In Vitro Evaluation of Multiobjective Hemodynamic Control ...antaki/articles/Gwak, Antaki et...

Original Articles

In Vitro Evaluation of Multiobjective Hemodynamic Controlof a Heart-Assist Pump

KWAN-WOONG GWAK,* MICHAEL RICCI,* SHAUN SNYDER,* BRADLEY E. PADEN,† J. ROBERT BOSTON,‡ MARWAN A. SIMAAN,‡AND JAMES F. ANTAKI§

Ventricular assist devices now clinically used for treatment ofend-stage heart failure require responsive and reliable hemo-dynamic control to accommodate the continually changingdemands of the body. This is an essential ingredient to main-taining a high quality of life. To satisfy this need, a controlalgorithm involving a trade-off between optimal perfusionand avoidance of ventricular collapse has been developed. Anoptimal control strategy has been implemented in vitro thatcombines two competing indices: representing venous returnand prevalence of suction. The former is derived from the firstderivative of diastolic flow with speed, and the latter derivedfrom the harmonic spectra of the flow signal. The responsive-ness of the controller to change in preload and afterload wereevaluated in a mock circulatory simulator using a HeartQuestcentrifugal blood pump (CF4b, MedQuest Products, Salt LakeCity, UT). To avoid the need for flow sensors, a state estima-tor was used, based on the back-EMF of the actuator. Themultiobjective algorithm has demonstrated more robust per-formance as compared with controllers relying on individualindices. ASAIO Journal 2005; 51:000–000.

Congestive heart failure remains a leading cause of morbidityand mortality around the world, and heart transplantation, theonly accepted method to treat severe cases of the disease,cannot meet the vast demand. Consequently, considerableeffort has been put into development of implantable prostheticheart substitutes and ventricular assist devices (VADs).

Because the loading conditions are not static, these devicestypically require feedback control. As patients are rehabilitatedand return to a normal, active lifestyle, the demands for flowcapacity and responsiveness can challenge conventional con-trol. As the importance of the physiologic (demand-based)control for rotary blood pumps has now been recognized,modern control concepts have started to be evaluated for theseapplications. 1–11

Unlike pulsatile VADs that fill passively, the second gener-

ation of VADs are based on turbodynamic pump technologyand do not intrinsically respond to the availability of incomingblood. Furthermore, their characteristic response to alterationsin hydrodynamic load is precisely opposite to the requirementof the body: their pressure generation decreases with flow,whereas the body demands increased flow for increased pres-sure. Therefore, the speed of the pump must dynamicallyrespond to changes in both preload and afterload to meet thedemand for perfusion while avoiding the risk of outstrippingthe available blood flow capacity. The consequences of bothunderpumping it and overpumping it will limit the quality oflife and can pose serious risks to the health of the patient.Underpumping, for example, may cause pulmonary conges-tion, and overpumping may cause the heart and vessels tocollapse.

Therefore, the basic objective of a controller for a pumpoperating as a LVAD (LVAD) is to operate within a range offlow (hence speed) that matches the blood flow capacity of theright ventricle. This, in turn, requires the pump to operatewithin proximity of suction but without actually achievingsuction. In the absence of sensors to directly detect the immi-nence of suction or the hemodynamic load, we have intro-duced a variety of indices, including a pulsatility index, avenous return index, and harmonic spectral index as surro-gates.4,5,11

In this article, the results of in vitro studies are reported thatevaluate these indices, both independently and in combina-tion. Experiments were conducted using a HeartQuest centrif-ugal blood pump (MedQuest Products, Salt Lake City, UT) inan apically cannulated LVAD configuration within a mockcirculatory simulator. The response to changes in preload andafterload are presented.

