Minimizing left ventricular stroke work with iterative learning flow profile control of rotary blood pumps

Biomedical Signal Processing and Control 31 (2017) 444–451

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Biomedical Signal Processing and Control journal homepage: www.elsevier.com/locate/bspc

Minimizing left ventricular stroke work with iterative learning flow profile control of rotary blood pumps Daniel Rüschen a,∗ , Frederik Prochazka b , Raffael Amacher c , Lukas Bergmann a , Steffen Leonhardt a , Marian Walter a a

Philips Chair for Medical Information Technology, Helmholtz-Institute for Biomedical Engineering, RWTH Aachen University, Aachen, Germany Institute of Flight Systems and Automatic Control, Technische Universität Darmstadt, Darmstadt, Germany c Wyss Translational Center Zurich, ETH Zurich, 8092 Zurich, Switzerland b

a r t i c l e

i n f o

Article history: Received 8 April 2016 Received in revised form 22 August 2016 Accepted 3 September 2016 Keywords: Hybrid mock circulatory loop Iterative learning control Rotary blood pump Ventricular assist device

a b s t r a c t Rotary blood pumps are gaining importance in the successful treatment of advanced heart failure. However, the application of fixed pump speeds is discussed controversially. Since the natural heart delivers pulsatile flow, many physicians presume that pulsatile pumping provides therapeutical advantages. To address this, we combine the technical advantages of continuous flow devices with the supposed physiological advantages of pulsatile flow. We present an iterative learning control (ILC) strategy for continuous flow ventricular assist devices that minimizes the left ventricular stroke work (LVSW). For that, a comprehensive nonlinear model for rotary blood pumps that is used for simulation and controller design is introduced. The controller is tested using a hardware-in-the-loop cardiovascular system simulator with a Medos deltastream DP1 blood pump. The tracking performance of the proposed ILC approach is compared to a benchmark controller that uses additional sensor information, both controllers significantly reduce the residual LVSW compared to the fixed speed case. In addition to decreasing ventricular load, the proposed ILC strategy can be used as an inner control loop to any physiological controller that sets reference flow profiles. The introduced controller might be useful for the investigation of effects of various pulsatile flow patterns independent from the type of VAD in future in vivo studies. The targeted manipulation of physiological quantities such as the residual cardiac work has the potential to considerably improve ventricular assist device therapy. © 2016 Elsevier Ltd. All rights reserved.

1. Introduction Patients with advanced heart failure are unable to perform any physical activity without discomfort [1]. Approximately 1–2% of the adult population in developed countries suffers from heart failure [2]. In case of an unfavorable progression of the disease, heart transplantation remains the gold standard therapy. Due to the limited availability of donor organs and the rapid development of ventricular assist device (VAD) technology, the number of patients bridged to transplant or receiving destination therapy by implantation of a VAD increased significantly [3]. This trend is confirmed by the latest Interagency Registry for Mechanically Assisted Circulatory Support (INTERMACS) report, which includes clinical information from 15,745 adult patients that received primary prospective implants

∗ Corresponding author at: Philips Chair for Medical Information Technology, RWTH Aachen University, Pauwelsstr. 20, 52074 Aachen, Germany. E-mail address: [email protected] (D. Rüschen). http://dx.doi.org/10.1016/j.bspc.2016.09.001 1746-8094/© 2016 Elsevier Ltd. All rights reserved.

between June 2006 and December 2014. The vast majority of these patients (84.4%) were treated with a left ventricular assist device (LVAD) [4]. The purpose of an LVAD is to relieve the native heart and to increase the cardiac output by pumping blood from the left ventricle into the aorta. In modern LVAD therapy, displacement pumps are virtually replaced by rotary blood pumps, as the latter are associated with dramatically lower overall adverse event rates [4]. These pumps are normally operated at a constant rotational speed; this leads to a reduced vascular pulsatility compared to physiological flow [5]. There is evidence that fixed speed support using continuous flow devices can cause aortic valve insufficiency [6,7], gastrointestinal bleeding [8], and thromboembolic events [9]. It is not yet known whether these complications are induced by the pump type or the lack of pulsatile flow. A systematic overview of clinical studies comparing pulsatile and continuous flow support and their conflicted findings is given in [10]. These studies cannot separate pump design from flow effects as they are limited to the comparison of previous pulsatile technology to recent continuous

