Conference of the IEEE EMBS
Cité Internationale, Lyon, France
August 23-26, 2007.
Abstract—A noninvasive approach to the task of pulsatile
flow estimation in an implantable rotary blood pump (iRBP)
has been proposed. Employing six fluid solutions representing a
range of viscosities equivalent to 20-50% blood hematocrit
(HCT), pulsatile flow data was acquired from an in vitro mock
circulatory loop. The entire operating range of the pump was
examined, including flows from -2 to 12 L/min. Taking the
pump feedback signals of speed and power, together with the
HCT level, as input parameters, several flow estimate models
were developed via system identification methods. Three
autoregressive with exogenous input (ARX) model structures
were evaluated: structures I and II used the input parameters
directly; structure II incorporated additional terms for HCT;
and the third structure employed as input a non-pulsatile flow
estimate equation. Optimal model orders were determined, and
the associated models yielded minimum mean flow errors of
5.49% and 0.258 L/min for structure II, and 5.77% and 0.270
L/min for structure III, when validated on unseen data. The
models developed in this study present a practical method of
accurately estimating iRBP flow in a pulsatile environment.
MPLANTABLE rotary blood pumps (iRBPs) are emerging
as a viable long-term treatment option for end-stage heart
failure patients. Indeed the so-called third generation iRBPs
are proving their worth as both bridge-to-transplant and
destination therapy devices . Developing an effective pump
control method, in which blood flow actively responds to
meet physiological demand, remains a vital objective for the
operation of such devices.
Estimating the blood flow rate through an iRBP is essential
if a pump control strategy based on flow is to be implemented.
While some groups  have incorporated an implanted flow
sensor into their left ventricular assist devices (LVADs), a
noninvasive approach for flow estimation is desirable.
Employing the feedback signals of pump impeller speed and
motor current (or power), as well as information regarding the
hematocrit (HCT) level (or viscosity) of the implant recipient,
it has been demonstrated [9-16] that an estimate of flow rate
under non-pulsatile or steady-flow conditions may be attained.
In a pulsatile environment however, the effects of impeller
inertia, speed control mechanisms, native heart interaction and
other fluid dynamic behavior must be considered. The aim of
the present study is the realization of a noninvasive estimate
of pulsatile pump flow that is accurate across a range of fluid
D.M. Karantonis (email: email@example.com), S.L. Cloherty
and N.H. Lovell are with the Graduate School of Biomedical Engineering,
University of New South Wales, Sydney NSW 2052, Australia. N.H. Lovell
is also with National Information and Communications Technology
Australia (NICTA), Eveleigh NSW 1308, Australia. D. G. Mason is with
the Dept Surgery, Monash University, Melbourne, Australia. P.J. Ayre is
with Ventracor Limited, Chatswood NSW 2067, Australia. This work was
supported in part by an Australian Research Council Linkage Grant.
viscosities, and is based on pump feedback signals and a value
for fluid viscosity. Information about the system, available to
such an estimation algorithm, is highly constrained; for
example, the magnitude of native cardiac contractions and the
flow resistance encountered by the pump are unknown. Thus,
rather than attempting to derive a flow estimate from a
theoretical pump model, the more empirical approach of
system identification was favored. In this paper we describe a
pulsatile flow rate estimation algorithm based on an
autoregressive with exogenous input (ARX) model and
measurements of pump speed, power and HCT obtained in a
mock circulatory loop.
A. Mock Loop Experiments
A series of laboratory experiments were conducted with the
VentrAssist™ (Ventracor Limited, Sydney, NSW, Australia)
LVAD – a centrifugal iRBP – in a pulsatile mock circulatory
loop (Fig. 1). The mock loop consisted of: a venous reservoir
tank; an arterial reservoir tank; a silicone bag representing the
left ventricle; the VentrAssist™ LVAD; and appropriate
tubing inter-connections. Each compartment was designed to
adhere to the appropriate physiological values (Table 1),
ensuring that a valid simulation of the human cardiovascular
system was performed.
Simulation of ventricular contraction was achieved by
Noninvasive Pulsatile Flow Estimation for an Implantable Rotary
Dean M. Karantonis, Graduate Student Member, IEEE, Shaun L. Cloherty, Member, IEEE, David G. Mason,
Peter J. Ayre, Member, IEEE, Nigel H. Lovell, Senior Member, IEEE
Fig. 1. Schematic diagram of the mock circulatory loop employed in this
study. The diamonds indicate the location of each pressure transducer: (1)
pump inlet; (2) pump outlet; (3) arterial pressure; and, (4) central venous
Proceedings of the 29th Annual International
1-4244-0788-5/07/$20.00 ©2007 IEEE1018
periodically compressing the mock ventricle with pneumatic
pistons mounted on adjustable stages. Both the in-stroke and
out-stroke periods, as well as the stroke length of the pistons,
could be independently set to predefined values, thus
approximating the desired heart rate and cardiac contractile
strength. Furthermore, the ventricle wall was open to air,
allowing passive filling to occur.
