Download Modeling and control of an implantable rotary blood pump for heart

2010 American Control Conference
Marriott Waterfront, Baltimore, MD, USA
June 30-July 02, 2010
ThB13.3
Modeling and control of an implantable rotary blood pump for
heart failure patients
Abdul-Hakeem H. AlOmari, Andrey V. Savkin, Peter J. Ayre, Einly Lim, and Nigel H. Lovell

Abstract—We propose a dynamical model for mean inlet
pressure estimation in an implantable rotary blood pump
(IRBP). Noninvasive measurements of pump impeller rotational
speed, motor power, and pulse width modulation signal (PWM)
to the motor controller were used as inputs to the model. Linear
regression between estimated and measured inlet pressure
resulted in a highly significant correlation (R2 = 0.9503) and
small mean absolute error (e = 2.31 mmHg). The proposed
model was also used to design a controller to regulate pump
inlet pressure using noninvasively measured pump rotational
speed and motor power. The control algorithm was tested using
both constant and square wave reference inputs. In the presence
of models uncertainties, the controller was able to track and
settle to the desired input within a finite number of sampling
periods with minimal error.
I. INTRODUCTION
H
EART failure is an abnormal health condition in which
the heart is unable to pump effectively and thus cannot
supply sufficient blood to cope with the body’s physiological
demands. The lack of donor organs for heart transplantation
has led to a range of treatment options for heart failure
patients. Implantable rotary blood pumps (IRBPs) are
emerging as a viable long-term treatment alternative for heart
failure patients. Small size and light weight are the most
important design aspects which make the third generation of
rotary blood pumps (RBPs) easily implanted inside the
patient’s body. This increases the potential for the patients to
leave the hospital and resume normal lives. The VentrAssist®
(Ventracor Limited, Sydney, NSW, Australia) left ventricular
assist device (LVAD) shown in Fig. 1 is a third generation
RBP. The pump is to be integrated with a cardiac assist
system primarily designed as a permanent option to heart
transplant. Fig. 2 shows a diagram of the LVAD connection
to the patient’s native heart and the controller.
Non-invasive control of an IRBP is one of the most vital
design goals in providing long-term alternative treatment for
congestive heart failure patients. Implantation of sensors is
not reliable as they result in thrombus formation and require
regular calibration due to measurement drifts which makes
Manuscript received September 22, 2009.
Abdul-Hakeem H. AlOmari and Andrey V. Savkin are with the School
of Electrical Engineering and Telecommunications, The University of New
South Wales (UNSW), Sydney, NSW 2052, Australia (phone: +61 (2) 9385
4918; fax: +61 (2) 9385 5993; (e-mail: [email protected]; a.
[email protected]).
Nigel H. Lovell, Einly Lim and Peter J. Ayre are with the Graduate
School of Biomedical Engineering, The University of New South Wales
(UNSW), Sydney, NSW 2052, Australia (e-mail: [email protected];
[email protected]; [email protected]).
978-1-4244-7425-7/10/$26.00 ©2010 AACC
long-term implantation of such devices problematic.
Previously, we developed stable dynamical models to
noninvasively estimate the pulsatile flow and differential
pressure in a rotary blood pump [1]. The proposed models
were successfully used to design control algorithms for
continuous and pulsatile flow [2]. Non-invasive
measurements of pump rotational speed, power, noninvasively estimated flow, and differential pressure were
used as inputs to the controller. The control algorithm was
evaluated using a lumped-parameter model of the
cardiovascular system (CVS) previously designed and
verified in our laboratory [3]. In the presence of model
uncertainty, our results showed that the pulsatile flow
controller was able to track the reference inputs with minimal
error, finite number of sampling periods and minimum
steady-state error.
Fig. 1. VentrAssist® as an example of a third generation IRBP (Ventracor
Limited, Sydney, NSW, Australia).
The existing most popular control strategies of IRBPs are
the pump differential pressure control [4, 5], pulsatility
control [6-11], and target speed control [12, 13]. Choi et al.
