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Influence analysis of thermophysical properties on temperature profiles on the breast skin surface
International Communications in Heat and Mass Transfer 111 (2020) 104453
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International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Influence analysis of thermophysical properties on temperature profiles on the breast skin surface
T
⁎
Alisson A.A. Figueiredoa, , Henrique C. Fernandesb,c, Fernando C. Malheirosd, Gilmar Guimaraese a
Department of Mechanical Engineering, Federal University of Ouro Preto, Ouro Preto 35400-000, Brazil School of Computer Science, Federal University of Uberlandia, Uberlandia 38408-100, Brazil c Fraunhofer IZFP Institute for Nondestructive Testing, Saarbrücken 66123, Germany d Minas Gerais State University, Ituiutaba 38302-192, Brazil e School of Mechanical Engineering, Federal University of Uberlandia, Uberlandia 38408-100, Brazil b
A R T I C LE I N FO
A B S T R A C T
Keywords: Breast cancer Infrared thermography Normalized temperatures Thermophysical properties Diagnosis simplification
This work presents a simplified approach for the early detection of breast cancer using thermographic images, showing that several thermophysical properties of the bio-thermal problem does not need to be previously known to locate the geometric center of tumors. A 3D hemispheric breast model composed of different layers (muscle, gland, fat and skin) was constructed to evaluate the thermal behavior on the skin surface from numerical simulations using commercial software COMSOL. The effects of changes in depth, size, metabolism, blood perfusion and thermal conductivity of the tumor at surface temperatures were systematically analyzed to provide important information and guidelines for future medical diagnoses. Variations in blood perfusions and thermal conductivities of healthy tissue layers were also evaluated. It has been found that changing the size, metabolism, blood perfusion and thermal conductivity of a centralized tumor in the same coordinate does not modify the profiles of normalized temperature variations on the breast skin surface. Regarding the properties of healthy tissue, if a specific region of the breast surface is taken, there is the possibility that the normalized temperature profiles also do not depend on these properties. Thus, knowing that one of the main limitations in the estimation of tumors from thermographic images is related to the difficulty of previously knowing the thermophysical properties of human tissues, the results obtained in this study provide valuable simplifications for the early diagnosis of breast cancer using infrared thermography.
1. Introduction Among women, breast cancer is the most commonly diagnosed type of cancer and the leading cause of cancer death in the world. Of the 8.6 million new cases of cancer estimated for 2018 among women, 24.2% corresponds to breast cancer. Regarding the 4.2 million cancer deaths among women estimated for 2018, 15.0% corresponds to breast cancer [1]. Breast cancer accounts for 30% of new estimated cancer cases among women in the USA and 28.2% in Europe [2,3]. Several imaging techniques are used to aid in the diagnosis of breast cancer, especially mammography, magnetic resonance imaging and ultrasonography. Mammography is the breast cancer screening tool with the best combination of sensitivity and specificity. However, mammography still has limitations, such as the emission of ionizing radiations, high false-negative or false-positive rates, inefficiency for women with dense breasts (especially young women), among others ⁎
[4]. It is known that cancer cells have a different blood flow and metabolism than healthy cells [5]. This change due to the presence of the tumor can be transmitted to the surrounding tissue, and may change the temperature on the breast surface [6]. Infrared thermography (IRT) is a non-destructive technique, non-invasive, contactless, which enables the mapping of thermal patterns, i.e., thermograms, on the surface of objects, bodies and systems through the use of an infrared (IR) imaging instrument, such as an IR camera [7]. According to some institutions such as the American Cancer Society, American College of Clinical Thermology and the International Academy of Clinical Thermology, IRT is unable to identify the location of tumors and can not replace, for example, mammography examination. However, the addition of thermographic images along with other types of exams significantly increases the chances of early diagnosis of the disease [8–10]. A large number of researches have been carried out
Corresponding author. E-mail addresses: alisson.fi[email protected] (A.A.A. Figueiredo), [email protected] (H.C. Fernandes), [email protected] (F.C. Malheiros), [email protected] (G. Guimaraes). https://doi.org/10.1016/j.icheatmasstransfer.2019.104453
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Hemispherical model of the breast: (a) 3D view, (b) x-z cutting plane in the center of the y-axis.
In a previous work, Figueiredo et al. [26] proposed a new technique to determine the geometric center of mammary tumors from correlations of superficial skin temperatures obtained by infrared images. The presented methodology was able to estimate tumors inside silicone samples without the need of previous knowledge of the properties of tumors with an error of less than 4%. In [27], Figueiredo et al. adapted the technique proposed in [26] to estimate the presence of the main types of breast cancer from superficial skin temperatures from numerical simulations of a real 2D anatomical model of the breast. This work demonstrated the ability of the technique to estimate tumors in real breast geometries without the need for prior knowledge of the properties of carcinogenic inclusions. In this work, a detailed thermal analyzes is presented which allows to affirm that it is possible to estimate the presence of the geometric center of tumors from superficial temperatures without the need of previous knowledge of the thermophysical properties of the thermal problem. The phenomenon is analyzed in a 3D hemispheric breast made up of different layers of tissues. The main goal is to present a set of possible simplifications in the process of early detecting breast cancer using IR imaging. The computational model was created using COMSOL Multiphysics and systematically considers the superficial thermal responses in the skin for tumors of different sizes, depths, blood perfusions and thermal conductivity. The influence of the thermophysical properties of the healthy tissue region on the surface thermal profiles is also analyzed.
with the aim of making IRT a method capable of early detecting and diagnosing breast and other kinds of tumors [11–14]. Several clinical tests for the detection of breast abnormalities have been performed based on thermograms and the results are very consistent [15]. A study using the conjugate gradient method in screening breast lesions in patients undergoing thermal mapping demonstrated great potential, obtained 96% efficacy in the detection of breast abnormalities [16]. The thermal impedance technique was recently applied experimentally in hyperplastic materials in order to qualify IRT for the detection of mammary tumors, obtaining high sensitivities for small sizes of inclusions [17]. Those works applied IRT together with an optimization method to characterize the presence of breast tumors. To better understand and interpret the thermal behavior on the breast surface caused by tumors, different theoretical models must be studied. The transmission line matrix (TLM) method was used to model the heat transfer in a 3D breast in Cartesian coordinates with a built-in tumor. In this study, the skin surface temperature increase was significant only for tumors located in the superficial region at a depth up to 20 mm [18]. In [19,20], estimations of the blood perfusion rate, size and depth of breast and brain tumors in 1D and 2D models were performed from the surface temperatures simulated by the finite volume method along with a direct search method and genetic algorithmns (GA). Estimations of the tumor parameters had maximum errors of 5.5%. In [21,22], the effect of tumor size and depth on breast surface temperatures was analyzed. Infrared images were used in [23] for the early detection of cutaneous melanomas based on a 2D multilayer heat transfer model. The transient temperature signals capture from the skin surface were demodulated according to the lock-in principle to calculate both the phase and the amplitude of the lesions. The results of this demodulation allow the detection of melanomas at an early stage when the penetration depth of the lesion is less than 0.1 mm. In [24], three types of cooling in lesions close to the skin surface were analyzed from infrared images in 2D models. The results suggest that it is possible to apply a moderate temperature of about 20 °C to achieve effective skin cooling, with an acceptable cooling duration (¡2 min) in a clinical setting. This level of cooling is not likely to cause discomfort to the patient. The duration of the cooling can be adjusted considering the characteristics of the lesion to optimize the thermal contrast. The optimization of skin cooling by 2D computational model for the early detection of breast cancer was performed by [25]. In this work it was concluded that 5 min of cooling time is enough to increase the thermal contrast in infrared images, which is an acceptable value in clinical applications. One can observe that the cited works present several alternatives to increase the sensitivity of the superficial thermal profiles and methodologies for the estimation of tumors from the thermal mapping on the surface of the tissue.