Materials and Methods

Robust Multiobjective Control

Previous in vivo studies with rotary LVADs have revealedcorrespondences between several features of the flow wave-form and the appearance of suction.10 Those observationssuggest that these features may be used to provide closedfeedback control algorithms. A harmonic suction index (HSI)has been presented based on the observation of altered mor-phology of the flow waveform near suction. Specifically, high-er-order harmonic content is amplified as suction occurs. Be-cause of the continued beating of the native heart, the flowwaveform is observed to vary periodically with the cardiac

From *LaunchPoint Technologies, LLC, Goleta, CA; †Department ofMechanical Engineering, University of California, Santa Barbara, CA;‡Department of Electrical Engineering, University of Pittsburgh, Pitts-burgh, PA; and §Department of Biomedical Engineering, CarnegieMellon University, PA.

Submitted for consideration September 2004, accepted in revisedform February 2005.

Reprint Requests: Dr. James F. Antaki, Carnegie Mellon University,700 Technology Drive, PTC 4321, Pittsburgh, PA 15219.

DOI: 10.1097/01.mat.0000169122.64794.28

ASAIO Journal 2005

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cycle. However, as suction approaches, it becomes increas-ingly asymmetric.5,10 The HSI is, therefore, defined as the ratioof the power of harmonics above the fundamental to the total

power:HSI � �

i�2

ai ⁄ �

j�1

aj

where ai is the coefficient of the Fourier power spectrum of theflow waveform.

A venous return index (VRI) has been defined as the firstderivative of pump flow with respect to pump speed. As pumpspeed increases, the mean flow rate increases at an incremen-tally decreasing rate. When venous return is matched by thepump, the rate of change is approximately zero. Ventricularsuction occurs within close proximity of this point.

Although VRI is particularly sensitive for flows below thesuction point, it is relatively insensitive above this point. Con-versely, HSI is more sensitive above the suction point. There-fore, it is advantageous to combine the two indices to achieveadded robustness to the control.

Furthermore, clinicians typically may wish to satisfy addi-tional, sometimes competing objectives, such as:

● Left atrial pressure should be maintained below approxi-mately 10 to 15 mm Hg to avoid pulmonary edema.

● Systolic arterial pressure should be maintained betweenpatient-specific limits to avoid consequences of hyperten-sion (and hypotension).

● However, VRI and HSI do not explicitly consider atrial orarterial pressure. If afterload is high, excessive arterialpressure can be developed when the pump produces max-imum flow.5 This motivates the use of multiple indices orthe multiobjective control approach.1,2,5

● Our group has studied various approaches to combiningindices. Baloa et al.5 proposed statistical methods, andBoston, Antaki et al.1 introduced penalty-based convolu-tion of indices. However, as a preliminary evaluation offeasibility, we implement a simple weighted sum of twoindices (HSI and VRI).

In Vitro Experimental Setup

Mock Circulatory System. Figure 1 shows a diagram of thein vitro experimental setup. A flexible sac within a pressurizedcontained rigid chamber represents the left ventricle. The com-pressed air source is controlled by pneumatic driver to createthe pumping action of the sac. Two accumulators are used torepresent the pulmonary and systemic compliances. A needlevalve between accumulators is used to impose the systemicresistance (afterload). To mimic the ventricular suction phe-nomenon, a collapsible “suction element” is inserted betweenthe left ventricle and the LVAD (Figure 2). Preload is varied byadjusting the valve between the ventricle and the suctionelement.

A transit time flowmeter (Transonic, Ithaca, NY) is used tomeasure flow through the LVAD and a differential pressuretransducer is used to measure the pressure rise across theLVAD, a magnetically levitated centrifugal pump (HeartQuestCF4b, MedQuest Products). Data I/O is achieved at 200 Hzusing an A/D D/A board (Quanser MultiQ). The acquisitionand control algorithms are programmed using WinCon real-

time software and MATLAB/Simulink. The output of the con-troller is a reference voltage representing the speed setpoint,and the inputs include the electrical current from the motorand the output of the motor drive tachometer.

