f

Simulation study of the Hemopump as a cardiac assist device X. Li I

J. Bai I

P. He z

1Institute of Biomedical Engineering, Department of Electrical Engineering, Tsinghua University, Beijing, China 2 Wright State University, Dayton, Ohio, USA

dynamic mode/ was developed for a Hemopump that withdraws blood from the left ventricle and discharges it to the aorta through a miniature axial-flow pump. Incorporation of the Hemopump mode/in a previously established m o d e / f o r the canine circulatory system enabled the effects of the Hemopump on various haemodynamic variables of the circulatory system to be studied, and the benefit of the Hemopump to the failing heart was investigated. In addition, the influence of the physiological status of the right ventricle on the Hemopump performances was examined, and the synchronous and non-synchronous operations of the Hemopump were compared. Results verified that the Hemopump assists the failing heart by increasing the oxygen supply, while reducing the oxygen consumption of the heart through a reduction in the workload of the left ventricle. These beneficial effects were enhanced when the pump's rotation speed was increased. When pump speed was increased from 17 000 to 23 000 revolutions min 1, the oxygen supply increased 101%, and the oxygen consumption decreased 60%. However, when the pump rotation speed was too high, the inflow to the pump could be impaired and the pump performance could be negatively affected. Predications from the model were in good agreement with the results previously obtained in animal experiments and in vitro measurements.

Abstract--A

Keywords--Cardiac assist device, Computer simulation, Hemopump, Ischaemia

\

Med. Biol. Eng. Comput., 2002, 40, 344-353

1 Introduction

MECHANICAL HEART assistance has been used as a bridge to heart transplant, it can also be used temporarily for patients affected by severe heart failure and drug resistance, with the goal of recovering the failing heart and preventing multi-organ failure. Many types of assist device, including the intra-aortic balloon pump and abdomen left-ventricular assist device (FREED et al., 1988, NORMAN et al., 1977; 1981), have been put into clinical use since DeBakey first inserted a mechanical cardiac assist pump in an open chest operation in 1964 (DEBAKEY,1971). in 1988, a new kind of cardiac assist device, the Hemopump, was introduced by BULTERet al. (1990), and its first human trial was reported by FRAZlER et al. (1990). The Hemopump consists of a disposable pump assembly, a high-speed motor and a control console. The miniature axialflow pump itself is situated in the aorta. The inlet flow cannula of the pump passes retrogressively through the aortic valve, with its tip located in the left ventricle. Power to drive the pump is transmitted from an external electric motor by a flexible cable threaded through a sheath. When the device is activated, the pump impellers rotate, and blood is drawn through the inlet cannula into the pump and then discharged into the aorta, in this process, the left ventricle is relieved of its major workload.

Correspondence should be addressed to Dr Jing Bai; emaih [email protected] Paper received 26 November 2001 and in final form 6 March 2002 MBEC online number: 20023669 © IFMBE: 2002 344

J The capability to be inserted into the circulatory system without major surgery makes the pump as safe and convenient as the intra-aortic balloon pump (IABP). On the other hand, the pump may be more effective than the IABP in assisting the left ventricle, owing to its ability to pump the blood actively and adjust the flow rate with no restraints from the function of the natural heart. All these advantages make this device a promising alternative to transplantation in the furore. Although it has been more than ten years since its first introduction, the benefits and operation of the Hemopump are still under investigation, and its clinical applications have been limited (DREYFUS, 1996). Assessment of the performance of the Hemopump in a clinical setting is difficult, owing to the lack of a sophisticated pump management system (SIESS et al., 1996). The variability of the human physiological system and possible administration of various medicines further complicate the assessment of the assistant effects of the Hemopump. in this paper, we propose a mathematical model for the Hemopump, based on published experimental data, and incorporate it into a canine circulatory system model that was developed previously by our group (ZHOU et al., 1998; BAI and ZHAO, 2000). Using this model, the operation mode of the Hemopump and the parameters of the circulatory system can be adjusted easily, and the haemodynamic parameters can be observed conveniently, so that the performance and assistant effects of the Hemopump can be assessed under different conditions. 2 M o d e l description

2.1 Steady model of Hemopump

Assuming that the inflow of the pump is not hampered, the flow produced by the Hemopump is a function of the rotation Medical & Biological Engineering & Computing 2002, Vol. 40

120

speed of the pump and the pressure difference between the outlet and inlet of the pump (MEYNS et al., 1996). In a typical clinical application, the pressure difference is the aortic pressure minus the left-ventricular pressure. The idealised relationship between the steady pump flow Qsteady and the pump pressure head Ah can be described by the following equation (IONEL, 1986): Ah -

APstat p----~

-

-

80 -

........................................... ×

~ '