The mock loop was instrumented to measure: arterial (AP),
central venous (CVP), pump inlet (Pin) and pump outlet (Pout)
pressures using pressure transducers (ADInstruments, Castle
Hill, NSW, Australia); and, pump flow (Qp) by means of an
ultrasonic flow probe (Transonics Systems Inc., Ithaca, NY,
USA). The noninvasive pump feedback signals of
instantaneous pump impeller speed, motor current and supply
voltage were monitored from the pump controller, filtered
appropriately and also recorded for analysis. A Powerlab data
acquisition system (ADInstruments) was employed to record
all the aforementioned signals, with all pressure signals pre-
conditioned using a Quad Bridge amplifier (ADInstruments).
Six experiments were performed, each with an aqueous
glycerol solution of different viscosity used to simulate
human blood (2.05-3.56 mPas). The range of viscosities was
chosen to coincide roughly with a blood haematocrit (HCT)
range of 20-50%, based don previous experiments by the
authors. For each test fluid, a series of speed ramp tests was
conducted, whereby the target pump speed setting was
varied between 1800-3000 rpm (in step increments of 100
rpm, with each speed setting lasting 30 s) at several systemic
resistance settings, providing a range of flow rates from -2 to
12 L/min. The level of contractility introduced via mock
ventricle compression was also varied from no pulsatility to
high pulsatility (at which the pump flow amplitude reached a
maximum of 3 L/min) for all operating points, with a fixed
heart rate of 72 bpm. The aortic valve was closed for all
tests, consistent with clinical observations of implant
recipients. The sampling rate was 4kHz for data acquisition,
however subsequent analysis dealt with data at 50Hz.
B. System Identification Methods
In approaching the problem of accurately estimating pump
flow in a pulsatile environment, a number of system
identification methods were examined. This methodology was
chosen due to its ability to describe, in terms of an appropriate
transfer function, discrete time-series data where the input(s)
sufficiently describe the target output. The only inputs
available are the noninvasive feedback signals of pump speed
and power. It is also assumed that the patient’s HCT level is
known (within a range of 5%).
There are a number of potential model structures that may
be chosen, such as the ARX, output error (OE) or Box-Jenkins
(BJ) types. Each of these treats the system dynamics and the
disturbance dynamics in a different manner. Due to the
excellent signal-to-noise ratio of our system, and the tight
coupling between inputs and external disturbances, the ARX
model structure was employed for this study. The generic
form of an ARX model may be described by the difference
a y t ib u tN
where: y(t) = (vector of) output signal(s)
u(t) = (vector of) input signal(s)
Na = output order = number of poles
Nb = input order = number of zeroes
Nk = input delay (samples)
Flow rate in the VentrAssist™ pump may be described, for
the non-pulsatile case, by the polynomial relationship in (2)
Qa b VIc VId VI
=+ ⋅ + ⋅+ ⋅
where: Q = pump flow (L/min)
VI = pump power (W)
N = pump speed (rpm)
Thus, the initial approach involved developing separate
models based on the data for each experiment (i.e., for each
solution), according to the inputs of (2) and as depicted in Fig.
2a. The relationship between each of the ARX model
coefficients and HCT was examined to determine whether a
single model incorporating HCT as an input could be
ascertained. However, unlike the four-dimensional non-
pulsatile flow equation described in  which contained
HCT as an input, no such useful relationship could be
identified in the presence of pulsatile flow.
Since this first approach proved ineffective, a second
structure which incorporated HCT directly was conceived and
evaluated (Fig. 2b). In this case, the model assumes that each
input term (VI, VI2, VI3 and N) is linearly related with HCT.
A third model structure based on a non-pulsatile flow
estimate equation developed previously in our laboratory 
was also tested (Fig. 2c). In this case a static flow model is
applied to dynamic (or pulsatile) data, via an ARX model. The
advantage here is that the role of viscosity has already been
accounted for, and with far fewer inputs than Structure II,
computational complexity is reduced.
C. Treatment of Data
The corpus of available data was divided into two pools:
the first contained data from three experiments employing
−=− − +
TABLE I. COMPARISON OF VARIOUS PHYSIOLOGICAL PARAMETERS
OCCURRING IN HEART FAILURE PATIENTS WITH THOSE EMPLOYED IN THE
MOCK CIRCULATORY LOOP. (VALUES ARE MEAN ± SD; DSC=DYNE.SEC.CM-5)
Parameter Human Mock Loop
1.38 ± 0.51  0.91-1.25
62.2 +/- 28.1 
2085 ± 560 ,
20  20
* The mean circulatory pressure refers to the pressure within the mock loop
compartments when the system is idle, and required for providing the initial
preload (central venous) pressure.
solutions of viscosity 2.05, 2.66, 3.26 mPas, while the second
pool contained data from the remaining three experiments
(2.35, 2.96, 3.56 mPas). The pools acted as a
training/validation pair, with a number of models being
trained using one pool while the other pool was used to
validate those models. Changes in pump target speed were
included in the data, in order to ensure the transient response
of the pump controller could also be identified.