2. Material and methods 2.1. Mathematical and physical model In this study, heat transfer in the breast is modeled in a 3D hemispherical domain, as shown in Fig. 1a. The breast is composed of four layers of tissues: skin, fat, mammary gland and muscle, which are shown in Fig. 1b (x-z cutting plane in the center of the y-axis of the Fig. 1a). Each layer is assumed as a homogeneous medium and its respective thermophysical properties are presented in Table 1. The spherical tumor of initial diameter d = 15 mm was centralized in three different coordinates in the center of the y axis within the region composed by the mammary gland. The simulations to be presented Table 1 Thermophysical properties of biological tissues [25,32,33].
2
Tissue layers
Thickness σ [mm]
Thermal conductivity, k [W/ (mK)]
Blood perfusion, w [s−1]
Heat source, Q [W/m3]
Skin Fat Gland Muscle Tumor
1.6 5.0 43.4 15 d = 15
0.45 0.21 0.48 0.48 0.62
0.00018 0.00022 0.00054 0.00270 0.01600
368.1 400 700 700 65,400
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considered the presence of only one tumor inside the breast. Based on the medical protocols that normalize the use of infrared thermography under steady state thermal conditions in clinical exams [28,29], the heat transfer in human tissue can be modeled at steady state according to the equation proposed by Pennes in 1948 [30] as
ki ∇2 Ti + ρb cb wb, i (Tb − Ti ) + Qi = 0
(1)
where i represents the layers of the breast, muscle (i = 1), gland (i = 2), fat (i = 3), skin (i = 4) and tumor (i = 5).The wb, i, and ki correspond to the blood perfusion rate and the thermal conductivity of the tissues, respectively. The variables ρb, cb, and Tb represent the specific mass, the specific heat and the arterial temperature of the blood, respectively. The metabolic heat generation of each tissue layer is denoted by Qi, and Ti is the temperature of each tissue layer. The values of the thermophysical properties used in the simulations are listed in Table 1. The specific mass (ρb) and specific heat (cb) for blood were 1060 kg/m3 and 3770 J/(kgK), respectively [31]. Eq. 1 is solved with appropriate boundary conditions on the breast surface and the temperature and heat flux continuity conditions at each interface between breast tissue layers. The core body temperature is prescribed at the bottom of the muscle layer, the heat flux at the bottom horizontal skin boundaries is taken to be zero, and the skin surface is exposed to thermal convection, as illustrated in Fig. 1b. The continuity of temperature and heat flux at the interface between tissue layers is described by
Ti (x , y, z ) = Ti + 1 (x , y, z ), ∂T (x , y, z ) ∂T (x , y, z ) ki i = ki + 1 i + 1 ∂n ∂n
Fig. 2. Numerical mesh of the hemispherical 3D breast model.
(2)
The lower part of the muscular layer is maintained at constant body temperature Tcore = 37 ° C. The boundary condition of the lower horizontal layer adjacent to the muscle is
∂T1 ∂n
=0 (3)
bottom surface
Fig. 3. Analysis of thermal properties.
The thermal convection boundary condition on the skin surface of the breast is specified as
q′′ = h [T (x , y, z )|skin
surface
− T∞]
layers of the breast tissue. In this work, the thermal model of the breast is analyzed in different situations. The temperature profiles on the breast surface are analyzed first, then, the difference between the temperatures of breasts with tumor and without tumor, and, finally, evaluates the normalized temperature variations (each temperature variation profile is divided by its respective maximum value). The following list is all analyzes that are carried out in this work, also represented by the schematic of Fig. 3:
(4)
where h is the thermal convection coefficient equals to 5 W/(m2K) and room temperature, T∞, considered equals to 21 °C. These values refer to a natural convection and a relatively low temperature medical room. The thermal model showed in Fig. 1, Eq. 1 and their respective boundary conditions are solved using the software COMSOL Multiphysics 4.3b (license number 6386748) for dimensions and properties of the tissue specified in Table 1. Thermophyscal properties and boundary conditions were implemented using the COMSOL bioheat transfer module. For a steady state problem, mash convergence is a simpler task compared to transient problem. The skin surface is of particular interest, the discretized skin layer mesh has 45,429 tetrahedral elements. The total mesh of the breast domain (Fig. 2) has 384,061 tetrahedral elements (finer mesh). The change to the finer mesh (extra fine mesh) resulted in less than 0.5% difference in the solution, therefore the selected mesh size was adequate for our analysis.
1. Analysis of tumor depth variation, i.e., the thermal profiles on the breast surface are analyzed for three distinct problems, where the same tumor is positioned at three different depths in the center of the y-axis, represented by tumors T1, T2, and T3, as shown in Fig. 1b. 2. Analysis of tumor size variation, i.e., three different diameters are analyzed at the same tumor geometric center T2, d = 10, 15 and 20 mm. 3. Analysis of tumor heat generation, i.e., three different values of heat generation are analyzed for the tumor T2, Qtumor = 29,000, 50,000 and 65,400 W/m3. These values were selected based on the heat generation values of tumors found in the literature [32]. 4. Analysis of tumor blood perfusion, i.e., three different values of blood perfusion rate are analyzed for tumor T2, wb, tumor = 0.0063, 0.016 and 0.05 s−1. The maximum and minimum values were chosen from the central value found in the literature [33]. 5. Analysis of the thermal conductivity of the tumor, i.e., three different values for thermal conductivity are analyzed for tumor T2, ktumor = 0.1, 0.62 and 1.0 W/(mK). The maximum and minimum values were chosen from the central value found in the literature
2.2. Analyzed thermophisical properties Most studies published in the literature that propose the estimation of mammary tumors from superficial temperatures are based on numerical simulations that use some optimization technique, whose objective is to identify characteristics such as depth, size, heat generation, thermal conductivity and blood perfusion of tumors [34–36]. However, the estimation of such characteristics will generally occur depending on several other thermophysical properties of the tumor and the healthy 3
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Fig. 4. Breast thermal distribution: (a) without tumor, (b) tumor T1. 34.6
1 Healthy T1 T2 T3
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0.8 Temperature variation [°C]
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Fig. 5. Tumor depth variation in the breast: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
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34.6 Healthy d = 10 mm d = 15 mm d = 20 mm
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Fig. 6. Tumor size variation on the breast - T2: (a) Skin superficial temperatures, (b) Temperature variations and (c) Normalized temperature variations.
the breast on the skin surface temperatures (temperatures that can be obtained by IR images) was investigated. First, it is presented the steady-state distribution of temperatures on the healthy breast surface (Fig. 4a) and on the breast with the tumor T1 (Fig. 4b). Since T1 is only 6.6 mm from the surface of the skin, one can observe that this inclusion is capable of increasing the surface temperature in approximately 1 °C.
[33]. 6. Analysis of the blood perfusion of the healthy breast region, i.e., three different values of blood perfusion in the healthy tissue layers (without tumor) of the breast are analyzed. The blood perfusion of all layers are considered equals to wb, healthy = 0.00018 and 0.00054 s−1, and it is verified if the thermal behavior of the tumor T2 on the surface has changed when compared to the initial setting for blood perfusions (already listed in Table 1). 7. Finally, the thermal conductivity of the healthy breast region is evaluated, i.e., three different values of the thermal conductivity coefficient of the healthy layers are analyzed. The thermal conductivity of all healthy layers is considered to be equal to khealthy = 0.21 and 0.48 W/(mK), and it is verified if the thermal behavior of the tumor T2 on the surface has changed when compared to the initial setting for thermal conductivities (already listed in Table 1).
3.1. Tumor depth influence Fig. 5a shows the superficial temperatures in the skin for the numerical simulations of the breast without tumor and for the three tumor cases, T1, T2, and T3, already illustrated in Fig. 1b. Each tumor has a distinct thermal profile, and the further away from the skin surface, more similar are the temperatures between tumor and healthy cases, making it difficult to diagnose anomalies through thermographic images. Looking to analyze the temperature variations caused by the different tumor depths, Fig. 5b shows the difference between the surface temperatures of each case with and without tumor, highlighting the thermal disturbances that each tumor causes in the healthy breast.
