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Use of finite element analysis to optimize probe design for double sensor method-based thermometer
Journal of Thermal Biology 52 (2015) 67–74
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Journal of Thermal Biology journal homepage: www.elsevier.com/locate/jtherbio
Use of finite element analysis to optimize probe design for double sensor method-based thermometer Soo Young Sim a, Kwang Min Joo a, Kwang Suk Park b,n a b
Interdisciplinary Program in Bioengineering, College of Engineering, Seoul National University, Republic of Korea Department of Biomedical Engineering, College of Medicine, Seoul National University, Seoul 110-799, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2015 Received in revised form 19 May 2015 Accepted 19 May 2015 Available online 27 May 2015
Body temperature is an essential vital sign for assessing physiological functions. The double sensor method-based thermometer is a promising technology that may be applicable to body temperature monitoring in daily life. It continuously estimates deep tissue temperature from the intact skin surface. Despite its considerable potential for monitoring body temperature, its key design features have not been investigated. In this study, we considered four design factors: the cover material, insulator material, insulator radius, and insulator height. We also evaluated their effects on the performance of the double sensor thermometer in terms of accuracy, initial waiting time, and the ability to track changes in body temperature. The probe material and size influenced the accuracy and initial waiting time. Finite element analysis revealed that four thermometers of different sizes composed of an aluminum cover and foam insulator provided high accuracy ( o 0.1 °C) under various ambient temperatures and blood perfusion rates: R¼ 20 mm, H ¼ 5 mm; R¼ 15 mm, H ¼10 mm; R¼ 20 mm, H ¼ 10 mm; and R¼ 15 mm, H ¼15 mm. The initial waiting time was approximately 10 min with almost the same traceability of temperature change. Our findings may provide thermometer manufacturers with new insights into probe design and help them fabricate thermometers optimized for specific applications. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Body temperature Deep body thermometer Double sensor method Noninvasive body temperature monitoring
1. Introduction Body temperature is one of the most important factors in metabolic processes such as cell division and enzyme reactions (Davidovits, 2012). An abnormal body temperature range implies that these essential processes are not proceeding properly. Therefore, body temperature measurement is a routine procedure in health examinations. Body temperature can also be intentionally adjusted to suppress injury progression or damage cancer cells. Hypothermia therapy reduces the body temperature by approximately 33 °C and is a widely accepted procedure when clinicians operate on patients suffering from traumatic brain injuries or cardiac arrest (Nikolov and Anthony, 2003; H. Alex et al., 2012). In hyperthermia therapy for cancer treatment, the deep tissue layer is heated up to 42–45 °C (Mitobe and Noboru, 2011). Ever since Hippocrates diagnosed fever using the warmth of his hand in the 5th century, various kinds of thermometers have been developed (Togawa, 1985). In the operating room or intensive care unit of a hospital, body temperature is monitored by inserting a temperature sensor into a body cavity (e.g., rectum, esophagus) or n
Corresponding author. Fax: þ 82 2 745 7870. E-mail address: [email protected] (K.S. Park).
http://dx.doi.org/10.1016/j.jtherbio.2015.05.007 0306-4565/& 2015 Elsevier Ltd. All rights reserved.
a blood vessel (e.g., pulmonary artery) (Lefrant et al., 2003). Although these methods are expected to be accurate because the sensor directly measures the temperature of deep tissue, they are too invasive and intrusive to be applied to conscious individuals. Infrared ear thermometers and axillary thermometers are commonly used in everyday life and medical care settings because they are easy to use. However, the readings of infrared ear thermometers are influenced by the technique of the operator (Terndrup and Rajk, 1992). Furthermore, axillary thermometers require people to hold an arm down tightly at their side while measuring armpit temperature. Therefore, the application of these thermometers to continuous body temperature monitoring in daily life is restricted. Many researchers have sought to develop noninvasive body temperature monitoring devices that use the zero heat flow method (ZHFM), double sensor method (DSM), and dual heat flux method (DHFM) (Fox and Solman, 1971; Gunga et al., 2012; Kitamura et al., 2010) (Fig. 1). The ZHFM-based thermometer (Fig. 1a) (Fox and Solman, 1971) uses a servo-controlled heater to reduce the heat flow crossing the tissue to zero and estimates the deep tissue temperature from the skin surface (Fox and Solman, 1971; Fox et al., 1973). It yields temperature measurements similar to those directly measured in the rectum of stable infants in incubators, in muscle (vastus lateralis), and in the esophagus of
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Fig. 1. Structures of noninvasive deep body thermometers: (a) ZHFM-based thermometer, (b) DSM-based thermometer, and (c) DHFM-based thermometer.
healthy subjects in hot and stable ambient conditions (Dollberg et al., 2000; Brajkovic and Ducharme, 2005; Teunissen et al., 2011). The applicability of thermometers using the DSM (Fig. 1b) has been verified under diverse environments (Gunga et al., 2012). They provided similar results to that of rectal thermometers during intensive work under various ambient temperatures (mean72 S.D.: – 0.1670.90 °C at 10 °C, –0.0870.70 °C at 25 °C, –0.1170.68 °C at 40 °C) (Gunga et al., 2008). DSM-based thermometers have also exhibited the potential to monitor circadian body temperature rhythms or abnormal body temperatures during cardiac surgery (Gunga et al., 2009; Kimberger et al., 2009). DSM-based or DHFMbased thermometers are suitable for unconstrained body temperature monitoring because they do not require an AC power supply for heating. Although the usefulness of various types of deep body thermometers was verified, measurement errors still exist. A portion of the error is inherent because deep body thermometers assume that heat flows only in the longitudinal direction and do not take the transverse heat flow into account. Therefore, some studies have investigated the design of thermometers that create measurement conditions that accord closely with the assumption, thereby improving the accuracy. Togawa et al. modified the conventional ZHFM-based thermometer to improve its performance (Kobayashi et al., 1975; Togawa et al., 1976). Steck et al. (2011) carried out numerical simulations to discover the best performing sensor design for a ZHFM-based thermometer. Huang et al. (2014) recently evaluated the structural and thermophysical effects on
the accuracy of the DHFM-based thermometer. However, the design of the DSM-based thermometer has not been considered. Therefore, we studied the influence of probe design factors (size and material) on the accuracy, initial waiting time, and traceability of temperature changes. We expect that this study will help researchers obtain insights into the DSM-based thermometer design and fabricate thermometers optimized for specific applications.
2. Materials and methods We implemented finite element simulations to evaluate the effects of probe size (radius and height) and material (insulator and cover) on the performance of the DSM-based thermometer. 2.1. Principle of the double sensor method The DSM-based thermometer is comprised of two thermistors, an insulator, and a cover (Fig. 2). The vertical heat flow from deep tissue to the probe cover is used to estimate deep body temperature. Approximately 10 min after attaching the probe to the skin, the thermal conditions around the measurement area reach equilibrium (Kimberger et al., 2009). At thermal equilibrium, the heat flow from the core towards the skin layer and the heat flow across the sensor are balanced. Each heat flow can be expressed as:
⎧ H = Ktis × (Td − T1) ⎨ ⎪ ⎩ H = Kinsul × (T1 − T2 ) ⎪
Fig. 2. Schematic diagram of the double sensor method. Heat flows vertically from deep tissue to the cover. Td is the deep tissue temperature. T1 and T2 are the measured temperatures at each point. Td is estimated from T1 and T2 and the ratio of thermal conduction coefficient of the insulator to that of human tissue (K¼Kinsul/ Ktis) using Td = T1 + K × (T1 − T2 ) .