Suction Element. To simulate the anatomic collapse of theventricle caused by negative pressure, a “suction element” wasfashioned by inserting a collapsible tube within a rigid cylinder(Figure 2). The space there between was regulated with variouslevels of vacuum to simulate corresponding degrees of suctionsusceptibility.

Flow Estimator

Based on the uncertain reliability of indwelling sensors overseveral years as required by a long-term VAD use, sensorlessapproaches, using model-based estimators, have been pursued

Figure 1. Schematic of experimental setup. A pneumatically ac-tuated compliant bladder was used to simulate the function of theleft ventricle. Systemic and pulmonary loads were simulated bycompliance chambers and needle valves. A suction element placedbetween mock ventricle and LVAD simulated ventricular collapse.dP, differential pressure; LVAD, left ventricular assist device; Q,derivative of flow.

Figure 2. Detail of suction element comprised of collapsible bal-loon within rigid casing. Pressure (vacuum) within rigid casing de-fined the susceptibility of collapse of balloon.

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by our group and by others.9–12 The use of brushless-DCmotors for the LVAD actuator provides an opportunity to relateback-EMF to load, and thereby to estimate pressure and flowfrom current and speed.11,12 Briefly, the form of the stateestimator used in these studies is represented by a set ofdifferential equations:

Jd�

dt� K� � Tf �

1�

HQ � KtI

H � f�Q, ��

� � f�H, Q, ��

(1)

(2)

(3)

where J is the net moment of inertia (motor and load), � is theangular speed, Kt is the torque constant of the motor, Tf is thefriction torque, H is the pressure head of the pump, I is themotor current, and � is the hydraulic efficiency. Equations 2and 3 are two empirical relationships used for the hydrody-namics of the pump, both in nondimensional form accordingto widely accepted formulas.13 In other efforts,11,14 Equations 2and 3 have been approximated by reduced-order polynomialsresulting in the following form for the estimator:

H � k1�2 � k2Q� � k3

dQdt

� k4

d�

dt� k5Q

Q � c0 � c1

1�

� c2� � c3�2 � c4

1�

d�

dt� c5

I�

� c6I � c7

dIdt

� c8I

(4)

(5)

Because the calculation of VRI is based on derivative offlow, Q, the low-order polynomial coefficients expressed inEquation 5 were regressed to experimental data; but theseresulted in unsatisfactory fit. By directed trial-and-error, weobtained an alternative realization of the estimator using alookup table with cubic interpolation as follows:

At constant speed �d�

dt� 0�, Equation 1 becomes

K� � Tf �1

��H, Q, ��H�Q, ��Q � Kt

Tnet

IQ � f��, I� � f��,Tnet

Kt�

(6)

where Tnet is the net torque. Equation 6 implies that flow canbe obtained from an interpolation of measured data usingquasi-static speed and current information only. To account forthe dynamics ignored in the quasi-static assumption, the nettorque in Equation 6 is amended with a dynamic term as inEquation 7:

Tnet � KtI � Jd�

dt (7)

Hence, the alternate form of the flow estimator can beexpressed as:

Q � f��, I� � f��, I �

Jd�

dtKt

� (8)

The lookup table for cubic interpolation of flow versuscurrent and speed is shown in Figure 3.

Figure 4 shows a representative sample of the flow estimatorperformance for MedQuest CF4b pump operating at 1,500rpm in water. The estimator was found to track the mean,maximum, and minimum peaks over the specified range ofoperating speeds in which flow is positive. This enabled thefeedback control algorithm to use the estimated flow ratherthan the measured flow. (Note, however, that the performanceof the flow estimator is not guaranteed for regurgitant (reverse)flow; accordingly, the lookup table in Figure 3 is not defined inthis region.)

Implementation and Validation of Control Algorithm

The calculation of VRI is defined as the first derivative offlow with respect to speed. This is based on the relationship offlow to speed, as depicted in Figure 5. This is typically a

Figure 3. Lookup table for flow estimation based on quasi-staticspeed and current data.