3. Results and discussions In this work, the influence of various thermophysical properties of 5
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0.25 Q = 29000 W/m3
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Q = 50000 W/m3
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Fig. 7. Variation of tumor volumetric heat generation on the breast - T2: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
3.2. Tumor size influence
Tumor T1, the closest to the skin surface, causes a temperature variation of about 1 °C. Tumor T3, the furthest from the skin surface, increases the superficial temperature of the breast skin by less than 0.1 °C. The normalization of temperature variations is also performed, i.e., each thermal variation presented in Fig. 5b is divided by its respective maximum value. The result of this calculation is presented in Fig. 5c, where one observes how each tumor depth modifies the temperatures in the skin. T3, the deepest tumor, causes a thermal change on the skin surface in the less flat Gaussian shape and T1, the most superficial, is characterized by a flattened Gaussian shape. Therefore, normalized information on temperature variations characterize the way each tumor changes the skin surface temperatures. Analyzing only the change of depth for tumors of the same properties and parameters, it is concluded that tumors with different depths cause different forms of surface thermal perturbation. By using the normalized temperature variation profiles to estimate the presence of tumors, the depth parameter will be an unknown factor in the problem.
At this stage, only the diameter is changed to the same geometric center of the tumor T2. For these analyzes, the tumor T2 is considered to have diameters of d = 10, 15 and 20 mm. Fig. 6a shows the superficial skin temperatures for the numerical simulations of healthy breast and with these three different tumors. It is again observed that each tumor increases the temperatures in the breast with different intensities, due to the different volumes that result in the change in heat generation of tumors. The larger the tumor, the greater the amount of heat generated, causing a rise in temperature above the other smaller tumors. Small tumors produce a distribution of skin surface temperatures similar to healthy tissue, making it difficult to diagnose anomalies by thermographic images. The temperature variations caused by the different tumors can be seen in Fig. 6b. The biggest tumor (d = 20 mm) causes an increase in skin surface temperatures of approximately 0.45 °C. The smallest tumor (d = 10 mm) increases the skin superficial temperatures in only 0.1 °C. One can observe in the normalized temperature variation 6
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w b,tumor = 0.0063 s-1
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w b,tumor = 0.0160 s-1
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Fig. 8. Variation of tumor blood perfusion on the breast - T2: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
healthy case. However, tumor metabolism also does not change the normalized temperature variation profiles on the skin surface. This is because, the change in the tumor heat generation only modifies the intensity of the heat carried in the neighbourhood, and not the form of heat propagation. Thus, it is also not necessary to know in advance the tumor heat generation to perform the estimation of the tumor geometric center using the normalized temperature variation profiles.
profiles that both tumor produce the same result, as shown in Fig. 6c. This happens because the three tumors have the same geometric center, i.e., the normalized temperature variation profile is independent of the tumor size. The tumor size only increases the heat intensity being generate and not the way that heat propagates in the biological tissue. Therefore, estimation of the geometric center of tumors can be performed without prior knowledge of its size, since tumors of different sizes centered at the same coordinates produce the same normalized thermal effect on the skin surface.
3.4. Tumor blood perfusion influence 3.3. Tumor metabolism influence The blood perfusion influence of the tumor T2 was also evaluated. For these analyses, only the values of perfusion rate wb, tumor = 0.0063, 0.0160 and 0.0500 s−1 were changed. Fig. 8a, b and c show the temperature profiles, the temperature variation and the normalized temperature variation, respectively. The higher the blood perfusion rate of the tumor, the lower the temperature on the breast skin surface, also causing less thermal variations when compared to the healthy case. However, tumor blood perfusion also does not change the normalized
The relationship of tumor metabolism and the temperature profiles was also analyzed. For this purpose, only the volumetric heat generation of tumor T2 is changed to 29,000 W/m3 and 50,000 W/m3. Fig. 7a, b and c show the temperature profiles, the temperature variation and the normalized temperature variation, respectively. The higher the metabolism of the tumor, the higher the temperature on the breast skin surface, also causing greater thermal variations when compared to the 7
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0.3 ktumor = 0.10 W/(mK)
Healthy ktumor = 0.10 W/(mK)
34.4
ktumor = 0.62 W/(mK) 0.25
ktumor = 0.62 W/(mK) Temperature variation [°C]
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ktumor = 1.00 W/(mK)
ktumor = 1.00 W/(mK)
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0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0
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Fig. 9. Variation of tumor blood perfusion on the breast - T2: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
variations when compared to the healthy case. However, tumor thermal conductivity also does not change the normalized temperature variation profiles on the skin surface. This is because, the change in the tumor thermal conductivity also only modifies the intensity of the heat carried in the neighbourhood, and not the form of heat propagation. Therefore, the thermal conductivity of the tumor is not necessary for the estimation of the tumor geometric center using normalized temperature variation profiles.
temperature variation profiles on the skin surface. This is because, the change in the blood perfusion rate of the tumor modifies the heat exchange between the tumor tissue and its surrounding blood, i.e., changing this thermophysical property only changes the intensity of thermal energy from the tumor to the breast surface, and not the form of heat propagation. Therefore, the blood perfusion rate of the tumor is not necessary for the estimation of the tumor geometric center using normalized temperature variation profiles.
3.6. Healthy tissue blood perfusion rate influence 3.5. Tumor thermal conductivity influence Heat transfer on the breast also depends of the thermophysical properties of the healthy tissue layers (muscle, gland, fat and skin). In order to analyze the influence of these characteristics in the temperature profiles, it is necessary to obtain the thermal behavior on the breast with and without tumor, with the same characteristics in the healthy region, i.e., verify if superficial temperature profiles will change by changing these properties.
The thermal conductivity of the tumor was also evaluated for T2. For the thermal conductivity analyses, ktumor = 0.10, 0.62 and 1.00 W/(mK) were considered. Fig. 9a, b and c show the temperature profiles, the temperature variation and the normalized temperature profiles, respectively. The higher the thermal conductivity of the tumor, the higher the temperature on the breast skin surface, also causing greater thermal 8
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35 w b,healthy = 0.00018 s-1
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Fig. 10. Variation of blood perfusions of healthy tissue layers: (a) Surface temperatures on the skin of the breast without tumor, (b) Surface temperatures on the skin of the breast with tumor, (c) Temperature variations with and without tumor, (d) Normalization of temperature variations.
blood perfusion rate of the healthy layers, the more intense is the heat exchange between the blood and the healthy tissue, causing the effect of heat generated by the tumor to be attenuated by the thermoregulation process of the human body. After obtaining the normalized temperature variations profiles presented in Fig. 10d, it can be observed that these profiles are not exactly the same. In other words, the way the tumor alters the thermal field on the skin surface is influenced by the blood perfusion variation of healthy tissue layers. However, it should be noted that in the region close to the greater sensitivity of this graph, a significant similarity between the shapes of the thermal profiles is observed. Therefore, normalized temperature variation profiles are not totally independent of the blood perfusion values of the healthy breast layers. In order to estimate the geometric center of tumors, an approximate value of this characteristic will be needed.
Fig. 10a shows the skin surface temperatures for three cases of healthy breasts considering different configurations for the blood perfusions of the breast tissue layers. In addition to the original configuration shown in Tables 1, thermal behaviors were also obtained considering blood perfusions equal to wb, healthy = 0.00018 and 0.00054 s−1. These values were selected based on the lowest and highest value found for this thermal property (disregarding the muscle) in Table 1. It is observed that the higher the blood perfusion, the higher the temperature on the skin surface. Increased blood perfusion rate accelerates the heat exchange between the tissue layer and the surrounding blood, resulting in this increase in superficial temperatures. Fig. 10b shows the skin surface temperatures of the breast with tumor T2 considering the same three blood perfusion rates for healthy tissue. One can observe that temperature increases with the increase of blood flow. However, by observing Fig. 10c, which shows the temperature variations of the case with tumor for each value of blood perfusion, one can observe that the greatest thermal variations occur in breasts with lower blood perfusions. This is because the higher the
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Fig. 11. Variation of thermal conductivities of healthy tissue layers: (a) Variations in skin surface temperatures e (b) Normalized temperature variations.
variations for the breasts with three different values for the heat convection coefficient, h = 0.5, 5.0, and 10 W/(m2K). Such chosen values include well insulated thermal systems and natural convection in closed rooms [21,25]. The higher the heat convection coefficient, higher the temperature variation observed on the breast skin surface. This is because increasing convective coefficient allows a higher convection heat exchange between the skin and the external environment. Fig. 13b shows the normalized temperature variations for the simulated cases considering different values for h. It is observed that there is a minimal influence of this property in the form of the normalized thermal variation profile. Therefore, the estimation of the geometric center of tumors from IR images using normalized temperatures will be minimally altered by changes in convection coefficient in the measured range.
