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ADVANCED RESEARCHES
Control Method of a Rotary Blood Pump for a Left Ventricular Assist Device
DOI: 10.17691/stm2016.8.1.04 Received May 5, 2015
D.S. Petukhov, PhD Student, Department of Biomedical Systems;
D.V. Telyshev, PhD, Senior Researcher, Department of Biomedical Systems;
S.V. Selishchev, DSc, Professor, Head of the Department of Biomedical Systems
National Research University of Electronic Technology — MIET, 1 Shokin Square, Zelenograd, Moscow, 124498, Russian Federation
The aim of the investigation is to develop a control method of a rotary blood pump (RBP) to solve the following problems: estimation of the pump flow rate, achievement and maintaining of the desired flow level through the continuous adjustment of pump speed and prevention of adverse effects on the cardiovascular system.
Results. Functional chart of RBP control consists of several units: a unit for evaluation of instantaneous pump flow rate, unit for estimation of approximate and actual pump flow rate and identification of pumping states, and unit for speed adjustment forming a new speed value of the desired flow rate and current pumping state. The core of the functional chart is RBP unit presented by a mathematical model of RBP.
Waveforms of pump flow and speed changes and indices for RBP state identification are given in the work. Hemodynamic curves (the flow rate through aortic valve and minimum volume of the left ventricle during a cardiac cycle) are used to evaluate accuracy of pumping states identification. The possibility to adjust pump flow in various physiological conditions (variation of the heart rate and left ventricular contractility) is demonstrated. Control of the pumping states allows to avoid adverse conditions in the cardiovascular system, and to estimate physiological changes in its work such as aortic valve closure.
Conclusion. The proposed control method of a RBP allows to achieve and maintain the desired pump flow rate under various physiological conditions. This method is supposed to be used in the development of control system for the left ventricular assist devices.
Key words: ventricular assist device; rotary blood pump; adaptive rotary blood pump control.
One of the main requirements to the circulatory support system is supplying of the adequate cardiac output. Generally, this requirement is realized with the help of control algorithms or methods for the implanted part of circulatory support system, i.e. rotary blood pump (RBP).
Method of control using pressure difference across the pump for calculation of the pulsatility index is suggested in the work [1]. Depending on the aims of control, a certain value of the gradient of pulsatility index with respect to pump speed is assigned, providing either a highest feasible flow or an average flow with a controlled opening of the aortic valve (AV) without any negative effect on the cardiovascular system. Wang et al. [2] have developed a control algorithm for preventing ventricular collapse by maintaining differential pump speed above user-defined threshold value and providing a sufficient flow by maintaining a reference pressure difference between the left ventricle (LV) and aorta. In the work [3] a method of establishing a balance between a cardiac output of the right ventricle and a combined flow rate of the LV and a pump is suggested. The value of pump flow pulsatility is used as feedback parameter in order to adjust the RBP flow.
The aim of the investigation is to develop a control method of a rotary blood pump to solve the following problems: estimation of the pump flow rate, achievement and maintaining of the desired flow rate through the continuous adjustment of the pump speed and prevention of adverse effects on the cardiovascular system.
Methods. Pump flow rate estimation is performed using mathematical model of RBP, which takes into account inertial and viscous properties of blood. Adverse effect on the cardiovascular system is prevented by controlling pumping states (backflow of blood through the pump PBF, partial assist of the ventricle with a periodically opening aortic valve PPA, full assist of the ventricle with a constantly closed aortic valve PFA, partial and full ventricular collapse during cardiac cycle PPVC and PFvc).
A functional chart of the proposed control method is presented on Figure 1. The main part of the functional chart is a RBP unit. The principal component of this unit is a mathematical model of the RBP, described by the following equation:
L^-=aQ+bQl+CQ1+da>2+eQa>2+f(f a+g-H,
For contacts: Dmitriy S. Petukhov, e-mail: dmitry.spetukhov@gmail.com
28 СТМ J 2016 — vol. 8, No.1 D.S. Petukhov, D.V. Telyshev, S.V. Selishchev
ADVANCED RESEARCHES
where L is the parameter, characterizing blood inertia in the given pump, which equals to 0.2 mm Hg-min2-L-1; Q is pump flow rate (L/min); © is pump speed (min-1); H is pressure difference across the pump (mm Hg); a-g are coefficients, obtained by optimization on the basis of Levenberg-Marquardt method (their values are given in Table 1), each coefficient being related to the blood viscosity j (cP) by the following linear relationship: y(j)=k-j+x.
