Left ventricular assist devices (LVADs) have been widely accepted as a treatment option for advanced heart failure patients as a bridge to transplantation or as a destination therapy.1,2 LVADs need to provide adequate flow to maintain end-organ perfusion while avoiding ventricular suction, which can cause myocardial damage, pump flow stoppage, or ventricular collapse, or can trigger ventricular arrhythmias that may result in adverse events or death. Pulsatile flow LVADs minimized the risk of left ventricular (LV) suction by filling passively and also mimicked the Frank–Starling response by triggering device ejection when the LVAD chamber was fully filled with blood. Conversely, axial flow (AF) and centrifugal flow (CF) LVADs have a significantly lower preload and afterload sensitivity than that of the human heart.3,4 Subsequently, the potential risk for LV suction events while maintaining adequate perfusion over a wide range of physiologic conditions remains a significant clinical concern with current continuous flow LVADs.
Several methods for LV suction detection including threshold comparisons,5–7 classification and regression tree,8 discriminant analysis,9 neural networks,10 Lagrangian support vector machine,11,12 Gaussian mixture model,13 and motor current waveform analyses14,15 have been reported. While these methods are successful in detecting LV suction after its onset, they cannot prevent suction. There have also been a number of control strategies that provide physiologic flow while minimizing LV suction events, including sensorless control using LVAD motor current16,17; however, it was unable to consistently provide adequate perfusion over a wide range of clinical and physical activity scenarios. A fuzzy logic controller was developed to provide adequate perfusion while avoiding suction without using external flow or pressure sensors,18,19 but it assumes a linear relationship between flow and the heart rate and does not account for intrapatient variability or the nonlinearity in the relationship over a wide range of physical activity scenarios. Flow estimators for continuous flow LVAD have also been inadequate.20 Control algorithms that use multiple parameters and indices to provide physiologic LVAD flow and detect suction have been developed21–23; however, they can be complicated requiring input of patient status, integration of sensors for direct measurement, or cannot prevent suction under extreme conditions.
We propose a suction prevention and physiologic control (SPPC) algorithm for use with axial and centrifugal LVADs using two gain-scheduled, proportional-integral (PI) controllers that maintain a differential pump speed (ΔRPM) above a user-defined threshold to prevent LV suction, while also maintaining an average reference differential pressure (ΔP) between the LV and aorta to provide physiologic perfusion. The developed algorithm principles are device independent and may deliver a robust and reliable means to avoid suction events while providing physiologic perfusion.
Model of the Circulatory System
The proposed SPPC algorithm was tested in a computer simulation model of the human circulatory system in heart failure with models of an AF LVAD or a CF LVAD. The computer simulation model was validated and has been used in previous studies to develop and test physiologic control, timing, and fault detection algorithms for mechanical circulatory support devices.24–29 Briefly, the computer model subdivides the human circulatory system into an arbitrary number of lumped parameter blocks, each characterized by its own resistance, compliance, pressure, and volume of blood. Two idealized elements, resistance and storage, were used to characterize each block. The storage element provides zero resistance to flow, whereas the resistive element has zero volume. In the configuration used in this study, the model has 12 elements: four heart valves and eight blocks, including the LV, right ventricle (RV), pulmonary arterial and venous circulation, systemic circulation, coronary circulation, vena cava, and aorta. Ventricles were characterized by a time-varying compliance. The remaining blocks were characterized by passive elements. The coronary block consisted of time-varying resistive and compliance elements. The volume of blood in each block is described by a differential equation as a function of volume (V), pressure (P), compliance (C), and resistance (R), which is an expression for the macrosopic material balance for the block given by:
where dV n/dt is the rate of change of volume in block n, F in is the blood flow rate into the block, and F out is the blood flow rate out of the block. The computer simulation model was integrated with a dynamic model of an AF or a CF VAD.
