SMART MECHATRONIC DEVICE TO ASSIST HEART FUNCTION

           

SMART MECHATRONIC DEVICE TO ASSIST HEART FUNCTION  

Sebastian Schwandtner*, Dipl.-Ing. Martin Kortyka*, Dipl.-Ing. Steffen Leonhardt**, Prof. Dr. med. Dr.-Ing.

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Abiomed EUROPE Impella CardioSystems GmbH Neuenhofer Weg 3 D-52074 Aachen Tel.: +49 241 8860-0 FAX: +49 241 8860-111 http://www.impella.de

**

Philips Chair for Medical Information Technology RWTH Aachen University Pauwelsstr. 20 D - 52074 Aachen Tel.: +49 (241) 80 23211 Fax: +49 (241) 80 82442 www.medit.hia.rwth-aachen.de

  

Abstract: A model based observer for motor angle estimation and speed control of a permanent magnet synchronous motor is presented which serves to automatically control flow output in a cardiac assist rotary pump. After an introduction to the clinical problem, a model for a three-phase brushless synchronous motor is presented and a concept for sensor-less speed control is derived. Finally, some results for the specific application are given. Copyright © 2006 IFAC 

Keywords: Heart Assist Devices, Blood Pump, Three-phase Synchronous Motor, Electromechanical Model, Speed Control, Rotor Angle Estimation    

1. INTRODUCTION AND MEDICAL BACKGROUND 

For a patient suffering from heart failure, which may be due to e.g., a myocardial infarction (MI), an otherwise weakened heart muscle (cardiomyopathy) or a surgical procedure (cardiotomy), it is important to support the mechanical function of the heart for as long as possible (“bridging to transplant” or “bridging to recovery”). In case of a heart failure, the first therapeutic measure is to give proper medication (inotropes). This therapy immediately increases oxygen consumption of the already damaged heart. As the next step, the use of an intra-aortic ballon pump (IABP) may be considered (40 – 60 % of patient population). Due to rhythmic blow-up and relief of a balloon implanted temporarily in the aorta, this measure increases the diastolic blood pressure and thus enlarges the perfusion of the heart and other organs. However, usually only a mild support of the diseased heart is achieved. As the ultimate measure, a left ventricular assist device (VAD) may be used.

This is an expensive therapeutic measure (up to € 100.000) and requires invasive surgery to connect the external device directly to the heart or the large vessels. Thus, only a limited fraction of the patient population is treated with such a device (mid-term VAD 15 - 20%, long-term VAD 5 - 10%). As a future alternative, a new intracardial rotary blood pump (Siess and Reul, 2000) may be used which has recently been introduced (Autschbach et al., 2001). Fig. 1 shows the device

Fig. 1. Heart Assist Device (impella® recover LV).

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This heart assist device, called an impeller, can be placed inside the aorta and will pump blood during diastole similar to an IABP device, see Fig. 2.

Figure 4 gives some insight view into the actual electro-mechanical and the hydraulic components. Note that the synchronous motor has either a diameter of 6.4 mm (Recover 5.0 device, up to 5 l/min) or about 4 mm (Recover 2.5, up to 2.5 l/min). The corresponding speed of rotation typically varies between 10.000 … 33.000 rpm or 25.000 .. 50.000 rpm, respectively

Fig. 4. Inner components of the heart assist device including permanent magnet synchronous motor (PMSM) and impeller.

Fig. 2. Example of how to apply an impeller (impella® recover LV) to the left ventricle via an arterial femoral catheter. However, with up to 5.0 l/min the mechanical support of the weakened heart is much better than with an IABP device. In the specific design used for this research, the device mainly consisted of a catheter, a brushless three-phase synchronous motor and an impeller rotating continuously inside a small cage. In addition, the device features a blood directing tube connected to the impeller pump housing through which the blood can be sucked out of the ventricle and pumped into the aorta. Alltogether, the weight is less than 12 g. An external console is used to control motor speed and cardiac support (Fig. 3). To avoid clotting at the internal bearings, a purger is used to infuse a glucose solution through the catheter.

For optimal control of blood (hydraulic output), the rotor speed is an important parameter, mainly due to the fact that assisted flow output is a function of both the ventricular-aortic pressure difference and of motor speed Z, see Fig. 5. To control pump output under changing differential pressures is only possible by adjusting rotor speed.

Fig. 5. pump flow as a function of rotor speed and differential pressure for a Recover 5.0 LV device.

2.

DYNAMIC MODEL

The electric equivalent of the three-phase synchronous machine mainly features an ohmic resistance Rs and an inductance Ls in all three phases, see Fig. 6. ua A ia

Ea

ub B ib

Eb

uc C

Fig. 3. Console with electric power supply and purger to infuse glucose solution (20 … 40 %).

ic

Rs

Ls

Ec

Fig. 6. Dynamic model of the three-phase synchronous motor.

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The corresponding system of coupled differential equations is given by ªu « a «ub «u ¬ c

º » » » ¼

ªR « s « 0 « 0 ¬

­ªL d °« s  ® 0 dt ° «« 0 ¯¬

0 Rs 0 0 Ls 0

Separating the two coordinates leads to

0 º ª ia »« 0 » « ib L s »¼ «¬ i c

º » » » ¼ º½ »° »¾  »° ¼¿

ªE « a «Eb «E ¬ c

º » » » ¼


§ ua · 2S 2S 2 §¨ cos(T ) cos(T  3 ) cos(T  3 ) ·¸¨ ¸ ¨ ub ¸ 3 ¨  sin(T )  sin(T  2S )  sin(T  2S ) ¸¨ ¸ 3 3 ¹ u © © c¹

§U d · ¸ ¨ ¨U q ¸ ¹ ©

Ud

(4) and visualized by figure 7.

