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Experimental estimation of the emissivity of human enamel and dentin
Journal Pre-proofs Experimental estimation of the emissivity of human enamel and dentin Ahmad Soori, Farshad Kowsary, Shahin Kasraei PII: DOI: Reference:
S1350-4495(19)30890-4 https://doi.org/10.1016/j.infrared.2020.103234 INFPHY 103234
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Infrared Physics & Technology
Received Date: Revised Date: Accepted Date:
24 October 2019 7 February 2020 9 February 2020
Please cite this article as: A. Soori, F. Kowsary, S. Kasraei, Experimental estimation of the emissivity of human enamel and dentin, Infrared Physics & Technology (2020), doi: https://doi.org/10.1016/j.infrared.2020.103234
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Title page
Experimental estimation of the emissivity of human enamel and dentin Ahmad Sooria, Farshad Kowsarya, *, Shahin Kasraeib aSchool
bDepartment
of Mechanical Engineering, Tehran University, Tehran, Iran
of Restorative Dentistry, Dental School, Shahid Beheshti University of Medical Sciences, Tehran, Iran
Corresponding author: Corresponding author: Farshad Kowsary* Mailing address: School of Mechanical Engineering, College of Engineering, North Kargar St., Tehran, Iran Tel.: +9821-61119924; Fax: +9821-88013029 E-mail: [email protected]
Abstract
Heat transfer occurs frequently in numerous dental treatment procedures. In almost all of the related experimental studies, use of infrared camera for temperature measurement, is becoming more and more popular, considering the many advantages of this technique. This technique has been employed in some recent studies as a non-invasive method for disease diagnosis. However, use of the infrared camera for temperature measurements requires knowledge of the emissivity of the target surface. The present in vitro study aims to determine the emissivity of enamel and dentin. The emissivity of enamel was found to be 0.96±0.01 in the temperature range of 20°C to 40°C and 0.97±0.01 in the temperature range of 40°C to 60°C. The emissivity of dentin was found to be 0.92±0.01 at 20°C to 40°C and 0.93±0.01 at 40°C to 60°C. The difference in the emissivity of enamel and dentin can be attributed to their different composition and constituents, structure and surface quality.
Keywords: Emissivity; Infrared Thermography; Dental Enamel; Dentin; Heat Transfer
Introduction
Heat transfer is important in dental treatments and daily life [1]. Oral thermal alterations have been reported in the range of -5°C to 76.3°C [2]. Advances in contemporary dentistry led to the use of some heat generating equipment such as dental lasers [3, 4], light-curing units [5-7], and highspeed hand-pieces [8, 9] in the oral environment. The generated heat by such equipment can irreversibly damage the enamel and dentin. Enamel and dentin are sensitive to mechanical stresses
created by temperature rise. These stresses can cause microscracks and result in pain and tissue injury, and negatively affect the longevity of the tooth [10, 11]. Also, the nerve tissue present in dental pulp is heat sensitive, and temperature rise to 5.5°C in pulp-dentin complex can cause irreversible damage to the nerves [12]. The amount of temperature rise in use of the abovementioned equipment is affected by a number of controllable and uncontrollable parameters. For instance, the heat generated by laser irradiation or light-curing units is a function of intensity, power, and duration of radiation. The heat generated by hand-pieces is a function of type of irrigation, use of an old or new bur, shape and structure of bur, rotational speed, and the applied pressure [1, 13]. Studies on heat transfer can help assess the role of different parameters in heat generation and optimize the design and application strategy of equipment in clinical dentistry to increase the success of treatment and minimize complications. Heat transfer is also important in some procedures. For instance, it can be used for vitality testing of the teeth. Contact and non-contact methods are currently employed for measurement of temperature in heat transfer experiments. In contact measurement method, a temperature sensor, for example a thermocouple is used for temperature measurement. However, use of thermocouples is problematic due to the small size of the teeth and the contact resistance between the thermocouple and surface. Presence of contact resistance between the thermocouple and surface can cause significant errors in measurement of surface temperature. Among the non-contact temperature measurement methods, infrared thermography is a non-invasive and highly accurate technique for measurement of surface temperature in medicine and dentistry [14-16]. Kells et al. [17]used thermographic cameras to assess the vitality of the teeth and concluded that this method was comparable to laser Doppler flowmetry in terms of performance. Paredes et al,
[18] in an in vitro study assessed the efficacy of infrared thermography for dental diagnoses and concluded that thermographic recordings for 5 min can differentiate between a vital tooth and a tooth with necrotic pulp. On the other hand, Smith et al. [19] concluded that thermal changes at the tooth surface cannot serve as a simple and useful clinical tool for assessment of tooth vitality. Zakian et al. [20] used infrared imaging for detection of dental caries. They concluded that thermal imaging has the ability to discriminate between areas that are either sound or have an incipient carious lesion on the outer half of the enamel and areas with lesions extending deeper into the enamel. This method can be used for detection of incipient enamel caries in extracted teeth. Further in vivo investigations are required to assess the efficacy of this method for vital teeth [20]. Sakagami and Kubo [21] assessed a non-destructive thermographic method in a series of in vitro experiments based on measuring the transient surface temperature following a thermal pulse. They introduced it as a diagnostic modality in dentistry
It is necessary to know the emissivity value of a material to correctly read the temperature using a thermographic camera. Some recent studies that used an infrared camera coated the surface with a carbon spray to increase the emissivity. The disadvantage of this method is that this additional layer may alter the transient temperature variation [22, 23] and in some cases , the emissivity is presented without explanation of derivation [18, 21, 24, 25]. The emissivity: The emissivity [ε] of a material is a property which provides a measure of how efficiently a surface emits energy relative to a black body. The highest emissivity coefficient value is ε =1 for the surface of a perfect black body. The emissivity strongly depends on the nature of the surface, which