Model of the AF LVAD
A dynamic parameter-based AF LVAD model developed by Choi et al.30 was used in the computer simulation study. The AF LVAD was driven by a brushless DC motor, described by the equation31:
where J is the inertia of the rotor, ω is the rotor speed in rad/s, T e is the motor torque, T p is the load torque, and B is the damping coefficient. The motor torque can be related to the amplitude of the phase current, I, and the back EMF constant, K B, through the equation:
In addition, the load torque can be calculated as a function of pump rotational speed and LVAD generated flow, F p, with the following equation:
where a 0 and a 1 are correlation constants. To obtain a closed CV system-LVAD model, an equation for pump flow rate in terms of pump rotational speed and pressure difference across the pump, ΔP, was used30,32:
where b 0, b 1, and b 2 are experimental constants. The normal parameters are identified experimentally and are given as J = 9.16 × 10–7 kg m2, B = 6.6 × 10–7 kg m2/s, a 0 = 7.38 × 10–13 kg m2 s/ml3, a 1 = 1.98 × 10–11 kg m2 s/ml, b 0 = −0.296 mm Hg s/ml, b 1 = −0.027 mm Hg s2/ml, and b 2 = 9.33 × 10–5 mm Hg s2.30
Model of the CF LVAD
A parameter-based model for a CF LVAD developed by Kitamura et al.33 was used to test the proposed SPPC algorithm. The integration of the centrifugal LVAD and the CV system model is the same as with the axial VAD. We used a slightly modified centrifugal LVAD model, described by the following equations:
where F p , ω, and ΔP are as defined above, ϕ is the total inertance of the inlet and outlet cannulas, J 1 is the inertia of the rotor, T R is the kinetic friction coefficient, ω full is the rotor speed at full support, K 1 is the torque constant of the DC motor, I is the pump current, and c 1, c 2, c 3, c 4, and K 2 are viscosity-dependent parameters. The normal parameters are determined experimentally and are given as c 1 = 6.841 × 10–4 mm Hg s2/ml,c 2 = 4.718 × 10–3 mm Hg s2/ml2, c 3 = 2.636 × 10–4 kg m2/s, c 4 = 1.012 × 10–6 kg m2/ml, J 1 = 4.756 × 10–6 kg m2, K 1 = 0.0051 kg m2/(s2 A), K 2 = 4.7664 × 10–3 mm Hg s2, ϕ = 2 mm Hg s2/ml, and T R = 1.9992 × 10–3 kg m2/s2.29,33
The selected control objectives are (1) to maintain an average RPM difference between maximum and minimum pump speed (ΔRPM) above a specified reference value (ΔRPMr) to prevent suction, and (2) to maintain an average pressure difference, ΔP, between the LV and aorta close to the selected reference pressure head, ΔPr,24–26 to provide physiologic perfusion. Each of these opposing control objectives are implemented using a gain-scheduled PI controller. This approach enables the use of a fixed control configuration that only requires the selection of controller coefficients and setpoints. The pump motor current is manipulated according to the following control law:
where ΔRPM and ΔP are the measured RPM and measured (or estimated) pressure differential, respectively. K P1, τ 1, K P2, and τ 2 are user-defined gain-scheduled controller coefficients that were experimentally tuned. The schematic of the control algorithm is shown in Figure 1.
Efficacy and robustness of the proposed SPPC algorithm were evaluated during simulated rest and exercise test conditions for (1) normal ΔP setpoint of 75 mm Hg, (2) excessive ΔP setpoint (ES) of 115 mm Hg; (3) normal pulmonary vascular resistance (PVR); (4) an eightfold increase in PVR in 20 seconds; and (5) combined excessive ΔP setpoint of 115 mm Hg with a rapid eightfold increase in PVR in 20 seconds (ES + PVR). The simulated pulse rate was 80 beats per minute (bpm) during rest and 120 bpm during exercise. Before t = 0, unassisted perfusion was assumed. At time t = 0, arbitrarily selected as the end of the diastole, LVAD assistance was initiated with the reference differential pump speed (ΔRPMr = 1000 RPM for the AF LVAD, ΔRPMr = 150 RPM for the centrifugal LVAD) and reference differential pressure (ΔPr = 75 mm Hg or 115 mm Hg for both LVAD) sent to the two PI LVAD controllers. The ΔRPM was calculated as the difference between the maximum and minimum RPM values during the preceding one-second time period (moving one-second time window), irrespective of simulated native heart rate. The selected values for K P1, τ 1, K P2, and τ 2 were unchanged between test conditions for each LVAD. Initial LVAD flow rate and RPM were set to zero. The circulatory system reached a limit cycle within 150 cardiac cycles. The simulation was continued up to 600 cardiac cycles. The mean values of pressures, flows, and volumes were reported only for the last 20 cardiac cycles. The performance of the SPPC algorithm was compared to the performance of maintaining a constant ΔP and constant LVAD RPM. The computer model was assumed to have no process noise, and the deviation in steady-state value was less than 1 mm Hg for pressures, 0.05 L/min for flow rates, and 1 ml for ventricular volumes.
Differences in characterizing hemodynamic parameter values and ventricular pressure–volume loop responses were calculated using m-files developed in Matlab (MathWorks, Natick, MA). Pressure, flow, and volume waveforms were used to calculate the following hemodynamic parameters: cardiac output; aortic systolic, diastolic, and mean pressures; LV systolic, end diastolic, peak, and minimum pressures and volumes; and aortic, coronary artery, and left ventricular assist device flows. All hemodynamic parameters were calculated on a beat-to-beat basis. Characterizing hemodynamic parameters were calculated for all experimental and control conditions. Suction was defined to have occurred when the instantaneous ventricular pressure value was 1 mm Hg or lower.