3.7. Healthy tissue thermal conductivity influence The influence of the thermal conductivities of the healthy breast region was also investigated for the tumor case T2. Fig. 11a shows the superficial temperatures variations for the breasts with three different configurations for the thermal conductivity of healthy tissue layers (khealthy). In addition to the original configuration (Table 1), all healthy tissue layers were considered with khealthy = 0.21 and 0.48 W/(mK). Such chosen values include the lower and upper limits for the healthy layers shown in Table 1. The higher the thermal conductivity of healthy tissue layers, higher heat transfer efficiency from the tumor to the skin surface, causing higher surface thermal variation. Fig. 11b shows the normalized temperature variations for the simulated cases considering different values for khealthy. It is observed that there is a certain influence of this property in the form of the normalized thermal variation profile. Therefore, an approximate value of khealthy will be necessary to estimate the geometric center of tumors in breasts using normalized temperature variations obtained by IR images.
3.10. Ambient air temperature influence The influence of the ambient air temperature was investigated for the tumor case T2. Fig. 14a shows the superficial temperatures variations for the breasts with three different values for the ambient air temperature, T∞ = 15, 21, and 30 °C. Such values include a possible temperature values in a room with and without cooling. The higher the ambient air temperature, lower the temperature variation on the breast skin surface. This is because increasing air temperature decreases the convection heat exchange between the skin and the external environment. Fig. 14b shows the normalized temperature variations for the simulated cases considering different values for T∞. One can observe that changing these parameter also do not change the normalized thermal profiles on the skin surface. Table 2 presents a summary of the influence of each thermophysical property on normalized temperature profiles on the breast skin surface.
3.8. Fat layer thickness influence Finally, the effect of changing the thickness of the breast fat layer was also investigated for the tumor case T2. Fig. 12a shows the skin temperatures for three cases of healthy breasts considering different configurations for the fat layer thickness, σFat = 2, 5, and 8 mm. These values were selected based on a possible change to more or less of the breast fat percentage. It is observed that the higher the fat layer, lower the temperature on the skin surface. Increasing the fat layer thickness causes a thermal insulation effect, resulting in this decrease in superficial temperatures. Fig. 12b shows the skin surface temperatures of the breast with tumor T2 considering the same three fat layer thickness for healthy tissue. One can observe that temperature decreases with the increase of fat. However, by observing Fig. 12c, which shows the temperature variations for each value of fat layer, one can observe that the greatest thermal variations occur in breasts with higher fat layer thickness. Regarding the normalized temperature profiles presented by Fig. 12d, one can observe that changing the fat layer do not change the thermal profiles on the skin surface.
4. Conclusions In this work, a 3D hemispherical thermal model of the breast composed of different layers was created and analyzed to simulate IR images at steady state. The Pennes equation that mathematically characterizes the thermal model was solved numerically using commercial software COMSOL. Breast temperatures were obtained considering several situations in order to evaluate which thermophysical characteristics of the breast tissue (including the tumor) influence the superficial temperature profiles on the skin (temperatures that can be
3.9. Heat convection coefficient influence The influence of the heat convection coefficient was analyzed for the tumor case T2. Fig. 13a shows the superficial temperatures 10
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35.5
35.5 σ
= 2 mm
σ
= 2 mm
σ
= 5 mm
σ
= 5 mm
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35
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34
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33
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32.5 0
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σ
= 2 mm
Fat
0.9
σFat = 5 mm σFat = 8 mm
0.2
0.15
0.1
= 2 mm
σFat = 5 mm σFat = 8 mm
0.8 Normalized temperature
0.25
Temperature variation [ºC]
σFat = 8 mm
34.5 Temperature [ºC]
Temperature [ºC]
34.5
32.5 0
Fat
35
σFat = 8 mm
0.7 0.6 0.5 0.4 0.3 0.2
0.05
0.1 0 0
50
100 Arc length [mm]
150
0 0
200
50
100 Arc length [mm]
150
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Fig. 12. Variation of fat layer thickness: (a) Surface temperatures on the skin of the breast without tumor, (b) Surface temperatures on the skin of the breast with tumor, (c) Temperature variations with and without tumor, (d) Normalization of temperature variations.
on the breast surface. However, it is possible to evaluate a delimited region on the breast surface where these profiles have the same behavior. In this way, it would also be possible to detect the geometric center of tumors from IR images without prior knowledge of the properties of breast tissue layers, or by not having to know exactly these values. The fat layer thickness was evaluated. The results show that the fat layer thickness does not change the normalized temperature profiles, as long as the fat layer remains constant at both healthy breast and tumor breast temperatures. Variations in convective coefficient and ambient air temperature were also evaluated. Regarding the different convective coefficients analyzed, it was observed that small differences occur on the normalized temperature profiles. Thus, the convection coefficient must be the same on images without and with tumor. The change in ambient air temperature does not influence normalized temperature profiles on the breast skin surface. Finally, it is worth mentioning that by using IR imaging, even if it is in the steady state, one have the possibility of detect and estimate breast cancer without necessarily having to know several
obtained by IR images). Characteristics of the tumor, such as depth, size, metabolism, blood perfusion and thermal conductivity were varied in such a way that it was possible to evaluate the real influence of these on the superficial breast temperatures. A similar approach was adopted for the characteristics of the healthy breast region, blood perfusion, thermal conductivity and fat layer thickness were evaluated. By changing only the tumor depth, it has been found that the normalized temperature variations produced on the breast skin surface are different. However, when only size was changed for tumors of the same properties and centralized at the same coordinates, it was found that the normalized temperature variations are identical. Normalizations of temperature variations were also the same when evaluating the individual variation of metabolism, blood perfusion and thermal conductivity of the tumor. Therefore, these results demonstrated that a possible estimation of the geometric center of tumors from IR images can be performed without necessarily prior knowledge of tumor size, metabolism, blood perfusion and thermal conductivity. By individually changing the blood perfusion and thermal conductivity of the healthy tissue layers, it has been found that such properties influence the profiles of normalized temperature variations 11
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1 h = 0.5 W/(m2 K)
h = 0.5 W/(m2 K) 0.9
h = 5.0 W/(m2 K) h = 10 W/(m2 K)
h = 5.0 W/(m2 K) h = 10 W/(m2 K)
0.8 Normalized temperatute
Temperature variation [°C]
0.25
0.2
0.15
0.1
0.7 0.6 0.5 0.4 0.3 0.2
0.05
0.1 0
0 0
50
100 Arc length [mm]
150
200
0
50
100 Arc length [mm]
150
200
Fig. 13. Variation of heat convection coefficient: (a) Variations in skin surface temperatures e (b) Normalized temperature variations. 0.3
1 T = 15 ºC
T = 15 ºC
∞
∞
0.9
T∞ = 21 ºC T∞ = 30 ºC
T∞ = 30 ºC
0.8 Normalized temperature
Temperature variation [°C]
0.25
T∞ = 21 ºC
0.2
0.15
0.1
0.7 0.6 0.5 0.4 0.3 0.2
0.05
0.1 0 0
50
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150
0 0
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150
200
Fig. 14. Variation of ambient air temperature: (a) Variations in skin surface temperatures e (b) Normalized temperature variations.
breast cancer, thus reducing negative statistics related to the disease.
Table 2 Abstract on the influence of thermophysical properties on normalized temperature profiles on the breast skin surface. Tissue
Properties
Influence?
