Journal of Advances in Applied Mathematics
Transient Bioheat Equation in Breast Tissue: Effect of Tumor Size and Location
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Author(s)
- Sharmila Shrestha*
Department of Mathematics, School of Science, Kathmandu University, Kavre, Nepal - Gokul KC
Department of Mathematics, School of Science, Kathmandu University, Kavre, Nepal - Dil Bahadur Gurung
Department of Mathematics, School of Science, Kathmandu University, Kavre, Nepal
Abstract
Keywords
References
[1] American Cancer Society, Available: http://www.cancer.org/Cancer facts and Figures 2017.
[2] American Cancer Society, Available: http://www.cancer.org/Cancer facts and Figures 2019.
[3] Breast Cancer in Nepal, Available: World Life Expectancy, https://www.worldlifeexpectancy.com/nepal-breastcancer.
[4] Chapter 7: Vessels, lymphatic drainage and the breast, Available: https://.dartmouth.edu/~humananatomy /part_2/ chapter 7 .html.
[5] Global cancer statistics, 2012, Available: https://onlinelibrary.wiley.com/doi/full/10.3322/caac.21262.
[6] Singapore Cancer Registry, 1999, Ministry of Health, 3 Second Hospital Avenue, Singapore 168937, Available: http://www.gov.sg/moh/hfacts/hfacts.html.
[7] South Avenue Women’s Services, 2017, Available: https://www.southavewomensservices.com/whats-thedifference- between-mammography-and-thermography/.
[8] World Health Organization, 2018, Available: http://www.who.int/cancer/prevention/diagnosis-screening/breastcancer/ en/.
[9] S. Acharya, D.B. Gurung and V. P. Saxena, “Effect of metabolic reaction on thermoregulation in human males and females body”, Journal of applied mathematics, vol. 4, pp. 39-48, 2013.
[10] M. Agrawal, N. Adlakha and K. Padarsani, “Thermal distribution in dermal regions of human limbs involving metastasis of tumors”, International mathematical forum, vol. 5, no. 39, pp. 1903-1914, 2010.
[11] K. Das and S. C. Mishra, “Estimation of tumor characteristics in a breast tissue with known skin surface temperature”, Journal of thermal biology, vol. 38, pp. 311-317, 2013.
[12] S. C. Fok, E. Y. K. Ng and K. Tai, “Early detection and visualization of breast tumor with thermogram and neural network”, J Mech Med Biol, pp. 85-195, 2002.
[13] M. Gautherie, “Temperature and blood flow patterns in breast cancer during natural evolution and following radiotherapy”, Biomedical thermology, pp. 21-64, 1982.
[14] M. Giri, R. J. Thapa, B. Upreti and B. Pariyar, “Breast cancer in Nepal: Current status and future directions”, Biomedical reports, vol. 8, no. 4, 325-329, 2018. DOI: http://doi.org/10.3892/br.2018.1057.
[15] D. B. Gurung, V. P. Saxena and P. R. Adhikary, “Fem approach to one dimensional unsteady state temperature distribution in the dermal parts with quadratic shape function”, J.Appl. math and informatics, vol. 27, pp. 301- 313, 2009.
[16] C. Guyton and E. Hall, Text book of medical physiology. Elsevier, 2009.
[17] S. Jha, P. K. Sharma and R. Malviya, “Hyperthermia: role and risk factor for cancer treatment”, Achievements in the life sciences, vol. 10, pp. 161-167, 2016. DOI: http://doi.org/10.1016/j.als.2016.11.004.
[18] Gokul KC, D. B. Gurung and P. R. Adhikary, “Fem approach for transient heat transfer in human eye”, Applied mathematics, vol. 4, pp. 30-36, 2013.
[19] J. R. Keyserlingk, P. D. Ahlgren, N. Belliveau and E. Yu, “Infrared imaging of breast: Initial reappraisal using high-resolution digital technology in 100 successive cases of stage I and II breast cancer”, IEEE Transactions on Microwave Theory and Techniques, vol. 4, no. 4, pp. 241-251, 1998.