Thus, the pump flow rate at a given time Q(t) is calculated on the basis of speed value ©, pressure difference H and blood viscosity j, which value is set on the external control console.
The estimation unit of the functional chart is designed for storing the calculated value of Q(t), evaluation of the approximate and actual flow rate and identification of RBP states. Approximate flow QA is counted as a blood volume, pumped over by the pump during the time equal to nine cardiac cycles (6.75 s at a heart rate (HR) 80 beats per minute (bpm)); the obtained value is converted in liters per minute. The number of cardiac cycles necessary for estimation of the approximate flow may be arbitrary; in our case it was chosen to be nine in order to approximately evaluate a minute pump flow and to adjust it quickly if physiological conditions change. The actual flow QP is a blood volume pumped over by the pump per minute.
Table 1
Coefficients of rotary blood pump model
a=a,+a2y
a^-6.2332 mm Hg-L-1 a2=-0.0254 mm Hg-L-ЧР"1
Figure 1. The functional chart of rotary blood pump (RBP) control
Table 2
Indices for identification of rotary blood pump states
b=b,+b2y
b1=0.5339 mm Hg-L-2 b2=-0.0239 mm HgL-2cP-
c=c,+c2y
c1=-0.1594 mm Hg-L-3 c2=-0.0147 mm Hg-L^cP"1
d=d,+d2y
d1=1.0778 mm Hgmin2 d2=0.0495 mm Hgmin2cP-1
e=e,+e2y
e1=-0.0788 mm Hg-min2-L-1 e2=-0.0133 mm Hg-min2L"1cP-
/Ц+/2У
/1=0.1568 mm Hg-min-L-2 /2=0.0263 mm Hg-min-L-2-cP-1
g=g^grv
^=-0.6583 mm Hg g2=-0.6671 mm Hg-cP"1
SRf
- 2-min
e dQL
*—■Г-/ в
d2Q dQ . d2Q dQ
dt2 Ф
dt2 Ф
dt2 ф
dt d\x
. . dQ dQ .1 dQ dQ . dQ dQ
-2 -min—— •—=-/ max---min
dt ф
dt ф
max
dQdQ dt dm
„ . dQ J dQ . dQ
-2-min—/ max—-min— dt \ dt dt
Pumping states are identified by the analysis of changes in the dynamics of derivatives, obtained from the pump mathematical model. To simplify the description of these changes some indices were introduced: e.g. SBF uses to identify backflow of blood through the pump, SAV for identification of partial and full assist of LV, SPVC and SFVC for partial and full collapse of the ventricle during cardiac cycle. A list of used indices and their values is given in Table 2. A detailed description of the RBP mathematical model and method of pumping states identification is presented in work [4].
A new speed value ©(f+1) is formed in the speed adjustment unit. It depends on the difference between the approximate and desired flow QD and on the current pumping state. If QA and QD do not correspond, the pump speed will change with an increment of 100 rpm until their matching is set. When some undesired pumping state is identified (PBF or PFVC), which adverse effects on the cardiovascular system, the speed is forcibly increased or decreased independently of the pump flow at this moment.
The development and testing of the RBP control method was carried out using the mathematical model of the cardiovascular system in which RBP was connected between LV and aorta [4]. All results were obtained at blood viscosity value j=3.6 cP.
Results and Discussion. A waveform of flow rate
S
AV
S
PVC
S
FVC
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QP and Qa (L/min), pump speed &p (rpm/1,000) and indices for identification of pumping states at desired flow rate Qd=4.5 L/min is presented in Figure 2. After estimation of the approximate flow QA it is compared with the desired QD and, if necessary, the RBP speed is changed; in this case the speed increases by 100 rpm every time.