can be influenced by the method of fabrication. The emissivity of metallic surfaces is generally small and the emissivity of nonconductors is comparatively large, generally exceeding 0.6 [26]. Structure of the tooth: Human teeth have a composite, layered structure composed of enamel, dentin, cementum and dental pulp layers [27]. Enamel is the outermost layer with maximum mineral content, which is synthesized by ameloblasts. It is composed of 96wt% minerals and 4wt% organic substances and water [28]. Dentin is synthesized by odontoblasts and is covered by the enamel in the coronal part of the tooth and by cementum in roots. Dentin is composed of 60wt% minerals, 30wt% organic compounds and 10wt% water [29-31]. In dentin, dentinal tubules extend from the radicular pulp towards the cementum in roots and from the pulp chamber towards the dentinoenamel junction in the crown and contain dentinal fluids [32, 33] Kells et al, [34] in an in vitro study found the emissivity of teeth. For this purpose, they placed the teeth in a closed chamber at 70°C for 24 hours. After 24 hours, they opened the chamber and immediately photographed the teeth using a thermographic camera. They reported that the emissivity coefficient was 0.65 for the enamel. However, this method is not error-free since thermal alterations may occur upon opening the chamber and can disturb the equilibration. Dabrowski et al. [35] evaluated the emissivity of teeth and dental materials in an in vitro study. They reported that the emissivity of teeth was 0.92 in the range of 8 µm to 12 µm. also Lin et al. [36] reported the emissivity value of 0.92 for dentin. Ribeiro et al. [25] reported that the emissivity of dentin was 0.91. However, they did not describe the procedure of determination. Paredes et al. [18] discussed that the emissivity of the enamel had not been measured before and they were the first to measure it. They reported the emissivity value of 0.98 for the enamel after three measurements; however, they did not present any explanation of derivation. Sakagami and Kubo
[21] reported the emissivity of tooth surface to be 0.97 but did not present any explanation of derivation. Considering all the above, comprehensive data are not available regarding the exact value of emissivity of tooth, and since non-metal materials have a high emissivity coefficient [37], it seems that the results of Kells et al. [34] may not be adequately accurate since they opened the chamber prior to imaging. As soon as the chamber is opened, thermal alterations occur in the tooth surface and result in erroneous data. Some studies have assessed the emissivity of bone and reported this value to be 0.99 without describing the procedure through which, this value was obtained [38, 39]. This value does not seem correct since it is highly close to the value for a black body. Stumme et al. [40] determined the emissivity of bone using laboratory techniques and reported this value to be 1.01; whereas, this value is physically invalid and contrary to the Second Law of Thermodynamics. Feldmann and Zysset [41] determined the emissivity of bone using a thermographic camera. They compared the bone temperature with a reference material with a known emissivity. They determined the emissivity of bone in the rasnge of 8 µm to 12 µm. One shortcoming of this method is that it requires to use a reference material with a known emissivity. Uncertainty about the accuracy of emissivity of the reference material can cause uncertainty in the final results. They determined the emissivity of bone to be 0.96 at 40°C to 60°C. This value was 0.97 at 80°C. They suggested using a closed warm container with controlled environment for measurement of emissivity.
Material and Methods
Infrared thermometers determine the temperature as a function of emissivity. If the emissivity is correctly determined, the surface temperature is also determined correctly. One method of measurement of emissivity is to use a thermocouple to determine the temperature of an object and estimate its emissivity in order to match the temperature shown by the infrared sensor and the temperature measured by the thermocouple. For this purpose, we have to make sure that the surface of the object has a specific temperature. In order to do so, two thermocouples, one inside the root and the other one on the tooth surface, were used. An incubator was used to control the temperature of the environment. The incubator temperature could be adjusted as desired. A K-type thermocouple was placed inside the root and another one was placed on the tooth surface. This assembly was placed in an incubator. When the temperatures shown by the two thermocouples were equalized, the surface temperature was measured using an infrared thermometer. By estimating the emissivity, the temperature shown by the infrared thermometer was matched with the temperature measured by the thermocouples. In this situation, the emissivity of the surface was determined at the testing temperature. For this purpose, we had to ensure the optimal accuracy of thermocouples. In this experiment, two calibrated K-type thermocouples were used for measurement of the object temperature. In order to record the temperature measured by the thermocouples, a universal 4-channel thermometer SD card (LU-TM947SD) data logger with a certificate of calibration was used. Since the accuracy of thermocouples and data logger is highly important, to ensure the accuracy of the results, the thermocouples and data logger were tested in ice water and boiling water. An infrared thermometer sensor (OPTIRS CSLaser LT, Germany) was used to measure the temperature of tooth. This sensor can measure the local temperature at 15 cm distance from an object. The scanning rate of this sensor is 150 ms and it operates in the range of 8 to 14 µm. In this
study, an incubator (Paat Aria CPS) was used to create an isolated environment. This incubator operated at -5°C to 85°C and the temperature could be adjusted and measured with 0.1°C accuracy. In this study, sound mandibular first premolars of 3 patients aged 17, 18 and 21 years, which had been extracted as part of orthodontic treatment were used. The root cementum was removed by polishing to expose dentin, then the roots were cut at 8 mm below the cementoenamel. Next, a high-speed hand-piece was used under water irrigation to prepare a cavity with 1 mm diameter in the radicular pulp. A small excavator was used to remove the pulp tissue, and the remaining organic residues were dissolved by using 5.25% sodium hypochlorite for 5 min. The cavity was then rinsed with copious water, dried, and filled with a conductive paste. Next, the thermocouple was placed in the cavity. The tooth underwent radiography to ensure correct positioning of the thermocouple.Figure 1 shows the placement of thermocouples.
Figure 1. (Left) Site of temperature measurement on the enamel surface by infrared thermometer using a laser guide. Right) Radiograph showing K-type thermocouples placed within the root and on the tooth surface. (A) Inside pulp chamber thermocouple, (B) Surface thermocouple.
In order to control the temperature of the environment, the tooth along with the thermocouples and infrared thermometer sensor were placed in an incubator. The temperature of the incubator was adjusted between 20°C to 60°C. In this study, a try and error method was adopted to obtain the emissivity value. In this method, first an emissivity value that expected to match the substance was estimated. Then, the accuracy of this assumption was tested using the graphs obtained from infrared thermometer and thermocouples inside and outside of the tooth and by calculating the root mean square error (RMSE) and the mean absolute percentage error (MAPE), which quantitatively indicate the fit of the three graphs. The process of try and error was repeated for different emissivity values to find the emissivity value with minimal RMSE and MAPE values. Each test was repeated 4 times for each tooth at each temperature range.
