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An Automatic Control Algorithm for the Optimal Driving of the Ventricular-Assist Device Makoto Yoshizawa, Member, IEEE, Hiroshi Takeda, Member, IEEE, Takeshi Watanabe, Makoto Miura, Tomoyuki Yambe, Yoshiaki Katahira, and Shin-ichi Nitta

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Abstract-This paper presents a new method of keeping one of the most suitable driving conditions for regulating the outflow volume from the ventricular-assist device (VAD). The experimental results from a mock circulatory system have shown that the relationshipbetween the stroke volume and the systolic duration of the VAD can be specified by the combination of characteristic curves of the positive and negative drive pressures. The optimal operating point on the characteristic curve have been defined as the point at which thrombosis on the bloodcontacting surface and hemolysis due to mechanical damage can be avoided and at which the driving energy can be minimized. The present analysis has been revealed that the optimal operating point is the vertex of the triangular figure obtained from the characteristic curve. The algorithms for keeping the optimal operating point and for regulating the stroke volume have been also proposed.

time when f ( t ) becomes zero from negative stroke volume of LVAD target stroke volume of LVAD saturated value of PPCC when P,, = PPmax stroke volume as a function of w cardiac cycle Tc when the NPCC (PN = P N m l nmeets ) the saturating point on the PPCC (P,, = PPmax) Tc that satisfies Tc, < TCS Tc that satisfies Tc2 > Tcs sack volume of LVAD systolic duration reference systolic duration w at which sv(w) becomes positive as w increases time when f ( t ) becomes zero from positive correction factor included in (3)

NOMENCLATURE slope of PPCC approximated by (4) target slope of PPCC defined by (6) slope of NPCC approximated by ( 5 ) aN target slope of NPCC defined by (7) a; a,, when P,, = P P m x a p max when P,, = PNmin ffNmin A sampling interval of the controller error between CY: and a,,defined by (8) er, error between CY; and CY^ defined by (9) eN f (0 blood flow rate of LVAD defined by (1) HR heart rate k number of beats NPCC negative pressure characteristic curve of sv(w) positive drive pressure level PP negative drive pressure level PN Pp max approvable maximum of Pp approvable minimum of PN p N min PPCC positive pressure characteristic curve of sv(w) instantaneous value of drive pressure P(f)

a,,

Manuscript received April 10, 1990; revised July 18, 1991. This work was supported by Grant-in-Aid (No. 01890003 and No. 63750390) from the Japan Ministry of Education, Science, and Culture. M. Yoshizawa, T. Watanabe, and H. Takeda are with the Department of Electrical Engineering, Faculty of Engineering, Tohoku University, Sendai 980, Japan. M. Miura is with the Department of Thoracic Surgery, School of Medicine, Tohoku University, Sendai 980, Japan. T. Yambe, Y. Katahira and S . Nitta are with Research institute for Chest Diseases and Cancer, Tohoku University, Sendai 980, Japan. IEEE Log Number 9105592.

INTRODUCTION HE ventricular-assist device (VAD) is temporarily used in patients in the state of low cardiac output syn drome caused by postcardiotomy or myocardial infarction. The purpose of the VAD is to provide adequate blood perfusion for the systemic or coronary circulation and unload the damaged heart. The pneumatic drive system is most frequently used for pumping the VAD in clinical application because it acts on a relatively simple principle and can produce the drive pressure with a suitable rate of change for the cardiovascular system. The usual pneumatic drive system has three adjustable control inputs to regulate the outflow volume from the VAD, i.e., the positive drive pressure level (P,,), the negative drive pressure level ( P N ) ,and the systolic duration (w).One of the most important problems that confront an operator is how to adjust these control inputs [ 11, [2]. Optimal adjustment of the control inputs based on a certain criterion is urgently required for clinical application of the VAD [3]. In the case of the total artificial heart (TAH), the fullfill and full-ejection pumping has been defined as the optimal driving [4], [ 5 ] . When the TAH is driven in the fullfill and full-ejection pumping, the stroke volume of the pump becomes maximum and remains roughly constant. The average outflow volume is equal to the product of the stroke volume and the average pumping rate. Hence, the