Figure 2. A waveform of pump flow QP and QA (L/min), pump speed op (rpm/1,000) and indices SBF, SAV, SPVC and SFVC for Qq=4.5 L/min
As seen on the figure, the increase of RBP speed results in a certain dynamics of every index. Thus, partial assist of the ventricle PPA corresponds to the decrease of SBF index and increase of SAV, while partial ventricular collapse during a cardiac cycle corresponds to the decrease of SPVC and SFVC indices. Transitions from one state to another, which characterized by the changes in index dynamics, are pointed by color markers: a blue diamond-shaped marker on SBF(t) designates the moment of transition from PBF state to the state of partial LV unloading PPA. A red square marker on SAV(t) marks the moment of constant AV closure, which corresponds to the transition from partial assist state to the full assist state Pfa.
A red round marker on SPVC(t) corresponds to the transition in PPVC state, denoting a partial collapse of the ventricle during systole. A violet round marker on SFVC(t) corresponds to the transition in PFVC state, in this case the pump speed reduces by 500 rpm. As the desired flow level was not achieved, pump speed continues to increase.
A waveform of pump flow QP and QA (L/min), pump speed ap (rpm/1,000), flow through the aortic valve QAV (L/min), SAV index for the selected value Qd=3.8 L/min at LV contractility changes CLV (%) is shown on Figure 3. In this case the reduction of CLV by 10% does not alter the pump speed, which does not allow to detecting AV closure and transition to the PFA state. To trace the influence of such physiological changes, a differential index ASav was introduced, which is described by the following equation:
bSAV=(SAV[i]-SAr[i-l])-(SAV[i-l]-SAr[i-2]),
Figure 3. A waveform of pump flow QP and QA (L/min), pump speed ap (rpm/1,000), flow through the aortic valve QAV (L/min), SAV and ASav indices for Qd=3.8 L/min at left ventricle contractility changes CLV (%)
30 СТМ J 2016 — vol. 8, No.1 D.S. Petukhov, D.V. Telyshev, S.V. Selishchev
ADVANCED RESEARCHES
where i is the time step corresponded to estimation of current approximate flow QA; i-1 is the estimation of previous Qa value.
The increase of contractility by 10% is resulted in increase of pump speed due to the augmentation of AV flow, which is shown on QAV(t). The increase of SAV index with the consecutive increase of speed by 200 rpm corresponds to the partial assist pumping state PPA and AV opening, which is indicated by empty green square markers. At the same time, change of ASav is not considered — it is pointed by an empty black triangle marker on ASAV(t).
The next characteristic change of ASav is related to the reduction of LV contractility to the initial level. Such alteration simultaneously with the decrease of SAV index corresponds to the AV closure and transition to PFA state; it is pointed by a red triangular marker. Following decrease of speed by 100 rpm corresponds to the state of full assist state also due to the increase of SAV index at the decrease of the pump speed. However following reduction of the speed by 100 rpm and decrease of SAV index denotes the change in index dynamics and corresponds to the transition from the PFA state to the state of partial LV unloading (pointed by a green square marker).
The decrease of CLV by 10% does not lead to the speed change, therefore ASAV index is used to trace the effect of this physiological change on the pumping state. In this case the characteristic change of ASav from the negative to positive value at a decreased SAV corresponds to the constant AV closure and to the transition in PFA state; it is pointed by a red triangular marker.
The increase of contractility to the initial value results in increase of SAV and the characteristic change of ASav, which corresponds to the transition in partial assist state and pointed by a green triangular marker on SAV(t).
A waveform of pump flow QP and QA (L/min), pump speed ap (rpm/1000), flow through the aortic valve Qav (L/min), SAV and ASav indices for QD=3.8 L/min HR changes demonstrates, that decrease of HR to 70 bpm does not alter the pump speed (Figure 4). In this case ASAV index is also used to determine effect of physiological changes on the pumping state — its characteristic change in case of SAV decrease allows to detect AV closure (pointed by a red triangular marker).
Increase of SAV at a characteristic change of ASAV, which is the opposite of the previous one, corresponds to the transition in PPA state and AV opening (marked by a green triangle). With further HR changes pump speed at first increases and then reduces by 100 rpm. In the first case the speed increase is accompanied by the increase of SAV index, in the second one speed decrease results in the decrease of the index. Both of these changes corresponds to the PPA state and, therefore, are pointed by the empty square green markers.