Figure 4. Estimator performance of MedQuest CF4b pump op-erating at 1,500 rpm with water.

3MULTIOBJECTIVE HEMODYNAMIC CONTROL

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unimodal relationship, in which the extremum of flow is foundin the neighborhood of the suction zone. The slope of therelationship may be found through the chain rule:

dQdN

�dQdt

dtdN

(9)

where N is the pump speed. However, at constant pumpspeed

dtdN

→ � (10)

Therefore, real-time calculation of VRI requires a continualchange (modulation) of speed. Hence we applied sinusoidaldither signal with small amplitude (� 50 rpm) and excitationfrequency at 1 rad/s. The excitation frequency of the dithersignal was set to be slow: almost one decade below the heartrate (11.07 rad/s assuming a heart rate of 70) to uncouple fromthe fundamental cardiac modulation of flow, and to averagethe response over several cardiac cycles.

As depicted in Figure 5, at low operating speed Nlow, thedither signal creates large fluctuation in the flow Q, but smallfluctuation at high operating speed Nhigh. Assuming dithersignal amplitude is small enough to guarantee the linearity ofthe slope, the amplitude of the flow fluctuation is directlyproportional to the slope at the operating point. Hence, with-out using numerical differentiation, the flow fluctuation fol-lowing dither excitation can be used to calculate VRI. The flowfluctuation signal is passed through the signal conditioningloop depicted in Figure 6 to calculate DC level VRI.

The pass band for band-pass filter was set at approximately0.16 Hz (approximately 1 rad/s) to sense variations caused bydither signal only. The low-pass filter cutoff frequency was setat 0.015 Hz to compute the DC baseline of the slope.

The second index, HSI (defined above), was approximatedby the power of the second harmonic to the fundamental.Figure 7 shows the calculation process of the harmonics com-ponent. The first and second harmonics of the flow signal isobtained by passing the estimated flow signal through a low-pass filter first. A notch filter was then used to eliminate the firstharmonic at approximately 1.16 Hz (assuming a heart rate of70). The cutoff frequency of the low-pass filter for DC levelingwas set to approximately 0.042 Hz. This approach wasadopted for convenience, and is applicable only to this con-trolled in vitro experiment wherein the fundamental frequencyis known in advance. When implemented in vivo, additionalsignal processing would be required to adapt the filters basedon the heart fundamental frequency.

Controllers using these two indexes were implemented us-ing proportional-integral (PI)-type control loops. The integratorin the PI controller acted as the primary pump speed set point.The initial condition for the integrator was set to the pumpstartup speed. The controller was implemented to generate animmediate pump speed change based on the error between themeasured speed and the set point via the proportional gain.The integral gain causes the integrator speed set point to slewin the direction to correct the error. When the pump speedreaches a new set point, minimizing the error, the proportionalterm ceases to effect a change in pump speed while theintegrator locks the new equilibrium speed set point. To pre-vent integrator windup when using the combined indices,saturation limits were imposed on the integrators. (See Figure8 for the block diagram of the controller.)

Mock-Circulatory Loop Experiments

In vitro studies were performed using a HeartQuest centrif-ugal pump in a LVAD configuration within a mock circulatoryloop (Figure 1). The inflow cannula to the pump was modifiedwith a collapsible section (suction element, Figure 2) to sim-ulate the hemodynamics of ventricular collapse.

Figure 9 presents a typical set of hemodynamic data foropen-loop control of the pump through its full operating range:from 0 rpm (demonstrating regurgitant flow) through maximumspeed (demonstrating suction). The online calculation of con-trol signals, VRI and HSI, is also presented. Here it is importantto note that VRI is most sensitive to underpumping conditions

Figure 5. Principle of VRI based on first derivative of flow (Q) withrespect to speed (N)

Figure 6. Signal conditioning loop for VRI calculation based oncascaded filters. Flow signal is band passed, rectified, and low-passfiltered to provide estimate of the first derivative of speed withrespect to speed (dQ/dN).