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average outflow volume from the VAD can be regulated at a desired level if the average pumping rate is adjusted. In the case of the VAD, its pumping action is often synchronized with the natural heart beat in order to keep its systolic delay equal to the desired value [6]. In such synchronized driving, the pumping rate of the VAD is equal to that of the natural heart and cannot be changed arbitrarily. Hence, the stroke volume have to be adjusted in stead of the pumping rate in order to regulate the average outflow volume. If the stroke volume is changed, the condition of the full-fill and full-ejection driving will be no longer satisfied. The aim of this study is to develop an automatic control algorithm of the pneumatic drive system of the VAD synchronizing with the natural heart for satisfying the following three conditions: 1) avoiding thrombosis and hemolysis in the VAD, 2) minimizing the driving energy, and

3 ) regulating the outflow volume from the VAD under the condition of neither full-fill nor full-ejection driving. It is needless to say that the condition 1) is the most important criterion for driving the artificial heart [6]. Condition 2) is also important even though the VAD can be driven by a pneumatic drive unit outside the body because this aim is useful for minimizing electrical power consumption. This promotes the development of a smallsized and portable drive system of the VAD. Furthermore, the external force working on the sack in the VAD or the artificial valves can be decreased by decreasing in driving energy. Hence, minimization of driving energy also contributes to increasing their durability. When we are trying to wean the VAD from the patient, its output should be controlled at less than the maximum available. Condition 3 ) is used for this purpose. In general, in order to keep the patient’s hemodynamics normal, it is not always optimal to drive the artificial heart with the available maximum of the stroke volume [ 11. Hence, it will be necessary to regulate the assisted blood flow volume in accordance with the physiological demand of the circulatory system if the demand can be precisely known in the future. This requires condition 3 ) . In this paper, the variations of the stroke volume or the blood flow rate with P p , P,, and w are analyzed to obtain the most suitable driving pattern that satisfies the above conditions 1) and 2). The pattern is given as the optimal operating point on the function curve of the stroke volume. The algorithms for keeping the optimal operating point and for regulating the stroke volume are also proposed. EXPERIMENTAL PROCEDURE

In vitro and in vivo experiments were carried out by using a mock circulatory system and two adult goats weighing 60 and 65 kg. In in vivo experiments, anesthesia

r V A D simulating natural heart

I

~ t r i avolume ~ limiter3

Fig. 1. Schematic illustration of in vitro experiment consisting of the LVAD, the pneumatic drive unit and the mock circulatory system.

was induced with intramuscular ketamine hydrochloride (0.8 mg/kg), followed by 4% halothane, intubation, and ventilation with a volume respirator. Fig. 1 illustrates the in vitro experiment. The experimental apparatus consists of a VAD, its pneumatic drive unit and a mock circulatory system. The mock circulatory system includes another VAD that simulates the natural heart. Each VAD used in our system [7] is a sack type pump made of polyurethane with two Bjork-Shiley valves. The pneumatic drive unit provides positive and negative pressure alternately for the VAD in order to pump blood out of the sack. Total volume of water contained in the mock circulatory system is 8L. The measures of the closed tank are as follows: base area = 100 cm2, height of water = 19 cm and height of air = 6 cm. The measures of the open tank are as follows: base area = 286 cm2 and height of water = 19 cm. It was assumed that the device was implanted between the left atrium and the aorta for clinical use as the leftventricular-assist device (LVAD), and that the pneumatic drive unit was synchronized with the natural heart beat using the pulse signal triggered by R wave of ECG. The closed and open tanks correspond to the arterial compliance and the venous reservoir of the circulatory system, respectively. Two electromagnetic flow meters were used to measure the inflow and outflow rates at the inlet and outlet cannulae connected with the LVAD, respectively. Our pneumatic drive unit has three manipulated variables; i.e., the control signals of the positive and negative pressure saturating levels (P,, and P N ) , and the systolic duration (w).The systolic duration is the length of the time interval during which the positive pressure is provided for the LVAD. The values of these manipulated variables were decided by the personal computer system every 10 ms on the basis of the sampled information of the outflow rates. ANALYSIS OF STROKE VOLUME AND FLOWRATE

Let su denote the stroke volume of the LVAD, p ( t ) the instantaneous value of the drive pressure, HR the heart rate, Tc the cardiac cycle, and u(t) the volume of the

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The positive and negative parts of f ( t ) correspond to outflow rate from the LVAD and inflow rate into the LVAD, respectively.

