System Identification of Integrative Non Invasive Blood Pressure Sensor Based on ARMAX Estimator Algorithm

Abstract

Varieties of the oscillometric non-invasive blood pressure (NIBP) measuring devices are based on recording the arterial pressure
pulsation in an inflated cuff wrapped around a limb during the cuff deflation. The recorded NIBP data contain the pressure
pulses in the cuff, called oscillometric pulses, superimposed on the cuff deflation. Some of NIBP devices have also implanted
microphone inside the cuff, which enables measurements of Korotkoff sounds The objectives of this contribution are, first,
to extract the transfer characteristics of the oscillotonometric method of NIBP deflation from the pressure pulses, and second,
to extract the Parametric coefficient of the NIBP system with regression path with ARMAX algorithm.

Full text

385
System Identification of Integrative Non Invasive Blood Pressure Sensor Based
on ARMAX Estimator Algorithm
Noaman M. Noaman1, Abbas K. Abbas2
1 Department of Computer Engineering, Computer Man College, Khartoum, Sudan
2 Tuebingen University, Department of Biocybernetics, Germany
Abstract— Varieties of the oscillometric non-invasive blood
pressure (NIBP) measuring devices are based on recording the
arterial pressure pulsation in an inflated cuff wrapped around
a limb during the cuff deflation. The recorded NIBP data
contain the pressure pulses in the cuff, called oscillometric
pulses, superimposed on the cuff deflation. Some of NIBP
devices have also implanted microphone inside the cuff, which
enables measurements of Korotkoff sounds The objectives of
this contribution are, first, to extract the transfer characteris-
tics of the oscillotonometric method of NIBP deflation from the
pressure pulses, and second, to extract the Parametric coeffi-
cient of the NIBP system with regression path with ARMAX
algorithm.
Keywords— NIBP, system dynamics, ARMAX, estimator,
identification.
I. INTRODUCTION
Routine methods for noninvasive arterial pressure
evaluation are based on a simple idea, which has remained
almost unchanged in its essence for more than one century:
an arterial vessel, usually placed in a limb, is compressed by
an external load, which causes the artery to rhythmically
collapse or reopen at each heart beat. Some effects of the
arterial collapse (either alterations in pressure pulse ampli-
tude, blood volume changes, blood velocity perturbations,
or audio-frequency sounds) are then detected by means of
an external noninvasive transducer. The belief is that artery
obliteration and the consequent phenomena measured by the
transducer are closely related to the incoming arterial pres-
sure waveform, particularly to the diastolic, mean, and sys-
tolic arterial pressure values. [1, 2]
II. THEORETICAL BASIS OF BLOOD RESSURE MODELLING
ESTIMATION
A. Non invasive technique of the blood pressure
characteristics estimation based on the ARMAX system
There are two ways to validate noninvasive blood pres-
sure estimation techniques and improving their perform-
ance. The first consists of comparing values provided by the
indirect technique with those obtained simultaneously by a
catheter inserted into an artery. The most important results,
however, can be summarized as follows. The auscultatory
method seems to underestimate systolic blood pressure by
5-20 mm Hg, while it overestimates diastolic blood pressure
by 12-20 mm Hg. [7, 3]
In particular subjects, however, such as in the elderly, in
individuals with increased vascular rigidity (such as in ad-
vanced atherosclerosis), or in individuals with large arms
(such as in the obese), the auscultatory method may overes-
timate the intra-arterial pressure (a phenomenon often called
pseudo hypertension). Just a few experimental results on the
oscillometry technique can be found in the literature. Ged-
des et al. [5] used the value of cuff pressure pulse amplitude,
normalized to the maximum, to estimate systolic and dia-
stolic pressure. Comparison with intra-arterial pressure in
the dog suggests that these ratios are quite imprecise, rang-
ing from 0.45 to 0.57 for the systolic, and from 0.75 to 0.86
for the diastolic [6].
Basically, two main classes of models can be distin-
guished: the lumped parameter models, which neglect wave
propagation phenomena along the artery and provide a
compartmental description of tissue and artery segments
(i.e., they do not consider a spatial coordinate explicitly);
and the distributed parameter models, which consider the
spatial coordinates (i.e., the longitudinal coordinate of the
artery and of the arm and, in some instances, the arm radial
coordinate, too). Both models exhibit some advantages and
shortcomings.
Fig. 1 the oscillometric non-invasive blood pressure waveform and major
phases of NIBP waveform [4].