Figure 2. The schematic of experimental method for estimation of the emissivity of human enamel and dentin.
Figure 3. Experimental set-up for estimation emissivity using infrared thermometer and K-type thermocouples all placed in an incubator. (A) Infrared thermometer, (B, C) K-type thermocouples and (D) tooth specimen.
Results
The recorded temperature data by the thermocouple inside the tooth, the thermocouple on the tooth surface and the infrared thermometer were superimposed to estimate the emissivity. When the recorded data by the thermocouple inside the tooth and the one located on the tooth surface are well fitted, one can be almost certain of the fact that temperature uniformity within the tooth has
been achieved. At this point, the recorded data by the infrared sensor is matched with that of the surface thermocouple by modulating the emissivity setting on the infrared camera. In order to assess the degree of conformity between the two recorded data in a steady state condition, the obtained mean temperatures were compared. Moreover, calculation of the root mean square error (RMSE) could help determine the standard deviation and error of thermal alterations and the mean absolute percentage error (MAPE) can be used to assess the conformity of the recorded data by different sensor types. In transient conditions when comparison of the mean temperatures is meaningless, these parameters can be used to compare the conformity of the recorded datum [42, 43]. The RSME and MAPE are calculated for the data as:
𝑅𝑆𝑀𝐸 =
1 𝑛
𝑛
∑𝑒
2 𝑖
(1)
𝑖=1
100% 𝑀𝐴𝑃𝐸 = 𝑛
𝑛
∑ |𝑇 |
𝑖=1
𝑒𝑖
𝑖
(2)
Where 𝑇𝑖 is the infrared sensor data and 𝑒𝑖 is the difference between the infrared sensor and the thermocouple measured data. Figure 4 shows the recorded data for enamel at 24°C for 3 minutes. The emissivity in this test was set to be 0.95. As shown in Figure 4, the two-thermocouple data had a relatively near-optimal fit; however, the mean temperature shown by these two graphs had a significant difference with the recorded data of the infrared sensor. The fluctuations and gyrations observable in the data are due to the unavoidable electrical noise within the lab environment and the instrumentation
Figure 4. Comparison of enamel temperature measured by the infrared sensor and the thermocouples considering enamel emissivity=0.95 as a low accurate estimation.
As shown in Figure 4, the difference in the mean temperature measured by the two thermocouples was 0.07°C and the RMSE was 0.14°C. To assess the fit of graphs of the thermocouples with that of infrared sensor in 0.95 emissivity, the maximum difference in the mean values was calculated, which was found to be 0.43 for Figure 4, and was significant. Also, the maximum RMSE between the temperature measured by the sensor and thermocouples was found to be 0.45°C. The maximum MAPE between the temperature recorded by the infrared thermometer and thermocouples was found to be 2%. The two parameters of RMSE and MAPE showed the fit of graphs of temperatures measured by the thermocouples and infrared thermometer. When these two parameters are
minimum, it may be concluded that the most accurate estimation of emissivity is achieved. For this purpose, these two parameters were calculated for different emissivity settings of the enamel at 24°C. Figures 5 and 6 show the changes in RMSE and MAPE by varying the emissivity values on the infrared camera within 0.9 and 0.98 for the enamel at a steady state mean temperature of 24°C.
RMS Error in the emissivity range 0.90 to 0.98 1.8 1.6
RMS Error (°C)
1.4 1.2 1 0.8
A
0.6 0.4
B
0.2 0 0.89
0.9
0.91
0.92
0.93 0.94 0.95 Emissivity
0.96
0.97
0.98
0.99
Figure 5. Changes in RMSE by estimating different enamel emissivity values at 24°C. (A) RSME for emissivity=0.95 as a low accurate estimation. (B) RSME for emissivity=0.96 as an accurate estimation with minimum RMSE.
MAP Error in the emissivity range 0.90 to 0.98 5
MAP Error (%)
4
3
A 2
B
1
0 0.89
0.9
0.91
0.92
0.93 0.94 0.95 Emissivity
0.96
0.97
0.98
0.99
Figure 6. Changes in MAPE by estimating different enamel emissivity values at 24°C. (A) MAPE for emissivity=0.95 as a low accurate estimation. (B) MAPE for emissivity=0.96 as an accurate estimation with minimum MAPE. Referring to figures 5 and 6, it can be noticed by an increase in emissivity, the RMSE and MAPE decreased. When the emissivity reached 0.96, the RMSE and MAPE were minimum, and by an increase in emissivity, the RMSE and MAPE values increased. Thus, the most accurate estimation of enamel emissivity is found to be 0.96 at 24°C.
Figure 7 shows the temperature measured by infrared sensor in 0.96 emissivity for the enamel compared to the temperature measured by the thermocouples in the root and on the tooth surface.
Figure 7. Comparison of enamel temperature measured by the infrared sensor and thermocouples considering enamel emissivity=0.96 as an accurate estimation.
As shown in Figure 7, the recorded data for both sensors are relatively well-fitted. To more accurately assess the fit of graphs, the mean value, RMSE and MAPE were compared. The difference in the mean temperature measured by the thermocouples in the root and on the tooth surface was 0.05°C and the measured RMSE for the two thermocouples was 0.11°C. To assess the fitness of temperature measured by the infrared sensor, the maximum difference between the mean temperature measured by the infrared sensor and the temperatures measured by the thermocouples was calculated and found to be 0.09°C. The maximum RMSE between the temperature measured by the infrared sensor and thermocouples was 0.15°C. The maximum MAPE was <0.5%. Thus, it may be concluded that emissivity=0.96 is a more accurate estimate of enamel emissivity at 24°C. The emissivity of dentin
was also estimated in a similar manner. The location of thermal sensor was adjusted such that the measurement was made exactly on the dentin surface. As mentioned, for measurement of the enamel emissivity, a thermocouple was used in the root and another one on the tooth surface. When both thermocouples showed the same temperature, the emissivity was estimated and its accurate value was chosen such that the temperature measured by the infrared sensor matched the value measured by the thermocouples. Figure 8, shows the dentin temperature measured at 23°C considering emissivity=0.92.