(1)
where H, Td, T1, and T2 denote the heat flow, deep tissue temperature, skin temperature under the insulator, and the temperature above the insulator, respectively. Ktis and Kinsul are the heat conduction coefficient of the human tissue and insulator, respectively. Solving the simultaneous equation in Eq. (1), the deep tissue temperature can be estimated using the temperatures measured from two thermistors:
Td = T1 + K × (T1 − T2 ) where K =
Kinsul Ktis
(2)
S.Y. Sim et al. / Journal of Thermal Biology 52 (2015) 67–74
Fig. 3. The four design factors considered in this study: r, h, Mins, and Mcov. The parameters r and h represent the radius and height of the insulator, respectively. Mins and Mcov indicate the material of insulator and cover, respectively. To determine the effect of material, we considered cork, foam, hard rubber, and nylon as the insulators. Acrylic and aluminum were employed for the cover. We varied the insulator size to investigate its influence on body temperature estimation. We changed the insulator radius from 10 mm to 30 mm and its height from 5 mm to 15 mm. The human tissue under DSM-based thermometer was composed of skin, fat, and bone layers. The cover thickness was fixed at 2 mm.
where K is the ratio of the heat conduction coefficient of the insulator to that of tissue layer. The thermal resistance of a multitissue layer can be calculated as the sum of the thermal resistances of each layer (e.g. skin, fat, and bone). The heat conduction coefficient of multi-layer tissue (Ktis) can be computed using
x fat xtis x skin x bone = + + Ktis⋅A K skin⋅A K fat⋅A Kbone⋅A
(3)
where xtis, xskin, xfat, and xbone are the thicknesses of the total tissue, skin, fat, and bone layers, respectively, and the corresponding thermal conduction coefficients for these layers are denoted as Ktis, Kskin, Kfat, and Kbone, respectively. A is the heat conduction area. 2.2. Simulation study 2.2.1. Simulation model and design factors Heat transfer analysis was performed using the finite element method (FEM) simulation package COMSOL Multiphysics (COMSOL Inc., Sweden). As shown in Fig. 3, the simulation model was divided into five parts: the skin layer, fat layer, bone layer, insulator, and cover. A human tissue layer was established to model the forehead, which is one of the most common sites for measuring
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deep body temperature because the anatomy is relatively similar across individuals (Finvers et al., 2006; Werner et al., 2009; Zeiner et al., 2010). The forehead model was derived from a previous study (Steck et al., 2011). The thicknesses of the skin, fat, and bone layers were 2 mm, 3 mm, and 5.4 mm, respectively. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. Metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The radius of the tissue model was 60 mm. When modeling the insulator and cover, we considered four design factors: the radius (r), height (h), and the materials of the insulator (Mins) and the cover (Mcov). Cork, foam, hard rubber, and nylon were used to test the effect of the insulator material, all of which have previously been used as the insulator. Acrylic and aluminum were employed for the cover. In addition, we accounted for the anodized metal to examine the effect of the emissivity of the cover. The insulator size was varied to investigate its influence on body temperature estimation. The radius of the insulator was changed from 10 mm to 30 mm and its height from 5 mm to 15 mm. The values were manually altered rather than using a parametric sweep. The mesh was set using a user-controlled mesh. The maximum element size was 5 mm and the minimum element size was 1 mm. The maximum element growth rate was 1.3. The curvature factor was 0.5. The resolution of narrow regions was 0.6. Table 1 shows the thermal properties of the materials (Steck et al., 2011; Huang et al., 2014; Apache-Tables, IES VE). In all trials, the minimum mesh quality was maintained above 0.1, which is a typical criterion for acceptable mesh quality. 2.2.2. Mathematic formulation for understanding temperature distribution in model The Pennes bioheat equation (Pennes, 1998) is widely used to understand temperature distributions in human tissue and is given by
ρt ct
∂Tt = ∇⋅(kt ∇Tt ) + ωρ b cb (Ta − Tt ) + Q met ∂t
(4)
where kt, ρt, and ct represent the thermal conductivity, density, and specific heat of tissue, respectively. Tt is the tissue temperature and Ta is the arterial blood temperature. The arterial blood temperature was assumed to be equivalent to the deep tissue temperature. The third term is related to heat transfer by blood perfusion, where ω, ρb, and cb are the blood perfusion rate, density, and specific heat of blood, respectively. The thermal equilibrium between the blood and the surrounding tissue was assumed (Xuan. and Roetzel, 1997). And the blood is uniformly perfused in each tissue layer. Qmet is the heat transfer by metabolism.
Table 1 Thermal properties of the materialsa. Specific heat (J/kg °C)
Density (kg/m3)
Thermal conductivity (W/m °C)
Emissivity
Tissue (forehead)
Skin Fat Bone Blood
3766 2510 1590 3900
1000 850 1500 1050
0.21 0.16 1.16 –
0.98 – – –
Insulator
Cork Foam Hard rubber Nylon
1800 1900 1000 1700
120 24 1200 1150
0.04 0.06 0.15 0.26
– – – –
Cover
Acrylic Aluminum Aluminum (anodized)
1433 896
1140 2800
0.14 200
0.95 0.05 0.77
a
The thermal properties of each material were cited from Steck et al. (2011), Huang et al. (2014), and Apache-Tables guide (IES VE).
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The outer surface of the cover and skin exchange heat with the surrounding air through convection and radiation. However, the convection effect was ignored as in a previous study because the probe is covered by a cloth (Huang et al., 2014). We applied the Stefan–Boltzmann law to express the radiative heat exchange around boundaries:
(
∇⋅(k∇T) = εσ T A4 − T 4
)
(5)
where k is the thermal conductivity of the boundary substance, TA and T are the ambient and boundary temperatures of the material, respectively, and s and ε are the Stefan–Boltzmann constant and emissivity of the boundary substance, respectively. The thermal insulation boundary condition was used on the vertical boundaries of the tissue layers. 2.3. Performance analysis of DSM-based thermometer We assessed the performance of the DSM-based thermometer in terms of measurement accuracy, initial waiting time, and traceability of temperature changes. 2.3.1. Accuracy To evaluate accuracy, we calculated the estimation error, defined as the absolute difference between the estimated and actual deep body temperatures. To compute the accuracy of each design, we implemented a stationary solver, which assumes a thermally steady-state condition. The Multifrontal Massively Parallel Sparse (MUMPS) direct solver was used to solve the system of equations. For the stopping criterion, a relative tolerance was 0.001. The ambient temperature and blood perfusion rate can differ depending on the measurement environment. In particular, the blood perfusion rate can change depending on the subject’s activity (Dittmar et al., 2006). To identify the DSM-based thermometer design that accurately estimates body temperature under diverse conditions, we varied the ambient temperature and blood perfusion rate. The ambient temperature was increased from 20 °C to 30 °C in steps of 2 °C. The variation in the blood perfusion rate was derived from a previous approach (Steck et al., 2011) where ωskin was changed from 0.00013 (1/s) to 0.01213 (1/s) and ωfat was changed from 0.000019 (1/s) to 0.002019 (1/s). 2.3.2. Initial waiting time The initial waiting time is the time required for the DSM-based thermometer to reach thermal equilibrium. Reducing the initial waiting time is a challenge for noninvasive deep body thermometers. Kimberger et al. (2009) stated that a long initial waiting time can preclude the practical monitoring of body temperature. To evaluate the initial waiting time, we used a time-dependent solver. Deep body temperature was maintained at 37 °C and we obtained data from 0 to 120 min over intervals of 1 min. MUMPS direct solver was used to solve the system of equations. We used a relative tolerance of 10 3 and an absolute tolerance of 10 6 for the local error control in the solver. The backward differentiation formula (BDF) was used as the time stepping method. The maximum and minimum BDF orders were 2 and 1, respectively. The steps taken by the solver were strictly controlled, which the maximum step set 1 min. We then identified the time when the gap between the estimated body temperature and temperature at thermal equilibrium decreased to below 0.1 °C. 2.3.3. Traceability of temperature changes A body temperature monitor should reflect the temperature variation. To evaluate the traceability of temperature changes, we used a time-dependent solver. During the initial 60 min, deep body temperature was maintained at 37 °C. The deep body
temperature was then decreased from 37 °C to 35 °C at a rate of – 0.2 °C/min (Kitamura et al., 2010). When the deep body temperature reached 35 °C, it was maintained for the remaining 60 min. We obtained data for 130 min in intervals of 1 min. The solver configuration was the same as in Section 2.2.2.
