Proceedings of the 7th World Congress on Mechanical, Chemical, and Material Engineering (MCM'21)
Prague, Czech Republic Virtual Conference – August, 2021
Paper No. ICMIE 124
DOI: 10.11159/icmie21.124

Detection of Tumours Using Breast Surface Thermal Patterns
Y.S. Yu1, G.S. Hu1, S.C. Fok1

Sichuan University Pittsburgh InstituteSichuan University, Chengdu, China
yuanshengyu1999@outlook.com; gengshuohu1023@gmail.com; Saicheong.fok@scupi.cn
1

Abstract – Influencing factors are important considerations in the application of non-invasive thermal diagnostics for the early detectionof breast tumour. In this paper, experimental studies of artificial tumours embedded inside silicone breasts coupled with numericalsimulations using 3D finite-element method in ANSYS were used to investigate the effects of tissue conductivity, tumour size and tumour
depth on the heat patterns at the breast skin surface. After validating the numerical breast model, the analysis was extended to examine
the heat patterns of a growing tumour. The findings revealed that thermal patterns of the breast surface over time could be useful for thedetection of tumours. The existence of tumours would be more noticeable from thermal images of breasts with more fatty tissues, andbreasts of lower density. The method would be more suitable for the detection of large tumours near the skin surface. The simulated
results suggested that it is possible to detect an initial 4 mm HER2-positive tumour at a depth of 44 mm after about 196 days when it had
grown to 7 mm using a temperature sensor with resolution of 0.01 ℃.
Keywords: thermal images; breast tumour; finite-element method; non-invasive diagnostics

1. Introduction

Body temperature is commonly used as a health indicator and thermal data had been applied for the diagnosis of manyillnesses [1]. Recently, thermal patterns had been suggested for the early detection of breast tumours [2-4]. This technique isrelatively inexpensive, non-invasive, and temperature sensors can be easily embedded into wearable computers forcontinuous real-time monitoring of health status. These advantages would facilitate the early detection of breast tumours sothat the disease can be treated in the early stages, which would ensure higher probability of successful treatment.
The changing thermal characteristics associated with a growing tumour is the result of the rapid volumetric development
and acceleration of local metabolism directly related to the speed of cell division [5]. Clinical results had shown that the
blood flow to a growing tumour was greater than the blood flow of surrounding normal tissues [6], and the subsurface of thebreast tumour lesion is hotter than the surrounding tissues. Gautherie [7] found that the temperature of a cancerous tumour
inside the breast can be about 3 ℃ higher than normal tissue. As the tumour grows, the heat pattern would change. The
escalation in temperature over time on the breast surface for a growing tumour can be captured using temperature sensors or
infrared cameras. By comparing the changing temperature profiles between the lift and right breasts with respect to time,
abnormality that warrants further investigation can be detected.
Although the concept of using temperature profiles over time for the detection of growing tumour is relatively simple,
factors influencing the thermal patterns had not been fully investigated. This paper examines the effects of the changes intissue conductivity, tumour size and tumour depth on the surface heat patterns. Experimental studies were conducted onbreasts made from three types of silicone rubbers with different material properties. Heated resistors were inserted into theartificial breasts to simulate heat generated from tumours of specific sizes and locations. The steady state heat patterns ofthese breasts were captured using an infrared camera. At the same time, numerical models of these breasts were developed
using finite-element method (FEM) in ANSYS. After the verification of the numerical models with experimental results, theFEM model was then extended using realistic tissue properties, body temperature, and tumour heat generation characteristics
to examine the changes in heat patterns over time for a growing tumour. Through this study, the resolution of the infrared
camera or temperature sensor required for detection of a tumour of a certain size and depth can be determined, along withconsiderations of factors that could influence the heat patterns.