Tumor
Depth Size Metabolism Blood perfusion Thermal conductivity Blood perfusion Thermal conductivity Fat layer thickness Heat convection coefficient Ambient air temperature
Yes No No No No Partly Partly No Partly No
Healthy
Acknowledgements This study was funded in party by the Coordination for the Improvement of Higher Education Personnel (CAPES) - Brazil - Finance Code 001; FAPEMIG, Minas Gerais Research Funding Foundation; and the National Council of Technological and Scientific Development (CNPq) - Brazil - Grand number 150661/2018-5; and the Founded by the Alexander von Humboldt foundation. References [1] F. Bray, J. Ferlay, I. Soerjomataram, R.L. Siegel, L.A. Torre, A. Jemal, Global cancer statistics, Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA Cancer J. Clin. (2018), https://doi.org/10.3322/caac.21492. [2] R.L. Siegel, K.D. Miller, A. Jemal, Cancer statistics, 2017, CA Cancer J. Clin. 6 (1) (2018) 7–30, https://doi.org/10.3322/caac.21442. [3] J. Ferlay, M. Colombet, I. Soerjomataram, T. Dyba, G. Randi, M. Bettio, A. Gavin, O. Visser, F. Bray, Cancer incidence and mortality patterns in europe: estimates for 40 countries and 25 major cancers in 2018, Eur. J. Cancer 103 (2018) 356–387, https://doi.org/10.1016/j.ejca.2018.07.005.
thermophysical characteristics of the breast tissue. It is known that one of the great problems in estimating tumors from thermographic images is related to the difficulty in knowing the thermophysical properties of the tissues. Thus, this work contributes with information that can simplify the use of infrared thermography in the early diagnosis of 12
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International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt
Influence analysis of thermophysical properties on temperature profiles on the breast skin surface
T
⁎
Alisson A.A. Figueiredoa, , Henrique C. Fernandesb,c, Fernando C. Malheirosd, Gilmar Guimaraese a
Department of Mechanical Engineering, Federal University of Ouro Preto, Ouro Preto 35400-000, Brazil School of Computer Science, Federal University of Uberlandia, Uberlandia 38408-100, Brazil c Fraunhofer IZFP Institute for Nondestructive Testing, Saarbrücken 66123, Germany d Minas Gerais State University, Ituiutaba 38302-192, Brazil e School of Mechanical Engineering, Federal University of Uberlandia, Uberlandia 38408-100, Brazil b
A R T I C LE I N FO
A B S T R A C T
Keywords: Breast cancer Infrared thermography Normalized temperatures Thermophysical properties Diagnosis simplification
This work presents a simplified approach for the early detection of breast cancer using thermographic images, showing that several thermophysical properties of the bio-thermal problem does not need to be previously known to locate the geometric center of tumors. A 3D hemispheric breast model composed of different layers (muscle, gland, fat and skin) was constructed to evaluate the thermal behavior on the skin surface from numerical simulations using commercial software COMSOL. The effects of changes in depth, size, metabolism, blood perfusion and thermal conductivity of the tumor at surface temperatures were systematically analyzed to provide important information and guidelines for future medical diagnoses. Variations in blood perfusions and thermal conductivities of healthy tissue layers were also evaluated. It has been found that changing the size, metabolism, blood perfusion and thermal conductivity of a centralized tumor in the same coordinate does not modify the profiles of normalized temperature variations on the breast skin surface. Regarding the properties of healthy tissue, if a specific region of the breast surface is taken, there is the possibility that the normalized temperature profiles also do not depend on these properties. Thus, knowing that one of the main limitations in the estimation of tumors from thermographic images is related to the difficulty of previously knowing the thermophysical properties of human tissues, the results obtained in this study provide valuable simplifications for the early diagnosis of breast cancer using infrared thermography.
1. Introduction Among women, breast cancer is the most commonly diagnosed type of cancer and the leading cause of cancer death in the world. Of the 8.6 million new cases of cancer estimated for 2018 among women, 24.2% corresponds to breast cancer. Regarding the 4.2 million cancer deaths among women estimated for 2018, 15.0% corresponds to breast cancer [1]. Breast cancer accounts for 30% of new estimated cancer cases among women in the USA and 28.2% in Europe [2,3]. Several imaging techniques are used to aid in the diagnosis of breast cancer, especially mammography, magnetic resonance imaging and ultrasonography. Mammography is the breast cancer screening tool with the best combination of sensitivity and specificity. However, mammography still has limitations, such as the emission of ionizing radiations, high false-negative or false-positive rates, inefficiency for women with dense breasts (especially young women), among others ⁎
[4]. It is known that cancer cells have a different blood flow and metabolism than healthy cells [5]. This change due to the presence of the tumor can be transmitted to the surrounding tissue, and may change the temperature on the breast surface [6]. Infrared thermography (IRT) is a non-destructive technique, non-invasive, contactless, which enables the mapping of thermal patterns, i.e., thermograms, on the surface of objects, bodies and systems through the use of an infrared (IR) imaging instrument, such as an IR camera [7]. According to some institutions such as the American Cancer Society, American College of Clinical Thermology and the International Academy of Clinical Thermology, IRT is unable to identify the location of tumors and can not replace, for example, mammography examination. However, the addition of thermographic images along with other types of exams significantly increases the chances of early diagnosis of the disease [8–10]. A large number of researches have been carried out
Corresponding author. E-mail addresses: alisson.fi[email protected] (A.A.A. Figueiredo), [email protected] (H.C. Fernandes), [email protected] (F.C. Malheiros), [email protected] (G. Guimaraes). https://doi.org/10.1016/j.icheatmasstransfer.2019.104453
0735-1933/ © 2019 Elsevier Ltd. All rights reserved.
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Fig. 1. Hemispherical model of the breast: (a) 3D view, (b) x-z cutting plane in the center of the y-axis.
In a previous work, Figueiredo et al. [26] proposed a new technique to determine the geometric center of mammary tumors from correlations of superficial skin temperatures obtained by infrared images. The presented methodology was able to estimate tumors inside silicone samples without the need of previous knowledge of the properties of tumors with an error of less than 4%. In [27], Figueiredo et al. adapted the technique proposed in [26] to estimate the presence of the main types of breast cancer from superficial skin temperatures from numerical simulations of a real 2D anatomical model of the breast. This work demonstrated the ability of the technique to estimate tumors in real breast geometries without the need for prior knowledge of the properties of carcinogenic inclusions. In this work, a detailed thermal analyzes is presented which allows to affirm that it is possible to estimate the presence of the geometric center of tumors from superficial temperatures without the need of previous knowledge of the thermophysical properties of the thermal problem. The phenomenon is analyzed in a 3D hemispheric breast made up of different layers of tissues. The main goal is to present a set of possible simplifications in the process of early detecting breast cancer using IR imaging. The computational model was created using COMSOL Multiphysics and systematically considers the superficial thermal responses in the skin for tumors of different sizes, depths, blood perfusions and thermal conductivity. The influence of the thermophysical properties of the healthy tissue region on the surface thermal profiles is also analyzed.