60

(1)

where APstat is the static pressure difference, p is the density of the fluid, g is the gravity acceleration, u is the linear velocity of the liquid (e.g. blood), fi is the angle of the impeller outlet, d is the diameter at the impeller output, and b is the width of the pump impeller. if we express u as a function of the rotation speed n in revolutions rain-1 u=

~

E

U cotfl g ndb Qsteady

U2 g

100 t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

x

:

i '

100

120

,__

40

20 --; . . . . . . . . . . -;. . . . . . . . . . ;. . . . . . . . . . -;-

0 0

20

40

60

80

140

pressure difference, mmHg

ndn 60

(2)

Results o f least squares fit to reported data obtained from in vitro measurements" of Hemopump operated at seven rotation speeds': (+) 1; ([1) 2; (A) 3; (©) 4; (o) 5; ( x ) 6," (V) 7

Fig. 1

(1) can be transformed to Osteady = An - Bn" Aestat

(3)

where

By comparing (5) with (3), we obtain

nbn2d 2 An - 60 cot fi

and

60b Bn - np cot fi

Qn=An

(4)

Table 1

Rn=l/B n

(6)

and they both depend upon the rotation speed of the pump, as shown in Table 1. In (3), the idealised relationship between Qsteaay and APstat is described. Considering the viscous property of the blood, the viscous resistance R~ to the pump flow should be investigated. The value of R~ can be given approximately by the Poiseuille steady-state formula (RIDEOUT, 1991):

(3) shows a linear relationship between the pump flow and the pressure difference for a fixed rotation speed n. Given the values of An and Bn at a certain rotation speed, the steady pump flow under various pressure differences can be determined. In our present study, we chose to model the Hemopump type HP31 (Medtronic, Minneapolis, Minnesota, USA). This pump can be operated at seven different rotation speeds ranging from 17 000 (speed 1) to 26 000 revolutions min-* (speed 7), with an interval of 1500 revolutions min -1. MEYNS et al. (1996) performed in vitro measurements of the steady flow-pressure difference relationships of the pump at the above seven speeds under pressure differences of up to 230 mmHg. Their data (Fig. 2 in MEYNS et al. (1996)) showed a nearly linear relationship between the flow and pressure difference in the region of lowpressure difference. In the region of high-pressure difference, this linear relationship was broken down owing to flow separation within the rotor. In our present study, we only consider the pressure difference up to 140 mmHg and deliberately do not investigate the effects of flow separation. Consequently, we obtain the values of the two coefficients An and Bn, in the linear equation (3) by fitting a least squares line to the corresponding data of MEYNS et aL (1996) in the range of 0-140mmHg. Figure 1 shows the seven fitted straight lines, and Table 1 lists the values of An and Bn for each of the seven pump rotation speeds. A steady model of the pump based on (3), is shown in Fig. 2a; it consists of a constant flow source Qn and a resistance Rn. The model gives the following relationship between the pump flow Qste~ay and the pressure difference APst~t: 1 Qsteady = Qn - ~nAPstat

and

R,-

8ilL 7rr4

(7)

where fl is the blood viscosity, and L and r are, respectively, the length and internal radius of the pump cannula. Using the data from MEYNS et al. (1995; 1996): q = 3.48mPa-s, L = 8.5 cm, r = d/2 = 4.05 ram, we obtain the value of R~: R, = 2.7997 x 106 Pa- s m 3 = 2.1000x10 2 m m H g - s m l 1

(8)

Comparing the value of R~ with the values of Rn in Table 1, we found that R~ is about 100 times smaller than Rn. This indicates that, when the pump works at speeds 1-7, the blood viscosity has little effect on the pump flow. in fact, in Table 1, the values of the two coefficients An and Bn were not obtained directly from (4) but were calculated based on linear fit to the experimental data from MEYNES et al. (1996). As, in their measurements, a glycerol-in-water solution having the same viscosity as blood was used, Rn in Table 1 has incorporated the resistance to the pump flow due to the blood viscosity. 2.2 Dynamic model o f Hemopump Equation (3) is for steady flow under constant pressure difference. When the pump works in a living circulatory

(5)

Values"of parameters of linear model shown in (3) for pump operated at seven rotation speeds"

Speed level An, mls 1 Bn, ml/(s • mmHg) Rn, (mmHg. s)/ml

1 56.7 0.538 1.86

2 64.1 0.507 1.97

3 69.7 0.485 2.06

Medical & Biological Engineering & Computing 2002, Vol. 40

4 75.1 0.426 2.35

5 80.9 0.373 2.68

6 85.1 0.301 3.32

7 87.6 0.227 4.40 345

Qstat Pin

l

APstat = Pout Pin Rn

Qn

Pout

system, the pressure at the inlet (Pi, = pressure in left ventricle), the pressure at the outlet (Po,t = pressure in aorta) and the pump flow all change with time during a cardiac cycle, and the inertial property of the liquid needs to be considered. To include the effects of the inertial property of the blood in the pump, we modified the steady model of the Hemopump by including an inertia H in the dynamic model of the Hemopump, as shown in Fig. 2b. To determine the value of H i n terms of the mechanical property of the blood, we started from the fact that the inertial property of the blood manifests itself as a force that opposes any change in the flow velocity (SIESS et al., 1996): d am Ov Ov F = ~-~(m- v) = --~-v + ~--~m = ~-~m

