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Metaheuristics applied to the thermographic detection of multicentric breast tumor

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Abstract

In recent years, the clinical diagnosis of breast tumors employing thermal analysis has received increasing attention as a non-invasive and less expensive alternative to classic techniques. In this paper, we propose to use and compare different metaheuristics applied to the inverse problem for estimating a multicentric tumor geometric parameters through thermography. To this end, a multicentric circular tumor in a multilayered breast model comprised of five tissue layers is considered, and from simulated temperature measurements taken on the breast skin surface, the geometric parameters are then estimated by adopting metaheuristics. To assess the effects of real data in the inverse solution, a random noise with the same order of magnitude that occurs in modern infrared cameras is inserted into the simulated measurement data. A two-dimensional steady-state nonlinear bioheat model governed by the Pennes’ equation is considered for the forward problem, which is efficiently solved by the finite element method (FEM) via FEniCS through a Newton–Raphson scheme. The inverse problem is formulated as an optimization one and then solved here by three algorithms, namely, differential evolution (DE), genetic algorithm (GA), and a self-adaptive differential evolution (SaDE). Our numerical experiments with and without noise show that SaDE outperformed the remaining techniques, indicating that this approach is a suitable alternative in this type of inverse problem.

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Notes

  1. https://docs.python.org/3/library/profile.html.

  2. https://cran.r-project.org/package=irace.

References

  1. Sung H, Ferlay J, Siegel RL, Laversanne M, Soerjomataram I, Jemal A, Bray F (2021) Global cancer statistics 2020: Globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries. CA Cancer J Clin 71(3):209–249

    Google Scholar 

  2. Chakraborty S, Rahman T (2012) The difficulties in cancer treatment. Ecancermedicalscience 6(16)

  3. Hortobagyi GN (1998) Treatment of breast cancer. N Engl J Med 339(14):974–984

    Google Scholar 

  4. Rezo A, Dahlstrom J, Shadbolt B, Rodins K, Zhang Y, Davis AJ (2011) Tumor size and survival in multicentric and multifocal breast cancer. Breast 20(3):259–263

    Google Scholar 

  5. Andea AA, Wallis T, Newman LA, Bouwman D, Dey J, Visscher DW (2002) Pathologic analysis of tumor size and lymph node status in multifocal/multicentric breast carcinoma. Cancer 94(5):1383–1390

    Google Scholar 

  6. Egan RL (1982) Multicentric breast carcinomas: clinical-radiographic-pathologic whole organ studies and 10-year survival. Cancer 49(6):1123–1130

    Google Scholar 

  7. Fushimi A, Yoshida A, Yagata H, Takahashi O, Hayashi N, Suzuki K, Tsunoda H, Nakamura S, Yamauchi H (2019) Prognostic impact of multifocal and multicentric breast cancer versus unifocal breast cancer. Surg Today 49(3):224–230

    Google Scholar 

  8. Lang Z, Yanqiu W, Li C, Li X, Wang X, Guimei Q (2017) Multifocal and multicentric breast carcinoma: a significantly more aggressive tumor than unifocal breast cancer. Anticancer Res 37(8):4593–4598

    Google Scholar 

  9. Heywang-Köbrunner SH, Hacker A, Sedlacek S (2011) Advantages and disadvantages of mammography screening. Breast Care (Basel) 6(3):199–207

    Google Scholar 

  10. Ekici S, Jawzal H (2020) Breast cancer diagnosis using thermography and convolutional neural networks. Med Hypotheses 137:109542

    Google Scholar 

  11. Sun D, Yongming F, Yang Y (2020) Label-free detection of breast cancer biomarker using silica microfiber interferometry. Opt Commun 463:125375

    Google Scholar 

  12. Morrow M, Waters J, Morris E (2011) MRI for breast cancer screening, diagnosis, and treatment. Lancet 378(9805):1804–1811

    Google Scholar 

  13. Soltani M, Rahpeima R, Kashkooli FM (2019) Breast cancer diagnosis with a microwave thermoacoustic imaging technique–a numerical approach. Med Biol Eng Comput 57:1497–1513

    Google Scholar 

  14. Lima MG, Gilmar G (2019) Development of a new technique for breast tumor detection based on thermal impedance and a damage metric. Infrared Phys Technol 97:401–410