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flow devices. This issue may be addressed by pulsatile flow control of rotary blood pumps. A control strategy that restores pulsatility might be the solution for combining the benefits of smaller and more reliable rotary blood pumps with the positive hemodynamic effects of pulsatile devices [11]. A recent review of studies investigating cardiac cyclesynchronized speed modulation of continuous flow devices [12] confirmed that such strategies can increase pulsatility in the systemic arterial circulation and enhance the unloading of the left ventricle. These studies focused on the modulation of pump speed as this is the control variable in standard VAD therapy and hence clinically available. However, the quantity that directly affects hemodynamics is the pump flow, which depends not only on the pump speed, but also on the differential pressure across the pump. Hence, it is preferable to directly control the pump flow [12]. It enhances the comparability of studies conducted with different VADs and heterogeneous groups of subjects. Ising et al. [13] demonstrated in silico that the arterial pulsatility and ventricular work can significantly be affected by the modulation of the pump flow. The specific control of VADs might eventually lead to higher myocardial recovery rates [14]. In this paper, we present an iteratively learning flow controller for rotary blood pumps. It enables good reference tracking of numerically optimal flow profiles that minimize the left ventricular stroke work (LVSW). Moreover, we show that pump flow modulation outperforms the fixed speed control operation case in terms of LVSW reduction, which is consistent with the literature. Therefore, we present a comprehensive nonlinear model for continuous-flow VADs. It is used to design and test the iterative learning control (ILC) strategy. ILC was chosen because it exploits the repetitive nature of the changing differential pressure across the pump to improve the flow tracking performance. Besides, it was already successfully applied in clinical trials in other areas of biomedical engineering [15,16]. The improvement of the flow tracking performance is achieved by generating a control input trajectory that incorporates error information of previous heartbeats. The LVSW-optimal reference trajectories, which are solutions of a nonlinear program, allow a meaningful comparison of different control strategies. We tested two strategies: ILC combined with a PID feedback controller and a classical PID controller with PD disturbance feedforward control. Their performance was assessed in a hybrid mock circulatory loop with a cardiovascular system (CVS) model simulating severe heart failure. This paper is structured as follows. Section 2 presents our approach and the test setup. In Section 3, in vitro results are analyzed and discussed. Our conclusions are drawn in the final section. 2. Materials and methods This section begins by introducing a generic nonlinear model for rotary blood pumps. It is used to design and test the iteratively learning pump flow controller proposed in Section 2.2. The tracking performance of the ILC is tested with numerical optimal flow profiles described in Section 2.3 in a hybrid mock circulatory loop which is presented in Section 2.4. The last section gives a brief overview of the experimental procedure. 2.1. Rotary blood pump model The functional principle of a continuous-flow VAD is identical to that of conventional centrifugal pumps. As VADs are in direct contact with blood, their designs are optimized for hemocompatibility. Continuous flow devices include an impeller in the flow path that accelerates the blood stream. Different pump types can be distinguished by impeller design and position of the flow outlet. The

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Fig. 1. Medos deltastream DP1 rotary blood pump with a diagonally streamed impeller.

rotation axis and outlet are aligned in axial-flow pumps, whereas they are tangential in radial-flow pumps. Fig. 1 shows the rotary blood pump used in this study (deltastream DP1, Medos AG, Stolberg, Germany). It can be classified as a diagonal pump, because the blades are mounted diagonally on the impeller. The VAD is designed for extracorporeal operation, in which tubes connect the inlet of the pump to the apex of the left ventricle and the outlet of the pump to the ascending aorta. We developed a nonlinear dynamical model of the blood pump in order to design and test controllers in silico. For this purpose, the standard electro-hydraulic modeling approach was applied [17]. The overall model of the system is depicted in Fig. 2. The electrical subsystem consisting of an electronically commutated motor is modeled by applying Kirchhoff’s voltage law to the armature Larm

diarm = varm − Ke ω − Rarm iarm dt

(1)

with Larm armature inductance [mH], Ke back-EMF constant [Vs rad−1 ], Rarm armature resistance [m], iarm armature current [A], varm armature voltage [V], ω angular velocity of the rotor [rad s−1 ]. According to Newton’s third law, the torque generated by the electrical drive is transmitted over a motor shaft that is directly connected to the impeller. The resulting rotary motion of the mechanical subsystem can be described by Jrot

dω = Kt iarm − Kf ω − (ω, qpump ) dt

(2)

with Jrot moment of inertia of the rotor and impeller [kg m2 ], Kt motor torque constant [N m rad A−1 ], Kf viscous friction constant [N m s], qpump pump flow [L min−1 ],  load torque as a function of ω and qpump [N m rad]. Besides inertia and load torque, Eq. (2) only contains viscous friction as a complete stop of the impeller is prevented in normal operation in order to reduce the risk of blood clotting in the pump. Eqs. (1) and (2) model a conventional brushless DC electric motor which is very similar in all pump designs. In contrast, the hydraulic subsystem is different for every individual pump design. We determined a two-dimensional characteristic map of the pump in static differential pressure and flow measurements. From this measurement data, we derived a model for the differential pressure ppump = Aω2 − Rturb q2pump sign(qpump ) − Rlam qpump [mmHg s2

rad−2 ],

(3)

with A pump constant Rturb turbulent flow resistance [mmHg min2 L−2 ], Rlam laminar flow resistance [mmHg min L−1 ], ppump differential pressure generated by the pump [mmHg]. Note that [mmHg] is a manometric unit of pressure that is still widely used in the medical community. The pump constant A describes the relationship between rotational speed of the impeller and generated differential pressure ppump . Two hydraulic resistances in series model losses in the flow path due to laminar and turbulent flow. Although the rotational speed ω is strictly positive, the direction of flow can reverse at high negative differential