(for incompressible fluid), where F is the force, and v and m are, respectively, the velocity and mass of the fluid within the cannula of the pump. Equivalently, the inertial property of the blood can be modelled by a pressure difference AP' that is induced by the change in flow rate. Numerically, AP' is equal to the force Fdivided by the cross-sectional areaA of the cannula of the pump

Q(O

Ib

Pin( t)

T

(9)

F 1 dv AP'=~=~-d-7-m=L--~-

Rn

AP(t) = Pout Pin

Qn H

P dQu d----~

(10)

where L is the length of the cannula, p is the fluid density, and QH is the volumetric flow rate. Based on (10), the inertia H in Fig. 2b can be determined as H=L.-~ P

(11)

H

Using the data from MEYNES et al. (1995) and REUL (1994), L = 8.5 cm, A ~ ~zr2 = 51.53 m m 2, p = 1.06 × 10 3 kg m - 3 , w e obtain the value o f / / f o r our model

Pout( t)

Fig. 2

(a) Steady model and (b) dynamic model for Hemopump

H = 1.749 Pa- s2 ml 1

(12)

I 4 HI,,

i~ : ~ Pul i,

4 HI,,

Fig. 3 Block diagram of model for canine circulatory system. LA = left atrium," LVH = healthy portion of left ventricle," LVI= ischaemic portion of left ventricle," AV=aortic valve," AR = aortic root," HP=Hemopump; Cor=coronary circulation; RA = right atrium," RV= right ventricle," Pul =pulmonary circulation," An = aortic segment," Bn = branch of aorta; Pn =periphery segment," V= lumped venous system 346

Medical & Biological Engineering & Computing 2002, Vol. 40

2.3 Complete canine cardiovascular model including pump A canine cardiovascular model was developed previously that can simulate the dynamic relationship between the cardiac function and the vascular function, as well as be used as a tool to investigate the mechanism of heart failure and the effects of a cardiac assist device system (JARON et al., 1985; ZHOU et al., 1998; BAI and ZHAO, 2000). As shown in Fig. 3, the model consists of four heart chambers, a pulmonary circulation, 11 aortic segments and lumped venous and peripheral vascular systems. The detailed structure and operation of each block of the model can be found in BAI and ZHAO (2000) and ZHOU et al. (1998). Here, we just give a brief description of the model for the left ventricle with regional ischaemia. The left ventricle is functionally divided into two non-physiological compartments, one consisting of all the normal myocardium, and the other consisting of all the ischaemic myocardium. We use R m to denote the ratio of the ischaemic myocardial mass to the total myocardial mass. In this study, a value of 30% is used for Rm, which models the typical ischaemic condition of a canine heart 15 min after its left anterior descending coronary artery has been ligated (MOHL et al., 1984). During each cardiac cycle, each compartment generates its own pressure-volume loop that, in turn, determines the pressure and volume of the entire left ventricle. The maximum elasticity (which is related to myocardial contractility) of the normal compartment (Eesl) is 5 mmHgm1-1, and the maximum elasticity of the ischaemic compartment (Ees2) is 1.5 mmHg ml-1. The canine cardiovascular model shown in Fig. 3 also includes the dynamic model of the Hemopump shown in Fig. 2b. To simulate the typical clinic setting (FRAZIERet al., 1990), the inlet of the pump in our model is inserted into the left ventricle, where the pressure is denoted as PLY. The outflow of the pump is discharged into the descending aorta, where the pressure is denoted as Pa [4], where the number 4 refers to the forth aortic segment. As a result, Pin and Po,t in Fig. 2b become PLY and Pa [4], respectively.

explained by the fact that, when the pump speed is increased, more blood is expelled by the pump, and the ventricular cavity is reduced. As a result, the contribution of the heart to the pump flow is reduced, which is illustrated by the decrease in the upstroke in flow during the ejection phase at high speeds, in our simulation, the contractility and end-diastolic filling volume

70

"-~

,

oOoo o3O

.............................

10

20

,

..............................

