AN APPROACH OF REDUCING MEASURE TIME
OF NONINVASIVE THERMOMETER
Application of Curve-fitting Method and Autoregressive Model
for Reducing the Measure Time of Dual-heat-flux Thermometer
S. Y. Sim, H. J. Baek, G. S. Chung
Interdisciplinary program of Bioengineering, Seoul National University, Jongnogu, Seoul, Republic of Korea
K. S. Park
Department of Biomedical Engineering, College of Medicine, Seoul National University
Jongnogu, Seoul, Republic of Korea
Keywords: Core body temperature, Non-invasive thermometer, Autoregressive (AR) model, Curve fitting method,
Dual-heat-flux thermometer.
Abstract: Newly developed dual-heat-flux thermometer is expected to be useful in measuring core body temperature
noninvasively. However, as it takes more than 30 min to measure, the additional process is needed to reduce
the measure time. In this study, we made a dual-heat-flux thermometer to verify its performance and
obtained an hour-long data from three subjects. Dual-heat-flux thermometer estimated the core body
temperature very well in all subjects. In addition, least squares curve-fitting method predicted deep body
temperature well with within 100 sec data. Autoregressive model with 10 sec data also seemed to be
suitable method for shortening measure time of dual-heat-flux thermometer.
1 INTRODUCTION
Body temperature is a basic and vital signal when
monitoring health abnormality. In hospital, all
patient monitor devices observe body temperature
along with ECG, SPO
2
, respiration, NIBP and pulse.
And athletes could lose their lives due to continuous
high body temperature during exercise(Coris et al.,
2004). Moreover, body temperature has a strong
correlation with various physical conditions. S. S.
Yalçın reported that different individual
characteristics of children such as hypoalbuminemia
showed different RATD (Rectal–Axillary
Temperature measurement Difference)
values(Yalcin et al., 2010). The menstrual cycle of
female is also closely related to the temperature
rhythm(Nakayama et al., 1997). Therefore, varied
types of thermometers have been developed.
The first method of measuring body temperature
was offered by Hippocrates in the 5
th
century
B.C.(Cranston, 1966). He used comparative
measurements of heat and cold to distinguish certain
diseases. In these days, more complicated and
scientific thermometers are employed to measure
body temperature. Rectal thermometers,
oesophageal thermometers and auditory canal
thermometers are the typical thermometers of
today(Togawa, 1985). And these types of
thermometers are called invasive thermometers
because they insert a sensor into a body cavity for
checking deep body temperature. In spite of their
public use, these devices are not suitable for a long-
term monitoring especially when people are awake.
Taking a rectal thermometer for example, putting a
long and sharp probe in rectum would restrict most
movements and cause perforation of the rectum
moreover.
The first, innovative noninvasive thermometer
was produced in 1971(Fox and Solman, 1971). Zero-
heat-flow thermometer is based on the assumption
that if heat flow across the skin is zero, skin
temperature would be equivalent to deep body tissue
temperature. And for making heat flow zero, this
thermometer equips a heater which needs AC power
540
Sim S., Baek H., Chung G. and Park K..
AN APPROACH OF REDUCING MEASURE TIME OF NONINVASIVE THERMOMETER - Application of Curve-fitting Method and Autoregressive Model
for Reducing the Measure Time of Dual-heat-flux Thermometer .
DOI: 10.5220/0003287305400543
In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing (BIOSIGNALS-2011), pages 540-543
ISBN: 978-989-8425-35-5
Copyright
c
 2011 SCITEPRESS (Science and Technology Publications, Lda.)