3. Results We began by evaluating the influence of the probe material on the performance of the DSM-based thermometer. We analyzed the performance in terms of accuracy and initial waiting time. After identifying the optimal combination of insulator and cover material, we examined the effect of probe size. 3.1. Effects of probe material on performance We tested accuracy of the DSM-based thermometer for 12 material combinations derived from four insulator and three cover materials for either ambient temperatures between 20 °C and 30 °C (Fig. 4a) or a range of blood perfusion rates in the skin and fat layers of –0.00013rωskin r0.01213 and 0.000019rωfat r0.002019, respectively (Fig. 4b). In Fig. 4a, the blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. In Fig. 4b, the ambient temperature was 25 °C. In both trials, deep body temperature was 37 °C and metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The radius and height of the insulator were fixed at 20 mm and 10 mm, respectively. Under both measurement conditions, the acrylic cover had a lower accuracy than the aluminum or anodized aluminum cover irrespective of the insulator material. The anodized aluminum cover has a higher emissivity than aluminum. Its accuracy was lower than that of the aluminum cover. Therefore, the aluminum cover had the lowest emissivity and was the most accurate with a maximum absolute error of less than 0.2 °C in all trials. When the thermal conductivity of the insulator was higher, the maximum absolute error was larger. To determine the initial waiting time for each material combination, we observed the deep body temperature for 120 min. In this trial, the ambient temperature was maintained at 25 °C. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. And metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The initial waiting time was defined as the time when the difference between the estimated core temperature and the estimated temperature at thermal equilibrium fell below 0.1 °C. Two deep body temperature estimation curves were observed (Fig. 5a): a temperature curve that reaches thermal equilibrium at approximately 10 min and a temperature curve that reaches thermal equilibrium after 19 min. For example, the curve for the aluminum cover and foam insulator reached thermal equilibrium after 7 min. In contrast, the curve for the aluminum cover and nylon insulator reached thermal equilibrium after 25 min. In general, the initial waiting time was shortest for the acrylic cover. It was longer than 19 min for the probe with an aluminum or anodized aluminum cover and a hard rubber or nylon insulator (Fig. 5b). For the cork or foam insulator, the initial waiting time of approximately 10 min was similar to that of Kimberger et al. (2009). The green dotted line in Fig. 5b represents the thermal conductivity of each insulator. The DSM-based thermometer with the acrylic cover showed subtle changes in initial waiting time for four kinds of insulators. There was a strong positive correlation between the thermal conductivity and initial waiting time for aluminum or anodized aluminum covers (r ¼0.97). In contrast, there was a negative correlation between the thermal diffusivity and the initial waiting time with aluminum or anodized aluminum covers
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1.4
Max. Abs. Err.(°C)
1.2 1
acrylic cover aluminum cover anodized aluminum cover
0.8 0.6 0.4 0.2 0 Cork
Foam
Hard rubber
Nylon
Hard rubber
Nylon
1.4
Max. Abs. Err.(°C)
1.2 1
acrylic cover aluminum cover anodized aluminum cover
0.8 0.6 0.4 0.2 0
Cork
Foam Insulator
Fig. 4. The accuracy of 12 kinds of material combinations under various ambient temperatures (a, top) and blood perfusion rates in tissue (b, bottom). The y-axis of each figure represents the maximum absolute error. In (a), the ambient temperature ranged from 20 °C to 30 °C. In (b), the blood perfusion rate in the skin layer, ωskin, changed from 0.00013 (1/s) to 0.01213 (1/s) and that in the fat layer, ωfat, from 0.000019 (1/s) to 0.002019 (1/s). In both trials, deep body temperature was 37 °C. And the radius and height of the insulator were fixed at 20 mm and 10 mm, respectively.
(r ¼ 0.66). On the basis of these results, we decided to design a probe with an aluminum cover and foam insulator. This combination had superb accuracy ( o0.1 °C) in diverse measurement conditions and an initial waiting time of less than 10 min. Although the probe with the aluminum cover and cork insulator performed similarly, we opted for the foam insulator given its lower weight. 3.2. Effects of probe size on performance The area and height of the probe influences the accuracy of the deep body thermometer (Huang et al., 2014). To examine the effect of the probe size, we varied the insulator radius from 10 mm to 30 mm and the insulator height from 5 mm to 15 mm in 5 mm steps. We determined the accuracy of 15 DSM-based thermometers of different sizes under various measurement conditions (Fig. 6). In the first trial, the ambient temperature was increased
from 20 °C to 30 °C in steps of 2 °C and the error was calculated at deep body temperatures of 34 °C, 37 °C, and 40 °C. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. Metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The accuracy generally appeared to decrease as the radius or height of the insulator increased (Fig. 6a). The accuracy was the best overall at an insulator height of 5 mm and showed the least dependence on the radius. In contrast, under various blood perfusion rates in human tissue, the maximum absolute error was approximately 0.3 °C at a radius of 10 mm (Fig. 6b). In this trial, deep body temperature was 37 °C and the ambient temperature was 25 °C. The metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. Although the accuracy at a probe height of 5 mm was lower by approximately 0.1 °C compared with a probe of height 15 mm when the radius was 15 mm, there was no consistent trend
Fig. 5. The initial waiting time of 12 kinds of material combinations. (a) Typical temperature estimation curves. The y-axis of the figure represents the estimated deep body temperature. (b) Initial waiting time (Init. Wait. Time) for each material combination. The green dotted line represents the thermal conductivity of each insulator. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. The accuracy of 15 DSM-based thermometers of different sizes under various ambient temperatures (a, top) and blood perfusion rates in tissue (b, bottom). In (a), the maximum absolute error (Max. Abs. Error) was calculated when ambient temperature ranged from 20 °C to 30 °C. Three deep body temperatures (DBT: 34 °C, 37 °C, 40 °C) were considered. In (b), the blood perfusion rate in the skin layer, ωskin, changed from 0.00013 (1/s) to 0.01213 (1/s) and that in fat layer, ωfat, from 0.000019 (1/s) to 0.002019 (1/s). Deep body temperature was maintained at 37 °C. In both trials, the thermometer consisted of an aluminum cover and a foam insulator.
in the effect of height on accuracy. On the basis of these results, we selected probe sizes that offered a maximum absolute error of less than or equal to 0.1 °C under various measurement conditions. In addition, we restricted the radius of the probe to 20 mm, which would allow it to be stably fixed on the forehead. The probes with the following dimensions satisfied the selection criteria: R¼ 20 mm, H¼ 5 mm; R¼15 mm, H ¼10 mm; R¼ 20 mm, H ¼10 mm; and R ¼15 mm, H¼15 mm. Finally, we examined the effects of insulator size on initial waiting time and traceability of temperature changes (Fig. 7). The probe with a radius of 20 mm and a height of 5 mm required 11 min to reach thermal equilibrium (Fig. 7a) and showed good traceability when the core temperature decreased from 37 °C to 35 °C (Fig. 7b). The initial waiting time of other sizes of probes was approximately 10 min. The probe with radii and heights of R¼ 15 mm, H¼ 10 mm; R¼20 mm, H¼ 10 mm; and R ¼15 mm, H ¼15 mm required 9 min, 7 min, and 7 min to reach thermal equilibrium. All four sizes of DSM-based thermometers had almost the same traceability (data not shown). The DSM-based thermometer exhibited a lag of approximately 4 min until the measurement decreased to within 0.1 °C of the reduced temperature.