[8] developed a fuzzy logic controller for an axial blood
pump based on the blood flow pulsatility which was
estimated using a validated pump model. Using unrealistic
assumptions which included no heart valves, continuous flow
throughout the circulatory system, and linear correlation
between pump differential pressure, voltage, current, and
rotational speed, Waters et al. [13] developed a proportionalintegral (PI) controller to adjust the motor speed and
maintain the system reference differential pressure when
changes occurred in the natural heart. Zhou et al. [14] used a
nonlinear static model of the pump to model the
hemodynamic responses of the assisted circulatory system as
a function of different constant speeds of the pump and
concluded that the developed integrated circulatory system
ventricular assisted device (VAD) model could be used to
develop different VAD control algorithms.
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Others [15] have used a model-based estimation method to
estimate the differential pressure across the pump which was
used as an input to a control system of the IRBP. Using a
state-space model of the circulatory system together with
measurements of pump differential pressure, Wu et al. [16]
developed their control algorithms to control the aortic
pressure. On the other hand, Bullister et al. [17] have
designed hierarchical control algorithms to control the speed
of the pump based on feedback from pressure sensors
measuring pump inlet and outlet pressures.
stroke volume depends on left ventricle end diastolic volume
(Frank-Starling mechanism). Therefore, one design
requirement of an IRBP is to simulate the Frank-Starling
law. In patients with a left ventricle assisted by an IRBP,
when the volume in left ventricle is low, inlet pressure will
automatically decrease. This may cause suction if the same
target speed was maintained. By applying inlet pressure
control, target speed will be reduced to increase the inlet
pressure to avoid suction. This shows one example that
makes the problem of non-invasive estimation and control of
inlet pressure during the diastolic period of considerable
benefit. The primary objective of the proposed deadbeat
controller is to avoid undesired pumping states such as
suction by regulating the inlet pressure within a predefined
physiologically reasonable limit.
II. MATERIALS AND METHODS
Fig. 2. Illustration of how VentrAssist® is implanted and connected. As
shown, a short inflow cannula is attached to left ventricle. The outflow
cannula returns the blood to the ascending aorta and the percutaneous lead
connects the IRBP to the external controller and batteries (Ventracor
Limited, Sydney, NSW, Australia).
One limitation of the majority of the previously designed
control algorithms was that the estimation of differential
pressure and flow were performed using steady state models
without data relating to the transient response of the pump.
Furthermore, they required the implantation of additional
sensors to provide measurements of parameters used as
inputs to their corresponding control algorithms.
For the first time, in the present study, we used noninvasive measurements of rotational pump speed, motor
power, together with the pulse width modulation (PWM)
signal as inputs to a new dynamical autoregressive with
exogenous inputs (ARX) model to estimate average inlet
pressure during the diastolic period. The resulting model is
stable and simple, thus offering a tractable control design
problem. The average inlet pressure estimation model was
validated using in vivo animal data obtained from acute
implantation of a VentrAssist® (Ventracor Limited, Sydney,
Australia) LVAD in dogs under heart failure conditions.
Also, the model developed herein was used to design a
deadbeat controller that non-invasively controls and
regulates the inlet pressure of the pump.
In the VentrAssist®, during ventricular collapse state, the
inlet pressure during the diastolic period may be as low as 160 mmHg, and varies between + 10 mmHg during normal
pump operation. During diastole, the inlet pressure and left
ventricular end diastolic pressure (preload to the left
ventricle) are closely related. In normal human hearts, the
A. In vivo acute dog experiments
The VentrAssist® centrifugal heart pump was acutely
implanted in four healthy dogs. In each dog, the inflow pump
cannula was inserted into the apex of the left ventricle while
the outflow cannula was anastomosed to the ascending aorta
as shown in Fig. 3. The dogs were instrumented with
indwelling catheters (DwellCath, Tuta Labs, Lane Cave,
NSW, Australia) to measure the left ventricular (LVP), left
atrial (LAP), aortic (AoP), pulmonary arterial (PAP) , central
venous (CVP), pump inlet (Pin) and outlet pressures (Pout).
Pump (Qp) and aortic valve (Qao) flows were measured by
ultrasonic flow probes (Transonic Systems Inc., Ithaca, NY,
USA). Qp, Pin, and Pout were obtained near the inlet and
outlet of the pump. Furthermore, the instantaneous pump
impeller rotational speed (), motor current (I), supply
voltage (V), and pulse-width modulation signal (PWM) were
continuously monitored from the pump controller and
recorded for further analysis. All the aforementioned signals
were recorded using a Powerlab data acquisition system
(ADInstruments, Castle Hill, NSW, Australia).