Figure 8. Comparison of dentin temperature measured by the infrared sensor and thermocouples considering emissivity=0.92.
In this case, the mean difference in temperature measured by the two thermocouples was 0.01°C, and the RMSE indicating the fitness of the two graphs was found to be 0.1°C. The maximum difference between the mean temperature measured by the infrared sensor and the temperature measured by the thermocouples was 0.03°C. The maximum RMSE between the temperature measured by the infrared sensor and thermocouples was 0.09°C. The maximum MAPE was around 0.1%. Next, the transient condition was studied when the temperature fluctuated for about 1°C using incubator temperature control unit. After incubation, the two recorded data obtained from the two thermocouples were fitted. By estimating the correct emissivity, the recorded data of the infrared thermometer was fitted to the latter. The same test was performed for the enamel at 30°C (Figure 9).
Figure 9. Comparison of enamel temperature measured by the infrared sensor and thermocouples considering emissivity=0.96.
Figure 9 shows the fitness of the recorded data of different sensors for the enamel considering emissivity=0.96. Since the test was performed under the transient condition, comparison of the mean temperature was not possible. Thus, in order to assess the fitness of the three graphs, the maximum RMSE and MAPE for the temperatures measured by infrared thermometer and thermocouples were calculated. The maximum RMSE was found to be 0.18°. The MAPE was found to be 0.5%. Figure 10 shows temperature variations measured by the thermocouples on the tooth surface and inside the root as well as the infrared thermometer under transient conditions for dentin with a presumed emissivity of 0.92.
Figure 10. Comparison of dentin temperature measured by the infrared sensor and thermocouples considering emissivity=0.92.
Since the thermal alterations were transient, comparison of the mean temperature was not possible. Thus, the RMSE and MAPE were calculated to assess the fitness of graphs. Maximum RMSE between the temperature measured by the infrared thermometer and the thermocouples was found to be 0.13° and the MAPE was found to be 0.3%. Table 1 summarizes the values of estimated emissivities at temperatures between 20°C to 60°C for both the dentin and the enamel.
Table 1. Dentin and enamel emissivity at 20°C to 60°C and mean and standard deviation of RSME and MAPE.
Temperature (°C) 20-30 30-40 40-50 50-60
Emissivity
0.96 0.96 0.97 0.97
Enamel RMSE1 (°C) Ave. 0.15 0.19 0.20 0.16
Sd. 0.03 0.01 0.03 0.02
MAPE2
Emissivity
% Ave. 0.7 0.9 1.1 0.8
Sd. 0.20 0.11 0.21 0.16
0.92 0.92 0.93 0.93
Dentin RMSE (°C) Ave. 0.12 0.15 0.17 0.18
Sd. 0.02 0.02 0.03 0.02
MAPE % Ave. 0.5 0.6 0.7 0.8
Sd. 0.21 0.24 0.25 0.28
Discussion In this study, an infrared thermometer within 8 µm to 14 µm wavelength range was used to measure the emissivity of enamel and dentin. Previous studies have discussed a number of uncertainties for measurement of emissivity of bone by comparison of emissivity with a reference material, such as
1 2
Root Mean Square Error Mean Absolute Percentage Error
uncertainty about the emissivity of the reference material, temperature uniformity of the samples and assuming the temperature of samples to be the same as that of reference material [41]. In the current study, these uncertainties have been eliminated. In order to ensure temperature uniformity of the samples, two thermocouples were used, one inside the pulp chamber and the other one on the tooth surface. In order to control the temperature of the environment, the tests were performed in an incubator. There is no reference material in the methodology of the present work and the emissivity was estimated by fitting the temperature data of the infrared thermometer with that of the thermocouples. Since there was no reference material, uncertainty about its emissivity or temperature of the samples and reference material no longer affected the results. In this study, the emissivity of enamel was 0.96 at a temperature range of 20 to 40 ° C and increased to 0.97 with increasing temperature in the range of 40 to 60 °C. The emissivity of dentin was 0.92 in the range of 20 to 40 ° C and 0.93 in the range of 40 to 60 ° Which was in agreement with the results of Feldmann and Zysset [41] results Who showed an increase in emissivity following temperature rise. The emissivity of dentin estimated 0.92 in the temperature range of 20°C to 40°C. This result was in line with the emissivity value reported by Lin et al, [36] who reported the emissivity of dentin to be 0.92. Da Costa Ribeiro et al. [25] reported the emissivity of dentin to be 0.91 without explanation of derivation. The emissivity value of enamel found in our study between 40°C-60°C was in agreement with the value reported by Sakagami and Kubo [21], which was 0.97. However, they did not mention the method or temperature at which, they measured the emissivity. Our results regarding the emissivity of enamel was close to the value reported by Paredes et al, [18] which was 0.98.
It should be noted that similar to the study by Feldmann and Zysset [41], change in emissivity by 0.01 caused a change in temperature by approximately 0.5°C.
Conclusion This in vitro study evaluated the emissivity of enamel and dentin. For this purpose, three sound mandibular first premolars of 3 patients aged 17, 18 and 21 years extracted for orthodontic treatment were used. The emissivity was determined by fitting the recorded data of temperatures measured by an infrared thermometer and thermocouples placed inside the root and on the tooth surface. In order to create different environmental temperatures and controlled conditions, the test was performed in an incubator. The results showed that the emissivity of enamel was 0.96±0.01 between 20°C to 40°C and 0.97±0.01 between 40°C to 60°C. The emissivity of dentin was 0.92±0.01 at 20°C to 40°C and 0.93±0.01 at 40°C to 60°C. A significant difference was noted in the emissivity of enamel and dentin, which can be due to the difference in their structure. Enamel is composed of regularly aligned apatite-like crystals surrounded by a matrix of water, lipids and proteins [44]. These crystals have 30 nm to 40 nm diameter and around 10 µm length. However, dentin is composed of hydroxyapatite (45%), organic compounds (33%) and water (22%)[45].
Conflicts of Interest: None Funding: None Ethical Approval:
The Ethics Committee of Research Institute of Dental Sciences-Shahid Beheshti University of Medical Sciences approved the study (Code No. IR.SBMU.DRC.REC.1398.097).