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2. Experimental Study and Numerical Simulation

In the experimental studies, artificial breasts were made from three types of silicone rubbers: T00, T05, and T10.
The properties of the silicone rubbers are tabulated in Table 1. Fig. 1a shows a breast casted from T00 using the 3D
printed mould in Fig. 1b (the origin “O” and the Cartesian (x, y, z) coordinates are shown in Fig. 1b). Three breasts weremade entirely from a single type of silicone rubber, like the one shown in Fig. 1a. In addition, multi-layered breasts werealso made using different coatings of silicone rubbers with dissimilar thickness, like the examples shown in Fig. 2.
Resistors (of resistance 𝑅𝑅 = 78 kΩ with applied voltage of 5.14 V) were inserted at location with coordinates (85mm, 90 mm, 32 mm) inside all the breasts to simulate 4 mm diameter tumours with heat generation rate of 9818 W⁄m3 .
Before the start of each experiment, the room temperature as well as the temperature of the ground where the breast
was placed were measured. The voltage was then applied across the resistors and the heat pattern was captured with theFlir T630sc infrared camera at 20 min intervals. The images were captured perpendicular to the z-axis in the x-y plane.
The process stopped after the surface temperature had reached steady state. A final thermograph was taken for each of
one-layer breasts after 300 minutes and it took 260 minutes for each of multi-layer breasts to confirm the steady stateheat pattern. The process was repeated for all the breasts.
Table.1: Silicone rubbers’ properties

Silicone Type
Ecoflex0010 (T00)
Ecoflex0050 (T05)
Dragon Skin10 (T10)

Density(𝑘𝑘𝑘𝑘/𝑚𝑚3 )
1.12
1.07
1.07

Absolute
Viscosity (𝑃𝑃𝑃𝑃 ∙ 𝑠𝑠)
15
2
3

Tensile Strength(𝑀𝑀𝑀𝑀𝑀𝑀)
1.379
1.441-3.503
2.9992-4.999

Conductivity
Coefficient (𝑊𝑊/𝑚𝑚 ∙ 𝐾𝐾)
0.4
0.25
0.35

Fig. 1: A casted breast with mould

In the numerical model development, the 3D geometrical model of the breast, the heat conduction process along withappropriate equation boundary conditions, were utilized for the finite element analysis. The finite element analysis (FEA)
was based on solving Penne’s’ equation:
𝑑𝑑𝑑𝑑𝜌𝜌𝜌𝜌 𝑑𝑑𝑑𝑑 = ∇ ∙ (𝑘𝑘∇𝑇𝑇) + 𝜌𝜌𝑏𝑏 𝑤𝑤𝑏𝑏 𝑐𝑐𝑏𝑏 (𝑇𝑇𝑎𝑎 − 𝑇𝑇) + 𝑞𝑞𝑚𝑚
ICMIE 124-2(1)where 𝑘𝑘 is the thermal conductivity of the tissue, 𝜌𝜌𝑏𝑏 and 𝑐𝑐𝑏𝑏 are the density and the specific heat of the blood respectively, 𝑤𝑤𝑏𝑏
is the blood perfusion rate (𝑚𝑚𝑚𝑚/𝑠𝑠/𝑚𝑚𝑚𝑚), 𝑞𝑞𝑚𝑚 is the metabolic heat generation rate (𝑊𝑊/𝑚𝑚3 ), 𝑇𝑇𝑎𝑎 is the arterial blood temperature,
and T is the local temperature of the breast tissue. In the steady state, the equation can be expressed as:

𝑘𝑘∇2 𝑇𝑇 + 𝜌𝜌𝑏𝑏 𝑤𝑤𝑏𝑏 𝑐𝑐𝑏𝑏 (𝑇𝑇𝑎𝑎 − 𝑇𝑇) + 𝑞𝑞𝑚𝑚 = 0(2)

In the steady state, the heat convection is equal to the conduction inside the breast:−𝑘𝑘∇𝑇𝑇 = ℎ(𝑇𝑇𝑠𝑠 − 𝑇𝑇𝑎𝑎𝑎𝑎 )(3)where 𝑇𝑇𝑎𝑎 = 𝑇𝑇, ℎ is the convection heat transfer coefficient; 𝑇𝑇𝑠𝑠 is the surface temperature of the breast; 𝑇𝑇𝑎𝑎𝑎𝑎 is the ambient
temperature, which is the same as the room temperature. The convective heat transfer coefficient, ℎ = 5 𝑊𝑊/(𝑚𝑚2 ∙ ℃), wastaken from Chanmugam [8]. The tumour size and location in the numerical models and the experimental studies were similar.