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Fig. 2. Block diagram of the rotary blood pump consisting of the interconnection of an electrical, mechanical, and hydraulic subsystem.

pressures. This is considered using a signum function in the turbulent flow loss term. In Eq. (2), the load torque (ω, qpump ) acting on the drive is not based on a formal derivation. A common approach is to use a general function fitted to describe measurement data; we use (ω, qpump ) = k0 q2pump ω + k1 qpump ω2 + k2 ω + k3 ω3

(4)

as proposed in [18]. The dynamic behavior of the pump is also dependent on the hydraulic load. We assume a simple resistance/inertance load model Rfluid qpump + Mfluid

dqpump = ppump + pd , dt   

(5)

=p

where pd = plv − pao is the difference between the left ventricular and the aortic pressure. The parameters of the presented gray box model were identified with pseudo random binary noise as input for the setpoint of the armature current controller iarm,ref and the disturbance pd while measuring the rotational speed ω and the resulting pump flow qpump . The real system has armature current limitations, the impeller (depending on the differential pressure) starts spinning at approximately 0.3 A due to static friction. The motor of the pump (EC 22, maxon motor GmbH, Munich, Germany) has a nominal current of 1.56 A. The proposed system model was implemented in Simulink, where the current limitations are incorporated. The generic nature of the model should enable adaptation to other VADs simply by changing the parameters. The hydraulic part is most critical, because it depends on the viscosity of the patient’s blood which can change with fluid balance and medication. As these parameters normally change slowly, this drawback can be compensated by an iterative learning controller. 2.2. Iterative learning controller An LVAD pumps blood from the left ventricle into the ascending aorta, thus it is exposed to periodic changes of differential pressure due to natural heartbeats. An iterative learning control strategy can exploit the recurrent nature of this disturbance by incorporating error information from previous cardiac cycles. It generates a feed-forward control that adjusts to the repeating disturbance and enables the accurate tracking of arbitrary flow profiles. We combined ILC with a feedback controller for fast pump flow modulation during a heartbeat. This parallel structure incorporates both the advantages of learning over several cycles as well as rejection of instantaneous non-repeating disturbances. This combination is necessary because the iterative learning controller represents an open-loop controller in the time domain, where the feedback is incorporated by closing the control loop in the iteration domain. The learning nature of ILC guarantees high robustness

against model uncertainties [19] and slowly changing repetitive disturbances. The availability of entire time sequences from previous iterations allows the application of high-performing non-causal learning algorithms [20]. A widely used standard learning algorithm [21] for a first order ILC is





uj+1 (k) = Q (q) uj (k) + L(q)ej (k + m) ,

(6)

where the index j ∈ {0, 1, 2, . . . } indicates the iteration, k the discrete time step within this iteration and q the forward time-shift operator which is defined as q u(k) = u(k + 1). The control signals of the current and previous iteration are denoted as uj+1 (k) and uj (k), respectively. The control error of the previous iteration ej (k + m) is used to calculate a feed-forward trajectory for the current iteration. The relative delay m of the plant is compensated by using the previous control error at the time step k + m. The filters L(q) and Q(q) are called learning function and Q-filter. The learning function was selected to be a static gain L(q) =  with <

1 G(z = 1)

(7)

in order to guarantee stable ILC dynamics and monotone error convergence (for linear systems) [19]. G(z = 1) denotes the static gain of the time discrete plant model G(z) =

qpump (z) iarm (z)

(8)

introduced in Section 2.1, linearized at qpump = 3 L min−1 and pd = 0 mmHg. As the factor  also determines the convergence rate, it is beneficial to choose it close to the bound given in Eq. (7). The purpose of the Q-filter is to increase the robustness against model uncertainty and noise by reducing the learning bandwidth. Therefore, we implemented Q(q) as a non-causal zero-phase lowpass filter to cut off learning at higher frequencies which are predominated by noise and non-repeating disturbances. The zerophase filtering is achieved by subsequent forward and backward convolution of the low-pass filter and the filtered signal [22]. This leads to a higher attenuation above the chosen cutoff frequency and a compensation of the phase lag normally introduced by low-pass filters. As a result, it yields a better learning behavior. Fig. 3 shows the pump flow control loop, with the ILC in parallel to a feedback controller K. Both controllers receive the control error e = qpump,ref − qpump

(9)

as an input and the plant input iarm,ref is defined as the sum of both controller outputs. The change of the differential pressure pd due to remaining heart activity acts as a repeating disturbance on the VAD. It is compensated with an ILC that utilizes the control error and its own command signal of the preceding iteration stored in memory blocks. The learning function L and the Q-filter Q are applied in

