changing PVR or VCR (Tables 1 and 2). Importantly, the BiVAD control strategy prevented ventricular suction even during an abrupt step-transition from exercise to rest condition (Figure 5).

Figure 2

Figure 2

Figure 3

Figure 3

Figure 4

Figure 4

Figure 5

Figure 5

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Left-Right–Sided Balance

All control algorithms (BiVAD, constant ΔP, constant RPM) maintained left-right balance when the pulmonary or systemic vascular resistances were not perturbed for both AF and CF rotary pumps (Tables 1 and 2). BiVAD and constant ΔP control algorithms maintained left-right balance when PVR or VCR were increased, but constant RPM control was unable to maintain left-right balance.

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Performance During Ventricular Fibrillation

During ventricular fibrillation, the proposed BiVAD algorithm successfully transitioned to “safe mode” and maintained both AF and CF BiVAD flow rates between 3.5 and 4.0 L/min, which was similar to the cardiac output during HF condition at rest (Figure 6).

Figure 6

Figure 6

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Discussion

The results of this study demonstrated that the BiVAD control algorithm provided physiologic flow by adapting pump flow rates to match cardiac demand, prevented ventricular suction, and balanced left-right sided flow rates for all test conditions. Importantly, the performance of the BiVAD control algorithm was similar for both AF and CF VAD, demonstrating that the proposed approach is device independent.

Physiologic flow requires providing maximal device support that matches the cardiac demand to ensure adequate end organ perfusion. This necessitates the BiVAD to operate at pump speeds where the risk of suction is high. ΔPL or ΔPR setpoints were set to higher than physiologic values to ensure that the VAD provided maximum flow and decreased afterload sensitivity. Maintaining a ΔP setpoint also augmented the preload sensitivity of the BiVAD and ensured left-right–sided balance. If one side of the BiVAD overpumps, the preload decreased on that side with an increase in preload on the other side. The BiVAD controller reduced the VAD speed in response to a lower preload (increased ΔP and decreased ΔRPM) and augments VAD speed on the other side in response to an increased preload (reduced ΔP and elevated ΔRPM), inherently providing left-right–sided balance. Suction is prevented by having a greater weight on ΔRPM errors as the ΔRPM approached its setpoint by gain scheduling the PI controllers. With increasing VAD support, the ventricular pressure variation over a cardiac cycle diminishes, which in turn diminishes the pump speed differential. This phenomenon has been observed in vivo in both AF and CF devices and is referenced in instructions for use for HeartMate II and HeartWare HVAD. Gain scheduling ensured that the BiVAD provided maximum flows while maintaining a safety margin to avoid suction. Further, this control approach ensured a robust and rapid response both in terms of increasing BiVAD flow rates to meet cardiac demand as well as reducing BiVAD flow rates to prevent suction, even when there is a significant user-input error in ΔPL or ΔPR setpoints, rapid threefold increase in PVR or VCR or a step transition from exercise to rest.

The proposed BiVAD control structure requires two simple PI controllers that act against to each other for each VAD to satisfy the opposing objectives of maintaining physiologic flow and avoiding ventricular suction. This simple controller structure only requires input of controller coefficients and setpoints, which can be found a priori. However, the controller tuning parameters are unique and dependent upon the dynamic response characteristics of the device. This control approach ensured that the left ventricular and right ventricular end diastolic pressures remained within physiologic values for all test conditions, demonstrating that atrial pressures need not be measured or controlled directly. The proposed BiVAD control strategy may better adapt to changes in both preload and afterload compared with previously proposed control strategies39 of maintaining a reference pump inlet pressure (prevents suction but may not be able to adapt to changing afterloads) or maintaining a reference mean arterial pressure (allows for physiologic pump flow from rest to exercise but may not prevent suction). The LVAD and RVAD controllers in the proposed BiVAD algorithm act independently of each another and do not require any communication between them. The advantages of controllers acting independently are: 1) the controllers do not have to be in communication with each other and thus communication failure between controllers would not cause any degradation in performance, 2) removing the need for communication between controllers would make it easier to modify existing controllers. The proposed algorithm does not require any device or cannula modifications with the exception of incorporation of pressure sensors and prevents LV and RV suction, adapts to physiologic demand, and maintains left-right–sided flow balance.

During ventricular fibrillation, the BiVAD control algorithm will reduce BiVAD flows to zero as pump speed differentials (ΔRPM), which are generated by the beating heart, will be close to zero. During ventricular fibrillation, the safe mode maintained predetermined lower ΔP setpoints to generate 3.5–4.0 L/min of BiVAD flows sufficient to maintain life (similar to HF cardiac output) to minimize suction and device thrombosis. An alarm may be activated during safe mode operation to notify the patient to visit a medical facility.

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Limitations

The BiVAD control algorithm requires pressure sensors for the measurement of VAD inlet and outlet pressures to calculate ΔPL and ΔPR. Pressure sensors are unreliable for long-term implants due to sensor drift, measurement errors, and risk of septicemia.36 Significant pressure sensor drift would affect the performance of physiologic control only. Importantly, suction prevention is based solely on RPM measurements (intrinsic pump parameter) and would not adversely affect safety. It may be possible to estimate ΔP using intrinsic pump parameters36 eliminating the need for pressure measurements. In addition, suction prevention algorithms based on estimated flows have been integrated into current clinically approved LVAD. However, it has been shown that estimated flow is poorly correlated to measured flow (flow probes) in LVAD,40 which is also likely to be inaccurate for RVAD flow estimates. The calculation of ΔRPM using a 1 second time window requires the patient’s native heart rate to be above 60 beats per minute. However, extending the time window to 2 seconds for ΔRPM calculation did not lead to a significant BiVAD controller performance degradation.

The computer simulation model is not intended to replace the importance and significance of in vivo models and cannot reproduce all expected clinical responses. The lumped parameter in silico model used in this study assumes Newtonian blood, ideal heart valves, and does not account for inertial or gravitational effects. Despite these limitations, the computer simulation model provided a controlled test platform for demonstrating feasibility and robustness of the proposed BiVAD control algorithm. Mock flow loop and large animal models studies are needed to validate BiVAD controller efficacy, performance, and robustness.

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Keywords:

biventricular assist devices; flow balancing; physiologic control; suction prevention; sensor control algorithm

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