Modeling And Control Of AnExtracorporeal Heart Assist Device

Alexander Sievert ⇤ Wolfgang Drewelow ⇤ Torsten Jeinsch ⇤

Olaf Simanski ⇤⇤

⇤ Institute of Automation, University of Rostock, 18119 Rostock,Germany (e-mail: Alexander.Sievert@uni-rostock.de).

⇤⇤ Hochschule Wismar, University of Applied Sciences, Technology,Business and Design, 23952 Wismar, Germany, (e-mail:

olaf.simanski@hs-wismar.de).

Abstract:Heart assist devices provide mechanical circulatory support for patients with end-stage heartfailure. Extracorporeal heart assist devices are applied to adult and pediatric patients in thecase of uni- and biventricular assistance. Modern driving units provide more mobility what is animmense benefit to the quality of life of the patients. The treated heart assist device in this articleis the EXCOR system (Berlin Heart GmbH, Germany). This device is pneumatically operatedby a piston drive. Pump assistance for the native heart of the patient should be provided by anautomatic control system. This could be achieved by the control of the piston movement andthe enclosed air mass in the pneumatic system. The model based design of a control system forthe extracorporeal assist device is described in this paper.

1. INTRODUCTION

Terminal heart failure deceases is one major cause ofdeath in the industrialized countries. The pump outputof the native heart is reduced. This could be caused forexample by infects or genetic defects. In end-stage the onlyavailable treatment option is a heart transplantation or themechanical circulatory support by an assist device. Heartassist devices can be divided into three main categories.Intracorporeal systems are characterized by an implantedartificial blood pump. Examples are the Heart Mate II R�

(Thoratec, Pleasanton, USA), the HeartWare VentricularAssist System R� (Heart Ware, Framingham, USA) or theINCOR System R� (Berlin Heart GmbH, Berlin, Germany).Extracorporeal devices are nowadays used in special heartdecease situations and especially for pediatrics. Here theartificial blood pump is placed outside of the body. Avail-able systems are for example the Thoratec PVAD R� (Tho-ratec, Pleasanton, USA) or the EXCOR R� VAD (BerlinHeart GmbH, Berlin, Germany). The third category con-tains total artificial hearts. In that case the heart is re-placed completely by an artificial heart. An example isthe Aachen Total Artificial Heart ReinHeart (HelmholtzInstitute of RWTH Aachen University & Hospital, Aachen,Germany). For intracorporeal and extracorporeal systemsuni- and bi-ventricular heart support is possible, depend-ing of the patient needs. This contribution deals with anextracorporeal heart assist device. The operating principledi↵ers significantly between the varying kinds of heartassist devices. Also within the category of extracorporealsystems there are several types of devices. They di↵erby the available measurements and the driving concepts.Control approaches are not well known from publishedliterature. The modeling process of the addressed systemin this paper was presented in detail in [4]. A first presenta-

tion of the idea of a control system for the EXCOR heartassist system was published in [5, 6]. This paper shouldgive a detailed overview of the developed control systemfor a extracorporeal heart assist device. Finally, results ofthe control of pump assistance are presented.

2. THE HEART ASSIST DEVICE

This contribution deals with the control of an extracorpo-real ventricular assist system. A short description of thesystem is given in this section. Furthermore the controlgoal is defined.

System Description And Functionality Fig. 1 gives anoverview over treated heart assist system. The EXCORpump is operated by a battery powered, mobile drivingunit. Mobility greatly improves the quality of life of theventricular assist device (VAD) recipients [1]. An externalpump is the main component of an extracorporeal heartassist system. It is connected to the natural heart of thepatient via two cannulas. The inlet cannula is mostlycoupled to the ventricle. Other options are a cannulizationof the atrium or a direct connection to the pulmonary vein.The outlet cannula is connected to the aorta. Artificialvalves at the accesses of the artificial blood pump constrainthe possible flow direction. To separate the blood ofthe patient from the environment a flexible membrane isplaced inside the blood pump. This membrane also couplesthe pressure in the blood chamber to the driving pressurein the pneumatic system. The pneumatic part of the VADconsists of the air chamber of the artificial blood pump,an air tube and a pneumatic piston drive chamber. Apiston drive is used to generate the necessary pneumaticpressure to operate the system. The piston position canbe controlled by a settable motor torque. Additionally a