20 40 60 pressure difference, mmHg a

80

100

50

45

4O E _o 35

3O

25

3 Computer simulations and results The subject of the computer simulation was a dog in a lying position, with regional ischaemia in its left ventricle. The heart rate of the dog was 120 beats min- 1. The computer program was written in Delphi language and run on an IBM compatible computer. The time interval for computation was chosen to be 0.001 s. During each time interval, the pressure, flow and volume of each block were computed and updated sequentially, starting from the left and fight ventricles. 3.1 Pump flow and pressure difference during normal cardiac cycle In the current applications, the Hemopump always runs at a constant rotation speed. Consequently, we studied the assistant effects of the pump operated at a certain constant speed. For the HP31, the speed can be chosen from between 17 000 revolutions min -1 (speed 1) and 26 000 revolutions min -1 (speed 7) with an increment of 1500 revolutions min -1. In Fig. 4, the flow-pressure difference (Q-AP) relationships of the working pump at speeds 1, 3 and 5 are shown. At each speed level, the Q-AP curve shows hysteresis, resulting in a loop that proceeds clockwise during a cardiac cycle. This phenomenon, which is due to the inertial property of the blood within the cannula and pump, was also observed previously by MEYNS et al. (1996) in their in vivo study of the pump. The hysteresis of the loop decreases as pump speed increases. This can be Medical & Biological Engineering & Computing 2002, Vol. 40

20 60

40

80

1 O0

120

pressure difference, m m H g b

E "7-

38

37.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

129

130

131 132 pressure difference, m m H g

133

134

Fig. 4 Relationship of pump flow and pressure diffbrence of working

pump during cardiac cycle at (a) speed 1, (b) speed 3 and (c) speed 5. ( 0 ) systolic period," (--e-) diastolic period 347

of the left ventricle were set so that the resultant range of pressure differences across the pump was consistent with that reported by MEYNS e t al. (1996) in their in v i v o experiment. Fig. 5 depicts the pump flow during one cardiac cycle (0.5 s, corresponding to a heart rate of 120 mins -~) at pump rotation speeds 1-5. At each speed, especially at a low speed, the pump flow shows significant pulsation. As the pump speed rises, the pulsation of the pump flow decreases. This can be attributed to the decrease in the pulsation of the pressure difference from speed 1 to speed 5, as shown in Fig. 4. We also notice that at speed 1, backflow happens around end systole. The backflow may be deleterious to the failing heart and should be avoided.

70

oo[

,

5o

~:

40 E

30

&

.ol 10 [

3.2 Effects o f Hemopump on v a r i o u s haemodynamic variables

0-

k

Incorporating the Hemopump model into the canine circulatory model, we can study the effects of the pump on various haemodynamic variables at different rotation speeds. Fig. 6a shows the aortic pressure dunng a cardiac cycle at each of the five rotation speeds of the pump. As the rotation speed increases, the mean aortic pressure increases, and the pulsation

-10

150

E E

140 -

0.1

0

0.2

0.3 time,

Fig. 5

0.4

0.5

s

Waveform of pump flow during cardiac cycle when pump is operated at one offive speeds: ( I ) 1; ( [] ) 2; ( ,~, ) 3;

(

)4,.(-,-)5

o

50

160 -

£

J

40E 30-

130

-

110

, . ..~ . ~ _ ~ - . , ~ " ~ " ~ " ~ ~ , ~ ~ ,,- .... .

8

100-'

20

>

%

10-

'~ " = "

90:0

0.1

0.2

0.3

0.4

0 , : ii i : : i,i i: -i ii, i- :1 ii ,::1 ii :: ,11 i: .i 0 0.1 0.2 0.3 0.4 0.5 time, s b

0.5

time, s

120 90-

£

80 d E 70

E E d

60

g. 60-

"~.

40 [,'÷'S~.-.~.v ~ .

30

.

~,,, ~ . .

.

.

~.,.z,~

,~

8

0

40-

,~%

. ..;,..~/...~,

.

>

............ ill

20 10

80

©

50

%

1 O0

do

0.1

0.2

0.3

0.4

0.5

time, s

0 10

~

,;

• ~, .i, ~"

L

~

20-

20

30 left

c

40

ventricular

50 volume,

60

70

ml

d

14-

12-

.,

10,

•

8 "'

6"

., ....

2

~,'"'"

"

"

"

'),.. ~ ")~.

<,-"

II

',;

.~

II

I~

/

÷ ..........

i

0.2

0.3

•I

".:,~,=.

. ........