supply. Recently-introduced dual-heat-flux
thermometer is another kind of noninvasive
thermometer(Kitamura et al., 2009). However, it
doesn’t need a heater and AC power supply.
Therefore, except for a long measure time of 40
mins, dual-heat-flux thermometer is more promising
than zero-heat-flow thermometer when monitoring
patient’s core body temperature.
In this study, we made a similar dual-heat-flux
thermometer to Kitamura K.’s work for reassessing
its performance and applied curve-fitting method
and autoregressive (AR) model for reducing its long
measure time.
2 METHODS
We made a dual-heat-flux thermometer and
compared it with the measured values of an infrared
ear thermometer and an armpit thermometer. For
shortening measure time of dual-heat-flux
thermometer, curve-fitting method and AR model
were applied. We address each of these issues in
detail in the following sections.
2.1 Principles
2.1.1 Dual-heat-flux Thermometer
With an insulator on the surface of the body, a heat
flow from deep body tissue to skin and another heat
flow from skin to outside of the body are balanced.
Kitamura K. assumed that the heat flow from the
internal body to external is constant and vertical.
Therefore, as shown in figure.1 (a), there are two
heat flows passing the thermometer and four sensors
measure temperatures at each part. In the previous
study, based on these presumptions, following
equation was obtained by introducing the concept of
thermal resistance:
T

=T

+
T

T

T

T


K

T

T


T

T


(1)
K
=
T

T

T

T


T

T

T

T


(2)
where T
B
represents the core body temperature and
T
N
indicates the measured value at sensor number N.
To calculate T
B
, K-value has to be gained in
advance through the simulation experiment of
Nemoto and Togawa(Nemoto and Togawa, 1988).
In the present study, K-value is 0.2679.
(a)
(b) (c)
Figure 1: (a): Two heat flows through the probe (b): A
photograph of probe (c): A photograph of the experiment.
2.1.2 Curve-fitting Method
Dual-heat-flux thermometer needs more than 40 min
to measure, which makes subjects impatient to
remain motionless. Therefore, with data within 100
sec, we tried to estimate the core body temperature
using curve-fitting method.
For estimating the trend of outcome and
eliminating the noise effect, least squares curve-
fitting was used. Least squares method assumes that
the best-fit curve of outcome has the smallest sum of
the deviations squared from an experimental data.
To gain the best-fit curve, we used ORIGIN PRO 8
program which is a powerful tool for analyzing data,
especially for curve-fitting.
2.1.3 Autoregressive Model
An autoregressive (AR) model explains that the time
series value (y
t
) at particular point can be predicted
by a linear weighted sum of previous data:
y

=b

y

+ϵ



(3)
where b denotes the autoregressive coefficients and
ϵ

represents Gaussian white noise with unknown
variance. Firstly, to determine the regression
coefficient b, we used one subject’ data as training
data. And as Andrei V. Gribok confirmed that the
model trained for one subject is useful to predict the
AN APPROACH OF REDUCING MEASURE TIME OF NONINVASIVE THERMOMETER - Application of
Curve-fitting Method and Autoregressive Model for Reducing the Measure Time of Dual-heat-flux Thermometer
541