Preprints of the 19th World CongressThe International Federation of Automatic ControlCape Town, South Africa. August 24-29, 2014

Copyright © 2014 IFAC 6581

Fig. 1. Shematic representation of the treated VAD: EX-COR VAD (Berlin Heart GmbH, Berlin, Germany)

Fig. 2. Schematic of diastolic (a) and systolic (b) phase ofthe pump process of the EXCOR system

controllable balancing valve is present. This valve can beused to adjust the air mass in the pneumatic system.

The operation of the extracorporeal heart assist device canbe divided into two phases. The diastole corresponds tothe filling phase. Fig. 2 a) shows the piston movementtowards the diastolic reversal point x

d

. This movementexpands the volume in the pneumatic system. As a resultthe pressure in the pneumatic system decreases. Thepressure in the blood chamber is directly coupled to thepneumatic pressure by the flexible membrane. Due to thepressure gradient between the blood chamber and thecannulated heart (about 10 mmHg) a blood flow accruesinto the artificial pump. The membrane has a specifiedhydraulic capacity according to the applied pump size. Anoverstretching of the membrane should be avoided aftera complete filling is achieved. This would increase thepower consumption of the system and decrease battery lifetime significantly. After the diastole the piston movementdirection reverses and systole begins. Fig. 2 b) shows thepiston movement to the systolic reversal point x

s

. In thisphase the volume decreases and the pressure increases. Asa consequence the inlet valve closes. When the pressurein the blood chamber exceeds the pressure of the aorta(about 100 mmHg) the outlet valve opens. The obtainedblood is pumped into the circulation system of the patient.

The diastolic and systolic phase repeat cyclical with thegiven pump frequency.

Control Objective A heart assist system takes overthe functionality of the human heart. All organs need asu�cient supply with nutrients and oxygen. For a sanepatient the demand of cardiac output is not constantover the day. It depends on the physical load or stressconditions of the patient. A perfect control of a VADshould include these demands. The problem from thetechnical view is the availability of reliable measurementsof physiological states which represent the actual loadcondition of the patient. Due to this reason the controlgoal for current heart assist devices is to keep up adesired cardiac output. This value is parameterized by acardiologist and represents an estimated mean demand ofcardiac output. The cardiac output for a pulsatile workingextracorporeal heart assist system is the product of appliedpump size and pump frequency. The pump size is fixed.The cardiologist parameterizes the pump frequency. Thecontrol goal is defined by the task to achieve a completefilling end depletion of the artificial blood pump. Thecontrol is performed once within a pump cycle.

3. MODELING

The developed model should be the basic for the controllersynthesis. A model based controller design leads in mostcases to a better control accuracy than empirical designs[2]. Therefore a lumped parameter model structure waschosen. The essential characteristic e↵ects of the systemshould be reproduced to obtain comprehension of thesystem behavior. Models of di↵erent orders were analyzed.One of the developed models with a system order of nineo↵ers su�cient model accuracy. This model should bedescribed in the following.

v̇ =µ

2 · ⇡ · J (Mm �Mf (v)�Mp(pp)) (1)

ẋ = v (2)

ṗ

p

=(ṁ

v

(pp

) + ṁ(pp

, p

ac

)) ·R · T �A · v · pp

V

dpp+A · x (3)

ṗ

ac

=�ṁ(p

p

, p

ac

) ·R · T + (Qa

�Qv

) · pac

V

dpac+ V

bc

(4)

V̇

bc

= Qv

�Qa

(5)

Q̇

a

=f

m

(pac

, V

bc

)� pa

�Ra

(Qa

) ·Qa

L

a

(6)