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S1350-4495(19)30890-4 https://doi.org/10.1016/j.infrared.2020.103234 INFPHY 103234
To appear in:
Infrared Physics & Technology
Received Date: Revised Date: Accepted Date:
24 October 2019 7 February 2020 9 February 2020
Please cite this article as: A. Soori, F. Kowsary, S. Kasraei, Experimental estimation of the emissivity of human enamel and dentin, Infrared Physics & Technology (2020), doi: https://doi.org/10.1016/j.infrared.2020.103234
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Title page
Experimental estimation of the emissivity of human enamel and dentin Ahmad Sooria, Farshad Kowsarya, *, Shahin Kasraeib aSchool
bDepartment
of Mechanical Engineering, Tehran University, Tehran, Iran
of Restorative Dentistry, Dental School, Shahid Beheshti University of Medical Sciences, Tehran, Iran
Corresponding author: Corresponding author: Farshad Kowsary* Mailing address: School of Mechanical Engineering, College of Engineering, North Kargar St., Tehran, Iran Tel.: +9821-61119924; Fax: +9821-88013029 E-mail: [email protected]
Abstract
Heat transfer occurs frequently in numerous dental treatment procedures. In almost all of the related experimental studies, use of infrared camera for temperature measurement, is becoming more and more popular, considering the many advantages of this technique. This technique has been employed in some recent studies as a non-invasive method for disease diagnosis. However, use of the infrared camera for temperature measurements requires knowledge of the emissivity of the target surface. The present in vitro study aims to determine the emissivity of enamel and dentin. The emissivity of enamel was found to be 0.96±0.01 in the temperature range of 20°C to 40°C and 0.97±0.01 in the temperature range of 40°C to 60°C. The emissivity of dentin was found to be 0.92±0.01 at 20°C to 40°C and 0.93±0.01 at 40°C to 60°C. The difference in the emissivity of enamel and dentin can be attributed to their different composition and constituents, structure and surface quality.
Keywords: Emissivity; Infrared Thermography; Dental Enamel; Dentin; Heat Transfer
Introduction
Heat transfer is important in dental treatments and daily life [1]. Oral thermal alterations have been reported in the range of -5°C to 76.3°C [2]. Advances in contemporary dentistry led to the use of some heat generating equipment such as dental lasers [3, 4], light-curing units [5-7], and highspeed hand-pieces [8, 9] in the oral environment. The generated heat by such equipment can irreversibly damage the enamel and dentin. Enamel and dentin are sensitive to mechanical stresses
created by temperature rise. These stresses can cause microscracks and result in pain and tissue injury, and negatively affect the longevity of the tooth [10, 11]. Also, the nerve tissue present in dental pulp is heat sensitive, and temperature rise to 5.5°C in pulp-dentin complex can cause irreversible damage to the nerves [12]. The amount of temperature rise in use of the abovementioned equipment is affected by a number of controllable and uncontrollable parameters. For instance, the heat generated by laser irradiation or light-curing units is a function of intensity, power, and duration of radiation. The heat generated by hand-pieces is a function of type of irrigation, use of an old or new bur, shape and structure of bur, rotational speed, and the applied pressure [1, 13]. Studies on heat transfer can help assess the role of different parameters in heat generation and optimize the design and application strategy of equipment in clinical dentistry to increase the success of treatment and minimize complications. Heat transfer is also important in some procedures. For instance, it can be used for vitality testing of the teeth. Contact and non-contact methods are currently employed for measurement of temperature in heat transfer experiments. In contact measurement method, a temperature sensor, for example a thermocouple is used for temperature measurement. However, use of thermocouples is problematic due to the small size of the teeth and the contact resistance between the thermocouple and surface. Presence of contact resistance between the thermocouple and surface can cause significant errors in measurement of surface temperature. Among the non-contact temperature measurement methods, infrared thermography is a non-invasive and highly accurate technique for measurement of surface temperature in medicine and dentistry [14-16]. Kells et al. [17]used thermographic cameras to assess the vitality of the teeth and concluded that this method was comparable to laser Doppler flowmetry in terms of performance. Paredes et al,
[18] in an in vitro study assessed the efficacy of infrared thermography for dental diagnoses and concluded that thermographic recordings for 5 min can differentiate between a vital tooth and a tooth with necrotic pulp. On the other hand, Smith et al. [19] concluded that thermal changes at the tooth surface cannot serve as a simple and useful clinical tool for assessment of tooth vitality. Zakian et al. [20] used infrared imaging for detection of dental caries. They concluded that thermal imaging has the ability to discriminate between areas that are either sound or have an incipient carious lesion on the outer half of the enamel and areas with lesions extending deeper into the enamel. This method can be used for detection of incipient enamel caries in extracted teeth. Further in vivo investigations are required to assess the efficacy of this method for vital teeth [20]. Sakagami and Kubo [21] assessed a non-destructive thermographic method in a series of in vitro experiments based on measuring the transient surface temperature following a thermal pulse. They introduced it as a diagnostic modality in dentistry
It is necessary to know the emissivity value of a material to correctly read the temperature using a thermographic camera. Some recent studies that used an infrared camera coated the surface with a carbon spray to increase the emissivity. The disadvantage of this method is that this additional layer may alter the transient temperature variation [22, 23] and in some cases , the emissivity is presented without explanation of derivation [18, 21, 24, 25]. The emissivity: The emissivity [ε] of a material is a property which provides a measure of how efficiently a surface emits energy relative to a black body. The highest emissivity coefficient value is ε =1 for the surface of a perfect black body. The emissivity strongly depends on the nature of the surface, which