    Google Scholar 

  15. Figueiredo AAA, do Nascimento JG, Malheiros FC, da Silva Ignacio LH, Fernandes HC, Guimaraes G (2019) Breast tumor localization using skin surface temperatures from a 2d anatomic model without knowledge of the thermophysical properties. Comput Methods Programs Biomed 172:65–77

  16. Gonçalo Filho AM, Nogueira LL, Silveira JVC, Loureiro MMS, dos Santos Loureiro F (2017) Solution of the inverse bioheat transfer problem for the detection of tumors by genetic algorithms. In: Computational science and its applications—ICCSA 2017. Springer, Cham, pp 441–452

  17. Manu M, Pidaparti RM (2008) Breast tumor simulation and parameters estimation using evolutionary algorithms. In: Modelling and simulation in engineering 2008. https://doi.org/10.1155/2008/756436

  18. Melo AR, Loureiro MM, Loureiro F (2017) Blood perfusion parameter estimation in tumors by means of a genetic algorithm. Procedia Comput Sci 108:1384–1393. Intl. Conf. on Computational Science, ICCS, (2017) 12–14 June 2017. Zurich, Switzerland

  19. Alifanov OM (2012) Inverse heat transfer problems. Springer, Berlin

    Google Scholar 

  20. Özisik MN, Orlande HRB (2021) Inverse heat transfer: fundamentals and applications. CRC Press, Boca Raton

    Google Scholar 

  21. Iljaž J, Wrobel LC, Gomboc T, Hriberšek M, Marn J (2020) Solving inverse bioheat problems of skin tumour identification by dynamic thermography. Inverse Probl 36(3):035002

    MathSciNet  Google Scholar 

  22. Hristov J (2019) Bio-heat models revisited: concepts, derivations, nondimensalization and fractionalization approaches. Front Phys 7:189

    Google Scholar 

  23. Murthy JY, Minkowycz WJ, Sparrow EM, Mathur SR (2000) Handbook of numerical heat transfer. John Wiley & Sons Ltd, New York

    Google Scholar 

  24. Minkowycz W, Sparrow E, Abraham J (2009) Advances in numerical heat transfer, vol 3. CRC Press, Boca Raton

    Google Scholar 

  25. Bousselham A, Bouattane O, Youssfi M, Raihani A (2018) 3D brain tumor localization and parameter estimation using thermographic approach on GPU. J Therm Biol 71:52–61

    Google Scholar 

  26. Reis RF, dos Santos Loureiro F, Lobosco M (2016) 3D numerical simulations on GPUs of hyperthermia with nanoparticles by a nonlinear bioheat model. J Comput Appl Math 295:35–47

  27. Bousselham A, Bouattane O, Youssfi M, Raihani A (2018) Brain tumor temperature effect extraction from MRI imaging using bioheat equation. Proc Comput Sci 127:336–343. Proc. of the First Intl. Conf. on Intelligent Computing in Data Sciences, ICDS2017

  28. Bahador M, Keshtkar MM, Zariee A (2018) Numerical and experimental investigation on the breast cancer tumour parameters by inverse heat transfer method using genetic algorithm and image processing. Sādhanā 43(9): 142

  29. Gonzalez-Hernandez J-L, Recinella AN, Kandlikar SG, Dabydeen D, Medeiros L, Phatak P (2020) An inverse heat transfer approach for patient-specific breast cancer detection and tumor localization using surface thermal images in the prone position. Infrared Phys Technol 105:103202

    Google Scholar 

  30. André V, Felipe L, Di BL, João MW (2018) Computer simulation of hyperthermia with nanoparticles using an octree finite volume technique. Int Commun Heat Mass Transf 91:248–255

    Google Scholar 

  31. Arka B, Ramjee R (2016) Estimation of growth features and thermophysical properties of melanoma within 3-d human skin using genetic algorithm and simulated annealing. Int J Heat Mass Transf 98:81–95

    Google Scholar 

  32. Mukhmetov O, Mashekova A, Zhao Y, Ng EYK, Midlenko A, Fok S, Teh SL (2021) Inverse thermal modeling and experimental validation for breast tumor detection by using highly personalized surface thermal patterns and geometry of the breast. Proc Inst Mech Eng Part C J Mech Eng Sci 235(19):3777–3791

    Google Scholar 

  33. Azevedo FAA, Coelho FH, Gilmar G (2018) Experimental approach for breast cancer center estimation using infrared thermography. Infrared Phys Technol 95:100–112