with the aim of making IRT a method capable of early detecting and diagnosing breast and other kinds of tumors [11–14]. Several clinical tests for the detection of breast abnormalities have been performed based on thermograms and the results are very consistent [15]. A study using the conjugate gradient method in screening breast lesions in patients undergoing thermal mapping demonstrated great potential, obtained 96% efficacy in the detection of breast abnormalities [16]. The thermal impedance technique was recently applied experimentally in hyperplastic materials in order to qualify IRT for the detection of mammary tumors, obtaining high sensitivities for small sizes of inclusions [17]. Those works applied IRT together with an optimization method to characterize the presence of breast tumors. To better understand and interpret the thermal behavior on the breast surface caused by tumors, different theoretical models must be studied. The transmission line matrix (TLM) method was used to model the heat transfer in a 3D breast in Cartesian coordinates with a built-in tumor. In this study, the skin surface temperature increase was significant only for tumors located in the superficial region at a depth up to 20 mm [18]. In [19,20], estimations of the blood perfusion rate, size and depth of breast and brain tumors in 1D and 2D models were performed from the surface temperatures simulated by the finite volume method along with a direct search method and genetic algorithmns (GA). Estimations of the tumor parameters had maximum errors of 5.5%. In [21,22], the effect of tumor size and depth on breast surface temperatures was analyzed. Infrared images were used in [23] for the early detection of cutaneous melanomas based on a 2D multilayer heat transfer model. The transient temperature signals capture from the skin surface were demodulated according to the lock-in principle to calculate both the phase and the amplitude of the lesions. The results of this demodulation allow the detection of melanomas at an early stage when the penetration depth of the lesion is less than 0.1 mm. In [24], three types of cooling in lesions close to the skin surface were analyzed from infrared images in 2D models. The results suggest that it is possible to apply a moderate temperature of about 20 °C to achieve effective skin cooling, with an acceptable cooling duration (¡2 min) in a clinical setting. This level of cooling is not likely to cause discomfort to the patient. The duration of the cooling can be adjusted considering the characteristics of the lesion to optimize the thermal contrast. The optimization of skin cooling by 2D computational model for the early detection of breast cancer was performed by [25]. In this work it was concluded that 5 min of cooling time is enough to increase the thermal contrast in infrared images, which is an acceptable value in clinical applications. One can observe that the cited works present several alternatives to increase the sensitivity of the superficial thermal profiles and methodologies for the estimation of tumors from the thermal mapping on the surface of the tissue.
2. Material and methods 2.1. Mathematical and physical model In this study, heat transfer in the breast is modeled in a 3D hemispherical domain, as shown in Fig. 1a. The breast is composed of four layers of tissues: skin, fat, mammary gland and muscle, which are shown in Fig. 1b (x-z cutting plane in the center of the y-axis of the Fig. 1a). Each layer is assumed as a homogeneous medium and its respective thermophysical properties are presented in Table 1. The spherical tumor of initial diameter d = 15 mm was centralized in three different coordinates in the center of the y axis within the region composed by the mammary gland. The simulations to be presented Table 1 Thermophysical properties of biological tissues [25,32,33].
2
Tissue layers
Thickness σ [mm]
Thermal conductivity, k [W/ (mK)]
Blood perfusion, w [s−1]
Heat source, Q [W/m3]
Skin Fat Gland Muscle Tumor
1.6 5.0 43.4 15 d = 15
0.45 0.21 0.48 0.48 0.62
0.00018 0.00022 0.00054 0.00270 0.01600
368.1 400 700 700 65,400
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considered the presence of only one tumor inside the breast. Based on the medical protocols that normalize the use of infrared thermography under steady state thermal conditions in clinical exams [28,29], the heat transfer in human tissue can be modeled at steady state according to the equation proposed by Pennes in 1948 [30] as
ki ∇2 Ti + ρb cb wb, i (Tb − Ti ) + Qi = 0
(1)
where i represents the layers of the breast, muscle (i = 1), gland (i = 2), fat (i = 3), skin (i = 4) and tumor (i = 5).The wb, i, and ki correspond to the blood perfusion rate and the thermal conductivity of the tissues, respectively. The variables ρb, cb, and Tb represent the specific mass, the specific heat and the arterial temperature of the blood, respectively. The metabolic heat generation of each tissue layer is denoted by Qi, and Ti is the temperature of each tissue layer. The values of the thermophysical properties used in the simulations are listed in Table 1. The specific mass (ρb) and specific heat (cb) for blood were 1060 kg/m3 and 3770 J/(kgK), respectively [31]. Eq. 1 is solved with appropriate boundary conditions on the breast surface and the temperature and heat flux continuity conditions at each interface between breast tissue layers. The core body temperature is prescribed at the bottom of the muscle layer, the heat flux at the bottom horizontal skin boundaries is taken to be zero, and the skin surface is exposed to thermal convection, as illustrated in Fig. 1b. The continuity of temperature and heat flux at the interface between tissue layers is described by
Ti (x , y, z ) = Ti + 1 (x , y, z ), ∂T (x , y, z ) ∂T (x , y, z ) ki i = ki + 1 i + 1 ∂n ∂n
Fig. 2. Numerical mesh of the hemispherical 3D breast model.
(2)
The lower part of the muscular layer is maintained at constant body temperature Tcore = 37 ° C. The boundary condition of the lower horizontal layer adjacent to the muscle is
∂T1 ∂n
=0 (3)
bottom surface
Fig. 3. Analysis of thermal properties.
The thermal convection boundary condition on the skin surface of the breast is specified as
q′′ = h [T (x , y, z )|skin
surface
− T∞]
layers of the breast tissue. In this work, the thermal model of the breast is analyzed in different situations. The temperature profiles on the breast surface are analyzed first, then, the difference between the temperatures of breasts with tumor and without tumor, and, finally, evaluates the normalized temperature variations (each temperature variation profile is divided by its respective maximum value). The following list is all analyzes that are carried out in this work, also represented by the schematic of Fig. 3:
(4)
where h is the thermal convection coefficient equals to 5 W/(m2K) and room temperature, T∞, considered equals to 21 °C. These values refer to a natural convection and a relatively low temperature medical room. The thermal model showed in Fig. 1, Eq. 1 and their respective boundary conditions are solved using the software COMSOL Multiphysics 4.3b (license number 6386748) for dimensions and properties of the tissue specified in Table 1. Thermophyscal properties and boundary conditions were implemented using the COMSOL bioheat transfer module. For a steady state problem, mash convergence is a simpler task compared to transient problem. The skin surface is of particular interest, the discretized skin layer mesh has 45,429 tetrahedral elements. The total mesh of the breast domain (Fig. 2) has 384,061 tetrahedral elements (finer mesh). The change to the finer mesh (extra fine mesh) resulted in less than 0.5% difference in the solution, therefore the selected mesh size was adequate for our analysis.
1. Analysis of tumor depth variation, i.e., the thermal profiles on the breast surface are analyzed for three distinct problems, where the same tumor is positioned at three different depths in the center of the y-axis, represented by tumors T1, T2, and T3, as shown in Fig. 1b. 2. Analysis of tumor size variation, i.e., three different diameters are analyzed at the same tumor geometric center T2, d = 10, 15 and 20 mm. 3. Analysis of tumor heat generation, i.e., three different values of heat generation are analyzed for the tumor T2, Qtumor = 29,000, 50,000 and 65,400 W/m3. These values were selected based on the heat generation values of tumors found in the literature [32]. 4. Analysis of tumor blood perfusion, i.e., three different values of blood perfusion rate are analyzed for tumor T2, wb, tumor = 0.0063, 0.016 and 0.05 s−1. The maximum and minimum values were chosen from the central value found in the literature [33]. 5. Analysis of the thermal conductivity of the tumor, i.e., three different values for thermal conductivity are analyzed for tumor T2, ktumor = 0.1, 0.62 and 1.0 W/(mK). The maximum and minimum values were chosen from the central value found in the literature
2.2. Analyzed thermophisical properties Most studies published in the literature that propose the estimation of mammary tumors from superficial temperatures are based on numerical simulations that use some optimization technique, whose objective is to identify characteristics such as depth, size, heat generation, thermal conductivity and blood perfusion of tumors [34–36]. However, the estimation of such characteristics will generally occur depending on several other thermophysical properties of the tumor and the healthy 3
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Fig. 6. Tumor size variation on the breast - T2: (a) Skin superficial temperatures, (b) Temperature variations and (c) Normalized temperature variations.
the breast on the skin surface temperatures (temperatures that can be obtained by IR images) was investigated. First, it is presented the steady-state distribution of temperatures on the healthy breast surface (Fig. 4a) and on the breast with the tumor T1 (Fig. 4b). Since T1 is only 6.6 mm from the surface of the skin, one can observe that this inclusion is capable of increasing the surface temperature in approximately 1 °C.