386
1. First preparation of simple biomechanical description
of the cuff wrapped around the arm was proposed: in this
case a lumped parameter model may be sufficient to account
for the main biomechanical properties of the cuff model +
air surrounding system.
2. Subsequently, the analysis of pressure transmission
across the arm elastic tissue should achieve.
In the case of an ideal cuff, this can be studied as the
classic two-dimensional problem in cylindrical coordinates,
when stress distribution is symmetrical about an axis.
Hence, the analytical solution can be written independently
of the axial coordinate. With suitable simplifications, the
distributed parameter model is then simplified into a lumped
parameter one. Moreover, a more complex model for stress
propagation in the tissue is presented, to account for the
cases when pressure load is not uniformly distributed
around the arm. However, in this event analytical solutions
are not available and, thus, a finite-element numerical
method is adopted. The effect on the measurement of
changes in cuff dimension is analyzed with the finite-
element model of the arm, together with the effect of altera-
tions in the arm tissue elastic parameters (Young's modulus
and Poisson's ratio) [4].
3. The last portion of our mathematical analysis concerns
the description of the collapsing artery under the cuff. Most
emphasis is given to a lumped parameter description of
brachial hemodynamics. A monodimensional, distributed
parameter model of brachial hemodynamics is also pre-
sented for the sake of completeness, without entering in
specific mathematical details.
B. Techniques for noninvasive blood pressure Transfer
characteristics estimation
There are two ways to validate NIBP estimation tech-
niques and to improve their performance. The first consists
of comparing the values provided by the indirect technique
with those obtained simultaneously by a catheter inserted
into an artery. The most important results, however, can be
summarized as follows. The auscultatory method seems to
underestimate systolic blood pressure by 5-20 mm Hg,
while it overestimates diastolic blood pressure by 12-20 mm
Hg [7, 8]
Geddes et al.[5] used the value of cuff pressure pulse ampli-
tude, normalized to the maximum, to estimate systolic and
diastolic pressure. Comparison with intra-arterial pressure
in the dog suggests that these ratios are quite imprecise,
ranging from 0.45 to 0.57 for the systolic, and from 0.75 to
0.86 for the diastolic [8]
III. A LUMPED PARAMETER MODEL OF THE CUFF
The overall pressure-volume characteristic of the cuff
depends on the elasticity of the internal wall, of the air en-
closed in the bladder, and of the external wall. By assuming
that cuff thickness is negligible, where Ve denotes the volume
enclosed within the cuff external wall, Vc is the air volume
inside the cuff, and V I is the volume enclosed within the cuff
internal wall. Of course, when the cuff is wrapped around the
arm, the latter volume is approximately equal to the arm vol-
ume. In the following we shall denote by pc the pressure of air
inside the cuff and by pb the outer pressure acting on the cuff
internal wall, both evaluated with respect to the atmosphere.
During the measurement, when the cuff is wrapped around the
upper arm, pb is equal to pressure transmitted from the cuff to
the arm's outer surface. Moreover, pressure acting on the cuff
external wall is constant and equal to the atmospheric pressure.
A lumped-parameter model of the cuff consists in a rela-
tionship linking the cuff volume, Vc, with the pressures pc
and pb
By denoting with Ce the compliance of the cuff external
wall, and with Ci The compliance of the internal wall, we
have
d
t
dp
pC
d
t
dV c
ce
e).(= (1.1)
⎟
⎠
⎞
⎜
⎝
⎛−−= dt
dp
dt
dp
ppC
dt
dV cb
bci
i).( (1.2)
Where, in writing Eqs. (1.2) and (1.3) assumed that both com-
pliances are non-linear functions of the transmural pressure.
Finally, by deriving Eq. (1.1), eq(1.3) can be written as
⎟
⎠
⎞
⎜
⎝
⎛−−−=−= dt
dp
dt
dp
ppC
dt
dp
pC
dt
dV
dt
dV
dt
dV cb
bci
c
ce
iec ).().( (1.3)
Equation (1.4) characterizes the pressure-volume behavior of
the occluding cuff provided expressions for the internal and
external wall compliances are available. Such expressions can
be easily obtained for a given cuff by means of the following
experimental procedure. In order to achieve an expression for
the compliance of the cuff external wall, the cuff can be
wrapped around a rigid cylinder having a suitable diameter and
progressively inflated with air. Since the inner radius does not
change in this condition, we have (dVi/dt= 0), and so the pres-
sure-volume curve only reflects the elasticity of the external
wall, i.e.,
d
t
dV
pC
d
t
dp
pC
d
t
dV
d
t
dV c
ce
c
ce
ec =→== )().( (1.4)
Similarly, in order to characterize the compliance of the
cuff internal wall, the cuff can be enclosed within a rigid
cage, which prevents any outer expansion, while the internal