Fig.2: Examples of multi-layer breasts
Fig. 3 shows an example of the experimental and simulated temperature profiles for the T05 breasts. The temperature
distributions in Fig. 3 show that the experimental and simulated results were very similar. The locations of the maximum
and minimum temperatures in the experiments match those in the simulations. All the other experimental and simulated
temperature profiles on the breast surfaces were also in good agreement. The errors between the maximum and minimum
temperatures for single and multiple-layer breasts were less than 1 %. The results verified the numerical model.
Although the experimental and simulated results showed certain trends on the effects of material conductivity on theheat patterns, the comparison was difficult due to the fluctuations of the room and ground temperatures in the experiments.
To overcome this problem, the effects of the tissue conductivity, tumour size and tumour depths on the surface temperature
profiles were studied using the numerical model under a constant ground temperature of 20 ℃ and room temperature of
20.5 ℃.
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Fig. 3: Comparison of experimental and simulated surface temperature profiles for the T05 breast

3. Effects of Tissue conductivity, Tumour size, and Tumour locations
3.1. Tissue Conductivity
Table 2 tabulates the effect of the material conductivities on the differences between the maximum and minimum
temperatures on the breast surfaces for single-layered breasts with a 15 mm diameter tumour located at Cartesian coordinates(85 mm, 90 mm, 32 mm). The temperature difference increases with decreasing conductivity coefficients. The results fromthe multi-layered breasts also revealed that the layering of tissues with different conductivities in the breast will also affectthe surface heat pattern. For two breasts with the similar bottom layers, the differences between the maximum and minimum
temperatures on the breast surfaces will decrease when the conductivity of the top layer material increases. When the top
layers of two breasts are similar, the temperature difference between the maximum and minimum temperatures on the breast
surfaces will increase when the conductivity of the bottom layer material decreases. In some cases, the changes in temperature
differences can be too small to be picked up by the sensors with insufficient resolution. The temperature difference inmultilayer breasts is dependent on the material combination and is always between that of the materials with the least andlargest conductivities.
Table 2: Effect of conductivity on surface temperatures for single-layered breasts

Room
GroundConductivity Maximum
Minimum Temperature
Silicone
Temperature Temperature
Coefficient Temperature Temperature Difference
Type
(℃)
(℃)
(𝑊𝑊/𝑚𝑚 ∙ 𝐾𝐾)
(℃)
(℃)
(℃)
20.5

20

T00
T10
T05

0.4
0.35
0.25

20.80964
20.86983
21.02505

2020
200.809640.86983
1.02505

The findings have implications in practical situations. Generally, higher thermal conductivity is associated with higher
breast tissue density, which can change with age. The breasts of older women typically have lower density [9]. The result
indicates that age can be a consideration factor when using thermal patterns for the detection of breast tumours. The finding
suggests that it would be easier to use heat patterns to detect tumours in elderly women. Furthermore, the conductivity of fat
is much lower than other tissues and it should be easier to use the approach to detect tumours in breasts with higher fat
content. The result is in agreements with findings documented in Omranipour et al. [10].

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3.2. Tumour SizeFig. 4 shows a typical simulated heat patterns for a T05 breast subjected to a ground temperature of 20 ℃ and room
temperature of 20.5 ℃ with tumour sizes of 12 and 15 mm at Cartesian coordinates (85 mm, 90 mm, 32 mm). The tumour
size affects the temperature distribution on the breast surface. It was found that larger tumour will increase the difference
between the maximum temperature and the minimum temperature on the breast surface. The maximum surface temperature
can be below or above room temperature depending on the tumour size. In general, the hottest point on the surface can shift
as the tumour size increases to a location that is directly above the tumour. The shift of the hottest point is due to the breast
geometry. The finding indicated that it will be easier to detect larger tumour with thermal images. This finding agrees withthe result in [11].

