Deep body temperature (DBT) has yet to be measured continuously in everyday life, even though it is useful in physiological monitoring and chronobiology studies. We tried to address this issue by developing a transcutaneous thermometer based on the dual-heat-flux method (DHFM) invoking the principle of heat transfer, for which measurement error was mitigated by elaborate design. First, a structural modification based on the original design of the DHFM was implemented by the finite element method. Based on the results of the simulations, prototypes were then implemented and tested with an experimental system that mimicked the thermometer being applied to skin. The simulation phase proposed the adoption of an aluminum cover to boost measurement accuracy and suggested that thermometers of different height be chosen according to specified requirements. The results of the mock-up experiments support the modification put forward in the simulation phase: the standard type (15 mm in height) achieved the accuracy with error below 0.3°C while the thin type (9 mm in height) attained accuracy with error less than 0.5°C under normal ambient temperature ranging from 20 to 30°C. Even though the design should also be examined
Deep body temperature (DBT) is one of the vital signs for human beings and is typically referred to as the temperature of the natural cavities, for example, the abdomen and the thorax. Strictly speaking, DBT can only be measured by invasive methods such as catheter insertion into rectum [
However, noninvasive methods are more acceptable and are therefore more widely used. They can provide approximation to the DBT, which is the temperature at a certain depth under the skin reflecting the real DBT. One good alternative to the invasive methods is the zero-heat-flux method [
However, continuous DBT measurement is necessary in situations such as heat strain monitoring [
More often, it is the temperature fluctuations rather than absolute temperature readings that interest us in the healthcare domain. However, the changes in readings by the devices should be caused by actual changes in the physiological state and not by some external influence. From this viewpoint, an ear-inserted thermometer is not a good choice because its measurements are evidently influenced by the ambient environment. The infrared tympanic thermometer is able to reflect internal change but is sensitive to its positioning.
The mechanism of the thermometer should also be universal; it should be applicable to different people. More specifically, even in the same person, the thermal conductivity of the skin might differ temporally and spatially. A thermometer based on the exact value of the personal physiological condition [
The above concerns can be addressed properly by the dual-heat-flux method (DHFM) [
Illustration of dual-heat-flux method. The heat flows from deep body into the thermometer longitudinally and thus the DBT can be calculated with the four inlaid sensors (
The criterion of accuracy for clinical use is 0.1°C conventionally, which is not readily met by noninvasive methods [
At least four inlaid temperature sensors are necessary for a thermometer based on DHFM. They are
Generally speaking, DBT is strictly regulated by hypothalamus and it changes tardily in accordance to biorhythm. These characteristics make the measurement with DHFM applicable. For such a passive method with heat insulator as the substrate material, it takes time for initial response.
Bioheat transfer involves blood perfusion and metabolic processes. It can be well described by the Pennes equation [
The second and third terms on the right denote the heating effect of blood perfusion and metabolism. However, these two terms were not considered in this model because this kind of evenly distributed heat source would alter the actual value of the measurement somewhat but would not invalidate the qualitative relations from the simulation. Further, because the DBT should vary in a quasistatic manner, the temporal change was not considered.
Because we assumed that the thermometer and skin were covered by suitable clothing, heat convection was neglected. However, radiation was inevitable; therefore, the boundary conditions of the thermometer and its surrounding skin could be described by the Stefan-Boltzmann law [
In the simulation phase, we sought to improve the thermometer’s accuracy by structural modification, while reserving the wearability of the thermometer. Therefore, an additional component, a peripheral aluminum ring (PAR), was introduced in view of the high emissivity of the insulator component. There were two kinds of thermometers in this simulation, with and without the PAR, as shown in Figures
Sectional view of two models. The original structure is without PAR (a), while the modified structure with PAR is shown by (b).
As shown in Figure
In this model, the rubber was used as insulator and the aluminum was used as the metal. Necessary physical parameters are tabulated in Table
Thermal properties of various materials
Component | Conductivity | Density | Specific heat | Emissivity |
---|---|---|---|---|
(W/m·°C) | (kg/m3) | (J/kg·°C) | ||
Skin | 0.17 | 1100 | 3500 | 0.98 |
Rubber | 0.06 | 180 | 2010 | 0.95 |
Aluminum | 400 | 8700 | 385 | 0.05 |
In practical implementation, the values of the parameters or even the specified materials may be different. The lower the conductivity of the insulator, the higher the accuracy at the cost of a longer initial response in general. The simulation here serves as an examination of the new design.
Based on the results of the simulation, we fabricated two prototypes of different heights,
Prototypes of thermometers based on DHFM. Line-up of the standard type and thin type is shown.
The probe of the thermometer connects to the main processing board by USB cable (Mini to Standard plug). The main processing board consists mainly of the controlling unit (ATmega164A, Atmel RISC Microcontroller; Atmel, San Jose, CA), a memory unit with 8 Mb serial flash memory to store the infradian data, and a battery unit to supply three days of energy for the whole local system. Data stored locally can be retrieved with a specialized program run on the PC as a CSV file.
The structures suggested by the simulation phase should be validated by mock-up experiments before being applied in practical measurement. A standard experimental system [
Illustration of the mock-up experiment system. The temperature of the water was used to mimic the DBT, while the natural rubber was used to mimic the skin layer.
The prototypes were tested in three conditions: without PAR (N), with PAR (A), and without PAR but with sponge cover (S). Through this phase, we hoped to find out whether the new component (i.e., the PAR) would influence the measurements as predicted by the simulation. Condition S was adopted to confirm the effect of the sponge in measuring accuracy; although it is obstructive in practical measurement, it is reportedly indispensable [
The range of normal Combination 1: Combination 2: Combination 3:
For each combination, experiments were conducted three times and for each condition of the thermometer (N, A, and S) 30 minutes was given for the establishment of heat equilibrium inside the probes. The two probes (thin and standard types) were tested in rotation to remove the heat stored in the previous trial.