4. Discussion DSM-based thermometers are expected to be useful in noninvasive and continuous monitoring of body temperature. In previous studies, the validity of the DSM was verified by comparing it with other existing thermometers (e.g., esophageal). Although this method exhibited superior accuracy for skin, bladder, or tympanic temperatures, impermissible errors still occur (Kimberger et al.,
2009; Zeiner et al., 2010). A wireless bandage-type thermometer based on the double sensor method showed a discrepancy that was larger than 2 °C when compared with a bladder thermometer (Stelfox et al., 2010). Therefore, we investigated the effects of probe design to improve the capability of the DSM-based thermometer. In addition, we modeled the forehead because of its similarity across individuals and the thin skin layer above the temporal artery. In clinical trials, the probe can be attached to the forehead with medical adhesive tape. In daily life, the deep body temperature can be monitored from the forehead by wearing a headband or helmet in which the thermometer is embedded. In future studies, we will consider other body parts such as the chest for nonintrusive deep body temperature monitoring in daily life. We confirmed that the aluminum cover had the best accuracy amongst three kinds of covers. The emissivity of the cover material influenced the accuracy for the anodized aluminum and aluminum covers. The insulator material also affected accuracy. In general, accuracy was higher for insulator materials with low thermal conductivity (e.g., cork, foam). This corresponds to results from previous research on DHFM-based thermometers, which found that low conductivity insulators improved measurement accuracy (Huang et al., 2014). We inferred that the low thermal conductivity of the insulator helps to interrupt the transverse heat flow. This makes the thermometer correspond more closely to the assumption that heat flows only in the vertical direction in the DSM-based thermometer. This work also evaluated the dynamic performance of the DSMbased thermometer (i.e., initial waiting time, traceability of temperature changes). An assessment of material effects showed that an acrylic cover required a shorter initial waiting time than an aluminum or anodized aluminum cover. In addition, when the
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Fig. 7. The dynamic performance of a DSM-based thermometer with 20 mm radius and 5 mm height. (a) Deep body temperature estimation curve. The y-axis represents the estimated deep body temperature. The initial waiting time was 11 min. (b) Traceability of temperature changes of probe of 20 mm radius and 5 mm height. All four thermometers showed similar traceability of temperature changes: R ¼20 mm, H¼ 5 mm; R ¼15 mm, H¼ 10 mm; R ¼ 20 mm, H¼ 10 mm; and R ¼15 mm, H¼ 15 mm.
cover was made of aluminum or anodized aluminum, insulators with a higher thermal conductivity (e.g., hard rubber, nylon) required a longer time to reach thermal equilibrium. We assumed that the probe with an insulator of higher thermal diffusivity would require a shorter initial waiting time. When the thermometer cover was made of aluminum or anodized aluminum, the correlation coefficient between the thermal diffusivity of the insulator and the initial waiting time was –0.66. However, the DSMbased thermometer with the acrylic cover showed subtle changes in initial waiting time regardless of insulator materials. Therefore, the cover material also influenced the initial waiting time. After selecting the optimal combination of aluminum cover and foam insulator, we investigated the effects of the probe size on the performance of the DSM-based thermometer. Fifteen thermometers of different sizes exhibited a maximum absolute error below 0.15 °C under various ambient temperatures (20–30 °C). In particular, at an insulator height of 5 mm, the probe had a maximum absolute error below 0.05 °C and the radius did not affect the accuracy significantly. In contrast, the insulator radius influenced the measurement accuracy under various blood perfusion rates. As the insulator area increased, the maximum absolute error decreased. This result also coincided with previous work showing that the accuracy of a DHFM-based thermometer is proportional to the insulator radius (Huang et al., 2014). This was explained in terms of the large area of the insulator suppressing the transverse
heat flow, which in turn results in ideal measurement conditions for the DSM-based thermometer. There was a gap in the initial waiting time when the probe size differed. However, four probes of different sizes with the same materials showed a similar traceability of temperature changes.
5. Conclusions We investigated the effects of varying the probe design on the performance of a DSM-based thermometer. The combination of a cover with low emissivity (e.g., aluminum) and an insulator with low thermal conductivity (e.g., foam) provided accurate measurements. Both the cover and insulator material influenced the initial waiting time. In addition, the probe size influenced the measurement accuracy and initial waiting time. The accuracy was improved for insulators of larger radius and lower height. The probe size slightly affected the initial waiting time. However, there was no observable difference in temperature traceability as long as the material combination for the probe remained the same. We expect that the knowledge gained from this study could provide thermometer manufacturers with new insights into designing and fabricating probes optimized for specific applications.
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Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) Grant (No. NRF-2012R1A2A2A02010714) funded by the Ministry of Science, ICT and Future Planning, and by the Bio & Medical Technology Development Program of the NRF funded by the Korean government, MSIP (NRF-2014M3A9E3064623).
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Kimberger, O., Thell, R., Schuh, M., Koch, J., Sessler, D.I., Kurz, A., 2009. Accuracy and precision of a novel non-invasive core thermometer. Br. J. Anaesth. 103 (2), 226–231. Kitamura, K.-I., et al., 2010. Development of a new method for the noninvasive measurement of deep body temperature without a heater. Med. Eng. Phys. 32 (1), 1–6. Kobayashi, T., Zhu, X., Chen, W., Nemoto, T., 1975. Improvement of deep body thermometer for man. Ann. Biomed. Eng. 3 (2), 181–188. Lefrant, J.-Y., Muller, L., Emmanuel de La Coussaye, J., Benbabaali, M., Lebris, C., Zeitoun, N., Mari, C., Saïssi, G., Ripart, J., Eledjam, J.-J., 2003. Temperature measurement in intensive care patients: comparison of urinary bladder, oesophageal, rectal, axillary, and inguinal methods versus pulmonary artery core method. J. Intensive Care Med. 29 (3), 414–418. Mitobe, K., Noboru, Y., 2011. Low-invasive heating and temperature measurement method for hyperthermia treatment using the metal coated ferromagnetic implant with low Curie temperature. In: Proceedings of the 9th International Conference on Biomedical Electronics and Devices (BIODEVICES), pp. 341–344. Nikolov, M., Anthony, C., 2003. Mild therapeutic hypothermia to improve the neurologic outcome after cardiac arrest. Surv. Anesthesiol. 47 (4), 219–220. Pennes, H.H., 1998. Analysis of tissue and arterial blood temperatures in the resting human forearm. J. Appl. Physiol. 85 (1), 5–34. Steck, L.N., Sparrow, E.M., Abraham, J.P., 2011. Non-invasive measurement of the human core temperature. Int. J. Heat. Mass. Transf. 54 (4), 975–982. Stelfox, H.T., Straus, S.E., Khandwala, F., Conly, J., Haslett, J., Zwierzchowski, S., 2010. An observational study of a wireless temporal artery bandage thermometer. Can. J. Anesth. 57.9, 870–871. Terndrup, T.E., Rajk, J., 1992. Impact of operator technique and device on infrared emission detection tympanic thermometry. J. Emerg. Med. 10 (6), 683–687. Teunissen, L.P.J., Klewer, J., de Haan, A., De Koning, J.J., Daanen, H.A.M., 2011. Noninvasive continuous core temperature measurement by zero heat flux. Physiol. Meas. 32 (5), 559. Togawa, T., Togwa, T., Nemoto, T., Yamazaki, T., Kobayashi, T., 1976. A modified internal temperature measurement device. Med. Biol. Eng. Comput. 14 (3), 361–364. Togawa, T., 1985. Body temperature measurement. Clin. Phys. Physiol. Meas. 6 (2), 83. Werner, A., Schlykowa, L., Schlich, G., Koch, J., Sattler, F., Koralewski, H.E., Gunga, H. C., 2009. Preliminary data on a new non-invasive method to measure core temperature with the double sensor under cold conditions. In: NATO. ORTAN Rep. RTO-MP-HFM-168. Xuan, Y., Roetzel, W., 1997. Bioheat equation of the human thermal system. Chem. Eng. Technol. 20 (4), 268–276. Zeiner, A., Klewer, J., Sterz, S., Haugk, M., Krizanac, D., Testori, C., Losert, H., Ayati, S., Holzer, M., 2010. Non-invasive continuous cerebral temperature monitoring in patients treated with mild therapeutic hypothermia: an observational pilot study. Resuscitation 81 (7), 861–866.
