USING A THERMAL SENSING BRA IN EARLY LOCATING THE BREAST TUMORS

Rev. Roum. Sci. Techn. Électrotechn. et Énerg. Vol. 61, 1, pp. 89 93, Bucarest, 2016 Génie biomédicale USING A THERMAL SENSING BRA IN EARLY LOCATING THE BREAST TUMORS GABRIEL KACSO 1, IOAN FLOREA HANTILA 2, GEORGE MARIAN VASILESCU 2, OANA DROSU 2, MIHAI MARICARU 2 Key words: Thermal bra, Breast cancer, Contact thermography, Tumor location, Qualitative analysis. The intense metabolism of cancer cells may be an early source of information regarding the presence of breast cancer when using the thermal footprint of the tumor on the breast surface (obtained by infrared or contact thermography). The temperature deviation from the normal thermal field may prove an extremely effective tool for locating the tumor. This paper describes the procedure, in which the temperature is measured with a special bra, woven with thermal sensors of known coordinates. 1. INTRODUCTION According to [1], breast cancer is the most common form of cancer diagnosed among Romanian women. In 2007, breast cancer constituted for about 29 % of all the newly diagnosed cases [2] and was, at the same time, the main cause of death among women under the age of 55. Secondary prevention through periodic screening mammography (at most two years apart) improves surviving rates through early cancer detection. This requires a network of specialized medical centers possessing an advanced infrastructure such as digital mammography systems, together with ultrasound imaging equipment or nuclear magnetic resonance systems for uncertain cases. It may also necessitate a lengthy transit (sometimes hundreds of kilometers) for the patient that must reach such a center. Several new methods for cancer detection exist. Examining the thermal field on the breast surface is one such method. In the early stage, the cancer cell can have a much higher metabolism than that of a normal cell and, thus, a greater specific power. Also, the formation of blood vessels in the tumor tissue (neoangiogenesis) is not yet established. The thermal field can be measured with a high-sensitivity infrared thermal imaging camera or with an array of thermal sensors applied to the skin. Unlike mammography, thermography causes no radiation exposure, can be repeated as many times as necessary and, when using the thermal sensing bra, eliminates the need of a medical personnel presence. The method may detect precancerous or cancerous cells much earlier than mammography [5, 6]. Measuring the thermal radiation using a high-sensitivity infrared camera, places a number of special constrains on the measurement room (it must be free of infrared sources and must have a low constant maintained temperature) and on the way the patient is prepared prior to the process taking place (she must stay in the room, with her bra removed, for an extensive period of time). Contact thermography involves using a thermal sensing bra, equipped with an array of sensors with known coordinates whose output is numerically processed. The thermal field is analyzed using the data obtained from the sensors. There is no need for a specially designed measurement room. In [3] the authors perform a qualitative analysis of the way in which the surface thermal field of the breast changes, when modifying its physical parameters: breast size, adipose and glandular tissue size, thermal conductivity, blood perfusion coefficient, heat transfer coefficient, specific power of tissues, and tumor depth. They considered a cylindrical shaped breast containing a small tumor with its power exhibiting a Dirac pulse spatial distribution along the cylinder axis. The analytical method used for solving the problem delivered the surface thermal field for both the healthy breast and the one exhibiting the pathology. The fields were pointwise subtracted and the result was divided by the maximum value of this difference. The paper proved this newly obtained field was significantly influenced only by the tumor depth. The breast shape and structure are extremely diverse among female population and in practical settings these data are unattainable. Thus they cannot be used for computing the thermal field. For this reason, the findings in [3] are particularly important and will by used in this paper with the goal of developing a procedure for locating the early tumor. The obtained location may constitute a target for a diagnostic procedure (puncture or biopsy) or targeted therapy. 