To mimic acute heart failure conditions and reduce the
cardiac contractility, the beta blocker metoprolol was
administrated until the total cardiac output fell to
approximately 50% of its baseline. Responses to three
different blood volume levels: low, medium, and high, were
studied by varying the rate of the cardiotomy suction
machine. For each volume level, each dog underwent several
speed ramp tests in which impeller speed was increased from
1250 rpm to 3000 rpm in a stepwise increment of 100 rpm
with each step lasting for 30 seconds. Blood samples were
taken regularly during the experiments for measurements of
the hematocrit (HCT) values. The sampling rate was set at 4
kHz for data recordings, but, in further analysis, the data
were down-sampled to 50 Hz.
B. Dynamical modeling
In another study performed by our research group [1], we
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developed stable dynamical models for pulsatile flow and
differential pressure estimation in an IRBP. The main
requirement for the pulsatile flow model was that any steadystate solution of the model can be described by a previously
designed and verified static model. Also, any steady-state
solution for the dynamical model should be stable. Both
models were validated and verified using data obtained from
ex vivo pig experiments and pulsatile mock loop. To
summarize, a non-invasive, steady-state average flow (Qss)
estimator was designed in a non-pulsatile environment for
the IRBP. The estimator was based on the input power (P)
and rotational speed ().
u1 (kh)  P(kh), (5)
u2 (kh)  (kh) , (6)
u3 (kh)  f (kh), (7)
u4 (kh)  PWM (kh) f (kh). (8)
Here, P(kh) is the motor power, (kh) is the rotational speed,
f(kh) is the steady-state average flow estimator, and
PWM(kh) is the pulse-width modulation signal. The block
diagram of the system with an ARX model is illustrated in
Fig. 4. All input signals were averaged during the diastolic
period shown in Fig. 5.
ARX
P(kh)
f (kh)
g ( P(kh), (kh))
(kh)
yest (kh)
Model

PWM (kh)
Fig. 4. Input/ output block diagram for the dynamical system model used to
estimate the mean inlet pressure (yest(kh)) using as inputs the non-invasive
measurements of mean rotational speed, mean power, and mean PWM
signal during diastolic period.
120
The static equation for the flow estimator is based on the
work of Malagutti et al. [18] and Ayre et al. [19] and is of
the following form:
Qss  a1  a 2 P  a3 P 2  a 4 P 3  a5  a 6 2 , (1)
where P = VI is the product of supply voltage (V) and motor
current (I), and a1-a6 are functions of viscosity levels [18].
We introduced a variable f(kh) as follows [1]:
f (kh)  g ( P(kh), (kh)), (2)
where
g ( P(kh),  (kh))  a1  a 2 P(kh)  a3 P 2 (kh)
 a 4 P 3 (kh)  a5( kh)  a6 2 (kh).
(3)
Here, h > 0 is the sampling interval equals to 0.02s, P(kh) =
V(kh)I(kh) is the product of supply voltage (V(kh)) and motor
current (I(kh)), and (kh) is the pump rotational speed. Now,
we introduce a multi-input dynamical ARX model of the
form:
n
4
m
y est ( kh)   bi y est ([k  i ]h )   cij u j ([k  i  1]h ) (4)
i 1
j 1 i 1
 e1 ( kh),
where yest(kh) is the output of the system which represents
the estimated mean inlet pressure during the diastolic phase
of the cardiac cycle, n is the model output order, m is the
model inputs order, bi and cij are the output and input
parameters of the model respectively, e1(kh) represents the
model error, and uj(kh) are four exogenous inputs defined as
follows:
Inlet Pressure (mmHg)
Fig. 3. Schematic diagram showing the LVAD connected to the native
heart. The inlet cannula was inserted into the left ventricle and the outlet
cannula was connected to the aorta. Arrows show the flow direction.
100
80
60
T
Dias
T
Dias
T
Dias
T
Dias
T
Dias
40
20
0
2.73
2.74
2.75
Time (Samples)
2.76
2.77
4
x 10
Fig. 5. Example of extracted diastolic period (TDias) where “x” and “o”
represent the starting and the end of TDias respectively. Average values for
all signals were calculated during the diastolic period.