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Fig. 3. Pump flow control loop consisting of an iterative learning controller in parallel to a feedback controller.

lifted system form [23], so that the command trajectory for the current iteration is generated by using simple matrix operations. The feedback controller K was designed for good disturbance rejection using open loop shaping. This is sufficient because the contribution of K to reference tracking decreases as the ILC converges [24]. Standard ILC requires constant initial conditions in each iteration [25]. A relaxed version of this postulate allows for a variation of the initial states [26], as long as xj (0) − x(0) < ˇ, ∀ j ∈ {1, 2, . . .}. The initial states



xj (0) =

ωj (0)

A numerical optimization routine described in [29] has been used to construct reference flow profiles that minimize left ventricular stroke work. Briefly, this method implements a “first discretize, then optimize” approach based on direct transcription, which results in computationally efficient problem structures [30,31]. An optimal-control problem (OCP) is formulated in continuous time and, by discretizing it, converted into a nonlinear program (NLP). The NLP is solved using a commercially available solver [32]. The OCP consists of a lumped-parameter model of the CVS where the control input is chosen to be the pump flow, a set of constraints, as well as an objective function. The CVS model is implemented as a simplified version of a model introduced in [33]. The control input is the pump flow from the left ventricle to the aorta, in parallel to the aortic valve. The right heart is not modeled and it has been shown that its influence on the resulting optimized trajectories is negligible [29]. The model consists of eight ordinary differential equations related to eight state variables, and it includes an actively contracting left atrium and left ventricle. Two equality constraints are set: First, the systemic perfusion is required to be equal to a specific predefined value, and second, a periodic solution is enforced. The control input is bound by inequality constraints to lie between a predefined maximum and minimum flow level at all times. The objective function is chosen as



(10) L=

plv (qav + qpump − qmv )dt,

(12)

T



pd,j (0)

447

(11)

were checked over several hundred iterations. They deviated from their mean value by ˇ < 1%. Hence, the assumption of bounded initial states holds. ILC also requires the cycle length of the repeating disturbance to be constant, this was achieved in this first implementation by fixing the heart rate of the cardiovascular system simulation to 60 bpm. However, a changing heart rate and thus a varying cycle length as it occurs in real life situations could be incorporated as shown in [27]. The saturation of the armature current iarm to an interval of 0.3–1.56 A showed to be a limiting factor of the controller performance. Convergence and monotonicity can only be guaranteed as long as the control signal uj (k) remains within the saturation limits. The combination of ILC with a feedback controller yields the benefits of both methods. The learning part compensates for model errors and slowly changing model parameters such as blood viscosity. It utilizes knowledge of previous cardiac cycles to effectively reject repeating disturbances. The parallel feedback controller K speeds up convergence and counteracts non-repeating disturbances. The control design based on the inverse steady-state gain of the plant can easily be adapted for other blood pumps. The proposed control structure is able to track challenging arbitrary pump flow profiles.

such that the left ventricular stroke work of a heartbeat with duration T is minimized. Eq. (12) contains plv left ventricular pressure [mmHg], qav aortic valve flow [L min−1 ], qpump pump flow [L min−1 ], qmv mitral valve flow [L min−1 ]. The OCP was solved with respect to two different sets of constraints derived from the physical limits of the blood pump, yielding the optimal flow profiles henceforth called A and B. The lower boundary for pump flow was defined as qmin = 1 L min−1 , whereas the upper boundary was constrained to qmax,A = 7 L min−1 for flow profile A and to qmax,B = 5 L min−1 for flow profile B. These settings resulted in the optimized flow profiles presented in Fig. 4, which are nearly rectangular and a form of co-pulsation. Profile A applies the maximum flow from the start of the atrial systole until the end of the ventricular systole, while profile B applies the (lower) maximum flow at a larger percentage of the cardiac cycle. Note that the flow profiles were not constrained to be rectangular, this is a result of the optimization procedure. The flow profiles are obtained with the same routine as in earlier work [29], with the only exception that the pump flow is directly used as the control input, hence no pump dynamics are considered. The minimum and maximum flows are predefined parameters, and as such influence the optimized flow profiles. The CVS model used

2.3. Optimal flow profiles This section describes the method used for obtaining the flow profiles for the reference tracking controllers investigated in this paper. Changing the VAD flow profile compared to the one resulting from a constant speed strategy offers an increased control authority on hemodynamics, and can thus be used for e.g. altering the workload of the heart, the arterial pulsatility, or the degree of aortic valve opening [12,28]. Using a reference flow profile instead of a reference speed profile offers the advantage that it is independent of the VAD that is used, assuming that the reference tracking performance is of sufficient quality.

Fig. 4. Timing and shape of the flow profiles A and B with respect to the left ventricular pressure of a healthy subject.