[20] G. M. Khan, R. K. Thapa, D. S. Adhikari, M. Rajbhandari, P. Dwa, S. Shrestha and S. Oli, “Cancer prevalence trend in central region of Nepal”, Journal of chitwan medical college, vol. 3, no. 3, pp. 22- 25, 2013.
[21] R. N. Lawson, “Implications of surface temperatures in the diagnosis of breast cancer”, Canadian medical association journal, vol. 75, pp. 309-310, 1956.
[22] R. N. Lawson and M. S. Chughtai, “Breast cancer and body temperatures”, Canadian medical association journal, vol. 88, pp. 68-70, 1963.
[23] H. A. Leong, “Breast cancer kills: does early detection make a differnence? Public symposium on cancer”, Singapore Cancer Society, Singapore, 1998.
[24] A. Makrariya and N. Adlakha, “Two dimensional finite element method of temperature distribution in dermal tissues of human breast under different stages of development”, Available: http://www.researchgate.net/ publication/280623090, 2015.
[25] M. Milosevic, D. Jankovic and A. Peulic, “Thermography based breast cancer detection using texture features and minimum variance quantization”, EXCLI Journal, vol. 13, pp. 1204-1215, ISSN 1611-2156, 2014.
[26] M. Mital and R. M. Pidaparti, “Breast tumor simulation and parameters estimation using evolutionary algorithms”, Hindawi Publishing Corporation modelling and simulation in engineering, 2008.
[27] E. Y. K. Ng, “A review of thermography as promising non-invasive detection modality for breast tumor”, International journal of thermal sciences, vol. 48, pp. 849-859, 2008.
[28] E. Y. K. Ng, Y. Chen and L. N. Ung, “Computerized breast thermography: study of image segmentation and temperature cyclic variations”, Journal of medical engineering and technology, vol. 25, no. 1, pp. 12-16, 2001.
[29] E. Y. K. Ng and N. M. Sudarshan, “An improved three-dimensional direct numerical modeling and thermal analysis of a female breast with tumor”, Proceedings of the Institution of Mechanical Engineers. Part H, journal of engineering in medicine, vol. 215, no. 1, pp. 25-37, 2001.
[30] M. M. Osman and E. M. Afify, “Thermal modeling of the normal womans breast”, Journal of biomechanical engineering, vol. 106, no. 2, pp. 123-130, 1984. [PubMed: 6738016].
[31] K. R. Pardasani and N. Adlakha, “Exact solution to a heat flow problem in peripheral tissue layers with a solid tumor in the dermis”, Ind. J. Pure. Appl. Math., vol. 22, no. 8, pp. 679-687, 1991.
[32] H. H. Pennes, “Analysis of tissue and arterial blood temperature in resting forearm”, Journal of applied physiology, vol. 1, pp. 93-122, 1948.
[33] V. P. Saxena and D. Arya, “Steady state heat distribution in epidermis and subdermal tissue”, J. Theor. Biolo, vol. 102, pp. 227-286, 1983.
[34] V. P. Saxena and K. R. Pardasani, “Effect of dermal tumors on temperature distribution in skin with variable blood flow”, Bulletin of mathematical biology, vol. 53, no. 4, pp. 525-536, 1991.
[35] S. Shrestha and D. B. Gurung, “Finite element method approach for thermal analysis of female breast tissue tumor model. J Appl bioinforma Comput Biol, vol. 6, no. 3, 2017. DOI: http://doi.org/10.4172/2329- 9533.1000141.
[36] N. M. Sudarshan and E. Y. K. Ng, “Surface temperature distribution of a breast with and without tumour”, Computer methods in biomechanics and biomedical engineering, vol. 2. No. 3, pp. 187-199, 1999 [PubMed: 11264827].