C. System identification and data analysis
Inlet pressure (Pin), motor power (P), rotational speed (),
PWM, and f signals obtained from each animal data were
averaged during the diastolic phase (T Dias) of the heart.
Average values of all signals were stored for further analysis
and system identification. Data were divided into two sets:
one set was used for system identification while another set
was used to validate the model. The first set of data consisted
of one animal experiment corresponding to the three blood
volume levels changes: low, medium, and high, while the
other set contained data from the other three dog
experiments. The transient response of the pump inlet
pressure was identified and validated using data obtained
during changes in the pump target speed.
In the system identification process, an off-line least
squares method [20] was used to estimate the parameter
coefficients of the mean inlet pressure estimation model.
Values of parameter coefficients of the inlet pressure
estimation model described in (4) were chosen to minimize
the error between estimated (yest(k)) and measured (ymeas(k))
mean inlet pressure.
The output model order (n) together with the model inputs
orders (m) were chosen across a range of 1 to 10. The delay
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value was determined by estimating the impulse response of
the system using cross-correlation analysis between the
inputs and output signals. The mean absolute error (e) and
correlation coefficient (R) between yest(kh) and ymeas(kh) were
used to evaluate the accuracy of the estimation models.
Values of e and R were evaluated as follows:
1 N
e
 ( ymeas (kh)  yest (kh)) 2 , (9)
N i 1
N
R
( y
i 1
meas
( kh)  y meas )( y est ( kh)  y est )
N
N
i 1
i 1
(  ( y meas ( kh)  y meas ) 2  ( y est ( kh)  y est ) 2 )1 / 2
Here, N is the length of data.
.
(10)
y est and ymeas are the mean
values of the estimated and measured signal respectively. To
reduce the contributions of external sources in the
identification process of the system, all sets of data were
explicitly pre-treated to remove trends and offsets by direct
subtraction. All simulations and algorithms were performed
in MATLAB R2007b® (The Mathworks, Inc., Natick, MA,
USA).
D. Control algorithm
In order to design a control algorithm for mean inlet
pressure in an IRBP, two new ARX models were developed
in the present study. The first one describes the relationship
between the control input signal, i.e. the PWM signal u(.)),
the steady-state pump flow (f(.)), pump rotational speed
((.)), mean inlet pressure (Pin(.)), and motor power (P(.))
during the diastolic period. The resulting system model is
described by the following difference equation:
chosen so that the mean absolute error (e), obtained from (9),
between the estimated and measured values were minimized
with high correlation coefficient (R). In the control algorithm
represented in this paper, models described in equation (11)
and (12) were used to estimate the mean pump power (P(kh))
and mean pump rotational speed (kh) respectively.
The high variability in the preload and afterload
encountered by patients during their daily activities place a
restriction on the control design problem for an IRBP as it is
required that the controller should react fast to these changes
in order to avoid undesired pumping states such as
ventricular collapse. In order to track the desired input signal
within minimum possible sampling periods and minimum
steady-state error, we derived our control input, u(.) based on
(4), as follows:
u( kh) 
1
(l2 P ( kh)  l3 P ([k  1]h )  l4 P ([k  2]h )
l1 f ( kh)
 l5  ( kh)  l6  ([k  1]h )
 l7  ([k  2]h )  l8 f ( kh)  l9 f ([k  1]h )
 l10 f ([k  2]h )  l11u ([k  1]h ) f ([k  1]h )
 l12u([k  2]h ) f ([k  2]h )  r ([k  2]h )), (13)
Where r(kh) is the desired input signal, l1- l12 are constants
with values of 0.000665, 0.926, 0.4683, 0.462, 0.1517,
0.3625, 0.2097, 0.1096, 0.5384, 0.4774, 0.01216, and
0.00987 respectively.
In all simulations, we added uniformly distributed noise to
model error terms, e1- e3, in equations (4), (11), and (12)
respectively to represent model uncertainty.