SPPC Algorithm Performance During Normal Conditions
There were no significant differences between the performance of the SPPC algorithm and the control algorithm that maintained a constant ΔP setpoint of 75 mm Hg. Suction was not observed, and the ΔRPM was above the suction threshold. The hemodynamic waveforms and LVAD operational parameters were similar for both control algorithms (Figure 2). Left ventricular assist device flow rates and hemodynamic parameters were similar between axial and centrifugal flow LVADs (Tables 1 and 2).
SPPC Algorithm Performance with a High ΔP Setpoint
Constant suction was observed with the ΔP control strategy when the setpoint was set at a high value of 115 mm Hg for both axial and centrifugal LVADs, as indicated by negative ventricular pressures (Figure 3, A–D, I–L). The value of ΔRPM was significantly diminished, and axial and centrifugal LVAD flow was significantly higher (5.8 L/min) in comparison to the LVAD flows generated with a normal ΔP setpoint of 75 mm Hg (Tables 1 and 2). Suction was not observed with the SPPC algorithm even with a 115 mm Hg ΔP setpoint (Figure 3, E–H, M–P). Steady-state hemodynamic parameters and LVAD flow rates were similar to parameters observed with a ΔP setpoint of 75 mm Hg.
SPPC Algorithm Performance During a Rapid Increase in PVR
Intermittent suction was observed for both AF LVAD (Figure 4, A–D) and centrifugal flow LVAD (Figure 4, I–L) with the ΔP control strategy with a rapidly increasing PVR. Suction was avoided with the SPPC algorithm, but a transient reduction in LV pressures and volumes was observed with both axial and centrifugal LVADs with the onset of rapid reduction in PVR (initiated at time t = 150 seconds). The SPPC algorithm automatically reduced LVAD flow rates for both axial and centrifugal pumps to avoid suction (Figure 4, E–H, M–P).
SPPC Algorithm Performance with Combined High ΔP Setpoint and Augmented PVR
Constant suction was observed with the ΔP control strategy when the setpoint was set at a high value of 115 mm Hg for both axial and centrifugal LVADs, as indicated by negative ventricular pressures (Figure 5, A–D, I–L). A rapid increase in PVR increased the magnitude of suction, as indicated by higher negative ventricular pressures. Suction was not observed with the SPPC algorithm (Figure 5, E–H, M–P). However, a transient reduction in LV pressures and volumes was observed with both axial and centrifugal LVADs with the onset of rapid reduction in PVR (initiated at t = 150 seconds).
SPPC Algorithm Performance During Exercise
The SPPC algorithm augmented pump flow autonomously during exercise for both axial and centrifugal LVADs. The magnitude of the LVAD flow augmentation was comparable to the LVAD flow increase obtained with a ΔP control strategy with a setpoint of 75 mm Hg (Tables 1 and 2). The performance of the SPPC algorithm was compared to maintaining a constant RPM setpoint. RPM setpoints of 9827.2 and 1478.0 RPM were selected for the AF and centrifugal devices, as they were the average operational speeds observed with the ΔP controller with a setpoint of 75 mm Hg during rest. Maintaining a constant pump operational speed augmented LVAD flow during exercise. However, the augmentation in the LVAD flow was lower than what was observed with the SPPC and ΔP control strategies. Suction was not observed with the SPPC algorithm even with an abrupt step-transition from exercise to rest condition (Figure 6).
The simulation results demonstrated feasibility of the proposed SPPC algorithm to successfully prevent suction while maintaining physiologic LVAD flows even under extreme conditions of a high ΔP setpoint, rapid changes in PVR, or physical activity levels. The high ΔP setpoint condition represents a case in which a healthcare provider or patient accidentally inputs a high setpoint value into the LVAD controller. Coughing and valsalva maneuvers can cause a rapid temporary increase in PVR and transient reduction in blood flow into the native ventricle.6 A permanent eightfold increase in PVR in 20 seconds represents a nonphysiologic, worst-case scenario for suction. Similarly, a step transition from exercise to rest also represents a nonphysiologic, worst-case condition for suction. These worst-case conditions were simulated to demonstrate the robustness of the SPPC algorithm to avoid suction whilst providing physiologic LVAD flows.
The SPPC algorithm provides physiologic perfusion as evidenced by similarity in steady-state hemodynamic parameters and LVAD flow rates observed with a ΔP setpoint of 115 mm Hg compared to a normal ΔP setpoint of 75 mm Hg during rest and exercise. In earlier studies, it has been demonstrated that maintaining an average ΔP of 75 mm Hg provides LVAD flows equivalent to the cardiac output of a healthy heart during rest and exercise.24–26 Further, the SPPC algorithm significantly augmented LVAD flow rates during exercise in comparison to maintaining a constant pump operational speed (Tables 1 and 2). Similarly, the SPPC algorithm autonomously reduced the LVAD flow rate in response to a diminished ventricular blood inflow (increased PVR) and enables LVAD to mimic a Frank–Starling-like response and enhancing the LVAD preload sensitivity. Selection of device operational speed (RPM) or LVAD flow as the setpoint would necessitate frequent changes in the setpoint according to some expert rule, model prediction, or operator judgment to provide physiologic perfusion for a broad range of physical and clinical conditions. In contrast, the SPPC algorithm does not require frequent changes to the ΔP or ΔRPM setpoint.