For each model structure described, the model orders and
delays were optimized: the number of poles (Na) was varied
between 0 and 8; the number of zeroes (Nb) was varied
between 1 and 8; and the delay term (Nk) was determined via
cross-correlation of the input and output signals, with a value
of 2 used for all models. The modeling task was performed
using the MATLAB System Identification Toolbox (The
Mathworks, Inc., Natick, MA, USA).
The central performance measure used in the data analysis
was the normalized mean flow error (Qerr_norm) (3), while the
absolute mean flow error (Qerr_abs) (4) provided an additional
indicator of accuracy.
[ /min][ ]
where: Qest = estimated pump flow (L/min)
Qmeas = measured pump flow (L/min)
When calculating Qerr_norm, flows less than 1 L/min were
excluded in order to avoid the skew produced when
normalizing errors for flows close to zero.
Results attained for Structure II (Fig. 2b) demonstrated a
wide range of accuracy, depending on the selection of model
orders. In general, orders of Na = 0 and Nb = 4-6 provided the
smallest Qerr_norm and Qerr_abs (see Table II), with minimum
values of 5.49% and 0.258 L/min respectively. Thus, the
models purely dependent on previous inputs provided the best
For the third approach, using the non-pulsatile flow
estimate as an input to the ARX model, the best performance
was also obtained with Na = 0 and Nb = 4-6 (see Table II). For
example, a Qerr_norm of 5.77% and Qerr_abs of 0.270 L/min was
achieved for Na = 0 and Nb = 5.
In comparing approaches II and III, the results reveal that
slightly superior performance was attained for the structure II.
A visual comparison between these approaches is depicted in
Fig. 3, for Na = 0 and Nb = 4. As shown, there is a high level
of agreement between the simulated and measured flows,
including the ability to accurately track the step change in
target pump speed at time 3.7 s.
A limited number of research groups have addressed the
problem of pulsatile flow estimation. Tsukiya et. al. 
developed a non-pulsatile flow estimate equation and applied
it to pulsatile data, with a mean flow rate error “almost within
1 L/min”. The team headed by Tohoku University described
the development of a pulsatile flow estimator (in a mock
circulatory loop) via ARX modeling . When incorporating
a second ARX model to account for HCT variation, a mean
error of 1.66 L/min was obtained, with a correlation
coefficient (r) of 0.85 between estimates and measured flows.
For comparison, the current models resulted in an r value of
0.9926 (when using model II with Na = 0 and Nb = 6). In light
of these earlier results, the present study appears to have
produced a highly accurate flow estimation model. Perhaps
the only limitation of the approach presented above is the need
for information regarding the HCT value. Further research
into estimating this value online is being conducted.
Abnormal flow conditions, such as ventricular suction,
pump inlet obstruction and regurgitant flow, met varied
outcomes with the models tested. The relatively sharp
downward flow peaks associated with suction or inlet
obstruction were estimated to a high level of accuracy (not
shown). Regurgitant (or negative) pump flows did not fair as
well, with the flow estimates unable to follow the measured
flow into the negative region beyond -0.5 L/min. This is due
(a) Model Structure I
(b) Model Structure II
(c) Model Structure III
Fig. 2. Block representations of the structures used for each of the ARX
models evaluated. Qp = measured pump flow; Qp_np_est = non-pulsatile
pump flow estimate; VI = pump power; N = pump speed; HCT = blood
hematocrit; K1, K2 = constants.
TABLE II. PERFORMANCE SUMMARY OF THE FLOW ESTIMATION MODELS
UNDER EVALUATION. RESULTS REFER TO THE CASE WHERE A SINGLE
TRAINING SET IS VALIDATED AGAINST THE REMAINING DATA. A ROTATION OF
THE TRAINING AND VALIDATION SETS PRODUCES SIMILAR RESULTS.
Mean Error (%)
to the behavior of the pump power signal, which does not Download full-text
continue the trend of decline when the flow becomes negative,
but rather reaches a minimum plateau value.
As mentioned in the results section, model structure II
produced a marginally superior overall performance.
However, considering that structure III is far less complex and
considerably less computationally intensive, it may be
beneficial to implement this simpler method in a real-time
Since continuous flow measurements cannot be obtained in
implant recipients due to the invasiveness of the required
instrumentation, only an average flow estimate may be
compared in this case. As such, in vivo animal experiments
may be required to provide the appropriate real-time
measurements and physiological environment necessary to
validate these flow models.
Worthy of note is that the level of pulsatility in the
simulated cardiac contractions had no effect on the pump
flow-power-speed characteristic, in the time-averaged sense. It
was hypothesized that added pulsatility might assist in the
work done by the pump, thereby reducing the power
requirement to produce a given average flow rate at a fixed
speed. However the data demonstrated that this was not the
case. This confirms the assertion made by Ayre et. al. , that
non-pulsatile flow estimates are applicable to pulsatile flow
environments when an average estimate is all that is required.
A practical method of estimating pulsatile flow in an iRBP
to a high degree of accuracy has been described. A reliable
flow estimate is not only a clinically valuable parameter to be
monitored by the relevant clinicians, but also serves as a
fundamental variable for a pump control strategy.
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a target speed change at time 3.7s.