Stroke Volume Patterns Fig. 2 shows the changes of sv with w for a variety of P,,, P N ,and HR in the mock circulatory system. Let sv(w) denote the relationship between su and w. Fig. 2(a)-(d) correspond to sv(w)’s when the change in both P,, and P N , in only P,,, in only P N ,and in only HR, respectively. Fig. 2 reveals that the patterns of sv(w) can be classified into the following two patterns. Pattern I: svtw) with a trapezoidal shape like Fig. 3(a). Pattern ZZ: sv(w) with a triangular shape like Fig. 3(b). The pattern I occurs when P,, or PN is strong or when Tc is long; i.e., HR is low. The pattern I1 occurs when Pp or PN is weak or when Tc is short; i.e., HR is high. Fig. 4 illustrates how the patterns of sv(w) like Fig. 3 are generated. Each sv(w) can be decided by a combination of two characteristic curves. One curve mainly depends on P,,. Let us call it the positive pressure characteristic curve (PPCC). The solid lines in Fig. 4 represent the family of the PPCC. The other curve is influenced by

Fig. 3 . Two patterns of sv(w).

s v (w)

(a) (b) Fig. 4 How to generate the pattern of sv(w) Solid and broken lines represent the PPCC and NPCC, respectively (a) Effect of the drive pressure level, P, or PN.(b) Effect of the cardiac cycle T,

both PN and Tc (or HR). Let us call it the negative pressure characteristiccurve (NPCC). The broken lines in Fig. 4 represent the family of the NPCC. The PPCC has a plateau and the slope of the PPCC becomes steeper as P,,

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300

1200

f ( t ):Outf low r a t e

rFig. 5 . Time responses of the LVAD f l o w f ( t )and the drive pressure p(r). A , B, and E correspond to the operating points assigned by A , B , and E depicted in Fig. 2, respectively.

increases. In the same way, the slope of NPCC becomes steeper as -PN increases. The point of intersection of the NPCC and w-axis is equal to T,, and the NPCC shifts right as Tc increases; i.e., as HR decreases. Thus, the combination of PPCC and NPCC decides whether su(w) has a trapezoidal shape (pattern I) or a triangular shape (pattern 11). Chinzei et al. [8] have explained the presence of the pattern I1 by using a hydrodynamic model. Their model is consistent with the results mentioned above. However, they have never pointed out the occurrence of the pattern I. Flow rate patterns When the LVAD was operating at the point A, B, and E in Fig. 2(b), the flow ratef(t) and the drive pressure p(t) were as shown in Fig. 5 where Pp = 300 mmHg and PN = -60 mmHg. The positive outflow part off(t) has a sinuous shape open downwards and the negative inflow part off(t) is slightly similar to a rectangle. On the basis of the experimental results, the schematic diagram of typicalf(t)'s can be depicted as Fig. 6. Each figure in Fig. 6 corresponds to each operating point on sv(w) in Fig. 3. THE OPTIMALOPERATING POINT Operating Point a t which Thrombosis and Hemolysis can be Avoided In general, it has been already confirmed by the experiments [9], [lo] that thrombosis is caused by stagnation of blood flow on the inside walls of the cannulae and the sack, or around the artificial valves. In order to avoid

thrombosis, hence, it is necessary to reduce the occurrence time of such stagnation as much as possible. To do this, the length of the time interval in which the blood flow rate is zero should be minimized. Hemolysis which takes place in driving the artificial heart is chiefly due to excessive external force working on blood cells [ 111. The force may originate from 1) the large shear stress caused by excessively high blood flow rate, 2) the water hammer caused by quick closing of the artificial valve, or 3) the stress from the inside wall of the sack collapsed by the excessively long systolic duration. In order to avoid hemolysis, hence, it is necessary to decrease the shear stress and the water hammer mentioned above. To do this, the magnitude of the blood flow rate should be minimized. Furthermore, it is also necessary to keep an appropriate systolic duration and prevent the sack from collapsing and flattening. On the basis of these criteria, the most suitable operating point on ~ ( w for ) avoiding thrombosis and hemolysis can be given below. As depicted in Fig. 6, let z denote the time when the blood flow ratef(t) becomes zero from positive, and let q denote the time whenf(t) becomes zero from negative. In the interval on t axis from z to w(z c w) seen at C to E in Fig. 6, the VAD tends to have thrombosis because the absolute value off(t) is zero during this time interval, and then the blood flow is stagnating inside the cannulae and around the artificial valves. In the same interval, the VAD tends to have hemolysis because the sack is apt to be collapsed and flattened by the excessively long systolic duration. In the same way, in the interval from q to Tc which can be seen at A to C in Fig. 6, the VAD tends to have thrombosis becausef(t) is also zero. It is considered that such driving conditions should not be applied to clinical use. On the other hand, in the case of the point F in Fig. 6 corresponding to the vertex F of the triangle of sv(w) in Fig. 3(b), the length of the time interval in whichf(t) is zero is minimum. In this case, the occurrence time of blood-flow stagnation can be minimized and then thrombosis may be avoided most. The average flow rate is equal to the stroke volume divided by the length of time whenf(t) is not zero. This length becomes maximum at F. Hence, the operating point F can minimize the absolute value of the average flow rate subject to generating the same stroke volume as the other operating points. This suggests that driving the VAD at F can minimize the magnitude of shear stress and water hammer caused by excessive flow rate. Thus, hemolysis may be avoided most at F. It can be concluded that the vertex of a triangular figure of su(w), such as the point F , is the most suitable operating point for avoiding thrombosis and hemolysis. Operating Point a t which Driving Energy can be Minimized is also the most deThe vertex of the triangle of SZI(W) sirable operating point for saving the driving energy. Its reason is as follows: Let w* and su* denote the desired