III. RESULTS
P( kh)  d1u([k  1]h )  d 2 u([k  2]h )  d 3 ([k  1]h )
 d 4 ([k  2]h )  d 5 f ([k  1]h )  d 6 f ([k  2]h )
 d 7 Pin ([k  1]h )  d 8 Pin ([k  2]h )  d 9 P([k  1]h )
 d10P([k  2]h )  d11P([k  3]h )  e2 ( kh).(11)
Here, d1, d2, d3, d4, d5, d6, d7, d8, d9, d10, and d11 are constants
with values of 0.107, 0.0925, 0.0006232, 0.00044, 0.0365,
0.02183, 0.00306, 0.00202, 1.369, 0.6751, and 0.283
respectively and e2(kh) is the model error. Also, the second
ARX model relates u(.), f(.),  (.), Pin(.), and P(.). The
resulting model is as follows:
The performance of the model for mean inlet pressure
estimation given in equation (4) was evaluated based on the
mean absolute error e, equation (9), and correlation
coefficient R, equation (10), for different combinations of
model inputs orders m and model output order n. System
model orders of n = 3, m = 3, and delay value = 2 gave the
best results, i.e. with the minimal e and highest R value
between the estimated and measured inlet pressure. The
resulting system model is described by the following
difference equation:
4
m
n
yest ( kh)   cij u j ([k  i  1]h )   bi yest ([k  i ]h )
 ( kh)  g1u([k  3]h )  g 2 u([k  4]h )  g 3 P([k  3]h )
j 1 i 1
 g 4 P([k  4]h )  g 5 f ([k  3]h )  g 6 f ([k  4]h )
 g 7 Pin ([k  3]h )  g8 Pin ([k  4]h )  g 9 ([k  3]h )
 g10 ([k  4]h )  e3 ( kh), (12)
where g1 - g10 are constants with values of 2.865, 3.026,
20.74, 26.66, 12.89, 8.616, 1.182, 1.21, 1.593, and 0.7055
respectively, and e3(kh) is the model error. Parameter
coefficients, orders, and time delays for models (11) and (12)
were obtained using the system identification procedure
described in subsection C. Orders and parameters were
i 1
 e1 (kh).(14)
Here, b1= -1.119, b2= 0.5803, b3= -0.4472, c11= -0.926, c12=
-0.51517, c13= 0.1096, c14= -0.000665, c21= 0.4683, c22=
0.3625, c23= 0.5384, c24= -0.01216, c31= 0.462, c32= -0.2097,
c33= -0.4774, c34= 0.00987, and uj represents the four
exogenous inputs described previously in equations (5) – (8).
The dashed line in Fig. 6 shows the estimated and measured
mean inlet pressures. Note that the model was able to
accurately track the changes in mean inlet pressure with
3577
25
12
Measured P
in
20
Inlet Pressure (mmHg)
of inlet pressure. The resulting output is plotted against the
desired reference input and shown in Fig. 10. It was shown
that the simulated inlet pressure accurately tracked the
reference input signal within an error of + 0.92 mmHg.
Estimated pump power (Watt)
stable transient response at each volume change. Linear
regression analysis between measured and estimated mean
inlet pressure obtained from three dog experiments is
illustrated in Fig. 7. The analysis resulted in a high R2 =
0.9503 between the estimated and measured with small e =
2.31 mmHg. Also, the mean slope of the linear regression
line was very close to unity (1.174) with offset value of
0.9605. Linear regression analysis between estimated and
measured pump power resulted in a high R2 = 0.969 with
small e = 0.451 W. The mean slope of the linear regression
line is also close to unity (0.9439) (Fig. 8).
P
10
8
est
2
= 0.9439 * P
meas
6
4
2
0
0
Estimated P
2
4
6
Measured pump power (Watt)
in
15
+0.658
R = 0.969
e = 0.451
8
10
Fig. 8. Linear regression plot between estimated versus measured pump
power obtained from animal data (N = 3).
10
Estimated rotational speed (rpm)
5
0
-5
-10
0
500
1000
1500
2000
2500
Time (s)
3000
3500
4000
Fig. 6. Estimated mean inlet pressure compared with the measured pressure
obtained in one animal experiment where target rotational speed was varied
from  = 1250 to 3000 rpm in each period of blood volume changes. In this
dog, blood volume was changed from low to medium at t = 970s, then to
high at ts. The solid line shows the measured extracted mean inlet
pressure, while the dashed line shows the estimated mean inlet pressure.