Uq

uE

Us

const.

(9)

(10)

dI q dt

d L s I d  ZL s I q dt

(11)

Ls  Z L´s I d  < pm (12)

>

Rs I q 

@

dI q dt

Ls  Z< pm (16)

The mechanical model of the heart assist device includes friction JZ Tel  TLoad  T f (17)

Ud

Tf

ș

K RZ

(18)

The overall model is shown in Figure 8.

ua

uD

< pm

(8)

It can be shown that the torque Tel produced by the motor is 3 3 Tel p 
Uq

ub

dt

 Z
Ls I q

Rs I d 

Rs I q 

(3)

To model the dynamic behaviour of an three-phase synchronous machine, it is common practice to transform the stationary a,b,c system to the q,d coordinate system which is rotating synchronously with the rotor (rotor-oriented reference frame). This transformation is given by

d
(7)

Combining Eq. (9) and Eq. (10) with Eq. (7) and (8) leads to

Uq

& d< Ri  dt

Ls I d  < pm ,


^ `

any voltage vector may be represented by &

d
Rs I q 

Uq

(1) where Ea, Eb and Ec are induced voltages (electromagnetic forces). Considering the flux equation & & & d< d (2) L ˜ i  E, dt dt

& u

Rs I d 

Ud

0 º ª ia »« 0 » « ib R s »¼ «¬ i c

uc Fig. 7. Coordinate systems a,b,c and q,d. Applying the coordinate transformation introduced in Eq. (4) (here in complex notation), the following result is obtained & <

& U dq

& uDE e  jT

leading to & U dq

& Rs iDE e  jT 

& & & dT d
dq

*    jT d (
dt

(5)

& & & d
Fig. 8. Overall model of electric and mechanical parts of the heart assist device. Note the nonlinear multiplication blocks.

(6)

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The speed control concept given in Fig. 9 is known as “field-oriented control” approach (FOC).

4.2 Dynamic Operation Figure 10 shows the results on current control. It can be nicely seen that Id is indeed controlled to be around 0.

Fig. 9. Concept for cascaded field-oriented speed control using an observer for rotor angle estimation.

Fig. 10. Current control performance during start and subsequent dynamic operation.

3. SPEED CONTROL AND OBSERVER DESIGN

In reality, the rotor angle T is not known. However, this state is required for proper qd-abc transformation. Classical linear observer designs are known to be rather sensitive to unknown or partly known model parameters. Therefore, a robust sliding mode observer for angle estimation (and speed) was developed. This design was based on the work of Utkin, see (Utkin, 1992; Utkin et al., 1999). Note that the cascaded FOC speed and current control structure is similar to the one given in (Isermann, 2003), with the major difference that the speed acquisition unit is replaced by the model based rotor angle estimator.

Figure 11 gives an example of dynamic motor operation when subject to changing reference values for rotor speed.

Fig. 11. Speed control with changing reference value. 4. RESULTS 4.1 Offline Estimation of Motor Parameters Some of the motor parameters, like Rs and Ls, may be obtained from direct measurements with a standing motor. In the case of the Recover 5.0 LV, they were found to be

By contrast, Figure 12 shows the results obtained when changing the load torque (pumping in water at 32.000 rpm vs. no load torque in air).

• R s 5,14 : • L s 44 µH, see (Kortyka, 2005). By stiffly connecting two PMSMs with the second motor acting as a generator and connected to high-ohmic loads (Igenerator § 0), it is possible to determine the flux

•

< pm

0,797 mVs

From looking at the power dissipations, it was possible to evaluate the friction. KR was found to be

Fig. 12. Reaction to changing loads (pump in water vs. pump in air).

• K R 32 10 9 Nms It is rather difficult to directly compute or measure the inertia J. This parameter was approximated and set to be J= 8 x 10-7 kgm².

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5. DISCUSSION AND CONCLUSION

REFERENCES

An observer based field-oriented control concept for sensor-free speed control of a PMSM has been presented. As presented in this work, the control concept has successfully been implemented on a real-time digital signal processor (DSP) and was applied to a catheter-based rotary heart assist device. From a clinical perspective, there is an increasing demand for advanced physiological control concepts in heart assist device. One important example is adaptation to physiological demands (e.g., mechanical exercise) of the body. The model based approach in this paper serves as a potent basis for such future work.

Autschbach, R., Rauch, T., Engel, M., Brose, S., Ullmann, C., Diegeler, A. and Mohr, F.W. (2001). A New Intracardiac Microaxial Pump: First Results of a Multicenter Study. Artificial Organs, Vol. 25, No. 5, pp. 327-330. Isermann, R. (2003), Mechatronic Systems, Springer Verlag, Heidelberg. Jurmann, M.J. and Hetzer, R. (2003). Erste klinische Erfahrungen mit miniaturisierten AxialflussHerzunterstützungssystemen bei postoperativem Herzversagen, Zeitschrift für Herz-, Thorax-, Gefässchirurgie, Vol. 17, pp. 102-107, Kortyka, M. (2005), Entwicklung, Aufbau und Inbetriebnahme einer elektronischen Ansteuerung für Mikroaxialblutpumpen zur Herzunterstützung, M.Sc. Thesis, Chair of Medical Information Technology, RWTH Aachen University. Siess, T. and Reul, H. (2000), Basic Design Criteria for Rotary Blood Pumps. Reprint from H. Matsuda (Ed.), “Rotary Blood Pumps“, Springer Verlag, Tokyo. Utkin, V.I. (1992), Sliding Modes in Control Optimization, Springer Verlag, Moskau. Utkin,V.I., Guldner, J. and Shi, J. (1999), Sliding Mode Control in Electromechanical Systems, Taylor & Francis, London.

                                                                 

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