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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