2. THE THERMAL FIELD ON THE BREAST SURFACE 2.1. THE MEASURED THERMAL FIELD T m The thermal sensing bra cups are padded with an array of thermal sensors with known positions. A thermo-insulating layer covers the array and reduces the heat transfer outside the bra. The bra cup is sufficiently rigid and customized so that the breast completely fills it. The surface temperature is measured at regular time intervals (e.g. at every three months). To improve thermography accuracy, in the absence of menopause, the thermal images should be taken in a suitable period relative to the first day of the menstrual cycle: between the 7 th and 10 th day. Also, the patient must lie down on her back for a period of 10 minutes during the imagining process. The measured thermal field T m is defined by the sensors output. 1 Iuliu Hatieganu University of Medicine and Pharmacy, 8 Babeş St., Cluj-Napoca, 400012, E-mail: gabi.kacso@gmail.com 2 Politehnica University of Bucharest, The Department of Electrical Engineering, Spl. Independentei 313, Bucharest, 060042, Romania, E-mails: hantila@elth.pub.ro, marian.vasilescu@upb.ro, oana.drosu@upb.ro, mm@elth.pub.ro

90 Gabriel Kacso et al. 2 2.2. THE HEALTHY BREAST THERMAL FIELD T 0 One way we can obtain this field is by analyzing the thermal fields given by both cups. Only one is likely to exhibit the pathology. In this case, the breast showing the lower temperatures is the healthy one and its mirror thermal image may be used as a valid healthy breast field. Fig. 1 The tumor location search algorithm. 2.3. THE DIFFERENCE THERMAL FIELD T d This field is obtain by pointwise subtracting the two previously described fields Td = Tm T 0 (1) and attains a maximum value Tmax = maxtd ( Rk ). (2) k at a position given by R max. Vectors R k describe the thermal sensors positions. The normalized thermal field is defined as Tr = Td T max. (3) The normalized field given by a tumor depends only on the tumor depth. A deeper tumor causes a flatter field appearance. It also gives a larger sum of normalized temperatures N S = T r k = 1 (R, (4) k ) where N is the number of sensors. 3. THE NUMERICAL SOLUTION OF THE BIOHEAT TRANSFER PROBLEM The numerical analysis of the thermal field, shown in [4], is applied here. The bioheat transfer problem is modeled using Pennes equation in the steady state λ T + γ( T T b ) = p s, (5) where T( C) is the temperature, T b is the blood temperature, λ(wm 1 C 1 ) is the tissue thermal conductivity, γ=c b w b is the blood perfusion coefficient, c b (J kg 1 C 1 ) is the blood specific heat, w b (kgs 1 m 3 ) is the mass flow rate of blood per unit volume and p s (Wm 3 ) is the tissue specific power (metabolic heat generation per unit volume). The term γ(t-t b ) expresses the blood flow contribution to tissue heating. The boundary condition on the breast surface S air is T λ' = α( T T air ), (6) n where T air is the air temperature, λ' is the adipose tissue thermal conductivity and α(wm -2 C -1 ) is the heat transfer coefficient. By approximating the thorax with a half-space, we obtain the boundary condition on the breast surface S t neighboring it and (5) simplifies to 2 d Tt λ + γ ( Tt Tb ) = p 2 s dz, (7) where T t is the thorax temperature; we assume its thermal conductivity λ'', blood perfusion coefficient γ'' and tissue specific power p s are the same as those of the breast glandular tissue. Equation (7) is solved assuming the boundary conditions is lim z dt t dz = 0 and T t (z = 0)= T 0, where T 0 is the temperature at the breast base. A new boundary condition, similar to (6) is obtained, and combining them both gives where α T T λ = αech ( T Tech ), (8) n ech = T = α air α, on S γλ, on St, on Sair p s + T γ air, on S ech. ech b t The numerical solution of equation (5) subjected to the boundary condition (8) is obtained with the help of the finite element method, using a tetrahedral discretization mesh and implementing shape functions of order 1 [4]. The tumor specific power is ptum p s =, (10) Vtetrahedron where p tum is the power of the tumor (Table 1 [5]) occupying an elementary volume V tetrahedron of a breast spatial discretization (tetrahedron in our paper). Table 1 The specific power p s and the power p tum of the tumor tissue Tumor diameter 10 15 20 25 30 (mm) p s (W/m 3 ) 65400 13600 8720 6827 5790 p tum (W) 0.034226 0.024021 0.036508 0.055825 0.081813 4. THE TUMOR SEARCH ALGORITHM The employed Cartesian coordinate system has the Oz axis, of unit vector k, perpendicular to the thorax (Fig. 1); its origin is placed on the thorax. A sufficiently small step δ is used for the successive advancements made inside the breast during searching., (9)