Figure 7. Calculation of HSI. Estimated flow signal is filteredsuccessively to extract first and second harmonic content.

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at low speed, whereas HSI is most sensitive to overpumping(suction) conditions at high speed.

We evaluated the response of the closed-loop controllerunder two disturbances: (1) step changes in preload caused byclosing the venous return valve, and (2) change in afterloadcaused by closing the corresponding systemic resistance valve.

Figures 9–13 illustrate the system response under closed-loop control described previously. Figure 10 demonstratesfeedback control based on VRI alone, using a set-point of0.0013. In this experiment, afterload was suddenly increased,causing an initial transient decrease in flow. The controllercompensated by increasing speed to normalize flow and return

VRI to normal. This is to be contrasted with open-loop re-sponse, where an increase in SVR, caused by, for example,sympathetic response, would cause a drop in flow and eleva-tion in inflow pressure (thus LAP)—which is precisely theopposite response as would be needed. Figure 11 shows theopen loop response to step decrease in preload. Pump flowand inlet pressure drops suddenly and suction insues as aresult. HSI is shown to increase due to the suction and ismaintained high because pump speed is maintained high.

Figure 12 demonstrates feedback control based on HSIalone. In this experiment, the preload was reduced, and thecontroller responded by dramatically reducing speed (rpm) to

Figure 8. Saturating PI controllers showing equal weighting for the HSI and VRI.

Figure 9. Open-loop response to ramp speed increase demon-strating behavior of control indices: HSI and VRI.

Figure 10. Closed-loop response of VRI control to step increasein afterload, in vitro.


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mitigate ventricular suction. However, even at reduced speed,there is still evidence of suction, indicated by downwardspikes in the flow signal, and negative inflow pressure. Nev-ertheless, the controller behaved rapidly and stably to reducespeed.

This observed settling error is suspected to be related to thesensitivity of the HSI used in this experiment. Future develop-ment of this controller will require additional investigation ofthe sensitivity of different forms of HSI to this phenomenon,and consideration of the set point for eliminating suction. Inthis experiment, the set point for HSI was 0.09. Ideally, itshould be set to near-zero.

Note that there may be circumstances when complete elim-ination of suction may result in excessive reduction of speed,thereby reducing flow and perfusion pressure dangerouslylow. This is our motivation for adding pressure and/or flow tothe overall control objective. We aim to explore this in thefuture. For the purpose of the current study, we explored the

benefit of combining VRI to HSI to counteract the tendency toreduce speed excessively.

Figure 13 demonstrates the performance of the feedbackcontroller based upon the linear combination of two separatePI-type controllers for HSI and VRI control, respectively. Here,two controllers are equally weighted. We observed avoidanceof suction while still maintaining perfusion flow.

In this case, at the start of the data record, the VRI loop iscommanding full speed, because the VR index has not yetreached its set point. Because there is no suction, the HSI loophas reached equilibrium, with a speed set point of 1,700 rpm.The linear combination of the two set points gives the initialspeed of 2,200 rpm. When the pump preload decreased, theHSI index rose because of the onset of suction, which causedthe HSI loop to decrease motor speed and decrease the HSIpump speed set point. The system reached its new equilibriumspeed when the HSI loop saturated at 0 speed command,leaving the VRI loop controlling the pump speed. The VRI loopprevented the HSI loop from excessively reducing pumpspeed.

The weighting coefficient for the linear combination of thetwo separate indices can be tuned for a better performancebecause the sensitivity of each controller is different dependingon the operating condition. Saturation limits and controllergains are also candidates for further tuning. Fuzzy logic couldbe considered to mix indices that have validity for differentregions.