0.1

i ,

- ".'k .,.

i

0

"

,,~-"~-~"

~.~"

S'

,,

0.4

l 0.5

time, s e

Fig. 6 Effects on various haemodynamic variables of Hemopump when operated at diffbrent speeds. With exception of(d), value of each variable is plotted as function of time during one cardiac cycle. (a) Aortic pressure; (b) blood flow pumped out through aortic valve by left ventricle; (c9 volume of leJ~ ventricle (d) pressure-volume relationship of leJ~ ventricle during cardiac cycle; (e) volume of leJ~ atrium. (a), (c)-(e) speed." (+) 1; ( [] ) 2; ( A, ) 3; ( 0 ) 4; (--e-) 5; (b) speed: (+) 1; ( [] ) 2-5 348

Medical & Biological Engineering & C o m p u t i n g 2002, Vol. 40

of the aortic pressure diminishes. The same trends have been reported in clinical experiments (DREYFUS, 1996; MEYNS et al., 1995; LACHAT et al., 1999; PETERZEN et al., 1996; WALDENBERGEa et al., 1995). Fig. 6b plots the blood flow pumped out by the left ventricle. Only at speed 1 is there noticeable blood flow pumped out by the left ventricle during early systole. As the pump rotation speed is further increased, the amount of blood pumped out by the left ventricle becomes negligible. This observation is also consistent with the results reported by PETEP,ZEN et al. (1996). They noticed that the aortic valve was almost always closed when the pump was working. The reason that, so far, we have not reported the simulation results for speeds 6 and 7 can be explained by Fig. 6c, which shows the volume of the left ventricle during the cardiac cycle when the pump is in operation. As the rotation speed of the pump is increased from speed 1 to speed 5, the volume of the left ventricle decreases to a rather small value. When the pump speed is further increased to speed 6 or speed 7, the volume of the left ventricle approaches zero at some moment, and the simulation comes to a halt. This situation is discussed in Section 3.4. Fig. 6d depicts the pressure-volume loop of the left ventricle in one cardiac cycle. As the pump speed increases, the loop moves to the left (the mean volume decreases), and the area of the loop decreases, indicating a decrease in the workload of the left ventricle (WALDENBEaGEa et al., 1995). Finally, Fig. 6e shows the changes in the left atrial volume during the cardiac cycle. As the pump speed increases, the left atrial volume decreases, which may explain the potential collapse of the left atrium at high speeds reported in literature (CHEN and YU, 2000).

20

15

~3

g

~ 10 o o 5

1

2

3 speed level 8

4

5

1

2

3 speed level b

4

5

0.15

0.10

z ~3

0.05

3.3 Beneficial effects o f Hemopump on a failing heart The main beneficial effects of the Hemopump to a failing heart include an increase in the stroke volume, a reduction in oxygen consumption, as a result of the decreased workload of the left ventricle, and an improved oxygen supply due to an increase in the coronary blood flow. Each of these beneficial effects becomes more significant when the pump rotation speed increases, as shown in Fig. 7. in Fig. 7a, the stroke volume is the combined volume of the blood pumped out by the left ventricle and that pumped out by the Hemopump during a cardiac cycle. As the contribution of the left ventricle to pumping blood quickly becomes insignificant as the pump rotation speed increases (see Fig. 6b), the increase in the stroke volume is almost entirely due to the increase in the pump flow. in Fig. 7b, the myocardial oxygen consumption Vo2 of the left ventricle is determined by the following three equations, based on the work of SUGA (1979): Vo2 = Vo:(a ) + Vo:(2)

(13)

Vo2(1) = B . PVA(a) ÷ C . Ees 1" (1 - Rm) ÷ D . (1 - Rm) (14) Vo2(2) = B . PVA(2) ÷ C . Ees2 " R m ÷ D . R m

(15)

where Vo2 (1)and Vo: (2)are the volumes of oxygen consumed by the normal compartment and by the ischaemic compartment of the left ventricle, respectively; PVA(1) and PVA(2) are the areas of the individual pressure-volume loop of each compartment (see Section 2.3); and Ee~ and Ee~ are the maximum elasticities of the normal region and the lschaemlc region of the left ventricle, respectively. The values of the three coefficients B, C and D are obtained from the work of SUGA et al. (1987). (13)-(15) indicate that the oxygen consumption is directly related to the area of the pressure-volume loop. Figure 6d indicates that, when the pump speed increases, the area of the pressure-volume (P-V) loop of the left ventricle •

1

~

.

Fig. 7 Assistant effects of Hemopump at diffbrent rotation speeds: (a) stroke volume (total blood volume pumped out by left ventricle and Hemopump during one cardiac cycle); (b) ([1) myocardial oxygen consumption and (11) myocardial oxygen supply

decreases (although not plotted, the individual P-V loop of the normal compartment or that of the ischaemic compartment shows a similar trend). As a result, the oxygen consumption decreases as the pump speed increases. Alternatively, the decrease in oxygen consumption of the left ventricle can be explained by the reduction in its preload that is related to the left atrium volume and the left ventricular end-diastolic volume. When the pump speed increases, both the left atrium volume and the left ventricular end-diastolic volume decrease, as indicated in Figs 6e and c. Consequently, the oxygen consumption decreases. Figure 7b also shows the volume of the myocardial oxygen supply (Vos) at each of the five pump speeds. The volume of the myocardial oxygen supply is calculated from the total coronary flow during one cardiac cycle F T C

V°s =

( A . T)o2. F T C

100

(16)

.