Fig. 4: Surface temperature profiles for T05 breasts with tumour

3.3. Tumour Depth
It is well known that it is very difficult to use thermography to detect a small tumour developing deep within the breast.
To study this situation, the numerical simulated surface heat patterns of a small 8 mm tumour at different depths were
examined at ground temperature of 20 ℃ and room temperature of 20.5 ℃. The results for the T05 silicone breast aresummarized in Table 3, which shows the maximum and minimum surface temperatures along with their differences. The
results indicated that as the tumour approaches the surface, the maximum surface temperature increases, while the minimum
surface temperature remains constant at 20 ℃. The changes in the tumour depths did not affect the location of the coldest
point, which was always located at the bottom corner on the breast surface. However, the location of the hottest point canshift as the tumour approaches the surface. This is mainly due to the geometry of the breast. The effect of the changing
locations of the hottest point to a position directly above the tumour is very similar to that encountered in the changing
tumour size.
Table 3: Some surface temperatures for an 8 mm tumour in the T05 breast

Tumour Location(mm)(85,90,25)(85,90,32)(85,90,40)

Maximum Temperature(℃)
20.40461
20.40967
20.41843

Minimum Temperature
(℃)
20
20
20

Temperature Difference(℃)
0.40461
0.40967
0.41843

The result indicated that heat generated from a small tumour at different depths may not significantly influence thetemperature difference between the hottest and coldest points on the skin surface. The location of the coldest point on thesurface where the temperature remains consistent may also be useful as a reference point for the detection of abnormality
through comparison of the heat patterns between the left and right breasts.

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4. Tumour Growth

The main advantage of the numerical model is that the simulation can be used to further predict the effects of tumour
growth in human breasts on the heat patterns. This is accomplished by changing the parameters and conditions based on
tissues’ properties and human body temperature. In this study, it is assumed that human breast consists entirely of gland,
which has a thermal conductivity of 0.48 𝑊𝑊/𝑚𝑚 ∙ 𝐾𝐾. It is worth noting that the most of breast tissues have conductivity of
0.48 𝑊𝑊/𝑚𝑚 ∙ 𝐾𝐾. This would imply that the assumption is valid if the breast has insignificant amount of fat. The thoracic wall
was assumed to be maintain at a constant temperature of 37 ℃.
It is reasonable to assume that the heat generation from the tumour will increase with the tumour diameter. The
relationship between tumour diameter and heat generated is assumed to be linear, i.e., heat generation varying between 14000
𝑊𝑊/𝑚𝑚3 and 70000 𝑊𝑊/𝑚𝑚3 for tumour diameter between 0.005 to 0.0015 m. The simulation examined the heat patterns as thetumour diameter increased by 1 mm starting from 4 mm. The tumour is located at Cartesian coordinates (85 mm, 90 mm, 32mm). The specific growth rates (SGRs) determined by ultrasonography in a recent study [12] for triple-negative tumours andHER2-positive tumours were 10.03 × 10−3 𝑑𝑑𝑑𝑑𝑑𝑑 −1 and 8.59 × 10−3 𝑑𝑑𝑑𝑑𝑑𝑑 −1 respectively. A referenced healthy breast withno tumour was also simulated. By comparing the heat patterns of the tumour growth with the referenced breast, the feasibilityof using thermal patterns for tumour detection can be examined. The process would be useful to determine the resolution of
the thermal sensors needed to distinguish the heat patterns between the breasts with and without tumour at different stagesof the tumour growth. The study would also be useful to determine the stage of the tumour growth that could be detected by
the thermal patterns. Fig. 5 shows heat patterns as the tumour grows from 4 mm to 14 mm diameter.