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f

(t)

i (t)

D r i v e pulse signal

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

k/

;

t i A

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

Fig. 6. Schematic illustration of the variation of flow rate f ( r ) with the systolic duration w . The width of the drive pulse signal is equal to w . A to Fcorrespond to the operating points assigned by A to F depicted in Fig. 3.

This algorithm has been derived from the fact that if z < w, the operating point always creates the interval at whichf(t) is equal to zero such as the interval between z

Fig. 7. Explanation on the reason why the optimal operating point minimizes the driving energy of the VAD.

systolic duration and the desired stroke volume, respectively. Three cases can be considered to realize the operating point Q(w*, su*) as shown in Fig. 7. One is the case where the VAD is driving at the operating point Q on the right edge of the triangle SPT when P,, is relatively large. The second is the case where the VAD is driving at the operating point Q on the left edge of the triangle SRT when PN is relatively large. The third is the case where the VAD is driving on the vertex of the triangle SQT. It is clear that the third case can minimize the driving energy used to produce the drive pressure. The case where su(w) has saturation such as the pattern I is no longer optimal because Pp and/or PN are excessive in this case.

CONTROL ALGORITHM Algorithm that Keeps the Optimal Operating Point The algorithm that keeps the optimal operating point, even if P,,, P N ,or Tc changes, can be proposed as follows:

if z > w then increase w else let w

=

z.

(2)

and w seen at C to D in Fig. 6. The algorithm guarantees the operating point to maintain the point which satisfies z = w ;i.e., the optimal operating point when su(w) is triangular. This can be explained below. The inequality z > w suggests that the sack can continue to pump blood at a longer interval than the current w. Hence, in the case of z > w, if w increases, the operating point will approach the optimal operating point. On the other hand, if the operating point enters any region where z < w and if w at the next step is chosen as w = z, then the diastolic period at the next step will increase and the sack will be filled with more amount of blood. Hence, the operating point at the next step will satisfy z > w and can approach the optimal operating point if w is increased as shown in the previous case. To apply this algorithm to an actual digital controller, Equation (2) have to be modified as follows: Let k denote the number of beats; w(k)the current w ;w(k 1) the next w; z(k) the current z; and A the sampling interval of the controller. The concrete digital control algorithm is represented by if z(k) - t > w(k)then w(k 1) = w(k) A

+

+ + else w(k + 1) = z(k) - (

(3)

where is the correction factor that compensates for the delay from the drive pulse signal to the output signal of the flow meter and for the influence of inertia of blood. In our system, { was equal to about looms. At the first step, w(0) should be large enough, for example, w(0) = Tc/2, to reach the optimal operating point as fast as possible.

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Algorithm to Regulate the Stroke Volume In order to regulate the stroke volume while keeping the optimal operating point, both P,, and PN must be manipulated as shown below. Even if so, the degree of freedom with respect to the systolic duration w can be still left. Let Q and Q* denote the current optimal operating point and the desired optimal operating point, respectively. Let them have coordinates ( w , sv) and (w*, sv*), respectively. The purpose of the regulation is to make Q close to Q* by adjusting both P,, and P N .Let CY,, denote the slope of the current PPCC and aN(< 0) the slope of the current NPCC. Let w,, denote w at which su(w) becomes positive from zero as w increases. CY,, and CY^ can be approximated by CY,, = s u / ( w - w,,) (4) CYN = S U / ( W -

Tc).

=

sv*/(w* - w,,),

(6)

CY; =

S U * / ( W *- Tc).

(7)

Define the errors of these slopes as

e,, =

CY; - CY,,,

(8)

eN = a; - ayN.