Conclusions

In vitro studies were performed to validate the hemody-namic control indices VRI and HSI for suction avoidance in theoperation of a rotary LVAD. Cubic spline interpolation wasimplemented for flow estimation and, accordingly, the calcu-lation of the control indices. Calculation of VRI was obtainedby dither modulation of the speed, which obviated numericaldifferentiation. An in vitro suction element made of a collaps-ible balloon was found to be effective to create the suctionphenomenon in vitro and to validate the suction-avoidance ofthe physiologic controller.

Figure 11. Open-loop response of HSI to step decrease in pre-load, in vitro.

Figure 12. Closed-loop response of HSI control to step decreasein preload, in vitro.

Figure 13. Performance of multiobjective feedback controllerbased on equally weighted HSI and VRI. A step decrease in preloadcauses a reduction of speed to avoid suction.

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A physiologic controller based on the VRI and HSI indicesshowed a synergistic benefit as compared with control basedon a single index. It was shown that those indices have differ-ent sensitivities for different operating condition (pump speed)so that their combination could provide additional controlla-bility of the system. The success of this preliminary implemen-tation of multiobjective control demonstrates the validity ofthis approach for achieving a trade-off between optimal LVunloading and avoidance of suction.

Ongoing research is seeking to implement more robustmeans of identifying the dynamically changing indices, com-bining these indices, and driving the system to its set point. Itis hoped that this approach will provide additional robustnesswithout introducing unnecessary complexity.

Acknowledgments

The authors gratefully acknowledge the support of the Na-tional Institutes of Health/NHLBI (1R43HL66656-01) and theNational Science Foundation – Control, Networks, and Com-putational Intelligence (ECS-0300097).

References

1. Boston JR, Antaki JF, Simaan MA: Hierarchical control of heart-assist devices. IEEE Rob Autom Mar: 54–64, 2003.

2. Baloa, L: A certainty-weighted system for the detection of suctionin ventricular assist devices [PhD dissertation]. Department of

Electrical Engineering, University of Pittsburgh, Pittsburgh, PA,2001.

3. Yu YC, Boston JR, Simaan MA, Antaki JF: Minimally invasiveestimation of systemic vascular parameters for artificial heartcontrol. Control Eng Pract 10: 277–285, 2002.

4. Choi S, Antaki JF, Boston JR, Thomas D: A sensorless approach tocontrol of a turbodynamic left ventricular assist system. IEEETrans Control Syst Technol 9: 473–482, 2001.

5. Baloa LA, Liu D, Boston JR, Simaan MA, Antaki JF: Control ofrotary heart assist devices, in Proceedings of the AmericanControl Conference, 2982–2986, 2000.

6. Gridharan GA, Skliar M, Gillars KJ, Koenig SC, Pantalos GM:Physioligic control of rotary blood pumps: An in-vitro study.Artif Organs 27: 332, 2003.

7. Giridharan GA, Skliar M: Control strategy for maintaining physi-ological perfusion with rotary blood pumps. Artif Organs 27:639–648, 2003.

8. Giridharan GA, Skliar M: Nonlinear controller for ventricularassist devices, Artif Organs 26: 980–984, 2002.

9. Amin DV, Antaki JF, Litwak P, et al: Controller for an axial flowblood pump. Biomed Instrum Technol 31: 483–487, 1997.

10. Konishi H, Antaki JF, Amin DV, et al: Controller for an axial flowblood pump. Artif Organs 20: 618–620, 1996.

11. Choi S: Modeling and control of left ventricular assist system [PhDthesis]. University of Pittsburgh, 1998.

12. Antaki JF, Boston JR, Choi S: Speed Control System for ImplantedBlood Pumps. US Patent 5,888,242, March 30, 1999.

13. Stepanoff AJ: Centrifugal and Axial Flow Pumps: Theory, Design,and Application, 2nd ed. New York, Wiley, 1957.

14. Wu J, Antaki JF: Flow estimation of Nimbus/TCI Heartmate-II.McGowan Center, University of Pittsburgh, 1999.



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