[33]. 6. Analysis of the blood perfusion of the healthy breast region, i.e., three different values of blood perfusion in the healthy tissue layers (without tumor) of the breast are analyzed. The blood perfusion of all layers are considered equals to wb, healthy = 0.00018 and 0.00054 s−1, and it is verified if the thermal behavior of the tumor T2 on the surface has changed when compared to the initial setting for blood perfusions (already listed in Table 1). 7. Finally, the thermal conductivity of the healthy breast region is evaluated, i.e., three different values of the thermal conductivity coefficient of the healthy layers are analyzed. The thermal conductivity of all healthy layers is considered to be equal to khealthy = 0.21 and 0.48 W/(mK), and it is verified if the thermal behavior of the tumor T2 on the surface has changed when compared to the initial setting for thermal conductivities (already listed in Table 1).
3.1. Tumor depth influence Fig. 5a shows the superficial temperatures in the skin for the numerical simulations of the breast without tumor and for the three tumor cases, T1, T2, and T3, already illustrated in Fig. 1b. Each tumor has a distinct thermal profile, and the further away from the skin surface, more similar are the temperatures between tumor and healthy cases, making it difficult to diagnose anomalies through thermographic images. Looking to analyze the temperature variations caused by the different tumor depths, Fig. 5b shows the difference between the surface temperatures of each case with and without tumor, highlighting the thermal disturbances that each tumor causes in the healthy breast.
3. Results and discussions In this work, the influence of various thermophysical properties of 5
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Fig. 7. Variation of tumor volumetric heat generation on the breast - T2: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
3.2. Tumor size influence
Tumor T1, the closest to the skin surface, causes a temperature variation of about 1 °C. Tumor T3, the furthest from the skin surface, increases the superficial temperature of the breast skin by less than 0.1 °C. The normalization of temperature variations is also performed, i.e., each thermal variation presented in Fig. 5b is divided by its respective maximum value. The result of this calculation is presented in Fig. 5c, where one observes how each tumor depth modifies the temperatures in the skin. T3, the deepest tumor, causes a thermal change on the skin surface in the less flat Gaussian shape and T1, the most superficial, is characterized by a flattened Gaussian shape. Therefore, normalized information on temperature variations characterize the way each tumor changes the skin surface temperatures. Analyzing only the change of depth for tumors of the same properties and parameters, it is concluded that tumors with different depths cause different forms of surface thermal perturbation. By using the normalized temperature variation profiles to estimate the presence of tumors, the depth parameter will be an unknown factor in the problem.
At this stage, only the diameter is changed to the same geometric center of the tumor T2. For these analyzes, the tumor T2 is considered to have diameters of d = 10, 15 and 20 mm. Fig. 6a shows the superficial skin temperatures for the numerical simulations of healthy breast and with these three different tumors. It is again observed that each tumor increases the temperatures in the breast with different intensities, due to the different volumes that result in the change in heat generation of tumors. The larger the tumor, the greater the amount of heat generated, causing a rise in temperature above the other smaller tumors. Small tumors produce a distribution of skin surface temperatures similar to healthy tissue, making it difficult to diagnose anomalies by thermographic images. The temperature variations caused by the different tumors can be seen in Fig. 6b. The biggest tumor (d = 20 mm) causes an increase in skin surface temperatures of approximately 0.45 °C. The smallest tumor (d = 10 mm) increases the skin superficial temperatures in only 0.1 °C. One can observe in the normalized temperature variation 6
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Fig. 8. Variation of tumor blood perfusion on the breast - T2: (a) Skin surface temperatures, (b) Temperature variations and (c) Normalized temperature variations.
healthy case. However, tumor metabolism also does not change the normalized temperature variation profiles on the skin surface. This is because, the change in the tumor heat generation only modifies the intensity of the heat carried in the neighbourhood, and not the form of heat propagation. Thus, it is also not necessary to know in advance the tumor heat generation to perform the estimation of the tumor geometric center using the normalized temperature variation profiles.
profiles that both tumor produce the same result, as shown in Fig. 6c. This happens because the three tumors have the same geometric center, i.e., the normalized temperature variation profile is independent of the tumor size. The tumor size only increases the heat intensity being generate and not the way that heat propagates in the biological tissue. Therefore, estimation of the geometric center of tumors can be performed without prior knowledge of its size, since tumors of different sizes centered at the same coordinates produce the same normalized thermal effect on the skin surface.
3.4. Tumor blood perfusion influence 3.3. Tumor metabolism influence The blood perfusion influence of the tumor T2 was also evaluated. For these analyses, only the values of perfusion rate wb, tumor = 0.0063, 0.0160 and 0.0500 s−1 were changed. Fig. 8a, b and c show the temperature profiles, the temperature variation and the normalized temperature variation, respectively. The higher the blood perfusion rate of the tumor, the lower the temperature on the breast skin surface, also causing less thermal variations when compared to the healthy case. However, tumor blood perfusion also does not change the normalized
The relationship of tumor metabolism and the temperature profiles was also analyzed. For this purpose, only the volumetric heat generation of tumor T2 is changed to 29,000 W/m3 and 50,000 W/m3. Fig. 7a, b and c show the temperature profiles, the temperature variation and the normalized temperature variation, respectively. The higher the metabolism of the tumor, the higher the temperature on the breast skin surface, also causing greater thermal variations when compared to the 7
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variations when compared to the healthy case. However, tumor thermal conductivity also does not change the normalized temperature variation profiles on the skin surface. This is because, the change in the tumor thermal conductivity also only modifies the intensity of the heat carried in the neighbourhood, and not the form of heat propagation. Therefore, the thermal conductivity of the tumor is not necessary for the estimation of the tumor geometric center using normalized temperature variation profiles.
temperature variation profiles on the skin surface. This is because, the change in the blood perfusion rate of the tumor modifies the heat exchange between the tumor tissue and its surrounding blood, i.e., changing this thermophysical property only changes the intensity of thermal energy from the tumor to the breast surface, and not the form of heat propagation. Therefore, the blood perfusion rate of the tumor is not necessary for the estimation of the tumor geometric center using normalized temperature variation profiles.
3.6. Healthy tissue blood perfusion rate influence 3.5. Tumor thermal conductivity influence Heat transfer on the breast also depends of the thermophysical properties of the healthy tissue layers (muscle, gland, fat and skin). In order to analyze the influence of these characteristics in the temperature profiles, it is necessary to obtain the thermal behavior on the breast with and without tumor, with the same characteristics in the healthy region, i.e., verify if superficial temperature profiles will change by changing these properties.
The thermal conductivity of the tumor was also evaluated for T2. For the thermal conductivity analyses, ktumor = 0.10, 0.62 and 1.00 W/(mK) were considered. Fig. 9a, b and c show the temperature profiles, the temperature variation and the normalized temperature profiles, respectively. The higher the thermal conductivity of the tumor, the higher the temperature on the breast skin surface, also causing greater thermal 8
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blood perfusion rate of the healthy layers, the more intense is the heat exchange between the blood and the healthy tissue, causing the effect of heat generated by the tumor to be attenuated by the thermoregulation process of the human body. After obtaining the normalized temperature variations profiles presented in Fig. 10d, it can be observed that these profiles are not exactly the same. In other words, the way the tumor alters the thermal field on the skin surface is influenced by the blood perfusion variation of healthy tissue layers. However, it should be noted that in the region close to the greater sensitivity of this graph, a significant similarity between the shapes of the thermal profiles is observed. Therefore, normalized temperature variation profiles are not totally independent of the blood perfusion values of the healthy breast layers. In order to estimate the geometric center of tumors, an approximate value of this characteristic will be needed.