(9)

If ep is fedback to P,, and if eN is fedback to PN according to an appropriate automatic control algorithm as shown in Fig. 8, then CY,, will approach CY;, aNwill approach CY; and Q will become close to Q*. CY,, changes linearly with P,, to some extent and depends little on PN. In the same way, CY^ changes linearly with PN to some extent and depends little on P,,. Hence, the coupling characteristic between their dynamics is considered to be small and design of their controller can be quite simple. The controller used in our system consists of two independent PI (proportional and integral) controllers as depicted in Fig. 8. The control behavior of this controller is as follows:

+ sp(k +

Pp(k

1) = K,,,,e,,(k) + KIPS,,(k)?

(10)

1) = s,,(k) + e,,(k),

(1 1)

Pdk

+

.sdk

+ 1) = s d k ) + e&),

1) = K,,fldk)

+ Ki~s~(k),

*

a (6),

+

sv

G

(7)

>

5 V

(4),---3 (5)

-+

m

(5)

denote the slopes of the In the same way, let CY; and CY; desired PPCC and the desired NPCC, respectively. CY; and CY; can be approximated by CY;

SV

(12) (13)

where P,,(k), PN(k),e,,(k) and eN(k)are P,,, P N , e,,, and eN at the kth beat, respectively. K,,,,, K , , , K,,N and KIN are constant values which should be chosen such that the desired response can be realized in transient and steady states.

Fig. 9. The widest region of set point with respect to the stroke volume sv.

How to Choose the Reference Systolic Duration w* The reference systolic duration w* can be chosen arbitrarily to some extent. However, w* has to be changed in accordance with the heart rate HR or cardiac cycle Tc so as to make the set point region of sv* as wide as possible. A method of choosing w* is proposed as follows: and PN ( < 0) denote the approvable maxLet P,, imum of P,, and the approvable minimum of P N , respec-tively. Define CY,, and ( Tcs. In the case where Tc = T,, , the widest region of the set point of sv* corresponds to the line BD because the shape of sv(w) is the triangle ABC. In the case where Tc = Tc2, the widest region of the set point of su* corresponds to the line SG. because the shape of sv(w) is the trapezoid ASEF and the optimal operating point does not exist in the right side of the saturating point S . Thus, to make the region of the set point with respect to su* as wide as possible, w* has to be changed as

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We do not have to know the precise values of w,,,CY,,^,,^^, aNlnin and s,z, used in (14) to (15) because these values have little effect on the control characteristics of the whole system. Our controller adopted the following values: w,, = 20 ms, ap,,, = 0.2 mL/ms, = 0.08 mL/ms, s,z, = 40 mL and Tcs = 720 ms. OF THE PROPOSED ALGORITHMS APPLICATION Algorithm to keep the Optimal Operating Point Fig. 10 represents the responses of the circulatory system of an adult goat ( A ) when the optimal operating point was being searched according to the algorithm described by (3). The algorithm was applied under the conditions that l =90 ms, P,, = 160 mmHg and PN = -40 mmHg: both P,, and PN were constant. This figure shows the variations of w , the outflow volume from the LVAD(OUTFLOW), the inflow volume into the LVAD(INFLOW), the aortic pressure(A0P) and HR with the number of beats. w was set to be constant as w = 100 ms before the 10th beat. w began to be changed according to the algorithm at the 10th beat. The optimal operating point was found at the 23rd beat as w = 180 ms and sz, = 24 mL and kept at this position. Fig. 11 shows the time trajectories of p ( t ) andf(t) corresponding to Fig. 10. The point at t = 0 ms was based on the time corresponding to R wave of ECG. The LVAD was operating in counter-pulsation with the systolic delay of 190 ms. Our system had transport delay of 40 ms from the drive signal to the output signal of the flow meter. In this figure, hence, the curve o f f ( t ) has been shifted left by 40 ms to compensate for the delay. The figures assigned by (a) to (d) in Fig. 11 correspond to the figures assigned by the arrows (a) to (d) in Fig. 10, respectively. Parts (a)-(d) represent the initial state, the state searching the optimal operating point with increase in w , the state overshooting, and the state at the optimal operating point, respectively. It is shown that the area of the lump of the inflow rate seen in (a) or (b) is smaller than (c) and (d). This implies that w can afford to increase to approach the optimal operating point. The systolic duration w can be regarded as the time interval between the rise and fall time of p ( t ) . From the figure, it can be seen that the values of z - { - w at (a)-(d) are 10, 10, - 10, and 0 ms, respectively, where l is considered to be (90-40) ms instead of 90 ms with regard to the shifted value of the abscissa corresponding to the transport delay. Thus, it has been ascertained that the algorithm represented by (3) worked successfully.