Medical & Biological Engineering & Computing 2002, Vol. 40

where A is the volume percentage of the oxygen content in the coronary arterial blood, and Tis a variable that depicts the ability of the myocardial oxygen absorption. The typical values of A and T are determined from the work of WALLEY et al. (1988), and a final value of Vos = O.O015FTC is used in this study. As the pump rotation speed increases, the aortic pressure increases 349

Table 2 Values of various haemodynamic variables when Hemopump is operated at five diffbrent rotation steeds" Speed

Qmpm, ml s

1 P . . . . mmHg P,o~y, mmHg P, odi, mmHg

Ppao, mmHg

P1wy, mmHg V1v~y,ml V1,di, ml SE mlbeat ~ ~ , mlbeat ~ ~s, mlbeat ~

1

2

3

4

5

19.9 99.4 108.3 90.4 17.9 108.3 51.0 9.3 12.0 0.1 0.1

27.7 105.2 110.7 100.9 9.8 99.5 46.2 8.1 14.0 0.1 0.1

30.8 113.5 116.3 111.2 5.2 68.6 35.6 6.4 15.3 0.0 0.1

33.8 122.2 123.6 121.2 2.4 31.3 23.3 4.7 16.9 0.0 0.1

37.9 133.7 133.9 133.6 0.3 4.4 17.0 3.2 18.9 0.0 0.1

80

/

70 . . . . . . . . . . . . =. . . . . . . . . . . . I. . . . . . . . . . . . ~. . . . . . . . . . . . ' . . . . . . . . . . . . T. . . . . . . . . .

1

/ 60 50 co E

40

o

30

E-

~_ 2o 10 0

(Fig. 6a), and the left ventricular pressure decreases (Fig. 6d). As a result, the coronary flow increases, as does the oxygen supply. in summary, the Hemopump assists a failing heart by relieving its workload while supplying it with more oxygen. These beneficial effects o f the Hemopump are also reported by PETERZEN et al. (1996), based on their clinic experiments. The results o f our computer simulation regarding the pump's beneficial effects in terms o f the values o f several relevant haemodynamic variables at five pump speeds are summarised in Table 2. The notations used in Table 2 are as follows: Qmpm= mean pump flow; P .... = mean aortic pressure; Paosy = aortic peak systolic pressure; Paodi----aortic minimum diastolic pressure; Ppao = pulsation o f aortic pressure (Paosy -Paodi); Plvsy----left ventricle peak systolic pressure; Vl~y=left ventricle endsystolic volume; Vladi=left atrium end-diastolic volume; S V = s t r o k e volume; V o c = v o l u m e o f myocardial oxygen consumption; and Vos = volume of myocardial oxygen supply.

20

3.5 Effect o f physiological status o f right ventricle on p u m p performance

it has been suggested that the performance o f the pump depends upon the physiological status o f the heart, not only o f the left ventricle but also o f the right ventricle (SIESS et al., 1996; MEYNS et al., 1996; ROBERT, 2001). To study the effect o f the right ventricle on the operation and performance o f the pump, we decreased the elasticity of the myocardium o f the right ventricle from a maximum value o f 2 m m H g m1-1 to 1 m m H g m1-1 and then observed its effects on the loop of the pump flow and pressure difference (Fig. 8), as well as on the loop of the pressure and volume o f the left ventricle (Fig. 9), during a cardiac cycle. As indicated by the two Figures, when the contractility o f the right ventricle decreases, the pump flow and the range o f the pressure difference are both

350

20

40

60

80

1O0

pressure difference, m m H g 55

50

i

45

E 40

E- 35 30

25

20 40

3.4 'Over-unload' o f left ventricle at pump speeds 6 and 7 When the pump speed increased to speed 6 or speed 7, the computer simulation came to a halt after several cardiac cycles. By tracing the volume o f the left ventricle, which was given an initial value of 70 ml at end-diastole, we found the volume o f the left ventricle approached zero after several cardiac cycles, and the halt in our program was due to a restraint that the volume o f the left ventricle cannot be negative. Our program, in fact, simulated a condition referred to as the left ventricle being 'over-unloaded', which was observed by SIESS et al. (1996) in their experiment with a sheep having a rather small ventricular cavity and the pump being operated at speeds 6 and 7. According to these authors, left ventricle 'over-unloading' was accompanied by hampered inflow of the pump, randomised tip-to-wall contact and possible arrhythmia and therefore should be avoided.