temperature of others (Andrei V. Gribok, 2008), we
used the model which was established by ‘training
data’ for estimating the core body temperature of
others.
2.2 Experiments
Dual-heat-flux thermometer was made as according
to the method of Kitamura K. - 4 IC temperature
transducers (AD590, Analog Devices Inc, USA), a
rubber sponge as an insulator, and a urethane sponge
cover for avoiding air current effect. In addition, we
replaced copper cap with aluminum cap and
removed copper disks and rings to reduce the
thermal inertia of the probe.
Core body temperature was measured in three
healthy young subjects (26.5± 1.5 years old) and the
room temperature was controlled at about 27˚C.
Each subject sat on the chair and dual-heat-flux
thermometer was fastened on the left anterior
temporal region by hair band for an hour. To prevent
the increase of brain temperature, some activities
like computer games or doing homework which
accompany strong brain activity was sublated.
3 RESULTS
3.1 Core Body Temperature
Besides the core body temperature measured by
dual-heat-flux thermometer, auditory canal and
axillary temperature were checked by an infrared ear
thermometer and an armpit thermometer during the
experiment. Table.1. shows measured temperatures
of each body part of three subjects.
Table 1: Enumeration of measured temperatures.
Core body
temperature
Auditory
canal
temperature
Axillary
temperature
Subject 1
36.3˚C 36.7˚C 36.48˚C
Subject 2
36.35˚C 36.8˚C 36.35˚C
Subject 3
36.2˚C 36.9˚C 36.35˚C
3.2 Application of Curve Fitting
The shapes of each subject’s temperature curve were
similar. Therefore, one subject’s data (subject 3)
were used to determine the minimum time that
offers relevant result. The model is ‘Temperature =
Ae
×
+C’. And as shown in figure 2, the
estimation curves drawn within 95sec data and
100sec data are fitted well. For choosing the best-fit
curve, estimated core body temperatures and
residual sum of squares are listed (Table 2).
Figure 2: Estimated curves with different measure time.
Table 2: The results of curve-fitting method.
Measure
time
Estimated
core body
temperature*
(dual-heat-flux
thermometer)
Estimated
core body
temperature**
(curve-fitting
method)
residual
sum of
squares
90sec
36.2˚C 36.34˚C
170.57
95sec
36.2˚C 36.23˚C
74.80
100sec
36.2˚C 36.11˚C
40.78
105sec
36.2˚C 36.01˚C
90.51
* Estimated core body temperature of subject 3 by dual-heat-flux
thermometer is 36.2˚C, as shown in Table 1.
** Estimated core body temperatures of subject 3 by curve-fitting
method were determined as the temperature of time =∞.
3.3 Application
of Autoregressive Model
To seek more progressive way of reducing measure
time of dual-heat-flux thermometer, we set up the
10th order AR model. In other words, as the
sampling frequency was 1Hz, we used only 10 sec
data for estimating core body temperature. The
whole autoregressive coefficients were obtained
from training data (subject 3). By drawing the curve
contiguous to experiment curve, AR model suggests
a possible approach to estimate the core body
temperature in 10 seconds (Figure 3(a)). On the
contrary, the prediction curve of cross-subject model
was not fitted well with another individual’s data.
0 500 1000 1500 2000 2500 3000 3500 4000
34.5
35
35.5
36
36.5
37
t [sec]
Tem perature [C]
data
85
90
95
100
105
110
120
BIOSIGNALS 2011 - International Conference on Bio-inspired Systems and Signal Processing
542

(a)
(b)
Figure 3: (a): Core body temperature estimation using the
same-subject AR model (b): Core body temperature
prediction using the cross-subject AR model.
4 DISCUSSION
Core body temperatures measured by dual-heat-flux
thermometer and other thermometers showed a
narrow difference. Therefore, we could confirm the
performance of non-invasive thermometer.
Curve-fitting method offered the possibility of
cutting down the measure time of dual-heat-flux
thermometer to 100 sec and AR model to 10 sec. In
addition, as the AR model was not appropriate for
cross-subject temperature estimation, we would
consider other probability models in future work.
Finally, the probe is still inconvenient because
many wires are surrounding the probe. Thus, we are
supposed to transform the existing dual-heat-flux
thermometer in telemetry way.
ACKNOWLEDGEMENTS
This work was supported by the Seoul R&BD
Program (10606M0209725). And also in part by the
Technology Innovation Program (10035525) and the
Strategic Technology Development Program funded
by the Ministry of Knowledge Economy (MKE,
Korea).
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0 500 1000 1500 2000 2500 3000 3500 4000
30
32
34
36
38
40
t [sec]
Temperature [C]
data
AR model
0 500 1000 1500 2000 2500 3000
30
32
34
36
38
40
t [sec]
Tem perature [C ]
subject4 data
estimated temperature of subject4 by AR model
AN APPROACH OF REDUCING MEASURE TIME OF NONINVASIVE THERMOMETER - Application of
Curve-fitting Method and Autoregressive Model for Reducing the Measure Time of Dual-heat-flux Thermometer
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