    Google Scholar 

  34. Yan Z, Cila H (2018) Optimization of skin cooling by computational modeling for early thermographic detection of breast cancer. Int J Heat Mass Transf 126:864–876

    Google Scholar 

  35. Bezerra LA, Oliveira MM, Rolim TL, Conci A, Santos FGS, Lyra PRM, Lima RCF (2013) Estimation of breast tumor thermal properties using infrared images. Signal Process 93(10):2851–2863. Signal and Image Processing Techniques for Detection of Breast Diseases

  36. Jose-Luis G-H, Recinella Alyssa N, Kandlikar Satish G, Donnette D, Pradyumna MLP (2019) Technology, application and potential of dynamic breast thermography for the detection of breast cancer. Int J Heat Mass Transf 131:558–573

    Google Scholar 

  37. Zuluaga-Gomez J, Al Masry Z, Benaggoune K, Meraghni S, Zerhouni N (2021) A CNN-based methodology for breast cancer diagnosis using thermal images. Comput Methods Biomech Biomed Eng Imaging Vis 9(2):131–145

    Google Scholar 

  38. da Silva Rocha JPA, dos Santos Loureiro F (2020) An inverse geometric bioheat transfer problem for the detection of breast tumours. In: 18th Brazilian congress of thermal sciences and engineering

  39. Partridge PW, Wrobel LC (2007) An inverse geometry problem for the localisation of skin tumours by thermal analysis. Eng Anal Bound Elem 31(10):803–811. ISSN 0955-7997

  40. Zhuo-Jia F, Chu W-H, Yang M, Li P-W, Fan C-M (2020) Estimation of tumor characteristics in a skin tissue by a meshless collocation solver. Int J Comput Methods 18:02

    MathSciNet  Google Scholar 

  41. Rajwar K, Deep K, Das S (2023) An exhaustive review of the metaheuristic algorithms for search and optimization: taxonomy, applications, and open challenges. Artif Intell Rev 56(11):1573–7462

    Google Scholar 

  42. Luna JM, Romero-Mendez R, Hernandez-Guerrero A, Elizalde-Blancas F (2011) Inverse problem for the estimation of skin cancerous region parameters by thermal analysis. In: Volume 2: Biomedical and Biotechnology Engineering; Nanoengineering for Medicine and Biology of ASME International Mechanical Engineering Congress and Exposition, pp 361–370

  43. Sun S, Ji Y, Chang Z, Wang G, Wei L (2022) Application of stochastic particle swarm optimization algorithm for noninvasive determination of temperature-dependent thermal properties of biological tissue. Heat Transf Res 53 (11):45–60. ISSN 1064-2285

  44. Singhal M, Singla RK, Goyal K (2024) Detection of multiple tumors through temperature response of a human brain using inverse bioheat transfer based on swarm optimization. Therm Sci Eng Prog 47:102315. ISSN 2451-9049

  45. Meenal S, Kumar SR, Kavita G, Sarvjeet S (2023) Inverse optimization based non-invasion technique for multiple tumor detection in brain tissue. Int Commun Heat Mass Transf 141:106596

    Google Scholar 

  46. Agnelli JP, Barrea AA, Turner CV (2011) Tumor location and parameter estimation by thermography. Math Comput Model 53(7):1527–1534. ISSN 0895-7177. Mathematical Methods and Modelling of Biophysical Phenomena

  47. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Google Scholar 

  48. Mendonça MED, Coral SR, Hultmann AHV, Humberto LC (2020) Recent meta-heuristics improved by self-adaptation applied to nonlinear model-based predictive control. IEEE Access 8:118841–118852

    Google Scholar 

  49. Logg A, Mardal K-A, Wells G (2012) Automated solution of differential equations by the finite element method: The FEniCS book, vol 84. Springer, Berlin

  50. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338

    Google Scholar 

  51. Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology. In: Control artificial intelligence. MIT Press, Cambridge. ISBN 0262082136

  52. Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Darrell Whitley L (ed) Foundations of genetic algorithms, vol 2. Elsevier, pp 187–202

  53. Hinterding R (1995) Gaussian mutation and self-adaption for numeric genetic algorithms. In: Proc. of 1995 IEEE Intl. Conf. on evolutionary computation, vol 1, p 384. https://doi.org/10.1109/ICEC.1995.489178