Q̇

v

=p

v

� fm

(pac

, V

bc

)�Rv

(Qv

) ·Qv

L

v

(7)

ṗ

a

= fartcirc

(Qa

, p

a

, p

v

) (8)ṗ

v

= fvencirc

(Qa

, p

a

, p

v

) (9)

Equations 1 and 2 describe the electro-mechanical com-ponent of the heart assist device. The dynamic relationbetween the controllable motor torque M

m

and a resultingpiston velocity v and piston position x is modeled. Drivespecific constants are the spindle pitch µ and the momentof inertia J . The term M

f

(v) is a friction based countermoment. This moment includes the static and kinetic fric-tion. Another moment component is the pressure momentM

p

(pp

). The pneumatic pressure pp

onto the piston surface

19th IFAC World CongressCape Town, South Africa. August 24-29, 2014

6582

Fig. 3. Shematic of the system from a control point of view

generates a force during the pump cycle.Equations 3 and 4 model the pneumatic components ofthe system. This contains the piston drive chamber, theair tube and the air chamber of the artificial blood pump.The pressure in the piston drive p

p

and in the air cham-ber p

ac

is modeled under the assumption of the commongas equation for an isothermal process. The connectingair tube is described by its pneumatic resistance. Thepneumatic resistance determines the air mass flow functionṁ(p

p

, p

ac

) between the piston drive and the pump. Anadditional term for the air mass flow against the envi-ronment ṁ

v

(pp

) is defined by the pneumatic resistance ofthe controllable balancing valve. The constants R and Tin equations 3 and 4 represent the universal gas constantand the ambient temperature. Pneumatic dead volumesV

dppand V

dpacare given by the design of the piston drive

and the artificial blood pump. A volume change in thepiston drive is given by the product of piston movement vand the piston surface A. In the hydraulic blood chamberof the artificial pump a volume change V̇

bc

is defined by theincoming, venous blood flow Q

v

and the outgoing, arterialblood flow Q

a

. The pressure drop across the flexible mem-brane is modeled by the function f

m

(pac

, V

bc

). The flowthrough the cannulas is characterized by its hydraulic flowresistance R

a

(Qa

), Rv

(Qv

) and the hydraulic inductanceL

a

, L

v

. A severe simplified circulatory replacement modelf

artcirc

, f

vencirc

was used to describe the arterial and ve-nous pressure p

a

, p

v

of the human circulatory system. Sev-eral parameters of the introduced model are determined byphysical properties of the EXCOR system. The remainingparameters were determined by experiments and suitablefitting procedures. More details about the modelling pro-cess are given in [4].

4. CONTROL SYSTEM

In this section the developed control system will be pre-sented. At first an analysis from the control point of viewis performed. After that an approach for a model basedestimation of the control variable is given. Finally the basiccontrol strategy is explained.

Fig. 3 shows an overview of the appreciable values of thecontrol system. The available measurement variables of thetreated heart assist device are the piston position x andthe piston drive pressure p

p

. Due to reliability there is nofurther sensor information in the artificial blood pump.There are two control signals in the EXCOR VAD. Amotor torque can be applied to the electro-mechanicalpiston drive. Furthermore a balancing valve can be openedor closed to compensate the enclosed air mass in thepneumatic system. The controlled variable is the achievedpump filling and depletion state from one pump cycle tothe next one.

Fig. 4. Shematic of the relevant process values for theestimation equation of the blood flow

4.1 Estimation For Control Feedback Application

No direct measurement for a control loop feedback isavailable. An estimation equation was developed to de-termine the achieved filling and depletion state of the lastpump cycle. The benefit of the prediction of the bloodflow against pure pressure-based algorithms [3] are betterpossibilities for the adaptation to the circulatory afterloadof the patient. The estimation is based on the assumptionof the ideal gas law. The pneumatic system of the VADis supposed to be an isothermal process. This leads tothe description for the pneumatic system consisting of thepiston drive chamber, the air tube and the air chamber ofthe pump with