can be influenced by the method of fabrication. The emissivity of metallic surfaces is generally small and the emissivity of nonconductors is comparatively large, generally exceeding 0.6 [26]. Structure of the tooth: Human teeth have a composite, layered structure composed of enamel, dentin, cementum and dental pulp layers [27]. Enamel is the outermost layer with maximum mineral content, which is synthesized by ameloblasts. It is composed of 96wt% minerals and 4wt% organic substances and water [28]. Dentin is synthesized by odontoblasts and is covered by the enamel in the coronal part of the tooth and by cementum in roots. Dentin is composed of 60wt% minerals, 30wt% organic compounds and 10wt% water [29-31]. In dentin, dentinal tubules extend from the radicular pulp towards the cementum in roots and from the pulp chamber towards the dentinoenamel junction in the crown and contain dentinal fluids [32, 33] Kells et al, [34] in an in vitro study found the emissivity of teeth. For this purpose, they placed the teeth in a closed chamber at 70°C for 24 hours. After 24 hours, they opened the chamber and immediately photographed the teeth using a thermographic camera. They reported that the emissivity coefficient was 0.65 for the enamel. However, this method is not error-free since thermal alterations may occur upon opening the chamber and can disturb the equilibration. Dabrowski et al. [35] evaluated the emissivity of teeth and dental materials in an in vitro study. They reported that the emissivity of teeth was 0.92 in the range of 8 µm to 12 µm. also Lin et al. [36] reported the emissivity value of 0.92 for dentin. Ribeiro et al. [25] reported that the emissivity of dentin was 0.91. However, they did not describe the procedure of determination. Paredes et al. [18] discussed that the emissivity of the enamel had not been measured before and they were the first to measure it. They reported the emissivity value of 0.98 for the enamel after three measurements; however, they did not present any explanation of derivation. Sakagami and Kubo
[21] reported the emissivity of tooth surface to be 0.97 but did not present any explanation of derivation. Considering all the above, comprehensive data are not available regarding the exact value of emissivity of tooth, and since non-metal materials have a high emissivity coefficient [37], it seems that the results of Kells et al. [34] may not be adequately accurate since they opened the chamber prior to imaging. As soon as the chamber is opened, thermal alterations occur in the tooth surface and result in erroneous data. Some studies have assessed the emissivity of bone and reported this value to be 0.99 without describing the procedure through which, this value was obtained [38, 39]. This value does not seem correct since it is highly close to the value for a black body. Stumme et al. [40] determined the emissivity of bone using laboratory techniques and reported this value to be 1.01; whereas, this value is physically invalid and contrary to the Second Law of Thermodynamics. Feldmann and Zysset [41] determined the emissivity of bone using a thermographic camera. They compared the bone temperature with a reference material with a known emissivity. They determined the emissivity of bone in the rasnge of 8 µm to 12 µm. One shortcoming of this method is that it requires to use a reference material with a known emissivity. Uncertainty about the accuracy of emissivity of the reference material can cause uncertainty in the final results. They determined the emissivity of bone to be 0.96 at 40°C to 60°C. This value was 0.97 at 80°C. They suggested using a closed warm container with controlled environment for measurement of emissivity.
Material and Methods
Infrared thermometers determine the temperature as a function of emissivity. If the emissivity is correctly determined, the surface temperature is also determined correctly. One method of measurement of emissivity is to use a thermocouple to determine the temperature of an object and estimate its emissivity in order to match the temperature shown by the infrared sensor and the temperature measured by the thermocouple. For this purpose, we have to make sure that the surface of the object has a specific temperature. In order to do so, two thermocouples, one inside the root and the other one on the tooth surface, were used. An incubator was used to control the temperature of the environment. The incubator temperature could be adjusted as desired. A K-type thermocouple was placed inside the root and another one was placed on the tooth surface. This assembly was placed in an incubator. When the temperatures shown by the two thermocouples were equalized, the surface temperature was measured using an infrared thermometer. By estimating the emissivity, the temperature shown by the infrared thermometer was matched with the temperature measured by the thermocouples. In this situation, the emissivity of the surface was determined at the testing temperature. For this purpose, we had to ensure the optimal accuracy of thermocouples. In this experiment, two calibrated K-type thermocouples were used for measurement of the object temperature. In order to record the temperature measured by the thermocouples, a universal 4-channel thermometer SD card (LU-TM947SD) data logger with a certificate of calibration was used. Since the accuracy of thermocouples and data logger is highly important, to ensure the accuracy of the results, the thermocouples and data logger were tested in ice water and boiling water. An infrared thermometer sensor (OPTIRS CSLaser LT, Germany) was used to measure the temperature of tooth. This sensor can measure the local temperature at 15 cm distance from an object. The scanning rate of this sensor is 150 ms and it operates in the range of 8 to 14 µm. In this
study, an incubator (Paat Aria CPS) was used to create an isolated environment. This incubator operated at -5°C to 85°C and the temperature could be adjusted and measured with 0.1°C accuracy. In this study, sound mandibular first premolars of 3 patients aged 17, 18 and 21 years, which had been extracted as part of orthodontic treatment were used. The root cementum was removed by polishing to expose dentin, then the roots were cut at 8 mm below the cementoenamel. Next, a high-speed hand-piece was used under water irrigation to prepare a cavity with 1 mm diameter in the radicular pulp. A small excavator was used to remove the pulp tissue, and the remaining organic residues were dissolved by using 5.25% sodium hypochlorite for 5 min. The cavity was then rinsed with copious water, dried, and filled with a conductive paste. Next, the thermocouple was placed in the cavity. The tooth underwent radiography to ensure correct positioning of the thermocouple.Figure 1 shows the placement of thermocouples.
Figure 1. (Left) Site of temperature measurement on the enamel surface by infrared thermometer using a laser guide. Right) Radiograph showing K-type thermocouples placed within the root and on the tooth surface. (A) Inside pulp chamber thermocouple, (B) Surface thermocouple.
In order to control the temperature of the environment, the tooth along with the thermocouples and infrared thermometer sensor were placed in an incubator. The temperature of the incubator was adjusted between 20°C to 60°C. In this study, a try and error method was adopted to obtain the emissivity value. In this method, first an emissivity value that expected to match the substance was estimated. Then, the accuracy of this assumption was tested using the graphs obtained from infrared thermometer and thermocouples inside and outside of the tooth and by calculating the root mean square error (RMSE) and the mean absolute percentage error (MAPE), which quantitatively indicate the fit of the three graphs. The process of try and error was repeated for different emissivity values to find the emissivity value with minimal RMSE and MAPE values. Each test was repeated 4 times for each tooth at each temperature range.