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in the OCP is different from the one where the profiles are then applied experimentally in this study. In summary, our numerical optimization procedure represents a flexible framework that allows to define flow profiles that directly optimize a specific physiologic criterion. The optimized flow profiles yield the theoretical minimum stroke work and thus allow for a meaningful analysis of the performance of the different control approaches for pump flow reference tracking. 2.4. Hybrid mock circulatory loop The VAD control strategies were tested in vitro with a hydrodynamic CVS simulator [34]. This hybrid mock circulatory loop (MCL) enables hardware-in-the-loop simulation of a numerical CVS model [35] that is connected to a VAD under test via a hydrodynamic interface. In contrast to classical MCLs, most parts of the physiological model, such as the heart and the vascular system, exist solely in the numerical domain. The only states transferred to the physical domain are the left ventricular pressure and aortic pressure at the pump inlet and outlet, respectively. By controlling these pressures and feeding back the measured pump flow to the numerical CVS simulation, which in turn results in new pressure setpoints, we can simulate a time variant hydraulic impedance at the ports of the VAD similar to the in vivo application. Fig. 5 gives an overview of the hybrid MCL, the VAD under test is located centrally and connected to the points marked with (a) and (b) via standard tubing. These points highlight the only connecting elements in which pressure and flow have equivalent physiological states in the numerical simulation. Apart from these, no other hydraulic quantity corresponds to any state of the CVS simulation. This fact makes (physical) valves unnecessary, which frequently cause artifacts such as reflections and fluid hammers. Instead, three gear pumps are employed to generate a directed flow. Beyond that, these pumps are used to control the amount of fluid in the two compartments C1 and C2 in order to keep the attached voice coil actuators (VCAs) within their limited operating range. The compartments are made of polymethyl methacrylate, each of them is connected by a metal bellow to a VCA. The VCAs are used to perform the fast pressure changes needed to track the reference of the CVS simulation. The pressure settling time is less than 20 ms with an accuracy of ±1 mmHg, which is possible due to the high stiffness of the actuators and the structure. Both pin and pout are measured with invasive blood pressure sensors (Xtrans, CODAN pvb Critical Care GmbH,

Fig. 5. Hybrid mock circulatory loop consisting of the two compartments C1 and C2 , in which the pressures pin and pout at the pump inlet and outlet are controlled. The pressure setpoints are provided by a cardiovascular system simulation, that responds to the measured flow qpump .

Forstinning, Germany). The pump flow qpump is determined with an ultrasonic flow probe (H11XL, Transonic Systems Inc., Ithaca, USA). In order to mimic the hydrodynamic properties of blood, a glycol/water mixture with a dynamic viscosity of 2.5 mPa s at 298.15 K over a wide range of shear stress is used. The CVS simulation and the test rig controllers are implemented in Simulink (The MathWorks Inc., Natick, USA) and run on a real-time computer (DS 1103, dSPACE GmbH, Paderborn, Germany) with a sampling time of 1 ms. As hybrid MCLs offer the possibility to investigate the interaction of a simulated CVS with all included physiological control loops and real mechanical heart support systems, they enable flexible and highly reproducible test series. Hence, MCLs meet the growing demand to study hemodynamic effects of mechanical heart support systems in vitro before conducting animal experiments.

2.5. Experiments The ILC approach to VAD flow control described in Section 2.2 was compared to a benchmark controller and analyzed with regard to LVSW reduction and pulsatility in hardware-in-the-loop experiments. Both flow controllers were implemented in Simulink and executed on the same real-time computer as the CVS simulation and the hybrid MCL controls. This fact obviates the need for subsequent synchronization of several data streams. All necessary data for the controller performance evaluation were obtained using ControlDesk (dSPACE GmbH, Paderborn, Germany) and analyzed with MATLAB (The MathWorks Inc., Natick, USA). The control signal for the blood pump iarm,ref were transmitted to a 4-quadrant PWM servo controller (ESCON 50/5, Maxon Motor GmbH, Munich, Germany) which drives the electronically commutated motor of the deltastream DP1. The CVS model described in [35] was modified to simulate severe heart failure for the controller tests. The heart rate was fixed to 60 beats per minute and the contractility was reduced to 25% of its nominal value by deactivating all physiological control mechanisms that affect these quantities. Fig. 6 depicts the classical controller used as a benchmark for the ILC performance. For that, a PID controller designed for reference tracking is combined with a PD feedforward disturbance compensator. In contrast to the iterative learning controller, the classical controller depends on a measurement of the disturbance signal pd to achieve comparable results. A practical implementation would thus require additional sensors for the inlet and outlet pressure of the blood pump. The ILC approach only requires a flow sensor or a sufficiently good estimation of the pump flow. Prior to the measurements, the MCL was thoroughly deaerated to guarantee a stiff coupling of the high bandwidth actuators necessary for tight control of the pressures at the pump inlet and outlet. The fluid temperature was ensured to be 298 K during the controller tests. Each of these tests began with the VAD switched off which caused backflow from the aorta into the left ventricle during diastole. The flow controller was active during power-up of the pump. The CVS simulation and the controllers reached a steady state before error values and the LVSW were determined. All error

Fig. 6. PID controller with PD disturbance feedforward control used as a benchmark.