ṗ

p

=ṁ ·R · T � p

p

· V̇pneumatic

V

pneumatic

. (10)

Fig. 4 illustrates the composition of the pneumatic volumeV

pneumatic

with the equation

V

pneumatic

= Vdead

+ Vmembrane

+A · x. (11)

A constant pneumatic volume is defined as a dead volumeof the piston drive chamber V

dpac, the air tube V

at

anda dead volume of the air chamber of the artificial bloodpump V

dpac

V

dead

= Vdpac

+ Vat

+ Vdpac

. (12)

Two other parts of the pneumatic volume change over thetime. The first one is the volume defined by the actualpiston position x and the surface area of the piston A.The second volume is represented by the actual membranevolume V

membrane

. Based on this assumptions the dynamicvolume gradient V̇

pneumatic

is defined as

V̇

pneumatic

= A · ẋ+ V̇membrane

. (13)

The air chamber and the blood chamber are directlycoupled by the membrane. Blood is assumed to be an in-compressible fluid for the relevant pressure range. So amovement of the membrane V̇

membrane

is equal to a bloodflow Q in or out of the blood chamber

V̇

membrane

= Q. (14)

The application of the stated definitions to equation 10leads to the estimation equation

19th IFAC World CongressCape Town, South Africa. August 24-29, 2014

6583

Q =ṁ ·R · T

p

p

�ṗ

p

·�A · x+ V

dead

+RQdt

�

p

p

�A · ẋ (15)

for the flow Q in and out of the artificial blood pump.

The term ṁ is defined as an air mass flow throughthe controllable balancing valve. R is the universal gasconstant and T is the ambient temperature. The resultingestimation equation 15 delivers a value which can beused for control feedback. This value can be calculatedfrom the available measurements and from known constantparameters. For control application the reached fillingstate after the diastolic phase V

d

and systolic phase Vs

ofeach pump cycle is needed. So these values are calculatedadditionally from the estimation equation 15.

4.2 Control Principle

The basic idea of the developed control system shouldbe presented at first. As a reminder that the goal is toachieve a cyclic filling and depletion of the artificial bloodpump. This is realized by a cyclic, alternating pressurebetween over-pressure and below atmospheric pressure.The pressure is generated by a piston drive. Therefore alsoa cyclic piston movement is required.

Fig. 5. Shematic of the control principle

The developed control approach is outlined in Fig. 5. Sothe control task is separated into two control circuits. Thefirst loop contains the piston movement controller PMC.A control of the cyclic piston movement is implementedhere. The second loop regulates the enclosed air mass inthe pneumatic system by an airmass controller AC. Asa result each available control signal is associated to onecontrol loop. The motor torque M

m

is used to controlthe piston movement. The balancing valve u

bv

is used tocontrol the air mass. A control action is performed oncewithin a pump cycle. The introduced two control loops areused exclusively from each other. A manipulated variableselectorMV S was developed to choose the suitable controlloop. This decision is based on the estimated achievedpump filling and depletion state of the last pump cycle.This values are derived by the filling/ depletion state esti-mator FDSE from the estimation of the flowQ introducedin section 4.1.

4.3 The Piston Movement Controller

The piston movement controller PMC has the task tocontrol the piston in such a way that a cyclic filling and

Fig. 6. Schematic of the piston movement to achieve cyclicpumping

depletion of the pump can be achieved. The process istime variant since parameters like friction, flow resistancesor the patient itself change in wide range over the time.Due to this, the movement between the diastolic reversalpoint x

d

and the systolic reversal point xs

is controlledwith a fixed trajectory shape. The chosen trajectory isshown in Fig. 6. An o✏ine model based optimization leadto a cubic shape for best control results. The optimizationloss function was defined under technical and medicalconstraints. The loss function contains:

• energy consumption• mechanical wear• cavitation in the blood• shear strain in the blood