Figure 2. The schematic of experimental method for estimation of the emissivity of human enamel and dentin.
Figure 3. Experimental set-up for estimation emissivity using infrared thermometer and K-type thermocouples all placed in an incubator. (A) Infrared thermometer, (B, C) K-type thermocouples and (D) tooth specimen.
Results
The recorded temperature data by the thermocouple inside the tooth, the thermocouple on the tooth surface and the infrared thermometer were superimposed to estimate the emissivity. When the recorded data by the thermocouple inside the tooth and the one located on the tooth surface are well fitted, one can be almost certain of the fact that temperature uniformity within the tooth has
been achieved. At this point, the recorded data by the infrared sensor is matched with that of the surface thermocouple by modulating the emissivity setting on the infrared camera. In order to assess the degree of conformity between the two recorded data in a steady state condition, the obtained mean temperatures were compared. Moreover, calculation of the root mean square error (RMSE) could help determine the standard deviation and error of thermal alterations and the mean absolute percentage error (MAPE) can be used to assess the conformity of the recorded data by different sensor types. In transient conditions when comparison of the mean temperatures is meaningless, these parameters can be used to compare the conformity of the recorded datum [42, 43]. The RSME and MAPE are calculated for the data as:
𝑅𝑆𝑀𝐸 =
1 𝑛
𝑛
∑𝑒
2 𝑖
(1)
𝑖=1
100% 𝑀𝐴𝑃𝐸 = 𝑛
𝑛
∑ |𝑇 |
𝑖=1
𝑒𝑖
𝑖
(2)
Where 𝑇𝑖 is the infrared sensor data and 𝑒𝑖 is the difference between the infrared sensor and the thermocouple measured data. Figure 4 shows the recorded data for enamel at 24°C for 3 minutes. The emissivity in this test was set to be 0.95. As shown in Figure 4, the two-thermocouple data had a relatively near-optimal fit; however, the mean temperature shown by these two graphs had a significant difference with the recorded data of the infrared sensor. The fluctuations and gyrations observable in the data are due to the unavoidable electrical noise within the lab environment and the instrumentation
Figure 4. Comparison of enamel temperature measured by the infrared sensor and the thermocouples considering enamel emissivity=0.95 as a low accurate estimation.
As shown in Figure 4, the difference in the mean temperature measured by the two thermocouples was 0.07°C and the RMSE was 0.14°C. To assess the fit of graphs of the thermocouples with that of infrared sensor in 0.95 emissivity, the maximum difference in the mean values was calculated, which was found to be 0.43 for Figure 4, and was significant. Also, the maximum RMSE between the temperature measured by the sensor and thermocouples was found to be 0.45°C. The maximum MAPE between the temperature recorded by the infrared thermometer and thermocouples was found to be 2%. The two parameters of RMSE and MAPE showed the fit of graphs of temperatures measured by the thermocouples and infrared thermometer. When these two parameters are
minimum, it may be concluded that the most accurate estimation of emissivity is achieved. For this purpose, these two parameters were calculated for different emissivity settings of the enamel at 24°C. Figures 5 and 6 show the changes in RMSE and MAPE by varying the emissivity values on the infrared camera within 0.9 and 0.98 for the enamel at a steady state mean temperature of 24°C.
RMS Error in the emissivity range 0.90 to 0.98 1.8 1.6
RMS Error (°C)
1.4 1.2 1 0.8
A
0.6 0.4
B
0.2 0 0.89
0.9
0.91
0.92
0.93 0.94 0.95 Emissivity
0.96
0.97
0.98
0.99
Figure 5. Changes in RMSE by estimating different enamel emissivity values at 24°C. (A) RSME for emissivity=0.95 as a low accurate estimation. (B) RSME for emissivity=0.96 as an accurate estimation with minimum RMSE.
MAP Error in the emissivity range 0.90 to 0.98 5
MAP Error (%)
4
3
A 2
B
1
0 0.89
0.9
0.91
0.92
0.93 0.94 0.95 Emissivity
0.96
0.97
0.98
0.99
Figure 6. Changes in MAPE by estimating different enamel emissivity values at 24°C. (A) MAPE for emissivity=0.95 as a low accurate estimation. (B) MAPE for emissivity=0.96 as an accurate estimation with minimum MAPE. Referring to figures 5 and 6, it can be noticed by an increase in emissivity, the RMSE and MAPE decreased. When the emissivity reached 0.96, the RMSE and MAPE were minimum, and by an increase in emissivity, the RMSE and MAPE values increased. Thus, the most accurate estimation of enamel emissivity is found to be 0.96 at 24°C.
Figure 7 shows the temperature measured by infrared sensor in 0.96 emissivity for the enamel compared to the temperature measured by the thermocouples in the root and on the tooth surface.
Figure 7. Comparison of enamel temperature measured by the infrared sensor and thermocouples considering enamel emissivity=0.96 as an accurate estimation.
As shown in Figure 7, the recorded data for both sensors are relatively well-fitted. To more accurately assess the fit of graphs, the mean value, RMSE and MAPE were compared. The difference in the mean temperature measured by the thermocouples in the root and on the tooth surface was 0.05°C and the measured RMSE for the two thermocouples was 0.11°C. To assess the fitness of temperature measured by the infrared sensor, the maximum difference between the mean temperature measured by the infrared sensor and the temperatures measured by the thermocouples was calculated and found to be 0.09°C. The maximum RMSE between the temperature measured by the infrared sensor and thermocouples was 0.15°C. The maximum MAPE was <0.5%. Thus, it may be concluded that emissivity=0.96 is a more accurate estimate of enamel emissivity at 24°C. The emissivity of dentin
was also estimated in a similar manner. The location of thermal sensor was adjusted such that the measurement was made exactly on the dentin surface. As mentioned, for measurement of the enamel emissivity, a thermocouple was used in the root and another one on the tooth surface. When both thermocouples showed the same temperature, the emissivity was estimated and its accurate value was chosen such that the temperature measured by the infrared sensor matched the value measured by the thermocouples. Figure 8, shows the dentin temperature measured at 23°C considering emissivity=0.92.