Contents lists available at ScienceDirect
Journal of Thermal Biology journal homepage: www.elsevier.com/locate/jtherbio
Use of finite element analysis to optimize probe design for double sensor method-based thermometer Soo Young Sim a, Kwang Min Joo a, Kwang Suk Park b,n a b
Interdisciplinary Program in Bioengineering, College of Engineering, Seoul National University, Republic of Korea Department of Biomedical Engineering, College of Medicine, Seoul National University, Seoul 110-799, Republic of Korea
art ic l e i nf o
a b s t r a c t
Article history: Received 17 January 2015 Received in revised form 19 May 2015 Accepted 19 May 2015 Available online 27 May 2015
Body temperature is an essential vital sign for assessing physiological functions. The double sensor method-based thermometer is a promising technology that may be applicable to body temperature monitoring in daily life. It continuously estimates deep tissue temperature from the intact skin surface. Despite its considerable potential for monitoring body temperature, its key design features have not been investigated. In this study, we considered four design factors: the cover material, insulator material, insulator radius, and insulator height. We also evaluated their effects on the performance of the double sensor thermometer in terms of accuracy, initial waiting time, and the ability to track changes in body temperature. The probe material and size influenced the accuracy and initial waiting time. Finite element analysis revealed that four thermometers of different sizes composed of an aluminum cover and foam insulator provided high accuracy ( o 0.1 °C) under various ambient temperatures and blood perfusion rates: R¼ 20 mm, H ¼ 5 mm; R¼ 15 mm, H ¼10 mm; R¼ 20 mm, H ¼ 10 mm; and R¼ 15 mm, H ¼15 mm. The initial waiting time was approximately 10 min with almost the same traceability of temperature change. Our findings may provide thermometer manufacturers with new insights into probe design and help them fabricate thermometers optimized for specific applications. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Body temperature Deep body thermometer Double sensor method Noninvasive body temperature monitoring
1. Introduction Body temperature is one of the most important factors in metabolic processes such as cell division and enzyme reactions (Davidovits, 2012). An abnormal body temperature range implies that these essential processes are not proceeding properly. Therefore, body temperature measurement is a routine procedure in health examinations. Body temperature can also be intentionally adjusted to suppress injury progression or damage cancer cells. Hypothermia therapy reduces the body temperature by approximately 33 °C and is a widely accepted procedure when clinicians operate on patients suffering from traumatic brain injuries or cardiac arrest (Nikolov and Anthony, 2003; H. Alex et al., 2012). In hyperthermia therapy for cancer treatment, the deep tissue layer is heated up to 42–45 °C (Mitobe and Noboru, 2011). Ever since Hippocrates diagnosed fever using the warmth of his hand in the 5th century, various kinds of thermometers have been developed (Togawa, 1985). In the operating room or intensive care unit of a hospital, body temperature is monitored by inserting a temperature sensor into a body cavity (e.g., rectum, esophagus) or n
Corresponding author. Fax: þ 82 2 745 7870. E-mail address: [email protected] (K.S. Park).
http://dx.doi.org/10.1016/j.jtherbio.2015.05.007 0306-4565/& 2015 Elsevier Ltd. All rights reserved.
a blood vessel (e.g., pulmonary artery) (Lefrant et al., 2003). Although these methods are expected to be accurate because the sensor directly measures the temperature of deep tissue, they are too invasive and intrusive to be applied to conscious individuals. Infrared ear thermometers and axillary thermometers are commonly used in everyday life and medical care settings because they are easy to use. However, the readings of infrared ear thermometers are influenced by the technique of the operator (Terndrup and Rajk, 1992). Furthermore, axillary thermometers require people to hold an arm down tightly at their side while measuring armpit temperature. Therefore, the application of these thermometers to continuous body temperature monitoring in daily life is restricted. Many researchers have sought to develop noninvasive body temperature monitoring devices that use the zero heat flow method (ZHFM), double sensor method (DSM), and dual heat flux method (DHFM) (Fox and Solman, 1971; Gunga et al., 2012; Kitamura et al., 2010) (Fig. 1). The ZHFM-based thermometer (Fig. 1a) (Fox and Solman, 1971) uses a servo-controlled heater to reduce the heat flow crossing the tissue to zero and estimates the deep tissue temperature from the skin surface (Fox and Solman, 1971; Fox et al., 1973). It yields temperature measurements similar to those directly measured in the rectum of stable infants in incubators, in muscle (vastus lateralis), and in the esophagus of
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Fig. 1. Structures of noninvasive deep body thermometers: (a) ZHFM-based thermometer, (b) DSM-based thermometer, and (c) DHFM-based thermometer.
healthy subjects in hot and stable ambient conditions (Dollberg et al., 2000; Brajkovic and Ducharme, 2005; Teunissen et al., 2011). The applicability of thermometers using the DSM (Fig. 1b) has been verified under diverse environments (Gunga et al., 2012). They provided similar results to that of rectal thermometers during intensive work under various ambient temperatures (mean72 S.D.: – 0.1670.90 °C at 10 °C, –0.0870.70 °C at 25 °C, –0.1170.68 °C at 40 °C) (Gunga et al., 2008). DSM-based thermometers have also exhibited the potential to monitor circadian body temperature rhythms or abnormal body temperatures during cardiac surgery (Gunga et al., 2009; Kimberger et al., 2009). DSM-based or DHFMbased thermometers are suitable for unconstrained body temperature monitoring because they do not require an AC power supply for heating. Although the usefulness of various types of deep body thermometers was verified, measurement errors still exist. A portion of the error is inherent because deep body thermometers assume that heat flows only in the longitudinal direction and do not take the transverse heat flow into account. Therefore, some studies have investigated the design of thermometers that create measurement conditions that accord closely with the assumption, thereby improving the accuracy. Togawa et al. modified the conventional ZHFM-based thermometer to improve its performance (Kobayashi et al., 1975; Togawa et al., 1976). Steck et al. (2011) carried out numerical simulations to discover the best performing sensor design for a ZHFM-based thermometer. Huang et al. (2014) recently evaluated the structural and thermophysical effects on
the accuracy of the DHFM-based thermometer. However, the design of the DSM-based thermometer has not been considered. Therefore, we studied the influence of probe design factors (size and material) on the accuracy, initial waiting time, and traceability of temperature changes. We expect that this study will help researchers obtain insights into the DSM-based thermometer design and fabricate thermometers optimized for specific applications.