I

10

60

80 1 O0 pressure difference, m m H g b

120

42

40

,-

38

E

36

E~-

34

32

30 90

100

110

120

130

pressure difference, m m H g G

Fig. 8 Effbcts of myocardial contractility of right ventricle on relationship of pump flow and pressure diffbrence when pump is" operated at (a) speed 1, (b) speed 3 and (c9 speed 4. (-*-) right ventricular Ees = 2 mmHg ml l; ( © ) right ventricular Ees = 1 mmHg ml 1

reduced (Fig. 8), and the mean pressure and mean volume o f the left ventricle are also both reduced (Fig. 9). These effects are more pronounced at higher pump speed, an observation that is consistent with the results o f in vivo experiments obtained by MEYNS et al. (1996).

Medical & Biological Engineering & Computing 2002, Vol. 40

came to a halt. Such a phenomenon is not unexpected. As the contractility of the right ventricle decreases, less blood will be driven into the left ventricle and be available for the pump to withdraw. This observation suggests that, if the Hemopump is to be applied for a patient whose fight ventricular function is also hampered, bi-ventricular assistance should be considered to achieve the full efficacy of the pump.

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3.6 Comparisons o f synchronous and non-synchronous operations o f Hemopump

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left ventricular volume, ml a

E E

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left ventricular volume, ml b

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Thus far, we have only considered the Hemopump being operated at a constant speed throughout the cardiac cycle, referring to the non-synchronous (with the heart) operation. Fig. 6a indicates that, under such operation, the aortic pressure waveform becomes quite flat, especially at a high pump speed. Considering the prospective long-term usage of the Hemopump, we cannot ignore the long-standing controversy regarding the physiological effects ofa non-pulsatile circulation. Although NOSE (1993) reported that a long-term non-pulsatile biventricular bypass did not produce harmful physiological effects in animals, recent studies have suggested that a prolonged non-pulsatile left heart bypass can produce certain effects on the arterial structure and function, such as the wall thickness, smooth muscles and vasoconstrictive function of the vessels (NISHIMURA et al., 1998; NISHINAKAet al., 2001). To observe the effects of the Hemopump working in the synchronous mode, we let the pump operate at speed 1 during diastole (to avoid backflow) but at a different speed during systole. Fig. 10 compares the stroke volumes for the two operation modes, where the white bars are for the non-synchronous operation of the pump rotating at a constant speed from speed 1 to speed 5, and the black bars are for the synchronous operation. Under the synchronous mode, the pump always rotates at speed 1 during diastole, but the rotation speed changes from speed 1 to speed 7 during systole, as shown in Fig. 10. The broken horizontal line in Fig. 10 indicates the normal level of stroke volume, 14mlbeat -1, according to the work of MA

35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

25

E E

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&

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15 za E

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5 0 15

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left ventricular volume, ml c

Fig. 9 Effects of myocardial contractility of right ventricle on relationship between pressure and volume of left ventricle when pump is operated at (a) speed 1, (b) speed 3 and (c9 speed 4. (--e-) right ventricular E~ : 2 mm Hgml z; ( - G - ) right ventricular E~ : 2 mmHgml z

1

Medical & Biological Engineering & Computing 2002, Vol. 40

3

4

5

6

7

speed level

Fig. 10

Another observation made from our computer simulation is that, with a failing right ventricle, the left ventricle is more prone to be 'over-unloaded'. In fact, with decreased contractility of the right ventricle, our computer simulation can only be carried out up to pump speed 4. At speed 5, the volume of the left ventricle approached zero after several cardiac cycles, and the program

2

Comparison between two operation modes of pump: ([]) (non-aynchronous mode): stroke volume produced by model when pump is operated at constant speed throughout cardiac cycle; (ll) (synchronous mode): stroke volume produced by model when pump is operated at speed 1 during diastole and at speeds 1-7 during systole; ( - - -) level of typical stroke volume of 14 mlbeat z for normal heart

351

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,

,

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Fig. 11

Comparison between aortic"pressure waveforms when pump is" operated in two operation modes" to achieve same stroke volume o f l 4 ml beat z. For non-synchronous mode, pump is operated at constant speed 2 throughout cardiac cycle. For synchronous" mode, pump is" operated at speed 1 during diastole and at speed 6 during systole. (--*-) pump rotates" constantly during one cardiac cycle. ( © ) pump rotates" synchronously with natural heart

et al. (1979). Figure 10 indicates that the pump can produce a

stroke volume of 14mlbeat -1 at speed 2 under the nonsynchronous operation mode. On the other hand, to produce the same stroke volume under the synchronous operation mode, the pump has to rotate at speed 6 during systole. This observation suggests that the pump is more effective when operating in the non-synchronous mode. in Fig. 11, we compare the aortic pressure waveforms when the pump is operated in either the synchronous mode or the nonsynchronous mode to obtain the same stroke volume of 14 mlbeat -1. We notice that, under the synchronous operation mode, the pulsation of the aortic pressure is larger, and the waveform is closer to a natural one belonging to a normal circulatory system without assistance. This observation then suggests that, when the pump is operated in the synchronous mode, the resultant haemodynamic variables of the circulatory system are more compatible with those of a natural one. As a result, there may be fewer long-term negative physiological effects when the Hemopump is operated in the synchronous mode.

