Inverse heat transfer problems: an application to bioheat transfer

• Autorzy: Rojczyk M. , Orlande H. R. B. , Colaço M. J. , Szczygieł I. , Nowak A. J. , Białecki R. A. , Ostrowski Z.
• Języki publikacji: EN

Abstrakty

EN

In this work, we applied the Markov chain Monte Carlo (MCMC) method for the estimation of parameters appearing in the Pennes’ formulation of the bioheat transfer equation. The inverse problem of parameter estimation was solved with the simulated transient temperature measurements. A one-dimensional (1D) test case was used to explore the capabilities of using the MCMC method in bioheat transfer problems, specifically for the detection of skin tumors by using surface temperature measurements. The analysis of the sensitivity coefficients was performed in order to examine linear dependence and low sensitivity of the model parameters. The solution of the direct problem was verified with a commercial code. The results obtained in this work show the ability of using inverse heat transfer analysis for the detection of skin tumors.

Słowa kluczowe

EN

inverse problems; Bayesian framework; Markov chain Monte Carlo methods; Pennes equation; skin tumor

PL

problem odwrotny; ramy Bayesa; łańcuch Markowa Monte Carlo; równanie Pennesa; nowotwór skóry

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Methods in Engineering and Science
• Rocznik: 2015
• Tom: Vol. 22, no. 4
• Strony: 365--383
• Opis fizyczny: Bibliogr. 69 poz., tab., wykr.

Twórcy

autor

Rojczyk M.

• Departament of Mechanical Engineering Politécnica/COPPE, Federal University of Rio de Janeiro UFRJ Cid. Universitária, Cx. Postal: 68503, Rio de Janeiro, RJ, 21947-972, Brazil
• Institute of Thermal Technology Silesian University of Technology Konarskiego 22, 44-100 Gliwice, Poland

autor

Orlande H. R. B.

• Departament of Mechanical Engineering Politécnica/COPPE, Federal University of Rio de Janeiro UFRJ Cid. Universitária, Cx. Postal: 68503, Rio de Janeiro, RJ, 21947-972, Brazil

autor

Colaço M. J.

• Departament of Mechanical Engineering Politécnica/COPPE, Federal University of Rio de Janeiro UFRJ Cid. Universitária, Cx. Postal: 68503, Rio de Janeiro, RJ, 21947-972, Brazil

autor

Szczygieł I.

• Institute of Thermal Technology Silesian University of Technology Konarskiego 22, 44-100 Gliwice, Poland

autor

Nowak A. J.

• Institute of Thermal Technology Silesian University of Technology Konarskiego 22, 44-100 Gliwice, Poland

autor

Białecki R. A.

• Institute of Thermal Technology Silesian University of Technology Konarskiego 22, 44-100 Gliwice, Poland

autor

Ostrowski Z.

• Institute of Thermal Technology Silesian University of Technology Konarskiego 22, 44-100 Gliwice, Poland