2. Materials and methods We implemented finite element simulations to evaluate the effects of probe size (radius and height) and material (insulator and cover) on the performance of the DSM-based thermometer. 2.1. Principle of the double sensor method The DSM-based thermometer is comprised of two thermistors, an insulator, and a cover (Fig. 2). The vertical heat flow from deep tissue to the probe cover is used to estimate deep body temperature. Approximately 10 min after attaching the probe to the skin, the thermal conditions around the measurement area reach equilibrium (Kimberger et al., 2009). At thermal equilibrium, the heat flow from the core towards the skin layer and the heat flow across the sensor are balanced. Each heat flow can be expressed as:
⎧ H = Ktis × (Td − T1) ⎨ ⎪ ⎩ H = Kinsul × (T1 − T2 ) ⎪
Fig. 2. Schematic diagram of the double sensor method. Heat flows vertically from deep tissue to the cover. Td is the deep tissue temperature. T1 and T2 are the measured temperatures at each point. Td is estimated from T1 and T2 and the ratio of thermal conduction coefficient of the insulator to that of human tissue (K¼Kinsul/ Ktis) using Td = T1 + K × (T1 − T2 ) .
(1)
where H, Td, T1, and T2 denote the heat flow, deep tissue temperature, skin temperature under the insulator, and the temperature above the insulator, respectively. Ktis and Kinsul are the heat conduction coefficient of the human tissue and insulator, respectively. Solving the simultaneous equation in Eq. (1), the deep tissue temperature can be estimated using the temperatures measured from two thermistors:
Td = T1 + K × (T1 − T2 ) where K =
Kinsul Ktis
(2)
S.Y. Sim et al. / Journal of Thermal Biology 52 (2015) 67–74
Fig. 3. The four design factors considered in this study: r, h, Mins, and Mcov. The parameters r and h represent the radius and height of the insulator, respectively. Mins and Mcov indicate the material of insulator and cover, respectively. To determine the effect of material, we considered cork, foam, hard rubber, and nylon as the insulators. Acrylic and aluminum were employed for the cover. We varied the insulator size to investigate its influence on body temperature estimation. We changed the insulator radius from 10 mm to 30 mm and its height from 5 mm to 15 mm. The human tissue under DSM-based thermometer was composed of skin, fat, and bone layers. The cover thickness was fixed at 2 mm.
where K is the ratio of the heat conduction coefficient of the insulator to that of tissue layer. The thermal resistance of a multitissue layer can be calculated as the sum of the thermal resistances of each layer (e.g. skin, fat, and bone). The heat conduction coefficient of multi-layer tissue (Ktis) can be computed using
x fat xtis x skin x bone = + + Ktis⋅A K skin⋅A K fat⋅A Kbone⋅A
(3)
where xtis, xskin, xfat, and xbone are the thicknesses of the total tissue, skin, fat, and bone layers, respectively, and the corresponding thermal conduction coefficients for these layers are denoted as Ktis, Kskin, Kfat, and Kbone, respectively. A is the heat conduction area. 2.2. Simulation study 2.2.1. Simulation model and design factors Heat transfer analysis was performed using the finite element method (FEM) simulation package COMSOL Multiphysics (COMSOL Inc., Sweden). As shown in Fig. 3, the simulation model was divided into five parts: the skin layer, fat layer, bone layer, insulator, and cover. A human tissue layer was established to model the forehead, which is one of the most common sites for measuring
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deep body temperature because the anatomy is relatively similar across individuals (Finvers et al., 2006; Werner et al., 2009; Zeiner et al., 2010). The forehead model was derived from a previous study (Steck et al., 2011). The thicknesses of the skin, fat, and bone layers were 2 mm, 3 mm, and 5.4 mm, respectively. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. Metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The radius of the tissue model was 60 mm. When modeling the insulator and cover, we considered four design factors: the radius (r), height (h), and the materials of the insulator (Mins) and the cover (Mcov). Cork, foam, hard rubber, and nylon were used to test the effect of the insulator material, all of which have previously been used as the insulator. Acrylic and aluminum were employed for the cover. In addition, we accounted for the anodized metal to examine the effect of the emissivity of the cover. The insulator size was varied to investigate its influence on body temperature estimation. The radius of the insulator was changed from 10 mm to 30 mm and its height from 5 mm to 15 mm. The values were manually altered rather than using a parametric sweep. The mesh was set using a user-controlled mesh. The maximum element size was 5 mm and the minimum element size was 1 mm. The maximum element growth rate was 1.3. The curvature factor was 0.5. The resolution of narrow regions was 0.6. Table 1 shows the thermal properties of the materials (Steck et al., 2011; Huang et al., 2014; Apache-Tables, IES VE). In all trials, the minimum mesh quality was maintained above 0.1, which is a typical criterion for acceptable mesh quality. 2.2.2. Mathematic formulation for understanding temperature distribution in model The Pennes bioheat equation (Pennes, 1998) is widely used to understand temperature distributions in human tissue and is given by
ρt ct
∂Tt = ∇⋅(kt ∇Tt ) + ωρ b cb (Ta − Tt ) + Q met ∂t
(4)
where kt, ρt, and ct represent the thermal conductivity, density, and specific heat of tissue, respectively. Tt is the tissue temperature and Ta is the arterial blood temperature. The arterial blood temperature was assumed to be equivalent to the deep tissue temperature. The third term is related to heat transfer by blood perfusion, where ω, ρb, and cb are the blood perfusion rate, density, and specific heat of blood, respectively. The thermal equilibrium between the blood and the surrounding tissue was assumed (Xuan. and Roetzel, 1997). And the blood is uniformly perfused in each tissue layer. Qmet is the heat transfer by metabolism.
Table 1 Thermal properties of the materialsa. Specific heat (J/kg °C)
Density (kg/m3)
Thermal conductivity (W/m °C)
Emissivity
Tissue (forehead)
Skin Fat Bone Blood
3766 2510 1590 3900
1000 850 1500 1050
0.21 0.16 1.16 –
0.98 – – –
Insulator
Cork Foam Hard rubber Nylon
1800 1900 1000 1700
120 24 1200 1150
0.04 0.06 0.15 0.26
– – – –
Cover
Acrylic Aluminum Aluminum (anodized)
1433 896
1140 2800
0.14 200
0.95 0.05 0.77
a
The thermal properties of each material were cited from Steck et al. (2011), Huang et al. (2014), and Apache-Tables guide (IES VE).