4 Discussion and conclusions A dynamic model for the pump has been developed based on theoretical analysis as well as in vitro and in vivo experimental data. The pump model is incorporated into a canine circulatory system model to study the relationship between the pump flow and pressure difference relationship of the pump in a living circulatory system, the effects of the Hemopump on various haemodynamic variables of the circulatory system, the assistant effects of the Hemopump on a failing left ventricle, the effects of the physiological status of the right ventricle on the Hemopump performances, and the comparison between the synchronous and non-synchronous operation modes of the pump. When the effects of inertial property of blood are included in the pump model, the curve of the pump flow against pressure difference during a cardiac cycle shows realistic hysteresis that was clearly observed in the in vivo experiments. Many other predictions from the model are also in good agreement with the reported results of clinical and animal experiments. The direct effects of the Hemopump on the haemodynamic variables of the circulatory system include an increase in mean 352

aortic pressure, an increase in stroke volume, a decrease in left ventricular volume, a decrease in blood flow pumped out by the left ventricle, a decrease in the area of the pressure-volume loop of the left ventricle during a cardiac cycle, and a decrease in left atrial volume. The increase in mean aortic pressure increases the coronary flow, which in turn increases the oxygen supply to the heart. On the other hand, the decrease in the left ventricular volume and the amount of blood pumped out by the left ventricle imply a reduction in the workload of the left ventricle, in addition, the decrease in the area of the pressure-volume loop of the left ventricle indicates a decrease in the oxygen consumption of the heart. As a result, the pump can effectively assist the failing heart by increasing the oxygen supply while decreasing the oxygen consumption. The increased mean aortic pressure and stroke volume also mean more blood flow being delivered to the vital organs of the body. The simulation results also indicate that all the beneficial effects of the Hemopump are enhanced when the pump rotation speed increases. However, when the pump is operated at a very high speed, both our simulation and in vivo experiments have shown that the volume of the left ventricle can approach zero at certain time during the cardiac cycle, a phenomenon referred to as the left ventricle being 'over unloaded'. As left ventricle 'over-unloading' can be accompanied by hampered inflow of the pump, randomised tip-to-wall contact and possible arrhythmia, such a situation should be avoided in clinical applications of the Hemopump. On the other hand, high shear stresses will occur owing to high rotational speed, and red blood cells can be damaged. The approaches of haemolysis analysis in such micro-axial blood pumps are now under investigation by means of computational fluid dynamics (APELe t al., 2001). The question of what the optimum pump speed is for a given heart may then arise, it has been suggested that, for a patient with low cardiac output, a lower pump speed may be more desirable to achieve a higher total cardiac output (SIESS et al., 1996). The main argument for such a strategy is to maintain better filling and inflow conditions into the pump. if there is no limitation to operate the pump at a constant speed during the entire cardiac cycle, a better strategy may be to operate the pump at a high speed when the left ventricular volume is large, and to reduce the pump speed when the left ventricular volume becomes small. Direct implementation of such a strategy requires a sensor that can read the instantaneous volume of the left ventricle. On the other hand, as the timing for the left ventricle to reach a minimum volume is known approximately (near end-systole), the desired control of the pump speed may be achievable by using the ECG waveform rather than a special volume sensor. Another interesting question is whether it is possible to find a target function to be either maximised or minimised by control of the operation of the Hemopump. The variables that need to be increased can include aortic pressure and stroke volume, and the variables that need to be reduced can include the area of the pressure-volume loop of the left ventricle and the highest pump rotation speed. The weight of each variable however, can be affected by the physiological conditions of the left ventricle, the right ventricle, and the aorta. The model described in this paper should provide a useful tool to investigate and test various strategies for optimum control of the Hemopump. Finally, the results from the modelling study should also provide useful guidelines for clinical testing of various control strategies.

This work is supported by National Natural Science Foundation of China and Tsinghua University.

Acknowledgment

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Author's biography XIONG LI was born in Hunan Province, China, in 1979. She received her BS in Biomedical Engineering from Tsinghua University, Beijing, China, in 2000. She is currently working towards her MS in the Department of Electrical Engineering at Tsinghua University. Her main research interests include modelling and computer simulation of the cardiovascular system and simulation studies of cardiac assist devices.

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