Algorithm to Regulate Stroke Volume Fig. 12 represents the responses of the circulatory system of a different adult goat (B) when the mean outflow from the LVAD was controlled so as to coincide with a reference rectangular signal according to the algorithm described by (3) and the PI-control algorithm described by (10) to (13). Fig. 12(a) shows the command flow, the mean outflow from the LVAD, the mean pulmonary ar-

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Fig. 10. The responses of the circulatory system of an adult goat ( A ) when the optimal operating point was being searched according to the algorithm described by (3).

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Fig. 11. Time responses of the flow rate of the LVAD f ( t ) and the drive pressure p ( t ) . (a)-(d) correspond to the beats assigned by (a)-(d) depicted in Fig. 10, respectively.

terial flow and the systolic duration w.In this experiment, the upper limit of the mean assistance flow was about 4L/min, because the capacity of the VAD was 40 mL and the heart rate HR was about 100/min (almost constant). The command flow amplitude was set to be two values; i.e., 2 and 3 L/min. They alternated with each other every 40 beats. Fig. 12(a) reveals that the outflow settled in about 20 beats. The positive and negative pressure levels, P,, and P N , manipulated by the PI-controller are shown in Fig. 12(b). It can be seen that both P,, and PN increase in absolute values when the reference signal is on the higher

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10 ILVADF

- Mean outf lor from LVAD (RLVADF)

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(b) Fig. 12. Tracking characteristic of the mean flow of the LVAD to a rectangular command flow. (a) Mean outflow from LVAD (mLVADF), mean pulmonary arterial flow (mPAF) and systolic duration ( w ) . (b) Drive pressure levels (P,and PN).

level, and vice versa. The reference systolic duration w* calculated from (15) is 150 ms because HR = 100/min (Tc % 600 ms). However, the actual systolic duration w decided by (3) changes as shown in Fig. 12(a). The inlet and outlet cannulae we used for the in vitro tests were different in length from the ones used for the above two in vivo tests. This difference might change the fluid resistance to some extent, and then the slopes of the PPCC and NPCC might change. However, the PI-controller definately worked so as to eliminate the errors with respect to the slopes. This suggests that as far as the characteristics of sv(w) as shown in Fig. 4 still exist, the algorithms for keeping the optimal operating point and for regulating the stroke volume do not have to be modified to compensate for small change in afterload, preload as well as fluid resistance.

Adaptation for Change in Heart Rate It is to be noted that the above acute animal experiments did not involve animals with variable heart rates, arrhythmias, or ventricular failure. However, the proposed regulation algorithms can realize an adaptive control behavior for the change in the heart rate HR. In the algorithms, aNdefined by (5) will

be mainly controlled if HR changes because the right-hand side of (5) includes the cardiac cycle: Tc = 6 0 / H R . Hence, output regulation can be carried out by manipulating the negative drive pressure PN chiefly even when the optimal operating point moves as a result of the change in T, like Fig. 4(b). To ascertain this behavior, the time response of the mock circulatory system to a sudden change in HR is shown in Fig. 13. The heart rate of the mock natural heart was changed as 120 90 --+ 120/min in a step-like manner shown in Fig. 13(a). In this case, the aim of regulation was to keep the mean outflow constant (2L/min). Fig. 13(b) shows the actual mean flow (mLVADF). It can be seen that the settling time of mLVADF is about 20 beats. The systolic duration w manipulated by (3) and the reference systolic duration w* decided by (15) are shown in Fig. 13(c). Note that the response speed of w in increasing in w after the 50th beat is lower than that in decreasing after the 100th beat. This was caused by the fact that the different manipulations were chosen for w on the basis of the algorithm (3). Fig. 13(d) and (e) show the changes in P,, and P N , respectively. They reveal that the response of the pneumatic controller was still stable and appropriate manipulations were carried out for the positive and negative pressure levels even when a wide and abrupt change happened in the heart rate. +

CONCLUSIONS The experimental results from a mock circulatory system have shown that the relationship between the stroke volume and the systolic duration of the VAD can be decided by a combination of the positive and negative pres-

YOSHIZAWA et a l . : CONTROL ALGORITHM FOR DRIVING OF VAD

sure characteristic curves. The analysis has revealed that the optimal operating point for avoiding thrombosis or hemolysis caused by the LVAD and for minimizing the driving energy is given as the vertex of the triangular figure made by the characteristic curve of the stroke volume. The algorithms for keeping the optimal operating point and for regulating the stroke volume have been proposed. In the experiments using the adult goats, it has been ascertained that these algorithms work successfully. In our system, a PI-control algorithm has been introduced to regulate the outflow from the VAD. It is considerably difficult to adjust the four coefficients included in the controller to be optimal. As a result, the settling time of the outflow response was fairly long. To realize the desired response even if the parameters of the cardiovascular dynamics change [ 121, some adaptive control algorithm [13]-[15] should be introduced instead of the PIcontrol algorithm.