3 Thermal sensing bra in early locating the breast tumors 91 i) Starting from R max (having components x max, y max, z max ), proceed along the direction of u= k and arrive at a point described by the vector Q 1 =R max δu. ii) Determine the tetrahedron containing vector Q 1 head and compute the normalized field T r,1, assuming Q 1 gives the tumor location. iii) If the field maximum is found in a new position described by R' max different from that of R max, then adjust the tumor position at Q' 1 =Q 1 +w(r max R' max ) and compute the thermal field once more. The factor w can be obtained with w = z Q z < 1 1 max. If the new field maximum position R' max is still different from R max, then reduce the step δ and return to i) iv) If R' max =R max, then Q' 1= Q 1 ; compute S N 1 = T r,1 k ) k = 1 (R. (11) If S 1 < S, continue further advancing with step δ, but along the direction of u = (Q' 1 R max )/ Q' 1 R max. Repeat ii) and iii) until S k > S at the k th iteration. The tumor location is given by Q k (or Q' k ). The breast surface shape and the measured thermal field are defined by the finite number of sensors padding the bra cup. The maximum value T max of the temperature corresponds to a vector R max, associated with a sensor. 5. AN ILLUSTRATIVE EXAMPLE We considered a simplified geometrical model of a spherical cap shaped breast of radius 84.5 mm and height 50.3 mm completely covered by the thermal sensing bra. The thickness of the breast fat bordering the thorax was 3 mm, while that of the fat bordering the skin was 6 mm. The breast tissue physical parameters are shown in Table 2. The heat transfer coefficient is α = 1 W. m 2. C 1 and the blood temperature is T b = 37 C. We numerically solved the problem by using a tetrahedral discretization mesh. We chose a spherical tumor of diameter d = 10 mm which, according to Table 1, has a specific power p tum = 65400 W/m 3. We further simplified the problem by assuming the tumor tissue occupied a full tetrahedron and that this abstract tetrahedral shaped tumor had the same power as that of the spherical one. Thus, its specific power was obtained using (10). The process of finding the tumor was based on the normalized thermal field T r. Tissue Table 2 Physical parameters of breast tissue Thermal conductivities λ (Wm 1 C 1 ) Blood perfusion coefficient γ (Wm 3 C 1 ) Specific power p s (Wm 3 ) Glandular 0.48 2400 450 Adipose 0.21 800 300 Fig. 2 The simulated thermal field T m of the breast containing the tumor. Fig. 3 The healthy breast thermal field T 0. Considering the blood vessels of the small tumor are not yet formed, we can accept the tumor having the same physical parameters as those of the surrounding tissue (glandular or, rarer, fat). The coefficients matrix obtained from the numerical form of (5) is independent of the tumor position. This matrix is computed only once. During the search, the thermal difference field is directly computed without solving the regular thermal field problem. In this case T ech = 0 in (9) and T b = 0. Only the right hand side of the equations associated with the nodes of the tetrahedron containing the tumor will be changed. The findings in [3] showed that the normalized field T r depends mainly on the tumor depth and very little on the tissue physical parameters. For this reason, the best procedure to obtain the healthy breast thermal field is the one described in section 2.2. However, in our investigation, instead of using this measuring procedure, we obtained the healthy breast thermal field by numerically solving the bioheat transfer problem with the method described in [4]. We obtained the sensors positions by starting off with a square grid of 31 31 nodes, placed beneath the spherical cap on the xoy plane. We projected each grid node on the cap, excluding those falling outside the base of the breast, and obtained a new grid covering the cap. We assigned a virtual sensor to each of the nodes covering the breast. Any other sensor arrangement can be used. The breast discretization mesh had: 591516 tetrahedrons, 106516 nodes, and 14142 triangular facets neighboring the bra surface. We placed the small tumor at point (x = 20 mm, y = 10 mm, z = 30 mm), inside a tetrahedron of volume 1.3 mm 3 (Fig. 8). We first assumed there were no measurement errors so that we could gauge the method error influence on the detection process. The simulated thermal field of the breast containing the tumor is shown in Fig. 2. We obtained the thermal field T 0 of the healthy breast by numerically solving the bioheat transfer problem and by sampling the temperatures at the positions occupied by the virtual sensors. The healthy breast thermal field T 0, the difference thermal field T d and the normalized thermal field T r are shown in Figs. 3, 4, and 5 respectively.