As shown in Fig. 6 the piston movement is defined bythe trajectory shape, the amplitude and the time scale.The systolic reversal point x

s

is fixed to zero. Thus theamplitude of the piston movement is defined by the valueof the diastolic reversal point x

d

. The time scale is definedby the parameterized pump frequency 1/f

stroke

. fstroke

isdetermined by a cardiologist o✏ine.The control of the pump process by the piston movement isreduced to one process variable. Instead of controlling thewhole trajectory dynamically, only the diastolic reversalpoint must be controlled. This scales the trajectory and thepiston movement can be adapted to the pump process.In section 4.1 the estimation equation to determine theachieved filling state V

d

(k) and depletion state Vs

(k) wasintroduced. These values are calculated once within apump cycle. So the control of the piston movement is alsodone once within a cycle. At the beginning of each diastolethe diastolic reversal point is controlled by

x

d

(k + 1) =xd

(k) +Kstroke

· ((Vd

(k)� Vd

ref

)

+ (Vs

(k)� Vs

ref

)).(16)

The controller parameter Kstroke

is pump size specific anddetermined by simulation tests. The reference values V

s

ref

and Vd

ref

are defined by the physical properties of the usedartificial pump. As a result the piston position trajectoryis generated once a cycle after the control of the diastolicreversal point.

Because the available control signal is a motor torqueand not the piston position, an underlying piston position

19th IFAC World CongressCape Town, South Africa. August 24-29, 2014

6584

Fig. 7. Schematic of the piston position controller

controller was developed. Its task is to control the pistonposition as exactly as possible to realize the calculatedtrajectory. This part of the process was described insection 3 by equations 1 and 2. Fig. 7 gives an overviewover the structure of the developed controller. It consistof a non-linear feed-forward controller FWC, a linearfeedback controller C, a disturbance compensation DC,a signal generator SG and a parameter estimator PE.The disturbance compensation DC uses the availablemeasurement of the piston drive pressure p

p

to compensatethe moment caused by the pressure on the piston. A feed-forward controller FWC controls the friction and theacceleration of the piston based on the given referencetrajectory and its gradients. This references are generatedby the signal generator SG. The used friction function isadapted by the parameter estimation PE by the equation

M

f

(v) = �2 · ⇡ · Jµ

· v̇ +Mm

�Mp

(pp

). (17)

So the corresponding friction moment Mf

(v) to the ac-tual piston velocity v can be calculated online from themeasurements. The piston is accelerated cyclical up tothe maximum necessary piston velocity. So a completenonlinear friction function can be determined during theterm of operation. To avoid problems of the dynamiccoupling of the adapted open-loop control and the closed-loop controller a filter and validation step is integratedinto the parameter estimation. Results of the introducedpiston position controller are given in section 5.1.

4.4 The Air Mass Controller

The air mass controller has to compensate pneumatic leak-ages during the pump process. Furthermore the enclosedair mass must be synchronized with the piston movement.This synchronization leads to an equal filling and depletionstate for the actual piston stroke. The control of the airmass follows heuristic motivated rules. For example, ifafter a pump cycle the artificial pump was filled completelybut the depletion was incomplete, the air mass in thepneumatic system was too low. The other way round atoo high air mass leads to a incomplete filling and a fulldepletion. The resulting control equation is given by

m

c

(k + 1) =Kair

· ((Vd

(k)� Vd

ref

)

� (Vs

(k)� Vs

ref

))(18)

where Kair

is determined by simulation tests.

As a reminder the existing manipulating variable besidethe motor torque is a balancing valve. This valve can beopened or closed by the control system. Thus the controlleroutput m

c

(k + 1) can not be directly applicated to thebalancing valve. Furthermore the compensation of air masscan only be done passively against the environmentalpressure p

e

. If the controller output mc

(k + 1) is negativea defined amount of air mass must be released to theenvironmental air. That is only possible during the systolicphase because the piston drive pressure p

p

exceeds theenvironmental pressure. An opening of the valve in thediastolic phase is performed if additional air mass in thepneumatic system is required. The valve is kept openeduntil an estimated air mass compensation m

e

is equal tothe controller output m

c

(k + 1). The estimation of theachieved compensated air mass is done by

m

e

=

Zt(close)

t(open)

rp

p

� pe

R

valve

dt. (19)

Experiments were performed to determine the parameterR

valve

.