REFERENCES [ I ] N. N. Puri, J. K-J. Li, S. Fich and W. Welkowitz, “Control system for circulatory assist devices: Determination of suitable control variables,” Trans. Amer. Soc. Art$ Intern. Organs, vol. 28, pp. 127132, 1982. [2] J. B. Mays, M. A. Williams, L. E. Barker, M. A. Pfeifer, J. M. Kammerling, S. Jung, and W. C. DeVries, “Clinical management of total artificial heart drive systems,” J . Amer. Med. Assoc., vol. 259, no. 6, pp. 881-885, 1988. [3] U. Tsach, D. B. Geselowitz, A. Sinha, J. Tirinato, H. K. Hsu, G . Rosenberg, and W. S. Pierce, “Minimum power consumption of the electric ventricular assist device through the design of an optimal output controller,” Trans. Amer. Soc. Art$ Intern. Organs, vol. 10, pp. 714-719, 1987. 141 E. Henning, “The artificial heart program in Berlin-technical aspects,” in Assisted Circulation 2, F. Unger, Ed. Berlin: SpringerVerlag, 1984, pp. 229-253. [5] H. Thoma, “Drive and management of circulation support system,” in Assisted Circulation 2, F. Unger, Ed. Berlin: Springer-Verlag, 1984, pp. 339-366. 161 W.Welkowitz, and J. K-J., Li, “Control aspects of intraaortic balloon pumping, An overview,” Proc. IEEE, vol. 76, pp. 1210-1217, 1988. [7] S . Nitta, Y. Katahira, T . Yanbe, M. Tanaka, Y. Kagawa, T. Hongo, N. Sato, and M. Miura, “Experimental and clinical evaluation of a sack-type ventricular assist device and drive system,” in Artijicial Heart 2 , T. Akutsu, Ed. Tokyo: Springer-Verlag. 1988, pp. 131138. 181 T. Chinzei, K. Imachi, K. Maeda, K. Mabuchi, Y. Abe, K. Imanishi, T. Yonezawa, I. Fujimasa, and K. Atsumi, “Development of multiparameter automatic control system of total artificial heart for analysis of circulation mechanism,” in Artijicial Heart 2, T. Akutsu, Ed. Tokyo: Springer-Verlag, 1988, pp. 295-301. 191 Y. Katahira, S . Nitta, M. Tanaka, Y. Kagawa, T . Hongo, and T. Horiuchi, “Flow visualization of artificial heart and its quantitative analysis,” in Fluid Control and Measurement. Oxford: Pergamon, 1985. [IO] S. Hashimoto, K. Nishiguchi, Y. Abe, M. Nie, T. Takayama, H. Asari, S. Kazawa, A. Ishihara and T. Sasada, “Thrombus formation under pulsatile flow: Effect of periodically fluctuating shear rate,” Japan. J . Artif. Organs, vol. 19, No. 3, pp. 1207-1210, 1990. [ 1 I] C. S . Kwam-Gett, H. J. Zwart, A. C. Kralios, T. Kessler, K. Backman, and W. J. Kolff, “Prosthetic heart with hemispherical ventricles designed for low hemolysis action,” Trans. Amer. Soc. Art$ Intern. Organs, vol. 16, pp. 409-415, 1970. 1121 G . Avanzolini, P. Barvini, A. Cappello, G . Cevenini, V. Pohl, and T. Sikora, “Tracking time-varing propaties of the systemic vascular bed,” IEEE Trans. Biomed. Eng., vol. BME-36, pp. 373-381, 1989. 1131 B. C. McInnis, R. L. Everett, J. C . Wong, B. Vajapeyam, and T. Akutu, “A microcomputer based adaptive control system for the ar-

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tificial heart,” in Proc. IFAC 8th World Congress, vol. XXI, 1981, pp. 130-137. [14] T. Kitamura and H. Akashi, “A design of an adaptive control system for left ventricular assist,” in Proc. 8th IFAC World Congress, vol. XXI, 1981, pp. 3767-3772. [15] B. C. McIniss, 2 . W. Cuo, P. C. Lu, and J. C. Wang, “Adaptive control of left ventricular bypass assist devices,” IEEE Trans. Automat. Cont., vol. AC-30, pp. 322-329, 1985.