Fig. 5: Tumour growth from 4 mm to 14 mm

The simulation results of human breast are different from that of the silicone breast. In the experimental studies using
silicone breasts, the room temperature was always higher than the ground temperature. However, the temperature of thoracic
wall in a human breast is assumed to be constant and always larger than the room temperature. Thus, the hottest point in thehuman breast is always inside the body while the minimum temperature is on the surface. This is important as the thermogramis 2D and will only display the surface temperatures. To overcome this issue, the coldest point on the breast surface (discussed
in section 3.3) was used as the basis for comparison.
By comparing the differences in surface coldest temperatures between breasts with and without tumours, the resolutionof the thermal camera needed and the earliest stage the tumour can be detected could be determined. Based on the numericalsimulation results, the thermal camera with a resolution of 0.1 ℃ will be able to detect the tumour located at a depth of 44mm when the diameter of tumour is 12 mm (total time of growth from 4 mm to 12 mm is about 329 for the triple-negative
tumours and 384 days for the HER2-positive tumours). However, using a camera with 0.01 ℃ resolution, simulation results
indicated that it should be able to detect a 7 mm tumour at a depth of 44 mm (total time of growth from 4 mm to 7 mm isabout 168 days for the triple-negative tumours and 196 days for the HER2-positive tumours). When the diameter is less than
this limit, it is hard for the camera to detect the presence of the breast tumour at this depth.

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5. Conclusion

This study presents the experimental and numerical investigation on the effects of the changes in tissue conductivity,
tumour size, and tumour depth on the heat patterns at the breast surface. Artificial breasts were made using single and multilayered coatings of three silicone rubbers with different material properties. Heated resistors were inserted into these artificial
breasts to simulate heat generated from tumours of specific sizes and locations. The heat patterns were captured with an
infrared camera. At the same time, numerical models of these breasts were developed using FEM in ANSYS and validatedby comparison of the surface heat patterns with the corresponding experimental results. It was determined that the surface
heat patterns of the experiments matched the simulated results of similar conditions in terms of temperature distributions
along with the magnitudes and locations of the maximum and minimum temperatures. The findings of these silicone breasts
revealed that decreasing the thermal conductivity, increasing the tumour size, and decreasing the tumour depth can increase
the difference between the maximum temperature and the minimum temperature on the breast surface. For the same breast
geometry, the maximum temperature at the breast surface will depend on the thermal conductivity and tumour size as wellas tumour depth. These results have direct implications as fatty tissues have lower conductivity and tissue conductivity isalso associated with breast density, which generally decreases with age. In addition, the findings indicated that different
layers of tissues with different conductivity and thickness can also affect the surface heat patterns.
The result showed that heat generated from a small tumour at different depths may not significantly influence thetemperature difference between the hottest and coldest points on the skin surface. For the same breast geometry, increasing
the tumour size and decreasing the tumour depth causes the location of the hottest point on the surface to gradually move toa point which is directly above the tumour. The shift in the location of the hottest point is a consequence of the breast
geometry and would be useful as the starting point for the inverse mapping to determine the tumour location using 2D thermal
patterns. On the other hand, the coldest point is always on the breast surface. The temperature and location of the coldest
point did not shift significantly with tumour depth. As a result, the coldest point may be useful as a reference for the detectionof abnormality through comparison of the left and right breasts.
Finally, the FEA were extended to examine the changes in heat patterns over time for a growing tumour in a humanbreast without fatty tissues. By comparing the differences in surface temperatures between breasts with and without tumours,
it was found that the thermal camera with a resolution of 0.1 ℃ will be able to detect the tumor located at a depth of 44 mm
when the diameter of tumor is 12 mm (total time of growth from 4 mm to 12 mm is about 329 days for the triple-negative
tumours and 384days for the HER2-positive tumours). However, using a camera with 0.01 ℃ resolution, simulation results
indicated that it should be able to detect a 7 mm at a depth of 44 mm with the time for detection reduced by half (i.e., total
time of growth from 4 mm to 7 mm is about 168 days for the triple-negative tumours and 196 days for the HER2-positive
tumours). Hence, to detect a growing tumour earlier, the improvement of the sensor resolution is critical.

Acknowledgements

The authors want to thank Prof. Y. Zhao of Nazarbayev University for sharing the breast geometry used in his work.

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