Fig. 10a shows the skin surface temperatures for three cases of healthy breasts considering different configurations for the blood perfusions of the breast tissue layers. In addition to the original configuration shown in Tables 1, thermal behaviors were also obtained considering blood perfusions equal to wb, healthy = 0.00018 and 0.00054 s−1. These values were selected based on the lowest and highest value found for this thermal property (disregarding the muscle) in Table 1. It is observed that the higher the blood perfusion, the higher the temperature on the skin surface. Increased blood perfusion rate accelerates the heat exchange between the tissue layer and the surrounding blood, resulting in this increase in superficial temperatures. Fig. 10b shows the skin surface temperatures of the breast with tumor T2 considering the same three blood perfusion rates for healthy tissue. One can observe that temperature increases with the increase of blood flow. However, by observing Fig. 10c, which shows the temperature variations of the case with tumor for each value of blood perfusion, one can observe that the greatest thermal variations occur in breasts with lower blood perfusions. This is because the higher the
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variations for the breasts with three different values for the heat convection coefficient, h = 0.5, 5.0, and 10 W/(m2K). Such chosen values include well insulated thermal systems and natural convection in closed rooms [21,25]. The higher the heat convection coefficient, higher the temperature variation observed on the breast skin surface. This is because increasing convective coefficient allows a higher convection heat exchange between the skin and the external environment. Fig. 13b shows the normalized temperature variations for the simulated cases considering different values for h. It is observed that there is a minimal influence of this property in the form of the normalized thermal variation profile. Therefore, the estimation of the geometric center of tumors from IR images using normalized temperatures will be minimally altered by changes in convection coefficient in the measured range.
3.7. Healthy tissue thermal conductivity influence The influence of the thermal conductivities of the healthy breast region was also investigated for the tumor case T2. Fig. 11a shows the superficial temperatures variations for the breasts with three different configurations for the thermal conductivity of healthy tissue layers (khealthy). In addition to the original configuration (Table 1), all healthy tissue layers were considered with khealthy = 0.21 and 0.48 W/(mK). Such chosen values include the lower and upper limits for the healthy layers shown in Table 1. The higher the thermal conductivity of healthy tissue layers, higher heat transfer efficiency from the tumor to the skin surface, causing higher surface thermal variation. Fig. 11b shows the normalized temperature variations for the simulated cases considering different values for khealthy. It is observed that there is a certain influence of this property in the form of the normalized thermal variation profile. Therefore, an approximate value of khealthy will be necessary to estimate the geometric center of tumors in breasts using normalized temperature variations obtained by IR images.
3.10. Ambient air temperature influence The influence of the ambient air temperature was investigated for the tumor case T2. Fig. 14a shows the superficial temperatures variations for the breasts with three different values for the ambient air temperature, T∞ = 15, 21, and 30 °C. Such values include a possible temperature values in a room with and without cooling. The higher the ambient air temperature, lower the temperature variation on the breast skin surface. This is because increasing air temperature decreases the convection heat exchange between the skin and the external environment. Fig. 14b shows the normalized temperature variations for the simulated cases considering different values for T∞. One can observe that changing these parameter also do not change the normalized thermal profiles on the skin surface. Table 2 presents a summary of the influence of each thermophysical property on normalized temperature profiles on the breast skin surface.
3.8. Fat layer thickness influence Finally, the effect of changing the thickness of the breast fat layer was also investigated for the tumor case T2. Fig. 12a shows the skin temperatures for three cases of healthy breasts considering different configurations for the fat layer thickness, σFat = 2, 5, and 8 mm. These values were selected based on a possible change to more or less of the breast fat percentage. It is observed that the higher the fat layer, lower the temperature on the skin surface. Increasing the fat layer thickness causes a thermal insulation effect, resulting in this decrease in superficial temperatures. Fig. 12b shows the skin surface temperatures of the breast with tumor T2 considering the same three fat layer thickness for healthy tissue. One can observe that temperature decreases with the increase of fat. However, by observing Fig. 12c, which shows the temperature variations for each value of fat layer, one can observe that the greatest thermal variations occur in breasts with higher fat layer thickness. Regarding the normalized temperature profiles presented by Fig. 12d, one can observe that changing the fat layer do not change the thermal profiles on the skin surface.
4. Conclusions In this work, a 3D hemispherical thermal model of the breast composed of different layers was created and analyzed to simulate IR images at steady state. The Pennes equation that mathematically characterizes the thermal model was solved numerically using commercial software COMSOL. Breast temperatures were obtained considering several situations in order to evaluate which thermophysical characteristics of the breast tissue (including the tumor) influence the superficial temperature profiles on the skin (temperatures that can be
3.9. Heat convection coefficient influence The influence of the heat convection coefficient was analyzed for the tumor case T2. Fig. 13a shows the superficial temperatures 10
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Fig. 12. Variation of fat layer thickness: (a) Surface temperatures on the skin of the breast without tumor, (b) Surface temperatures on the skin of the breast with tumor, (c) Temperature variations with and without tumor, (d) Normalization of temperature variations.
on the breast surface. However, it is possible to evaluate a delimited region on the breast surface where these profiles have the same behavior. In this way, it would also be possible to detect the geometric center of tumors from IR images without prior knowledge of the properties of breast tissue layers, or by not having to know exactly these values. The fat layer thickness was evaluated. The results show that the fat layer thickness does not change the normalized temperature profiles, as long as the fat layer remains constant at both healthy breast and tumor breast temperatures. Variations in convective coefficient and ambient air temperature were also evaluated. Regarding the different convective coefficients analyzed, it was observed that small differences occur on the normalized temperature profiles. Thus, the convection coefficient must be the same on images without and with tumor. The change in ambient air temperature does not influence normalized temperature profiles on the breast skin surface. Finally, it is worth mentioning that by using IR imaging, even if it is in the steady state, one have the possibility of detect and estimate breast cancer without necessarily having to know several
obtained by IR images). Characteristics of the tumor, such as depth, size, metabolism, blood perfusion and thermal conductivity were varied in such a way that it was possible to evaluate the real influence of these on the superficial breast temperatures. A similar approach was adopted for the characteristics of the healthy breast region, blood perfusion, thermal conductivity and fat layer thickness were evaluated. By changing only the tumor depth, it has been found that the normalized temperature variations produced on the breast skin surface are different. However, when only size was changed for tumors of the same properties and centralized at the same coordinates, it was found that the normalized temperature variations are identical. Normalizations of temperature variations were also the same when evaluating the individual variation of metabolism, blood perfusion and thermal conductivity of the tumor. Therefore, these results demonstrated that a possible estimation of the geometric center of tumors from IR images can be performed without necessarily prior knowledge of tumor size, metabolism, blood perfusion and thermal conductivity. By individually changing the blood perfusion and thermal conductivity of the healthy tissue layers, it has been found that such properties influence the profiles of normalized temperature variations 11
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breast cancer, thus reducing negative statistics related to the disease.
Table 2 Abstract on the influence of thermophysical properties on normalized temperature profiles on the breast skin surface. Tissue
Properties
Influence?
Tumor
Depth Size Metabolism Blood perfusion Thermal conductivity Blood perfusion Thermal conductivity Fat layer thickness Heat convection coefficient Ambient air temperature
Yes No No No No Partly Partly No Partly No
Healthy
Acknowledgements This study was funded in party by the Coordination for the Improvement of Higher Education Personnel (CAPES) - Brazil - Finance Code 001; FAPEMIG, Minas Gerais Research Funding Foundation; and the National Council of Technological and Scientific Development (CNPq) - Brazil - Grand number 150661/2018-5; and the Founded by the Alexander von Humboldt foundation. References [1] F. Bray, J. Ferlay, I. Soerjomataram, R.L. Siegel, L.A. Torre, A. Jemal, Global cancer statistics, Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA Cancer J. Clin. (2018), https://doi.org/10.3322/caac.21492. [2] R.L. Siegel, K.D. Miller, A. Jemal, Cancer statistics, 2017, CA Cancer J. Clin. 6 (1) (2018) 7–30, https://doi.org/10.3322/caac.21442. [3] J. Ferlay, M. Colombet, I. Soerjomataram, T. Dyba, G. Randi, M. Bettio, A. Gavin, O. Visser, F. Bray, Cancer incidence and mortality patterns in europe: estimates for 40 countries and 25 major cancers in 2018, Eur. J. Cancer 103 (2018) 356–387, https://doi.org/10.1016/j.ejca.2018.07.005.
thermophysical characteristics of the breast tissue. It is known that one of the great problems in estimating tumors from thermographic images is related to the difficulty in knowing the thermophysical properties of the tissues. Thus, this work contributes with information that can simplify the use of infrared thermography in the early diagnosis of 12
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