387
cuff is free to expand against the atmospheric pressure. This
means that dVe/dt= 0 in Eq. (1.4) and, moreover, pb=0.
Hence, we can write
()
bc
cc
bce
c
bci
ic
ppd
dV
dt
dV
ppC
dt
dp
ppC
dt
dV
dt
dV
−
==−→−== )().( (1.5)
Fig. 2 Sensors array transducer based on NIBP oscillometry measurement
technique [4]
IV. ESTIMATION OF THE NIBP OSCILLOMETRIC TRANSFER
CHARACTERISTICS BASED ON ARMAX ALGORITHM
The use of blood pressure input paradigm for system
identification process as actuation signal for monitoring the
response in order to estimate and making a robust prediction
for the NIBP transfer function , here we test for the 6 para-
digm for 8 subject simulated inputs and figure (1.3) illus-
trate the signals and simulated ARMAX estimation kernel
schemes multiplexed into error rate value is range between
(0.036- 0.0211) as the tolerance index is indicated that sys-
tem simulation is stable and pass the transient region with
raising time tr= 1.3 sec as it indicated for physiological
index.
A. Simulation result of NIBP system.
The simulation results are illustrated with figure templates
as in fig(3) ,fig(4) in which illustrate the system dynamics
and steady state characteristics for the oscillometric
proposed system as output from ARMAX method , the
platform is used with SIMULINK® software from
Mathworks.
B. Estimation method for NIBP
The oscillometric input signal where its simulate and in-
teracted to this ARMAX Kernel in order , the duration of
simulation is range between 120 msec to 3500 msec accord-
ing to the No. of samples for the parameterized blood pres-
sure waveform . The method for estimation NIBP when
defining the input paradigm of characteristic for the NIBP
waveform in which six different paradigm of blood pressure
waveform from 7 subject were selected and supplemented
to the ARMAX estimator kernel mask , as in the proposed
model figure(2) ,the sampling frequency for the S/H system
The resultant transfer function of simulated system can
be shown in table (1.1) with corresponding calibrating gain.
must be set so that is embedded inside the S-function of
the kernel and set to (0) in order to inhibit harmonics com-
putation for the input signal and avoid any frequency over-
loaded to the system or in other words attenuated the asso-
ciated harmonics of estimated model and decreasing the
polynomial orders of estimated transfer characteristics The
100 120 140 160 180 200 220 240 260 280
0
1
2
3
4
5
6
Time (secs)
Actual Output (Red Line) vs. The Predic ted Predict ed Model output ( Blue Line)
100 120 140 160 180 200 220 240 260 280
-0.6
-0.4
-0.2
0
0.2
0.4
Time (secs)
Error In Predict ed Model
Fig. 3 simulated Blood pressure signal of oscillometric unit based
form ARMAX estimator unit
.
00.05 0.1 0.15 0. 2 0.25 0.3 0.35 0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
Step Response of NIBP oscillometric system
with sampling time (Ts)=0.7567
Time in second (sec)
Amplitude of t he Blood pr ess ure (mmHg)
Fig. 4 A- step response of the extracted (estimated transfer function of the
ARMAX model).
00.5 11.5 22.5 33.5 44. 5
0
20
40
60
80
100
120
140
160
180
200
Step Response of NIBP oscillometric system
based on ARMAX method
Time in s ec  (sec)
Amplitude of Blood Pressure (mmHg)
Fig. 4 B- step response of the extracted (estimated transfer function of the
ARMAX model).