5. RESULTS

The results of the developed control system are presentedin this section. At first the quality of the piston positioncontroller is shown. Finally the control output of the pumpdepletion state is presented.

5.1 Control Results Of The Piston Movement

Fig. 8. Piston position control results immediate afterpower on

The control approach is based on a cyclic piston move-ment with a given trajectory. Therefore a good controlperformance must be achieved for the piston position. Anadaptive control approach was implemented. Fig. 8 showsthe control performance immediate after the power onof the system. The upper plot shows a moderate controlquality because a middle-rate starting value for the frictionestimation was chosen. A look to the control signal in thelower plot illustrates that the open loop control is not welladapted to the process. After 130 seconds (Fig. 9) theopen loop control is considerably better adjusted. Thatleads to a very high control accuracy. So a good control

19th IFAC World CongressCape Town, South Africa. August 24-29, 2014

6585

Fig. 9. Piston position control results 130 seconds afterpower on

performance can be achieved during the complete lifetimeof the heart assist device.

5.2 Control Results Of Pump Output

Fig. 10. Pump output during changing pump conditions

The task of a heart assist device is the maintenanceof a su�cient pump supply to the patient. Therefor anadaption to the patient needs is required. Fig. 10 showsthe achieved pump output per cycle for di↵erent operatingconditions. The achieved pumped blood volume per cycleis determined by external sensor equipment. Additionallythe control signal of the balancing valve and the controlledpiston position is plotted. Up to the twentieth second thepump drive operates against a very high arterial counterpressure of the patient. For test conditions a real patientis replaced by a mock simulation. For a very high counterpressure the control of the heart assist device operateswith control signal limitation. The maximum stroke of thepiston drive is limited to 0.045 m due to design aspects.That is the reason for a decreased output of 70 ml per cyclein the first phase. The nominal output of the applied bloodpump is 80 ml. After the twentieth second the arterialcounter pressure is decreased in the test scenario to anexpectable value of a nominal patient. The control systemdecreases the piston stroke and a full output of 80 mlis achieved. A further variation of the arterial counterpressure is performed at about second 35 and 65. Asshown the developed control system is able to compensate

variations of the human circulatory system within a fewpump cycles. A su�cient pump supply to the patient isachieved.

REFERENCES

[1] G. Miller. Artificial Organs. Synthesis lectures onbiomedical engineering, Morgan & Claypool, Vol. 4,2006.

[2] WJ. Weiss, J. Cysyk, G. Rosenberg. Simulationof a pneumatic driver for a pediatric ventricularassistant device. American Society for ArtificialInternal Organs 56th Annual Conference, Vol. 56, p.95, Washington DC, 2010.

[3] K. W. Nam, J. J. Lee, C. M. Hwang, J. Choi, H. Choi,S. W. Choi, K. Sun. Development of an Algorithm toRegulate Pump Output for a Closed Air-Loop TypePneumatic Biventricular Assist Device. ArtificialOrgans, Vol.33 No.12 2009.

[4] A. Sievert, A.Arndt, W. Drewelow, B.P. Lampe,O. Simanski. A control oriented model design ofheart assistant devices. 18th IFAC World Congress,Mailand, 2011.

[5] A. Sievert, A. Arndt, W. Drewelow, B. Lampe, O.Simanski. Modellbasierte Regelung pneumatisch be-triebener Herzunterstuetzungssysteme. at Automa-tisierungstechnik Band 59, Heft 11, Oldenburg Ver-lag, 2011.

[6] A. Sievert, C. Wiesener, A. Arndt, W. Drewelow, O.Simanski. Control of extracorporeal Heart AssistantDevices. IEEE International Conference on ControlApplications, pp. 63-68, Dubrovnik, 2012.

19th IFAC World CongressCape Town, South Africa. August 24-29, 2014

6586