Bibliografia

• [1] J.P. Agnelli, A.A. Barrea, C.V. Turner. Tumor location and parameter estimation by thermography. Mathematical and Computer Modelling, 53: 1527–1534, 2011.
• [2] O.M. Alifanov. Inverse Heat Transfer Problems, Springer-Verlag, New York, 1994.
• [3] O.M. Alifanov, E. Artyukhin, A. Rumyantsev. Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems. Begell House, New York, 1995.
• [4] T. Bayes. An Essay towards solving a problem in the doctrine of chances, by the late Rv. Mr. Bayes, F.R.S. Communicated by Mr. Price in a letter to John Cannon. A.M.R.F.S., Phil. Trans., 53: 370–418, 1763.
• [5] J. Beck, K.J. Arnold. Parameter Estimation in Engineering and Science. Wiley Interscience, New York, 1977.
• [6] J.V. Beck, B. Blackwell, C.R. St. Clair. Inverse Heat Conduction: Ill-Posed Problems. Wiley Interscience, New York, 1985.
• [7] M. Bertero, P. Boccacci. Introduction to Inverse Problems in Imaging. Institute of Physics Publishing, 1998.
• [8] L.A. Bezerra, M.M. Oliveira, T.L. Rolim, A. Conci, F.G.S. Santos, P.R.M. Lyra, R.C.F. Lima. Estimation of breast tumor thermal properties using infrared images. Signal Processing, 93: 2851–2863, 2013.
• [9] D. Calvetii, E. Somersalo. Introduction to Bayesian Scientific Computing, Springer, New York, 2007.
• [10] C.K. Charny. Mathematical models of bioheat transfer. [In:] Advances in Heat Transfer, Young Cho [Ed.], 22: 19–156, Boston: Academic Press, 1992.
• [11] Tze-Yuan Cheng, C. Herman. Analysis of skin cooling for quantitative dynamic infrared imaging of near-surface lesions. International Journal of Thermal Sciences, 86: 175–188, 2014.
• [12] K. Das, S.C. Mishra. Estimation of tumor characteristics in a breast tissue with known skin surface temperature. Journal of Thermal Biology, 38: 311–317, 2013.
• [13] K. Das, S.C. Mishra. Non-invasive estimation of size and location of a tumor in a human breast using a curve fitting technique. International Communications in Heat and Mass Transfer, 56: 63–70, 2014.
• [14] K. Das, R. Singh, S.C. Mishra. Numerical analysis for determination of the presence of a tumor and estimation of its size and location in a tissue. J. Therm. Biol., 38: 32–40, 2013.
• [15] M. Diakides, J.D. Bronzino, D.R. Peterson. Medical Infrared Imaging: Principles and Practices, CRC Press, 2013.
• [16] J.H. Randrianalisoa, L.A. Dombrovsky, W. Lipiński, V. Timchenko. Effects of short-pulsed laser radiation on transient heating of superficial human tissues. International Journal of Heat and Mass Transfer, 78: 488–497, 2014.
• [17] D. Fiala. Dynamic Simulation of Human Heat Transfer and Thermal Comfort. PhD Thesis, Institute of Energy and Sustainable Development De Montfort University Leicester, UK, 1998.
• [18] D. Fiala, G. Havenith, P. Bröde, B. Kampmann, G. Jendritzky. UTCI-Fiala multi-node model of human heat transfer and temperature regulation. International Journal of Biometeorology, 56(3): 429–441, 2012.
• [19] A.A.A. Figueiredo, G. Guimarães. Estimation the intensity and location of a tumor using sequential function specification method. Proceedings of CHT-15, ICHMT International Symposium on Advances in Computational Heat Transfer, CHT-15-085, Rutgers University, USA, 2015.
• [20] A.P. Gagge. Rational temperature indices of man’s thermal environment and their use with a 2-node model of his temperature regulation. Fed. Proc., 32: 1572–1582, 1973.
• [21] D. Gamerman, H.F. Lopes. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference, Chapman & Hall/CRC, 2nd edition, Boca Raton, 2006.
• [22] J. Geweke. Evaluating the Accuracy of Sampling-Based Approaches to the Calculation of Posterior Moments. [In:] Bayesian Statistics, J. Bernardo, J. Berger, A. Dawid, A. Smith [Eds.], Oxford University Press, 1992.
• [23] R.G. Gordon. The Response of Human Thermoregulatory System in the Cold. PhD Thesis (in Mechanical Engineering), University of California, Santa Barbara CA, 1974.
• [24] H. Haario, E. Saksman, J. Tamminen. An adaptive Metropolis algorithm. Bernoulli, 7: 223–242, 2001.
• [25] J. Hadamard. Lectures on Cauchy’s Problem in Linear Differential Equations. Yale University Press, New Haven, CT, 1923.
• [26] J.D. Hardy, J.A.J. Stolwijk. Partitional calorimetric studies of man during exposures to thermal transients. J. Appl. Physiol., 21: 1799–1806, 1966.
• [27] W.K. Hastings. Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57: 97–109, 1970.
• [28] E. Hensel. Inverse Theory and Applications for Engineers. Prentice Hall, New Jersey, 1991.
• [29] K.R. Holmes. Native thermal conductivity of biomaterials (Appendix A) and the blood perfusion rates for special tissues and organs (Appendix B). [In:] The CRC Handbook of Thermal Engineering Advances in Heat Transfer, F. Kreith [Ed.], Springer Science & Business Media, 2000.
• [30] Ch-H. Huang, Ch-Y. Huang. An inverse problem in estimating simultaneously the effective thermal conductivity and volumetric heat capacity of biological tissue. Applied Mathematical Modelling, 31: 1785–1797, 2007.
• [31] J. Kaipio, E. Somersalo. Statistical and Computational Inverse Problems, Applied Mahematical Sciences 160, Springer-Verlag, 2004.
• [32] J.P. Kaipio, C. Fox. The Bayesian framework for inverse problems in heat transfer. Heat Transfer Engineering, 32(9): 718–753, 2011.