Estimated Inlet Pressure (mmHg)
30
Pin est = 1.174 *Pin meas+0.9605
25 R2 = 0.9503
e = 2.31 mmHg
20
15
10
5
0
-5
-5
0
5
10
15
Measured Inlet Pressure (mmHg)
20
25
Fig. 7. Linear regression plot between estimated versus measured inlet
pressure obtained from animal data (N = 3).
A square wave signal was used as the desired input signal,
r(kh), to the control algorithm to mimic the variability nature
w
est
2
= 0.9914 * w
meas
+ 26.39
3000 R = 0.975
e = 14.79 rpm
2500
2000
1500
1500
2000
2500
3000
Measured rotational speed (rpm)
3500
Fig. 9. Linear regression plot between estimated versus measured pump
rotational speed obtained from animal data (N = 3).
20
r
P
in
10
0
in
P / r (mmHg)
The proposed pump rotational speed estimation model,
represented by equation (12), was accurately able to track
target speed changes. Furthermore, linear regression analysis
between estimated and measured pump rotational speeds
resulted in a high R2 = 0.975 and small e = 14.79 rpm. The
slope of the regression line was very close to unity (0.9914)
with an offset value of 26.39 rpm (Fig. 9). In this study, the
models developed for estimation of mean inlet pressure
(shown in equations (14)), mean pump power (11), and mean
pump rotational speed (12) together with control signal (11)
were used to design a control algorithm to control mean inlet
pressure. In practical situations, pump speed and power are
measured, not estimated. In this study, we used estimated
pump values in order to complete the controller design.
3500
-10
-20
0
0.5
1
1.5
2
2.5
Time (s)
3
3.5
4
4.5
Fig. 10. Reference input (r) versus inlet pressure (Pin).
IV. DISCUSSION
The problem of non-invasive estimation and control of
inlet pressure in an IRBP has not been frequently studied.
This may be due to the highly variable nature of the inlet
pressure, especially during abnormal pumping states of the
pump such as ventricular collapse. In the present study, a
dynamical model for mean inlet pressure estimation during
the diastolic period was successfully designed and verified.
Also, the model was used to design a controller for the
control of mean inlet pressure during diastolic period. The
inlet pressure estimation model used as inputs the noninvasive measurements of pump motor power (P), rotational
speed (), steady-state flow (f), and the pulse-width
modulation signal.
One limitation of the current study is that in a
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VentrAssist® LVAD, the power coefficient values used in the
static flow estimator equation as well as our estimation
models were highly affected by the HCT values. This
required routine measurement of the HCT during the
experiment and adjustment of the model as described in [18].
Previously, Bullister et al. [17], developed a control
algorithm for pump speed using the pump inlet and output
pressures measured using pressure sensors as inputs. In their
study, while they were able to build a stable pressure-based
controller using pressure sensors on a standard mock-loop,
they required the use of these invasive additional sensors.
Giridharan et. al. [21] designed a control system which was
able to maintain the average pressure difference between the
left ventricle and the aorta at a desired reference differential
pressure. Although they were able to show that maintaining a
reference differential pressure between the left ventricle and
aorta leads to adequate blood supply for different pathologic
and physical activity situations, their proposed approach
required the implantation of two pressure sensors.
In comparison with the aforementioned studies, the
present paper proposed an inlet pressure estimation and
controller using non-invasive measurements of pump power
and rotational speed.
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
V. CONCLUSIONS
A stable and novel dynamical model was proposed for
mean inlet pressure estimation during diastolic period in an
IRBP. In the proposed model, non-invasive measurements of
motor power and impeller rotational speed were used as
inputs. Furthermore, in this paper, we developed a noninvasive controller that controls the mean inlet pressure
during the diastolic period. The performance of the
controller was tested in the presence of model uncertainty.
Simulation results showed that the controller was able to
track the reference input with minimal error and minimum
sampling periods. The model will help in the design of
robust control algorithm that control the operation of IRBP,
detect and avoid undesired abnormal pumping states.
[14]
[15]
[16]
[17]
[18]
ACKNOWLEDGMENT
This work was supported in part by the Australian
Research Council.
[19]
REFERENCES
[20]
[1]
[2]
[3]
[4]
A. H. AlOmari, A. V. Savkin, D. M. Karantonis, E. Lim, and N. H.
Lovell, “Non-invasive estimation of pulsatile flow and differential
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