A waveform of pump flow QP and QA (L/min), pump speed ap (rpm/1,000), minimum volume of LV during a cardiac cycle Vmm (ml) and SFVC and ASFVC indices for Qd=4.4 L/min at HR changes illustrates, that decrease of HR to 70 bpm leads to the increase of SFVC index (Figure 5). In spite of the fact that increase of SFVC with the increase of pump speed corresponds to the transition in PFVC state, this change is not associated with the transition to PFVC due to the characteristic change of
Figure 4. A waveform of pump flow QP and QA (L/min), pump speed mp (rpm/1,000), flow through the aortic valve QAV (L/min), SAV and ASav indices for QD=3.8 L/min at heart rate (HR) changes (bpm)
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Figure 5. A waveform of pump flow QP and QA (L/min), pump speed mp (rpm/1,000), minimum volume of left ventricle during a cardiac cycle VLV[mln] (ml) and SFVC and ASFVC indices for QD=4.4 L/min at heart rate (HR) changes (bpm)
ASfvc. The situation like this is pointed by empty violet markers over the whole time range (by the round markers on SFVC(t), and triangular markers on ASFVC(t)).
The increase of Sfvc with the increase of speed in other cases corresponds to the transition in full ventricular collapse (PFVC) state, i.e. to the decrease of volume lower reference value (120 ml), that corresponds to the zero pressure in the ventricle — in this situation pressure in the ventricular chamber during systolic phase is constantly negative. The moment of transition to this state is pointed by round violet markers on ASFVC(t), the pump speed also decreasing by 500 rpm.
It should be noted, that increase of HR to 100 bpm allows reaching the desired flow level without any LV collapse, which is seen at VLV[min](t).
Thus, the proposed control method of a RBP allows to achieve the desired flow rate under various physiological conditions by continuous adjustment of pump speed. The estimation of the RBP performance is carried out by means of the pump mathematical model, which uses values of blood viscosity, pressure difference across the pump and pump speed. The control of RBP states allows to avoid adverse states in the cardiovascular system associated with backflow of blood through the pump or full LV collapse. A long-term RBP operation in the full assist state (PFA) results in the valve leaflet fusion and thrombus formation, therefore assessment of the AV condition is also necessary [5].
The proposed control method has been tested
under changing LV contractility and HR. The results demonstrate feasibility of achievement and maintaining of RBP flow rate on the required level and control adverse states in the cardiovascular system under varying physiological conditions. Identification of RBP states is possible in all considered cases, including a case of constant pump speed.
Conclusion. The presented control method of a rotary blood pump provides the desired flow rate and prevents adverse effects on the cardiovascular system under different physiological conditions. This method is supposed to be used in the development of adaptive control system for the left ventricular assist devices.
Study Funding. The study was supported by the grant of the Russian Scientific Fund (project No.14-39-00044).
Conflicts of Interest. The authors declare no conflicts of interest related to this study.
References
1. Arndt A., NGsser P., Graichen K., Muller J., Lampe B. Physiological control of a rotary blood pump with selectable therapeutic options: control of pulsatility gradient. Artif Organs 2008; 32(10): 761-771, http://dx.doi.org/10.1111/j.1525-1594. 2008.00628.x.
2. Wang Y., Koenig S.C., Slaughter M.S., Giridharan G.A. Rotary blood pump control strategy for preventing left ventricular suction. ASAIO J 2015; 61(1): 21-30, http://dx.doi.org/10.1097/ MAT.0000000000000152.
32 СТМ J 2016 — vol. 8, No.1 D.S. Petukhov, D.V. Telyshev, S.V. Selishchev
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3. Bakouri M.A., Salamonsen R.F., Savkin A.V., AlOmari A.H., Lim E., Lovell N.H. A sliding mode-based starling-like controller for implantable rotary blood pumps. Artif Organs 2014; 38(7): 587-593, http://dx.doi.org/10.1111/aor. 12223.
4. Petukhov D.S., Telyshev D.V. Simulation of changes in
the dynamics of blood flow through the implantable axial flow pump. Meditsinskaya tekhnika 2014; 6: 44-47.
5. Granegger M., Schima H., Zimpfer D., Moscato F. Assessment of aortic valve opening during rotary blood pump support using pump signals. Artif Organs 2014; 38(4): 290-297, http://dx.doi.org/10.1111/aor.12167.