• [33] B. Kateb, V. Yamamoto, Ch. Yu, W. Grundfest, J.P. Gruen. Infrared thermal imaging: a review of the literature and case report. NeuroImage, 47: T154–T162, 2009.
• [34] K. Kurpisz, A.J. Nowak. Inverse Thermal Problems. WIT Press, Southampton, UK, 1995.
• [35] P.M. Lee. Bayesian Statistics. Oxford Universty Press, London, 2004.
• [36] B. Lamien, H.R.B. Orlande, G. Eli¸cabe, A. Maurente. State estimation problem in hyperthermia treatment of tumors loaded with nanoparticles. Proc. of 15th Int. Heat Trans. Conf., IHTC15-8772: 1–14, 2014.
• [37] E. Majchrzak. Modelling and analysis of thermal phenomena. Part IV. Mechanics. Technical Mechanics [in Polish: Modelowanie i analiza zjawisk termicznych. Część IV. Mechanika Techniczna], Tom XII: Biomechanika, pod red. R. Będzińskiego, IPPT PAN, Warszawa, 223–361, 2011.
• [38] E. Majchrzak, B. Mochnacki. Sensitivity analysis and inverse problems in bio-heat transfer modeling. Computer Assisted Mechanics and Engineering Sciences, 13(1): 85–108, 2006.
• [39] E. Majchrzak, M. Paruch. Identification of electromagnetic field parameters assuring the cancer destruction during hyperthermia treatment. Inverse Problems in Science and Engineering, 19(1): 45–58, 2011.
• [40] MATLAB and Statistics Toolbox Release 2009b, The MathWorks, Inc., Natick, Massachusetts, United States, 2009.
• [41] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller. Equation of state calculation by fast computing machines. J. Chemical Phys., 21: 1087–1092, 1953.
• [42] V.A. Morozov. Methods for Solving Incorrectly Posed Problems. Springer Verlag, New York, 1984.
• [43] D.A. Murio. The Mollification Method and the Numerical Solution of Ill-Posed Problems. Wiley Interscience, New York, 1993.
• [44] H.R.B. Orlande. Inverse problems in heat transfer: New trends on solution methodologies and applications. Journal of Heat Transfer, 134: 031011, 2012.
• [45] H.R.B. Orlande, G.S. Dulikravich, M. Neumayer, D. Watzenig, M.J. Colaço. Accelerated Bayesian inference for the estimation of spatially varying heat flux in a heat conduction problem. Numerical Heat Transfer Part A: Applications, 65: 1–25, 2014.
• [46] H.R.B. Orlande, F. Fudym, D. Mailet, R. Cotta. Thermal Measurements and Inverse Techniques. CRC Press, Boca Raton, 2011.
• [47] Z. Ostrowski, P. Buliński, W. Adamczyk, A.J. Nowak. Modelling and validation of transient heat transfer processesin human skin undergoing local cooling. Przegląd Elektrotechniczny, R. 91 NR 5/2015.
• [48] M.N. Ozisik, H.R.B. Orlande. Inverse Heat Transfer: Fundamentals and Applications. Taylor and Francis, New York, 2000.
• [49] K. Parsons. Human Thermal Environments. Taylor & Francis, 2003.
• [50] M. Paruch, E. Majchrzak. Identification of tumor region parameters using evolutionary algorithm and multiple reciprocity method. Engineering Applications of Artificial Intelligence, 20(5): 647–655, 2007.
• [51] H.H. Pennes. Analysis of tissue and arterial blood temperatures in the resting human forearm. Journal of Applied Physiology, 1(2): 93–122, 1948.
• [52] P.C. Sabatier. Applied Inverse Problems. Springer Verlag, Hamburg, 1978.
• [53] N. Severens. Modelling hypothermia in patients undergoing surgery. PhD Thesis, TU/e, Eindhoven, 2008 [54] N. Silver. The Signal and the Noise. Penguin Press, New York, 2012.
• [55] C.F.L. Souza, M.V.C. Souza, M.J. Cola¸co, A.B. Caldeira, F. Scofano Neto. Inverse determination of blood perfusion coefficient by using different deterministic and heuristic techniques. J. Braz. Soc. Mech. Sci. Eng., 36: 193–206, 2014.
• [56] S. Tan, C. Fox, G. Nicholls. Inverse Problems. Course Notes for Physics 707, University of Auckland, 2006.
• [57] A. Tarantola. Inverse Problem Theory. Elsevier, 1987.
• [58] A.N. Tikhonov, V.Y. Arsenin. Solution of Ill-Posed Problems. Winston & Sons, Washington, DC, 1977.
• [59] D.M. Trujillo, H.R. Busby. Practical Inverse Analysis in Engineering. CRC Press, Boca Raton, 1997.
• [60] V. Umadevi, S.V. Raghavan, S. Jaipurkar. Framework for estimating tumour parameters using thermal imaging. Indian J. Med. Res., 134: 725–731, 2011.
• [61] L.A.B. Varon, H.R.B. Orlande, G.E. Eli¸cabe. Estimation of state variables in the hyperthermia therapy of cancer with heating imposed by radiofrequency electromagnetic waves. International Journal of Thermal Sciences, 98: 228–236, 2015.
• [62] C. Vogel. Computational Methods for Inverse Problems. SIAM, Philadelphia, 2002.
• [63] J. Werner, M. Buse. Temperature profiles with respect to inhomogeneity and geometry of the human body. J. Appl. Physiol, 65(3): 1110–1118, 1988.
• [64] R. Winkler. An Introduction to Bayesian Inference and Decision. Probabilistic Publishing, Gainsville, 2003.
• [65] E.H. Wissler. A mathematical model of the human thermal system. Bulletin of Mathematical Biophysics, 26: 147–166, 1964.
• [66] E.H. Wissler. Pennes’ 1948 paper revisited. Journal of Applied Physiology, 85: 35–41, 1998.
• [67] K. Woodbury. Inverse Engineering Handbook. CRC Press, Boca Raton, 2002.
• [68] P. Yuan, S-B. Wang, H-M. Lee. Estimation of the equivalent perfusion rate of Pennes model in an experimental bionic tissue without blood flow. International Communications in Heat and Mass Transfer, 39: 236–241, 2012.
• [69] A.G. Yagola, I.V. Kochikov, G.M. Kuramshina, Y.A. Pentin. Inverse Problems of Vibrational Spectroscopy. VSP, Netherlands, 1999.