388
duration of the simulating experiment should be at mini-
mum at least 3 folds grater than the signal duration of repi-
tion for BP waveform, this add more accuracy to the com-
putation algorithm of regression estimation For estimating
and derivation of the polynomial coefficient (α1…..αn-1) and
(β1…βn-1) for numerator and denumerator , one of the im-
portant aspect should be take into consideration which is the
calibrating factor or gain-weighting factor for oscillotono-
metric-transducer in this case sphynomanometric system
should be with in range of (0.89-1.9) to get the optimal
result for simulation. Trail simulation was done through
selection of different gain (calibrating factor) G in the path
of the NIBP signal
The step response of estimated transfer characteristics
shows enhancement of step response when increasing the
calibrating factor gain to reach 3 folds of the initial value in
which set in simulation system. The expected transfer func-
tion of NIBP system that is predicted using ARMAX meth-
ods are as following table in which 7 trials simulation with
two sampling time Ts was achieved and illustrate that inhi-
bition of the sampling time will lead to decrease of fre-
quency harmonics associated with real extracted model.
Table 1 estimated transfer characteristics of the NIBP system simulated
with ARMAX algorithm
Trail
No of
simulation
Transfer function
Ts=0.035 s
Transfer function
Ts=0.0745 s
1
G=0.89
4
.06.1
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00.5 11.5 22.5 33. 5 4
0
10
20
30
40
50
60
70
Step Response of estimated NIBP model based on varying Ts sampling time
Time (sec) (sec)
Amplitude of BP waveform mmHg
Fig. 5 step response of the NIBP system based on ARMAX estimator with
different sampling time Ts
V. CONCLUSIONS
The extraction the transfer function for the overall oscil-
lometric method for direct NIBP system as this work based
on ARMAX estimator algorithm that reflects partial dynam-
ics information when compared with IBP measurement this
is due to ARMAX lacking of compensation factor for resid-
ual harmonics unless we attenuate the sampling frequency
for the ADC of the unit ,this also add a systematic error
ration Δerr=0.0454 of total measurement errors , the meth-
ods should be comparable to models extracted from other
IBP and NIBP measurement to get significant of the tech-
niques used in estimation, in future work combination
methods for the estimation as MLE singular value decom-
position applied for both IBP and NIBP measurement with
hemodynamics performance comparison and analysis
ACKNOWLEDGMENT
We would like to thanks Tuebingen University Depart-
ment of Biocybernetics for providing research tools and
Computer Man College in Khartoum for giving opportunity
and scientific laboratory to complete this work in suitable
and reproductive profile.
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Author: Noaman M. Noaman
Institute: Department of Computer Engineering, Computer Man Col
lege, Sudan – Khartoum
Street:
City: Al Khartoum city
Country: Sudan
Email: noaman961@yahoo.com
Author: Abbas Kader Abbas
Institute: Tuebingen University, Biocybernetics department
Street: Waldhauser Ost, Fichtenweg 29 -D-72076
City: Tuebingen
Email: abbas.khudair@gmail.com