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that both controllers show adequate tracking performance for flow profile B, whereas the benchmark controller shows the same characteristic time lag as for flow profile A. This time lag is caused by the actuator saturation iarm > 0.3 A, which prevents the active deceleration of the pump flow. It demonstrates a clear advantage of the ILC approach, which reacts to the flow change before it occurs based on error information from previous cycles. This results in very short transition times. The ILC convergence behavior in terms of errors and left ventricular stroke work for flow profiles A and B is depicted in Fig. 8. The decreasing maximum absolute error for the consecutive heartbeats j ∈ [0, 200] calculated from emax (j) = max(|qpump,ref − qpump |).

Fig. 7. Performance of the converged iterative learning controller compared to the benchmark feedback controller over one heartbeat interval. Top: flow profile A. Bottom: flow profile B.

and LVSW measurements are mean values calculated over 10 cardiac cycles. 3. Results and discussion Fig. 7 shows the tracking performance of the ILC approach in comparison to the benchmark PID controller for the two LVSWoptimal flow profiles. The pump flow is depicted for one cardiac cycle whose start is defined as the onset of the ventricular systole (usually marked by the R peak in ECG). The isovolumic relaxation of the ventricle approximately ends at 45% of the cardiac phase. From late systole to early systole of the following heartbeat, the differential pressure pd is negative. The left ventricular pressure is lower than the aortic pressure and hence the aortic valve is closed. The ejection phase (20–40% of the cardiac phase) induces a slightly positive pd . This changing differential pressure is the main disturbance which affects the flow through the pump significantly. The top part of Fig. 7 shows that the benchmark controller (green line) does not reach the upper and lower setpoints of flow Profile A, besides the under- and overshoot around 55% and 90% of the cardiac phase, respectively. Moreover, we observe a time lag between the flow profile and actual flow generated by the benchmark controller. In contrast, the ILC strategy (blue line) reaches the upper setpoint and oscillates around the lower setpoint achieving the correct mean value of 1 L min−1 . The bottom part of Fig. 7 illustrates

(13)

is illustrated in Fig. 8(a). The large initial emax for flow profile A of approximately 8 L min−1 is caused by backflow through the pump at the beginning of the measurement. The magnitude of emax for flow profile A is higher compared to flow profile B due to the larger difference between the minimum and maximum flow setpoints. The maximum error reaches a steady state after 120 heartbeats or 2 min for both profiles. The benchmark controller achieves higher maximum error values with 4.5 L min−1 for flow profile A and 2.75 L min−1 for flow profile B. The ILC strategy performs superior after 41 s (A) and 16 s (B). The root mean square (RMS) error for heartbeat j is calculated with



eRMS (j) =

2 1 qpump,ref − qpump , n

(14)

n

where n = 1000 is the number of samples per heartbeat. In contrast to emax , the RMS error decreases monotonically (Fig. 8(b)). The iterative learning controller needs 87 heartbeats to outperform the RMS error of the benchmark controller for flow profile A (1.54 L min−1 ), whereas 35 heartbeats are sufficient for flow profile B (0.84 L min−1 ). Crucially, there is a positive correlation between the errors and the LVSW depicted in Fig. 8(c), which is calculated by evaluating the objective function given in Eq. (12). The ILC strategy shows a nearly monotonic learning behavior where convergence is reached within a timeframe comparable to the slowest time constants of the CVS simulation feedback loops. As the proposed control strategy is intended for long-term mechanical heart support, a convergence time of approximately 2 min seems acceptable. Fig. 9 compares the residual LVSW of the different control strategies for the two flow profiles. The theoretical optimum was calculated by directly applying the numerical optimal flow profiles to the CVS model in simulation. Flow profile A seems to be near the maximum possible reduction of LVSW with mechanical support. Even though the tracking performance of both the ILC strategy and the benchmark controller is moderate, the LVSW reduction is close to the optimal value. In contrast to that, the tracking performance of

Fig. 8. Transient behavior and asymptotic performance of the ILC approach in terms of errors and cardiac work. The maximum errors at converged state are emax,A (∞) =2.3 L min−1 and emax,B (∞) =1.5 L min−1 . The RMS errors are eRMS,A (∞) =1.07 L min−1 and eRMS,B (∞) =0.55 L min−1 .