Figure 8. Comparison of dentin temperature measured by the infrared sensor and thermocouples considering emissivity=0.92.
In this case, the mean difference in temperature measured by the two thermocouples was 0.01°C, and the RMSE indicating the fitness of the two graphs was found to be 0.1°C. The maximum difference between the mean temperature measured by the infrared sensor and the temperature measured by the thermocouples was 0.03°C. The maximum RMSE between the temperature measured by the infrared sensor and thermocouples was 0.09°C. The maximum MAPE was around 0.1%. Next, the transient condition was studied when the temperature fluctuated for about 1°C using incubator temperature control unit. After incubation, the two recorded data obtained from the two thermocouples were fitted. By estimating the correct emissivity, the recorded data of the infrared thermometer was fitted to the latter. The same test was performed for the enamel at 30°C (Figure 9).
Figure 9. Comparison of enamel temperature measured by the infrared sensor and thermocouples considering emissivity=0.96.
Figure 9 shows the fitness of the recorded data of different sensors for the enamel considering emissivity=0.96. Since the test was performed under the transient condition, comparison of the mean temperature was not possible. Thus, in order to assess the fitness of the three graphs, the maximum RMSE and MAPE for the temperatures measured by infrared thermometer and thermocouples were calculated. The maximum RMSE was found to be 0.18°. The MAPE was found to be 0.5%. Figure 10 shows temperature variations measured by the thermocouples on the tooth surface and inside the root as well as the infrared thermometer under transient conditions for dentin with a presumed emissivity of 0.92.
Figure 10. Comparison of dentin temperature measured by the infrared sensor and thermocouples considering emissivity=0.92.
Since the thermal alterations were transient, comparison of the mean temperature was not possible. Thus, the RMSE and MAPE were calculated to assess the fitness of graphs. Maximum RMSE between the temperature measured by the infrared thermometer and the thermocouples was found to be 0.13° and the MAPE was found to be 0.3%. Table 1 summarizes the values of estimated emissivities at temperatures between 20°C to 60°C for both the dentin and the enamel.
Table 1. Dentin and enamel emissivity at 20°C to 60°C and mean and standard deviation of RSME and MAPE.
Temperature (°C) 20-30 30-40 40-50 50-60
Emissivity
0.96 0.96 0.97 0.97
Enamel RMSE1 (°C) Ave. 0.15 0.19 0.20 0.16
Sd. 0.03 0.01 0.03 0.02
MAPE2
Emissivity
% Ave. 0.7 0.9 1.1 0.8
Sd. 0.20 0.11 0.21 0.16
0.92 0.92 0.93 0.93
Dentin RMSE (°C) Ave. 0.12 0.15 0.17 0.18
Sd. 0.02 0.02 0.03 0.02
MAPE % Ave. 0.5 0.6 0.7 0.8
Sd. 0.21 0.24 0.25 0.28
Discussion In this study, an infrared thermometer within 8 µm to 14 µm wavelength range was used to measure the emissivity of enamel and dentin. Previous studies have discussed a number of uncertainties for measurement of emissivity of bone by comparison of emissivity with a reference material, such as
1 2
Root Mean Square Error Mean Absolute Percentage Error
uncertainty about the emissivity of the reference material, temperature uniformity of the samples and assuming the temperature of samples to be the same as that of reference material [41]. In the current study, these uncertainties have been eliminated. In order to ensure temperature uniformity of the samples, two thermocouples were used, one inside the pulp chamber and the other one on the tooth surface. In order to control the temperature of the environment, the tests were performed in an incubator. There is no reference material in the methodology of the present work and the emissivity was estimated by fitting the temperature data of the infrared thermometer with that of the thermocouples. Since there was no reference material, uncertainty about its emissivity or temperature of the samples and reference material no longer affected the results. In this study, the emissivity of enamel was 0.96 at a temperature range of 20 to 40 ° C and increased to 0.97 with increasing temperature in the range of 40 to 60 °C. The emissivity of dentin was 0.92 in the range of 20 to 40 ° C and 0.93 in the range of 40 to 60 ° Which was in agreement with the results of Feldmann and Zysset [41] results Who showed an increase in emissivity following temperature rise. The emissivity of dentin estimated 0.92 in the temperature range of 20°C to 40°C. This result was in line with the emissivity value reported by Lin et al, [36] who reported the emissivity of dentin to be 0.92. Da Costa Ribeiro et al. [25] reported the emissivity of dentin to be 0.91 without explanation of derivation. The emissivity value of enamel found in our study between 40°C-60°C was in agreement with the value reported by Sakagami and Kubo [21], which was 0.97. However, they did not mention the method or temperature at which, they measured the emissivity. Our results regarding the emissivity of enamel was close to the value reported by Paredes et al, [18] which was 0.98.
It should be noted that similar to the study by Feldmann and Zysset [41], change in emissivity by 0.01 caused a change in temperature by approximately 0.5°C.
Conclusion This in vitro study evaluated the emissivity of enamel and dentin. For this purpose, three sound mandibular first premolars of 3 patients aged 17, 18 and 21 years extracted for orthodontic treatment were used. The emissivity was determined by fitting the recorded data of temperatures measured by an infrared thermometer and thermocouples placed inside the root and on the tooth surface. In order to create different environmental temperatures and controlled conditions, the test was performed in an incubator. The results showed that the emissivity of enamel was 0.96±0.01 between 20°C to 40°C and 0.97±0.01 between 40°C to 60°C. The emissivity of dentin was 0.92±0.01 at 20°C to 40°C and 0.93±0.01 at 40°C to 60°C. A significant difference was noted in the emissivity of enamel and dentin, which can be due to the difference in their structure. Enamel is composed of regularly aligned apatite-like crystals surrounded by a matrix of water, lipids and proteins [44]. These crystals have 30 nm to 40 nm diameter and around 10 µm length. However, dentin is composed of hydroxyapatite (45%), organic compounds (33%) and water (22%)[45].
Conflicts of Interest: None Funding: None Ethical Approval:
The Ethics Committee of Research Institute of Dental Sciences-Shahid Beheshti University of Medical Sciences approved the study (Code No. IR.SBMU.DRC.REC.1398.097).
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