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The outer surface of the cover and skin exchange heat with the surrounding air through convection and radiation. However, the convection effect was ignored as in a previous study because the probe is covered by a cloth (Huang et al., 2014). We applied the Stefan–Boltzmann law to express the radiative heat exchange around boundaries:
(
∇⋅(k∇T) = εσ T A4 − T 4
)
(5)
where k is the thermal conductivity of the boundary substance, TA and T are the ambient and boundary temperatures of the material, respectively, and s and ε are the Stefan–Boltzmann constant and emissivity of the boundary substance, respectively. The thermal insulation boundary condition was used on the vertical boundaries of the tissue layers. 2.3. Performance analysis of DSM-based thermometer We assessed the performance of the DSM-based thermometer in terms of measurement accuracy, initial waiting time, and traceability of temperature changes. 2.3.1. Accuracy To evaluate accuracy, we calculated the estimation error, defined as the absolute difference between the estimated and actual deep body temperatures. To compute the accuracy of each design, we implemented a stationary solver, which assumes a thermally steady-state condition. The Multifrontal Massively Parallel Sparse (MUMPS) direct solver was used to solve the system of equations. For the stopping criterion, a relative tolerance was 0.001. The ambient temperature and blood perfusion rate can differ depending on the measurement environment. In particular, the blood perfusion rate can change depending on the subject’s activity (Dittmar et al., 2006). To identify the DSM-based thermometer design that accurately estimates body temperature under diverse conditions, we varied the ambient temperature and blood perfusion rate. The ambient temperature was increased from 20 °C to 30 °C in steps of 2 °C. The variation in the blood perfusion rate was derived from a previous approach (Steck et al., 2011) where ωskin was changed from 0.00013 (1/s) to 0.01213 (1/s) and ωfat was changed from 0.000019 (1/s) to 0.002019 (1/s). 2.3.2. Initial waiting time The initial waiting time is the time required for the DSM-based thermometer to reach thermal equilibrium. Reducing the initial waiting time is a challenge for noninvasive deep body thermometers. Kimberger et al. (2009) stated that a long initial waiting time can preclude the practical monitoring of body temperature. To evaluate the initial waiting time, we used a time-dependent solver. Deep body temperature was maintained at 37 °C and we obtained data from 0 to 120 min over intervals of 1 min. MUMPS direct solver was used to solve the system of equations. We used a relative tolerance of 10 3 and an absolute tolerance of 10 6 for the local error control in the solver. The backward differentiation formula (BDF) was used as the time stepping method. The maximum and minimum BDF orders were 2 and 1, respectively. The steps taken by the solver were strictly controlled, which the maximum step set 1 min. We then identified the time when the gap between the estimated body temperature and temperature at thermal equilibrium decreased to below 0.1 °C. 2.3.3. Traceability of temperature changes A body temperature monitor should reflect the temperature variation. To evaluate the traceability of temperature changes, we used a time-dependent solver. During the initial 60 min, deep body temperature was maintained at 37 °C. The deep body
temperature was then decreased from 37 °C to 35 °C at a rate of – 0.2 °C/min (Kitamura et al., 2010). When the deep body temperature reached 35 °C, it was maintained for the remaining 60 min. We obtained data for 130 min in intervals of 1 min. The solver configuration was the same as in Section 2.2.2.
3. Results We began by evaluating the influence of the probe material on the performance of the DSM-based thermometer. We analyzed the performance in terms of accuracy and initial waiting time. After identifying the optimal combination of insulator and cover material, we examined the effect of probe size. 3.1. Effects of probe material on performance We tested accuracy of the DSM-based thermometer for 12 material combinations derived from four insulator and three cover materials for either ambient temperatures between 20 °C and 30 °C (Fig. 4a) or a range of blood perfusion rates in the skin and fat layers of –0.00013rωskin r0.01213 and 0.000019rωfat r0.002019, respectively (Fig. 4b). In Fig. 4a, the blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. In Fig. 4b, the ambient temperature was 25 °C. In both trials, deep body temperature was 37 °C and metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The radius and height of the insulator were fixed at 20 mm and 10 mm, respectively. Under both measurement conditions, the acrylic cover had a lower accuracy than the aluminum or anodized aluminum cover irrespective of the insulator material. The anodized aluminum cover has a higher emissivity than aluminum. Its accuracy was lower than that of the aluminum cover. Therefore, the aluminum cover had the lowest emissivity and was the most accurate with a maximum absolute error of less than 0.2 °C in all trials. When the thermal conductivity of the insulator was higher, the maximum absolute error was larger. To determine the initial waiting time for each material combination, we observed the deep body temperature for 120 min. In this trial, the ambient temperature was maintained at 25 °C. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. And metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The initial waiting time was defined as the time when the difference between the estimated core temperature and the estimated temperature at thermal equilibrium fell below 0.1 °C. Two deep body temperature estimation curves were observed (Fig. 5a): a temperature curve that reaches thermal equilibrium at approximately 10 min and a temperature curve that reaches thermal equilibrium after 19 min. For example, the curve for the aluminum cover and foam insulator reached thermal equilibrium after 7 min. In contrast, the curve for the aluminum cover and nylon insulator reached thermal equilibrium after 25 min. In general, the initial waiting time was shortest for the acrylic cover. It was longer than 19 min for the probe with an aluminum or anodized aluminum cover and a hard rubber or nylon insulator (Fig. 5b). For the cork or foam insulator, the initial waiting time of approximately 10 min was similar to that of Kimberger et al. (2009). The green dotted line in Fig. 5b represents the thermal conductivity of each insulator. The DSM-based thermometer with the acrylic cover showed subtle changes in initial waiting time for four kinds of insulators. There was a strong positive correlation between the thermal conductivity and initial waiting time for aluminum or anodized aluminum covers (r ¼0.97). In contrast, there was a negative correlation between the thermal diffusivity and the initial waiting time with aluminum or anodized aluminum covers
S.Y. Sim et al. / Journal of Thermal Biology 52 (2015) 67–74
71
1.4
Max. Abs. Err.(°C)
1.2 1
acrylic cover aluminum cover anodized aluminum cover
0.8 0.6 0.4 0.2 0 Cork
Foam
Hard rubber
Nylon
Hard rubber
Nylon
1.4
Max. Abs. Err.(°C)
1.2 1
acrylic cover aluminum cover anodized aluminum cover
0.8 0.6 0.4 0.2 0
Cork
Foam Insulator
Fig. 4. The accuracy of 12 kinds of material combinations under various ambient temperatures (a, top) and blood perfusion rates in tissue (b, bottom). The y-axis of each figure represents the maximum absolute error. In (a), the ambient temperature ranged from 20 °C to 30 °C. In (b), the blood perfusion rate in the skin layer, ωskin, changed from 0.00013 (1/s) to 0.01213 (1/s) and that in the fat layer, ωfat, from 0.000019 (1/s) to 0.002019 (1/s). In both trials, deep body temperature was 37 °C. And the radius and height of the insulator were fixed at 20 mm and 10 mm, respectively.