Makoto Yoshizawa (M’88) was born in 1955. He received the Bachelor’s, Master’s, and Ph.D. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1978, 1980, and 1983, respectively. He was a Research Associate from 1983 to 1990 and a Associate Professor from 1990 to 1991 in the Department of Electrical Engineering, Faculty of Engineering, Tohoku University, Sendai, Japan. Since April 1991 he has been a Associate Professor in the DeDartment of Knowledge-Based Information Engineering, Toyohashi University of Technology, Toyohashi, Japan. He is interested in biomedical engineering from the viewpoint of control theory. Dr. Yoshizawa is a member of the Japanese Society for Artificial Organs, the Japan Society of Medical Electronics and Biological Engineering, and the Society of Instrument and Control Engineers of Japan.

Hiroshi Takeda (M’83) was born in 1929. He received the Bachelor’s, Master’s, and Ph.D degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1954, 1956, and 1961, respectively. From 1959 to 1960 he was employed by Fujitsu Company. Since 1960 he has been with Tohoku University. Currently he is a Professor in the Department of Electrical Engineering, Faculty of Engineering. He is interested in estimation and control of stochastic systems and biomedical engineering from the viewpoint of control theory. Dr Takeda is a Fellow of the Society of Instrument and Control Engineers of Japan, a member of the Japanese Society for Artificial Organs, and the Japan Society of Medical Electronics and Biological Engineering.

Takeshi Watanabe was born in 1965. He received B.S. and M.S. degrees in electrical engineering from Tohoku University, Sendai, Japan, in 1989 and 1991, respectively. His master’s thesis involved the application of adaptive control and the optimal driving of the left-ventricular-assist device. He is currently employed at Mitsubishi Research Institute, Inc. Tokyo, Japan.

Makoto Miura was born in 1951 He received the Bachelor degree in applied physics from Tohoku University, Sendai, Japan, in 1975 and the M D. degree from Tohoku University, School of Medicine, in 1981 He joined the Department of Thoracic and Cardiovascular Surgery, Tohoku University, in 1983 after completing an internship in general surgery. He specializes in cardiac surgery. His main research interests includes design and application of cardiac assist devices

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Tomoyuki Yamhe was born in 1959. He received M.D. and D.M.Sc. from Tohoku University, Sendai, Japan, in 1985 and 1989, respectively. Since 1985 he has been with Tohoku University. Currently he is a Research Fellow in the Department of Medical Engineering and Cardiology, Research Institute for Chest Diseases and Cancer, Tohoku University. He is interested in clinical cardiology, development and evaluation of the ventricular-assist device and total artificial heart, and neurophysiology of the artificial heart. Dr. Yambe is a member of the American Society for Artificial Internal Organs, International Society for Artificial Organs, the Japanese Society for the Artificial Organs, and the Japan Society of Medical Electronics and Biological Engineering. Yoshiaki Katahira was born in 1955. He graduated from Tohoku University, School of Medicine in 1981 and the Ph.D. degree in medical science from Tohoku University, Sendai. Japan, 1988. Since 1983 he has been with Tohoku University. Currently he is a Research Associate in the Department of Medical Engineering and Cardiology, Research Institute for Chest diseases and Cancer, Tohoku University. He is interested in the artificial international organs and in the cardiology.

Dr. Katahira is a member of International Society for Artificial Organs and Japanese Society for the Artificial Organs, and the Japan Society of Medical Electronics and Biological Engineering.

Shin-ichi Nitta was born in 1939. He received the M.D. and Ph.D. degrees in the medical field from Tohoku University, Sendai, Japan, in 1966 and 1970, respectively. He was involved in cardiac surgery, Tohoku University, School of Medicine from 1971 to 1979. He was a Research Fellow of Texas Heart Institute, Houston, TX, from 1976 to 1977. Since April 1980 he has been at Tohoku University, Sendai, Japan, where he is currently an Associate Professor of Medical Engineering and Cardiology. Dr. Nitta is a member of the American Society for Artificial Internal Organs, International Society for Artificial Organs and the Japanese Society of Thoracic and Cardiovascular Surgery, the Japanese Society for Artificial Organs, the Japan Society of Ultrasound in Medicine, and the Japan Society of Medical Electronics and Biological Engineering.