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Fig. 9. Left ventricular stroke work of the flow profiles A and B as reference trajectories of ILC and PID controller in comparison to the theoretical minimum and the constant mean flow of these profiles, normalized to the LVSW without heart support of 410 mJ.

both controllers in terms of flow is better for flow profile B, but the achieved LVSW reduction compared to the theoretical minimum is inferior. This result underlines that a conclusive analysis of flow or speed profiles and their control can only be based on physiologically meaningful values. The absolute values of the residual LVSW given in Table 1 show that both flow profiles achieve a lower residual LVSW than the same mean flow (profile A: 4.5 L min−1 , profile B: 4.2 L min−1 ) constantly applied. The mean arterial pressure (MAP) is restored to physiological levels by all control strategies. These results concur well with [29] and also confirm previous findings [36,37]. Table 1 also reveals that the pulsatility of blood flow in the aortic arch is only marginally increased by both combinations of controllers and flow profiles. This is shown by analysis of the metrics of pulsatility: the energy equivalent pressure [38]



EEP =

(qpump + qav )pao dt



qpump + qav dt

(15)

[mmHg],

the surplus hemodynamic pressure [12] SHP = EEP − MAP

[mmHg],

(16)

and the more commonly used surplus hemodynamic energy [39] SHE = 1332 · SHP[erg cm−3 ].

(17)

SHE quantifies the energy density that is available additionally due to the pulsatility of blood flow, where [erg] is a unit of energy equal to 100 nJ. The SHE achieved in this study is negligible compared to the pulsatility generated by the healthy heart (see, e.g., [5]). This is consistent with [12], where an inherent trade-off between unloading the ventricle and increasing pulsatility in the downstream vessel is demonstrated. Thus, physiologic hemodynamic conditions in the aorta could be established with different

reference flow profiles, but only at the expense of a higher ventricular load. The optimal flow profiles were obtained with respect to the CVS model introduced in [33]. The fact that the application to a different CVS model as described in [35] shows similar effects indicates the transferability of the results. However, this study has limitations. In order to use the standard ILC algorithm, we did not take into account a changing heart rate or cardiac arrhythmias. We did investigate the effects of ventricular extrasystoles by randomly inducing LV contractions, this degrades the tracking performance but does not render the closed loop system unstable. Given that our findings are based on one condition of the CVS model (contractility 25%, nominal total peripheral resistance, etc.), it should be noted that control errors and LVSW may change with different conditions in the simulated CVS. Moreover, the ILC strategy relies on a high quality pump flow estimation or measurement which is not available for all clinically approved devices. The flowmeter used in this study has an accuracy of ±10%, this implies that proprietary or pump modelbased flow estimators with comparable or better accuracy may be used instead. In this proof-of-concept study, the flow profiles were chosen to minimize the LVSW although it is widely accepted that the systolic pressure-volume area is a better measure of left ventricular oxygen consumption [40]. However, the LVSW quantifies the energy delivered to the vascular system by the left ventricle. Hence, we opted for a minimal LVSW accompanied by a physiological cardiac output as this might be a suitable VAD control strategy. Furthermore, the analysis of other physiological or pathological consequences such as opening of the aortic valve, perfusion of the coronary arteries or hemolysis were not within the scope of this study. The introduced flow control strategies are intended to be used as an inner control loop, therapy and safety objectives such as preload sensitivity and suction prevention will have to be addressed by a superimposed control loop that adapts the reference flow trajectories. For example, the desired cardiac output is defined in a constraint equation of the OCP detailed in [29]. Furthermore, the proposed flow control strategy may be combined with a superimposed suction detector that adapts the mean flow of the reference trajectories. These adaptions of the flow profiles can be made, for instance, by a rule-based controller or an expert system. In this paper, we have shown that the accurate tracking of demanding flow profiles with a rotary blood pump can either be realized based on additional pressure sensor information that enables feedforward disturbance control or by utilizing a sophisticated control algorithm such as ILC. As pressure sensors are usually prone to drift over time and temperature, the ILC approach is more robust and hence more suitable for clinical practice. Our experiments show that a good tracking performance in terms of flow corresponds to a reduction of the left ventricular stroke work, which is the hemodynamic behavior that was aimed for in the flow profile optimization procedure.

Table 1 Hemodynamic effects of the two flow profiles with different controllers compared to the theoretical optimum and constant mean flow. Flow profile

Control strategy

LVSW [mJ]

MAP [mmHg]

EEP [mmHg]

SHP [mmHg]

SHE [erg cm−3 ]