(r ¼ 0.66). On the basis of these results, we decided to design a probe with an aluminum cover and foam insulator. This combination had superb accuracy ( o0.1 °C) in diverse measurement conditions and an initial waiting time of less than 10 min. Although the probe with the aluminum cover and cork insulator performed similarly, we opted for the foam insulator given its lower weight. 3.2. Effects of probe size on performance The area and height of the probe influences the accuracy of the deep body thermometer (Huang et al., 2014). To examine the effect of the probe size, we varied the insulator radius from 10 mm to 30 mm and the insulator height from 5 mm to 15 mm in 5 mm steps. We determined the accuracy of 15 DSM-based thermometers of different sizes under various measurement conditions (Fig. 6). In the first trial, the ambient temperature was increased
from 20 °C to 30 °C in steps of 2 °C and the error was calculated at deep body temperatures of 34 °C, 37 °C, and 40 °C. The blood perfusion rate in the skin and fat layers was 0.0072 (1/s) and 0.0000045 (1/s), respectively. Metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. The accuracy generally appeared to decrease as the radius or height of the insulator increased (Fig. 6a). The accuracy was the best overall at an insulator height of 5 mm and showed the least dependence on the radius. In contrast, under various blood perfusion rates in human tissue, the maximum absolute error was approximately 0.3 °C at a radius of 10 mm (Fig. 6b). In this trial, deep body temperature was 37 °C and the ambient temperature was 25 °C. The metabolic heat generation rate was 1040 W/m3 in the skin layer and 3.67 W/m3 in the fat layer. Although the accuracy at a probe height of 5 mm was lower by approximately 0.1 °C compared with a probe of height 15 mm when the radius was 15 mm, there was no consistent trend
Fig. 5. The initial waiting time of 12 kinds of material combinations. (a) Typical temperature estimation curves. The y-axis of the figure represents the estimated deep body temperature. (b) Initial waiting time (Init. Wait. Time) for each material combination. The green dotted line represents the thermal conductivity of each insulator. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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Fig. 6. The accuracy of 15 DSM-based thermometers of different sizes under various ambient temperatures (a, top) and blood perfusion rates in tissue (b, bottom). In (a), the maximum absolute error (Max. Abs. Error) was calculated when ambient temperature ranged from 20 °C to 30 °C. Three deep body temperatures (DBT: 34 °C, 37 °C, 40 °C) were considered. In (b), the blood perfusion rate in the skin layer, ωskin, changed from 0.00013 (1/s) to 0.01213 (1/s) and that in fat layer, ωfat, from 0.000019 (1/s) to 0.002019 (1/s). Deep body temperature was maintained at 37 °C. In both trials, the thermometer consisted of an aluminum cover and a foam insulator.
in the effect of height on accuracy. On the basis of these results, we selected probe sizes that offered a maximum absolute error of less than or equal to 0.1 °C under various measurement conditions. In addition, we restricted the radius of the probe to 20 mm, which would allow it to be stably fixed on the forehead. The probes with the following dimensions satisfied the selection criteria: R¼ 20 mm, H¼ 5 mm; R¼15 mm, H ¼10 mm; R¼ 20 mm, H ¼10 mm; and R ¼15 mm, H¼15 mm. Finally, we examined the effects of insulator size on initial waiting time and traceability of temperature changes (Fig. 7). The probe with a radius of 20 mm and a height of 5 mm required 11 min to reach thermal equilibrium (Fig. 7a) and showed good traceability when the core temperature decreased from 37 °C to 35 °C (Fig. 7b). The initial waiting time of other sizes of probes was approximately 10 min. The probe with radii and heights of R¼ 15 mm, H¼ 10 mm; R¼20 mm, H¼ 10 mm; and R ¼15 mm, H ¼15 mm required 9 min, 7 min, and 7 min to reach thermal equilibrium. All four sizes of DSM-based thermometers had almost the same traceability (data not shown). The DSM-based thermometer exhibited a lag of approximately 4 min until the measurement decreased to within 0.1 °C of the reduced temperature.
4. Discussion DSM-based thermometers are expected to be useful in noninvasive and continuous monitoring of body temperature. In previous studies, the validity of the DSM was verified by comparing it with other existing thermometers (e.g., esophageal). Although this method exhibited superior accuracy for skin, bladder, or tympanic temperatures, impermissible errors still occur (Kimberger et al.,
2009; Zeiner et al., 2010). A wireless bandage-type thermometer based on the double sensor method showed a discrepancy that was larger than 2 °C when compared with a bladder thermometer (Stelfox et al., 2010). Therefore, we investigated the effects of probe design to improve the capability of the DSM-based thermometer. In addition, we modeled the forehead because of its similarity across individuals and the thin skin layer above the temporal artery. In clinical trials, the probe can be attached to the forehead with medical adhesive tape. In daily life, the deep body temperature can be monitored from the forehead by wearing a headband or helmet in which the thermometer is embedded. In future studies, we will consider other body parts such as the chest for nonintrusive deep body temperature monitoring in daily life. We confirmed that the aluminum cover had the best accuracy amongst three kinds of covers. The emissivity of the cover material influenced the accuracy for the anodized aluminum and aluminum covers. The insulator material also affected accuracy. In general, accuracy was higher for insulator materials with low thermal conductivity (e.g., cork, foam). This corresponds to results from previous research on DHFM-based thermometers, which found that low conductivity insulators improved measurement accuracy (Huang et al., 2014). We inferred that the low thermal conductivity of the insulator helps to interrupt the transverse heat flow. This makes the thermometer correspond more closely to the assumption that heat flows only in the vertical direction in the DSM-based thermometer. This work also evaluated the dynamic performance of the DSMbased thermometer (i.e., initial waiting time, traceability of temperature changes). An assessment of material effects showed that an acrylic cover required a shorter initial waiting time than an aluminum or anodized aluminum cover. In addition, when the
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Fig. 7. The dynamic performance of a DSM-based thermometer with 20 mm radius and 5 mm height. (a) Deep body temperature estimation curve. The y-axis represents the estimated deep body temperature. The initial waiting time was 11 min. (b) Traceability of temperature changes of probe of 20 mm radius and 5 mm height. All four thermometers showed similar traceability of temperature changes: R ¼20 mm, H¼ 5 mm; R ¼15 mm, H¼ 10 mm; R ¼ 20 mm, H¼ 10 mm; and R ¼15 mm, H¼ 15 mm.
cover was made of aluminum or anodized aluminum, insulators with a higher thermal conductivity (e.g., hard rubber, nylon) required a longer time to reach thermal equilibrium. We assumed that the probe with an insulator of higher thermal diffusivity would require a shorter initial waiting time. When the thermometer cover was made of aluminum or anodized aluminum, the correlation coefficient between the thermal diffusivity of the insulator and the initial waiting time was –0.66. However, the DSMbased thermometer with the acrylic cover showed subtle changes in initial waiting time regardless of insulator materials. Therefore, the cover material also influenced the initial waiting time. After selecting the optimal combination of aluminum cover and foam insulator, we investigated the effects of the probe size on the performance of the DSM-based thermometer. Fifteen thermometers of different sizes exhibited a maximum absolute error below 0.15 °C under various ambient temperatures (20–30 °C). In particular, at an insulator height of 5 mm, the probe had a maximum absolute error below 0.05 °C and the radius did not affect the accuracy significantly. In contrast, the insulator radius influenced the measurement accuracy under various blood perfusion rates. As the insulator area increased, the maximum absolute error decreased. This result also coincided with previous work showing that the accuracy of a DHFM-based thermometer is proportional to the insulator radius (Huang et al., 2014). This was explained in terms of the large area of the insulator suppressing the transverse
heat flow, which in turn results in ideal measurement conditions for the DSM-based thermometer. There was a gap in the initial waiting time when the probe size differed. However, four probes of different sizes with the same materials showed a similar traceability of temperature changes.
5. Conclusions We investigated the effects of varying the probe design on the performance of a DSM-based thermometer. The combination of a cover with low emissivity (e.g., aluminum) and an insulator with low thermal conductivity (e.g., foam) provided accurate measurements. Both the cover and insulator material influenced the initial waiting time. In addition, the probe size influenced the measurement accuracy and initial waiting time. The accuracy was improved for insulators of larger radius and lower height. The probe size slightly affected the initial waiting time. However, there was no observable difference in temperature traceability as long as the material combination for the probe remained the same. We expect that the knowledge gained from this study could provide thermometer manufacturers with new insights into designing and fabricating probes optimized for specific applications.
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Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) Grant (No. NRF-2012R1A2A2A02010714) funded by the Ministry of Science, ICT and Future Planning, and by the Bio & Medical Technology Development Program of the NRF funded by the Korean government, MSIP (NRF-2014M3A9E3064623).
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