  54. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359

    MathSciNet  Google Scholar 

  55. Akbar B, Abd AMI, Abdul AZ (2016) A self-adaptive binary differential evolution algorithm for large scale binary optimization problems. Inf Sci 367(368):487–511

    Google Scholar 

  56. Figueiredo AAA, Fernandes HC, Malheiros FC, Guimaraes G (2020) Influence analysis of thermophysical properties on temperature profiles on the breast skin surface. Int Commun Heat Mass Transf 111:104453

    Google Scholar 

  57. Iljaž J, Carlos WL, Hriberšek M, Marn J (2019) Numerical modelling of skin tumour tissue with temperature-dependent properties for dynamic thermography. Comput Biol Med 112:103367

    Google Scholar 

  58. Bhattacharya A, Mahajan RL (2003) Temperature dependence of thermal conductivity of biological tissues. Physiol Meas 24(3):769

    Google Scholar 

  59. Deng Z-S, Liu J (2004) Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics. Comput Biol Med 34(6):495–521

    Google Scholar 

  60. Arka B, Ramjee R (2016) Estimation of growth features and thermophysical properties of melanoma within 3-d human skin using genetic algorithm and simulated annealing. Int J Heat Mass Transf 98:81–95

    Google Scholar 

  61. Nithiarasu P, Lewis RW, Seetharamu KN (2016) Fundamentals of the finite element method for heat and mass transfer. Wiley, London

    Google Scholar 

  62. Langtangen HP, Logg A (2017) Solving PDEs in python: the FEniCS tutorial I. Springer, Berlin

    Google Scholar 

  63. Spencer SW, Adam LD, Jacques C (2016) State of the practice for mesh generation and mesh processing software. Adv Eng Softw 100:53–71

    Google Scholar 

  64. Christophe G, Jean-François R (2009) Gmsh: A 3-d finite element mesh generator with built-in pre-and post-processing facilities. Int J Numer Methods Eng 79(11):1309–1331

    MathSciNet  Google Scholar 

  65. López-Ibáñez M, Dubois-Lacoste J, Cáceres LP, Birattari M, Stützle T (2016) The irace package: iterated racing for automatic algorithm configuration. Oper Res Perspect 3:43–58. ISSN 2214-7160

  66. Birattari M, Yuan Z, Balaprakash P, Stützle T (2010) F-Race and iterated F-Race: an overview. Springer, Berlin, pp 311–336

    Google Scholar 

  67. Alosaimi M, Lesnic D, Johansson BT (2021) Solution of the Cauchy problem for the wave equation using iterative regularization. Inverse Probl Sci Eng 29(13):2757–2771

    MathSciNet  Google Scholar 

  68. Manuel LJ, Ricardo R-M, Abel H-G, Francisco E-B (2012) Procedure to estimate thermophysical and geometrical parameters of embedded cancerous lesions using thermography. J Biomech Eng 134(3):03

    Google Scholar 

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Acknowledgements

Heder S. Bernardino has received financial support from CNPq and FAPEMIG. Felipe S. Loureiro has received financial support from CNPq (402832/2021-3). Alex Vieira has received financial support from CNPq and FAPEMIG. Jan Rocha has received research grants from Coordenação de Aperfeiçoamento de Pessoal de Nível Superior—Brasil (CAPES).

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Authors and Affiliations

  1. Graduate Program in Computational Modeling, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Jan P. A. S. Rocha, Heder S. Bernardino, Alex B. Vieira & Helio J. C. Barbosa

  2. Department of Thermal and Fluid Sciences, Federal University of São João del-Rei, São João del-Rei, Brazil

    Felipe S. Loureiro

  3. Department of Computer Science, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Heder S. Bernardino, Alex B. Vieira & Helio J. C. Barbosa

  4. National Laboratory for Scientific Computing, Petrópolis, Brazil

    Helio J. C. Barbosa

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  1. Jan P. A. S. Rocha
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Correspondence to Jan P. A. S. Rocha.

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Rocha, J.P.A.S., Loureiro, F.S., Bernardino, H.S. et al. Metaheuristics applied to the thermographic detection of multicentric breast tumor. J Braz. Soc. Mech. Sci. Eng. 46, 361 (2024). https://doi.org/10.1007/s40430-024-04907-w

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