The SPPC algorithm structure incorporates two controllers that act against each other to satisfy the opposing control objectives of providing physiologic LVAD flows and avoiding ventricular suction. The opposing control structure, while simple, is commonly and effectively used in nature for homeostasis. Gain-scheduled PI controllers were chosen for the SPPC algorithm as they are commonly used and simple to implement. Further, the SPPC algorithm has a defined controller structure, and only requires the selection of appropriate controller coefficients and ΔRPM setpoint. In this simulation study, different values of ΔRPM setpoints and controller coefficients were used for axial and centrifugal LVADs as each pump design has a different RPM range and dynamic response. However, once determined, these values were not altered between different test conditions for both devices. Thus, the controller coefficients and ΔRPM setpoint will need to be ascertained a priori, which is a common practice for tuning controllers. The controller structure is device independent as demonstrated by the use of the same controller structure for both axial and centrifugal LVADs. The dynamic axial and centrifugal LVAD models by Choi et al. and Kitamura et al. were chosen for this manuscript as they were readily available in literature with all parameters, correspond to LVAD used clinically, and have been used previously to verify physiologic control algorithms for LVAD.
Using the proposed SPPC algorithm, both the native heart and LVAD are contributing to the maintenance of an average ΔP. If cardiac function improves, the native heart will increase its contribution to maintaining the reference ΔP, with the LVAD controller autonomously and automatically reducing LVAD flow rate. Thus, the SPPC algorithm may potentially be useful in bridge-to-recovery applications. A reduction in LVAD flow rate in response to myocardial recovery would lead to a lower risk of suction. The reduced need for suction prevention during myocardial recovery would be evidenced by an augmentation in ΔRPM in response to increasing contractility.
A significant reduction in ventricular contractility would diminish ΔRPM and LVAD generated flows. We sought to minimize this effect in the SPPC algorithm by selecting the ΔRPM setpoint for a severely failing ventricle. However, the SPPC algorithm does require some native ventricular function. In the absence of native ventricular contractility (ventricular fibrillation), the SPPC algorithm will significantly diminish LVAD flows. However, maintaining systemic perfusion with an LVAD during ventricular fibrillation using other control strategies will not provide any pulmonary perfusion and will lead to mortality. Hypertension was not simulated as heart failure patients are medically managed with ACE inhibitors and beta-blockers to maintain normal blood pressure. Left ventricular assist device–generated flows with SPPC algorithm may be lower than cardiac demand with a ΔP setpoint of 75 mm Hg during hypertension. Selection of a higher ΔP setpoint (~115 mm Hg) may be necessary to provide physiologic perfusion in chronic hypertensive patients that are refractory to pharmacologic therapy. Importantly, suction would be prevented and physiologic LVAD flows would be generated with a higher ΔP setpoint of 115 mm Hg using the SPPC algorithm, should the mean arterial pressure diminish to normal values, as demonstrated in Tables 1 and 2. The SPPC algorithm currently requires the measurement of ΔP using implanted pressure sensors. However, it has been demonstrated that ΔP can be estimated using measurements of intrinsic LVAD parameters (RPM, voltage, and current), eliminating the need for any implantable sensors for implementing the SPPC algorithm.34,35
The performance of the computer simulation model is representative of clinical observations from a purely hemodynamic viewpoint. Clearly, this computer simulation is not intended to replace the importance and significance of in vivo models and is incapable of replicating all expected clinical responses, but it does provide a valuable initial step for early testing of hypotheses. For instance, this simulation cannot mimic neurohumoral responses, autonomous regulation, tissue remodeling, activation of regulatory proteins, or changes in genetic phenotype, but it can demonstrate feasibility of concepts. Computer models rely on many assumptions that may have a dramatic influence on the interpretation of simulation results. For example, the computer model for this study assumes ideal valves that open and close instantaneously, Newtonian blood, a constant diastolic ventricular compliance, does not account for inertial or gravitational effects, and the effects of wave reflection, but does enable prediction of hemodynamic and ventricular responses. Despite these limitations, the computer simulation model demonstrates the feasibility of the proposed SPPC algorithm and provides valuable insights into cardiovascular responses to these control algorithms.
This work was supported, in part, by an American Heart Association National Scientist Development Grant (0730319N).
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Keywords:Copyright © 2015 by the American Society for Artificial Internal Organs
ventricular assist device; suction prevention; physiologic control