A

Optimum ILC Benchmark Constant

121.7 122.8 124.1 201.4

97.9 97.9 99.2 97.5

98.2 98.2 99.3 97.5

0.28 0.28 0.14 0

378 376 188 0

B

Optimum ILC Benchmark Constant

130.6 148.2 161.8 242.2

91.7 91.3 91.7 91.7

91.7 91.4 91.8 91.7

0.06 0.06 0.04 0

76 75 53 0

D. Rüschen et al. / Biomedical Signal Processing and Control 31 (2017) 444–451

4. Conclusions Our study confirms that the appropriate pulsatile control of rotary blood pumps reduces the left ventricular stroke work. We presented a comprehensive model for rotary blood pumps that was used to design an iterative learning controller for the accurate tracking of optimal flow profiles. The tracking performance of the ILC approach is marginally better compared to the benchmark controller that utilizes additional sensors to measure the differential pressure across the pump. Importantly, the numerical optimal flow profiles applied with either one of the introduced controllers achieve a higher reduction of the LVSW than the same mean flow constantly applied. The presented control strategies can be used to investigate the effects of pulsatile flow independently from the type of blood pump. The translation to clinical practice might eventually lead to insightful contributions to the debate over the necessity of pulsatility during mechanical heart support. The ILC strategy in combination with the presented flow profiles provide the framework for clinicians that enables them to directly set a physiologically meaningful value as a therapy goal. Furthermore, the targeted manipulation of the residual cardiac work has the potential to improve the rate of myocardial recovery and successful weaning in VAD therapy. As we only considered a fixed heart rate in the hardware-in-the-loop experiments, future work will focus on the synchronization to and scaling for varying cardiac cycle lengths using intracardiac ECG. More broadly, research is also needed to enable the direct control of the residual cardiac power and with it the degree of support to be able to adapt the pump flow profile to the patient’s demand or individual therapy goal. References [1] J.J. McMurray, S. Adamopoulos, S.D. Anker, A. Auricchio, M. Böhm, K. Dickstein, V. Falk, G. Filippatos, C. Fonseca, M.A. Gomez-Sanchez, T. Jaarsma, L. Køber, G.Y. Lip, A.P. Maggioni, A. Parkhomenko, B.M. Pieske, B.A. Popescu, P.K. Rønnevik, F.H. Rutten, J. Schwitter, P. Seferovic, J. Stepinska, P.T. Trindade, A.A. Voors, F. Zannad, A. Zeiher, ESC guidelines for the diagnosis and treatment of acute and chronic heart failure 2012, Eur. J. Heart Fail. 14 (8) (2012) 803–869. [2] A. Mosterd, A. Hoes, Clinical epidemiology of heart failure, Heart 93 (2007) 1137–1146. [3] A. Cheng, M.S. Slaughter, Heart transplantation, J. Thorac. Dis. 6 (8) (2014) 1105–1109. [4] J.K. Kirklin, D.C. Naftel, F.D. Pagani, R.L. Kormos, L.W. Stevenson, E.D. Blume, S.L. Myers, M.A. Miller, J. Timothy Baldwin, J.B. Young, Seventh INTERMACS annual report: 15,000 patients and counting, J. Heart Lung Transplant. 34 (12) (2015) 1495–1504. [5] K.G. Soucy, S.C. Koenig, G.A. Giridharan, M.A. Sobieski, M.S. Slaughter, Defining pulsatility during continuous-flow ventricular assist device support, J. Heart Lung Transplant. 32 (6) (2013) 581–587. [6] S.V. Deo, V. Sharma, Y.H. Cho, I.K.P.S.J. Shah, De novo aortic insufficiency during long-term support on a left ventricular assist device: a systematic review and meta-analysis, ASAIO J. 60 (2) (2014) 183–188. [7] S.W. Pak, N. Uriel, H. Takayama, S. Cappleman, R. Song, P.C. Colombo, S. Charles, D. Mancini, L. Gillam, Y. Naka, U.P. Jorde, Prevalence of de novo aortic insufficiency during long-term support with left ventricular assist devices, J. Heart Lung Transplant. 29 (10) (2010) 1172–1176. [8] S. Crow, R. John, A. Boyle, S. Shumway, K. Liao, M. Colvin-Adams, C. Toninato, E. Missov, M. Pritzker, C. Martin, D. Garry, W. Thomas, L. Joyce, Gastrointestinal bleeding rates in recipients of nonpulsatile and pulsatile left ventricular assist devices, J. Thorac. Cardiovasc. Surg. 137 (1) (2009) 208–215. [9] H. Patel, R. Madanieh, C.E. Kosmas, S.K. Vatti, T.J. Vittorio, Complications of continuous-flow mechanical circulatory support devices, Clin. Med. Insights Cardiol. 9 (2) (2015) 15–21. [10] K.G. Soucy, S.C. Koenig, G.A. Giridharan, M.A. Sobieski, M.S. Slaughter, Rotary pumps and diminished pulsatility: do we need a pulse? ASAIO J. 59 (4) (2013) 355–366. [11] A. Cheng, C.A. Williamitis, M.S. Slaughter, Comparison of continuous-flow and pulsatile-flow left ventricular assist devices: is there an advantage to pulsatility? Ann. Cardiothorac. Surg. 3 (6) (2014) 573. [12] R. Amacher, G. Ochsner, M. Schmid Daners, Synchronized pulsatile speed control of turbodynamic left ventricular assist devices: review and prospects, Artif. Organs 38 (10) (2014) 867–875.

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