Abstract
Photothermal therapy (PTT) with combined use of laser radiation and photon absorber nanoparticles is a promising technique to treat cancer. Treatment planning and devising appropriate protocols for cancer photo thermal therapy require the computational simulation of coupled physical phenomena, such as radiation, conduction, and blood perfusion. The P1-approximation is a numerical method to solve radiation heat transfer which features the advantage of being computationally fast and, therefore, desirable for PTT simulations. However, the method is known to become inaccurate under certain conditions. In this study, the P1-approximation and the accurate discrete ordinate method were applied to solve a set of test problems idealized to portray conditions encountered in PTT. The test problems were one-dimensional, and the radiation scattering was assumed as isotropic. Tissues composed by layers with different properties were considered, including cases in which gold nanoparticles were embedded in the tissue to increase photon absorption. For the problems considered here, the P1-approximation and discrete ordinate method results presented quite good agreement for the time-dependent temperature distribution, which is the quantity of interest in PTT.
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References
Bayazitoglu Y, Kheradmand S, Tullius TK (2013) An overview of nanoparticle assisted laser therapy. Int J Heat Mass Transf 67:469–486
Dickerson EB, Dreaden EC, Huang X, El-Sayed IH, Chu H, Pushpanketh S, McDonald JF (2008) Gold nanorod assisted near-infrared plasmonic photothermal therapy (PPTT) of squamous cell carcinoma in mice. Cancer Lett 269:57–66
Gobin AM, Lee MH, Halas NJ, James WD, Drezek RA, West JL (2007) Near-infrared resonant nanoshells for combined optical imaging and photothermal cancer therapy. Nano Lett 7(7):1929–1934
Maksimova IL, Akchurina Garif G, Khlebtsovb BN, Terentyukc GS, Akchurina Georgy G, Ermolaeva IA, Skaptsova AA, Sobolevac EP, Khlebtsova NG, Tuchina VV (2007) Near-infrared laser photothermal therapy of cancer by using gold nanoparticles: computer simulations and experiment. Med Laser Appl 22:199–206
Gong F, Hongyan Z, Papavassiliou DV, Bui K, Lim C, Duong HM (2014) Mesoscopic modeling of cancer photothermal therapy using single-walled carbon nanotubes and near infrared radiation: insights through an off-lattice Monte Carlo approach. Nanotechnology 25:205101 (IOP publishing)
Huang X, El-Sayed IH, Qian W, El-Sayed MA (2006) Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods. J Am Chem Soc 128(6):2115–2120
Tjahjono IK, Bayazitoglu Y (2008) Near-infrared light heating of a slab by embedded nanoparticles. Int J Heat Mass Transf 51:1505–1515
Vera J, Bayazitoglu Y (2009) Gold nanoshell density variation with laser power for induced hyperthermia. Int J Heat Mass Transf 52:564–573
El-Sayeda IH, Huang X, El-Sayed MA (2006) Selective laser photo-thermal therapy of epithelial carcinoma using anti-EGFR antibody conjugated gold nanoparticles. Cancer Lett 239:129–135
Dombrovsky LA, Timchenko V, Jackson M, Yeoh GH (2011) A combined transient thermal model for laser hyperthermia of tumors with embedded gold nanoshells. Int J Heat Mass Transf 54:5459–5469
Dombrovsky LA, Timchenko V, Jackson M (2012) Indirect heating strategy of laser induced hyperthermia: an advanced thermal model. Int J Heat Mass Transf 55:4688–4700
Dombrovsky LA (2012) The use of transport approximation and diffuse-based models in radiative transfer calculations. Computational thermal sciences indirect heating strategy of laser induced hyperthermia: an advanced thermal model. Int J Heat Mass Transf 4:297–315
Zhou F, Xing D, Ou Z, Wu B, Resasco DE, Chen WR (2009) Cancer photothermal therapy in the near-infrared region by using single-walled carbon nanotubes. J Biomed Opt 14(2):021009
Tuersun P, Han X (2014) Optimal dimensions of gold nanoshells for light backscattering and absorption based applications. J Quant Spectrosc Radiat Transf 146:468–474
Yang K, Zhang S, Zhang G, Sun X, Lee ST, Liu Z (2010) Graphene in mice: ultrahigh in vivo tumor uptake and efficient photothermal therapy. Nano Lett 10(9):3318–3323
Huang X, Jain PK, El-Sayed IH, El-Sayed MA (2008) Plasmonic photothermal therapy (PPTT) using gold nanoparticles. Lasers Med Sci 23:217–228
Lim ZZJ, Li JEJ, Ng CT, Yung LYL, Bay BH (2011) Gold nanoparticles in cancer therapy. Acta Pharmacologica Sinica 32:983–990
An W, Zhu T, Zhu Z (2014) Numerical investigation of radiative properties and surface plasmon resonance of silver nanorod dimers on a substrate. J Quant Spectrosc Radiat Transf 132:28–35
Liu L, Wang B, Cao X, Xu X, Wang Y (2011) Investigation of resonant properties of metal core shell nanoparticles using T-matrix calculations. J Quant Spectrosc Radiat Transf 112:2733–2740
Pennes HH (1948) Analysis of tissue and arterial blood temperature in the resting human forearm. J Appl Physiol 1(2):93–122
Howell JR, Siegel R, Mengüç MP (2011) Thermal radiation heat transfer. Taylor & Francis Group, New York
Modest MF (2013) Radiative heat transfer. Academic Press, New York
Maurente A, Lamien B, Orlande HRB, Eliçabe GE (2013) Analysis of The P1-approximation for the radiative heat transfer in skin tissues loaded with nanoparticles. In: Proceedings of the 22nd International congress of mechanical engineering (COBEM 2013), Ribeirão Preto, SP, Brazil
Mengüç MP, Viskanta R (1983) Comaprison of radiative transfer approximations for a highly forward scattering planar medium. J Quant Spectrosc Radiat Transf 29:381–394
Maliska C (1995) Transferência de Calor e Mecânica dos Fluidos Computacional. LTC Editora, Rio de Janeiro
He Y, Shirazaki M, Liu H, Himeno R, Sun Z (2006) A numerical coupling model to analyze the blood flow, temperature, and oxygen transport in human breast tumor under laser irradiation. Comput Biol Med 36:1336–1350
Vo-Dinh T (2003) Biomedical photonics handbook. CRC Press, Boca Raton
Fantini S, Walker SA, Franceschini MA, Kaschke M, Schlag PM, Moesta KT (1998) Assessment of the size, position, and optical properties of breast tumors in vivo by noninvasive optical methods. Appl Optics 37(10):1982–1989
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Bruno, A.B., Maurente, A., Lamien, B. et al. Numerical simulation of nanoparticles assisted laser photothermal therapy: a comparison of the P1-approximation and discrete ordinate methods. J Braz. Soc. Mech. Sci. Eng. 39, 621–630 (2017). https://doi.org/10.1007/s40430-016-0553-3
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DOI: https://doi.org/10.1007/s40430-016-0553-3