In this phase, while the ambient temperature
For thermometers both with and without PAR, all 24 thermometers defined by the combinations of 4 different heights and 6 different radii were considered and modeled. The measurements from each thermometer are summarized in Figure
Results of simulation based on FEM. (a) and (b) show the measurements of thermometers in condition N and condition A, respectively.
From the results, we can see that the effects of the dimensions were different. For the thermometer without PAR, generally, the accuracy was proportional to the radius, but inversely proportional to the height. A change of dimensions influences the measuring accuracy greatly when the radius is less than 40 mm. Furthermore, the radius is more effective than the height. A twofold increase in radius benefits the accuracy much more significantly than does a half-size decrease in height.
For the thermometers with PAR, the accuracy was proportional to height and radius. It is easier for them to attain much greater accuracy with a radius greater than 20 mm. Moreover, the height is definitive in these thermometers, as no distinct improvement can be seen by changing the radius of thermometers of the same height, with a radius larger than 30 mm.
According to the simulation results, with both standard and thin types, we can attain the acceptable margin of error (<0.5°C) that is hard to attain in the designs without PAR.
In this phase, the combinations of experimental conditions (Combination 1, Combination 2, and Combination 3) were all tested and Combination 2 was the same as in the simulation phase. For both thermometers, all three conditions (A, N, and S) were tested three times each.
The results for these tests are shown in Figure
Results of mock-up experiments for both thermometers. Results of standard type were summarized in (a) and thin type in (b).
In condition N, the spans of the error were about 0.5 and 0.3°C for standard and thin type, respectively. By contrast, the spans were about 0.2°C for both types in condition A. This suggests that the PAR takes effect in resisting the influence of the ambient environment.
As we have introduced, the method is applicable in measuring the DBT that change at a slow manner. For extreme situation such as anesthesia or heatstroke, time delay happens. In a simulation whose results were not shown here, the standard type was used to monitor the abrupt change of DBT at a rate of 0.2°C/minute lasting for 10 minutes. The thermometer could indicate the change in about 4 minutes and became stable in 20 minutes after the change. For such situation, the thin type, whose reading will become stable in about 10 minutes, might be suited to trace the change.
If the thermometer is applied to the upper torso, for example, the thorax, the thermometer may come into contact with clothes from time to time. The physically thin layer and low conductivity of clothes would hardly change the resistance of the thermometer. However, the relatively high emissivity (0.75–0.90) [
The adoption of a PAR was based on the physical characteristics of metals, which usually have a much lower emissivity than heat insulators (e.g., rubber), and, at the same time, the radioactive energy exchange is the main reason for the horizontal heat flow distorting the practical situation from the theoretical assumption of DHFM. With a PAR, the influence of the ambient environment may be mitigated remarkably because this thermometer is designed to be worn on the torso with suitable clothing, which will shield the thermometer from the influence of airflow from concerted movement. It is also the reason why the convection was neglected in the boundary condition of the simulation.
In the simulation phase, only one pair of
By comparing the results with and without PAR, distinctly different patterns of the dimensional effects (height and radius) could be seen. Further, improvements in accuracy were attained for thermometers of the same size.
In the previous study on DHFM-based thermometers [
In the simulation phase, multiple sizes (height and radius) were tested, but only the 22.0 mm radius and the 15.0 and 9.0 mm heights were adopted in the fabrication stage; this limitation was imposed to retain only compact wearable sizes. An increase in radius to more than 30 mm gives minor improvement but will bring about difficulties in installation and an obstructive feeling.
Only 3 combinations of the ambient temperature and the DBT were investigated here. For ambient temperature, lower value results in lower accuracy due to radiation, while the relatively higher DBT would contribute to a more accurate result [
In the experimental phase, condition S was adopted to confirm the influence of the sponge in measuring accuracy. Its positive influence on measuring accuracy may be because of the heat-insulating effect shielding the thermometer and the surrounding surface of skin from the ambient environment. However, it is actually obstructive in practical measurement and may not be suitable for wearable use.
As previously mentioned, at the mock-up experiment stage, rubber sheets of different thicknesses were tested. As we expected, the thicker the sheet, the larger the measuring error. The two prototypes were able to measure the DBT (water temperature) accurately until the thickness was increased to 8.0 mm. The error became larger than 0.5°C for both thermometers when the sheet was increased to 10.0 mm in thickness. The main reason may lie in the abrupt decrease of the reading of sensor
For this kind of thermometer, which depends on a heat source from the human body, the resistance to the influence of ambient change is crucial. Judging from the results of these experiments, the error spans that came with the change of
The theory of this method suggests that
With the measurements in this study, we also tried to adjust
This was a preliminary study on the capability of a new kind of noninvasive DBT thermometer based on DHFM. The simulation study based on FEM brought this theory to a practical stage by proposing a new component, the PAR, to improve the accuracy and stability.
The designs were then implemented and validated through mock-up experiments. The measurement errors were mitigated to a level of less than 0.5°C for both designs. The standard type of 15 mm in height had better accuracy than the thin type, as the simulation predicted. Even though further
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study was supported by the Keihanna Science City Healthcare Project of the Ministry of Education, Culture, Sports, Science and Technology, Japan, and by Tateisi Science and Technology Foundation, Japan. The authors wish to thank Professor Yoshida Masaki for his kind support throughout the experiment stage.