92 Gabriel Kacso et al. 4 The search algorithm found the tumor in a nearby tetrahedron (Fig. 8); the distance between the centers of mass of the found and the proposed tetrahedron was 2.9 mm. A method error appears due to the fact that the breast surface temperature is measured only in a limited number of points (where the sensors are located). Therefore, the maximum registered temperature may differ from the real maximum that may be located between sensors. A denser grid of sensors may diminish this error: in our example a 69 69 grid completely removes the error. However, the small deviation is negligible in a practical setting and provides no justification for a denser grid that may reduce the product cost-effectiveness. We repeated the detection process, this time assuming a measurement error in the range [ 0.05, 0.05] C randomly distributed among the sensors. The thermal field T m of the breast containing the tumor and the normalized field T r are shown in Figs. 6 and 7 respectively. The algorithm found the tumor in a tetrahedron having its center of mass located 4.34 mm away from that of the proposed tetrahedron. Fig. 7 The normalized thermal field T r. A measurement error of 0.05 C was considered. Fig. 8 The tumor position. 6. CONCLUSIONS Fig. 4 The difference thermal field T d. Fig. 5 The normalized thermal field T r. Fig. 6 The simulated thermal field T m of the breast containing the tumor. A measurement error of 0.05 C was considered. The paper shows that, in theory, an early breast tumor can be located by measuring the breast surface temperature with the help of a thermal sensing bra and by implementing a search algorithm typically used in inverse thermal field problems. Since the procedure is non-invasive and is able to locate a small tumor with sufficient accuracy something a mammogram rarely does we believe it can be implemented in breast cancer screening procedures. Breast thermography is long known and various detection procedures (which used infrared thermal imaging camera or a thermal sensing bra) have already been proposed. This paper original contribution is that not only the proposed procedure is capable of detecting a tumor presence but it can also obtain its location. The location can aid in accomplishing a precise puncture or biopsy; it can also help in targeted therapy, following a confirmation of the diagnostic. The described procedure, however, does not conclusively identifies the tumor and can only integrate with other screening tests such as mammography, medical ultrasound, and magnetic resonance imaging. The theoretical model described here requires extensive clinical tests in order to establish its possibilities and limitations compared with established diagnostic methods such as mammography. ACKNOWLEDGEMENTS This work is supported by the Sectoral Operational Programme Human Resources Development (SOP HRD), financed from the European Social Fund and the Romanian Government under the contract number POSDRU/159/- 1.5/S/137390/. Received on July 10, 2015

5 Thermal sensing bra in early locating the breast tumors 93 REFERENCES 1. O. Suteu, N. Ghilezan, N. Todor, I. Petrache, Epidemiologia cancerului de sân în România, Cancer, o provocare la viaţă, 14, 2006. 2. A. Sabou, I. Georgescu, România, pe primul loc în Europa de Est la cancer, România Liberă, 2007. 3. G. Kacso, I. F. Hănţilă, O. M. Drosu, M. Maricaru, M. Stănculescu, Qualitative Analysis of the Temperature Field Produced by an Early Stage Tumor, Revue Roumaine Des Sciences Techniques-Serie Electrotechnique Et Energetique, 59, 4, pp. 433 443, 2014. 4. G. Kacso, I. F. Hantila, G. M. Vasilescu, O. Drosu, M. Maricaru, M. Stanculescu, The thermal field of an early breast cancer reflected on the breast surface, International Symposium on Fundamentals of Electrical Engineering, Bucharest, Romania, pp. 1 4, 2014. 5. J. Kwok, J. Krzyspiak, Thermal Imaging and Analysis for Breast Tumor Detection, BEE 453: Computer-Aided Engineering: Applications to Biomedical Processes, 2007. [Online]. Available: https://ecommons. library.cornell.-edu/handle/1813/7913. [Accessed: 01-Oct-2015]. 6. E.Y.-K. Ng, S.C. Fok, Y.C. Peh, F.C. Ng, L.S.J. Sim, Computerized detection of breast cancer with artificial intelligence and thermograms, J Med Eng Technol, 26, 4, pp. 152 157, 2002.