Abstract

In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens’ function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs.

© 2015 Optical Society of America

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2015 (6)

S. Eiichi, K. Hiroyasu, F. Hirosuke, F. Motoki, K. Tadashi, O. Yasutaka, Y. Susumu, T. Ryosuke, M. Tsuyoshi, and S. Michiyasu, “Diverse effects of hypothermia therapy in patients with severe traumatic brain injury based on the computed tomography classification of the traumatic coma data bank,” J. Neurotrauma 32(5), 353–361 (2015).
[Crossref]

G. Debaty, M. Maignan, S. Ruckly, and J-F Timsit, “Impact of intra-arrest therapeutic hypothermia on outcome of prehospital cardiac arrest: response to comment by Saigal and Sharma,” Intensive Care Med. 41(1), 172–173 (2015).
[Crossref]

K. M. Kelly, W. J. Moy, A. J. Moy, B. S. Lertsakdadet, J. J. Moy, E. Nguyen, A. Nguyen, K. E. Osann, and B. Choi, “Talaporfin sodium-mediated photodynamic therapy alone and in combination with pulsed dye laser on cutaneous vasculature,” J. Invest. Dermatol. 135(1), 302–306 (2015).
[Crossref]

E. Posadzka, R. Jach, K. Pitynski, and M. J. Jablonski, “Treatment efficacy for pain complaints in women with endometriosis of the lesser pelvis after laparoscopic electroablation vs. CO2 laser ablation,” Med. Phys. 30(1), 147–152 (2015).

S. Sinha, E. Hargreaves, N. V. Patel, and S. F. Danish, “Assessment of irrigation dynamics in magnetic-resonance guided laser induced thermal therapy (MRgLITT),” Lasers Surg. Med. 47, 273–280 (2015).
[Crossref] [PubMed]

A. Liemert and A. Kienle, “Novel analytical solution for the radiance in an anisotropically scattering medium,” Appl. Opt. 54(8), 1963–1969 (2015).
[Crossref] [PubMed]

2014 (7)

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[Crossref]

A. Willey, R. R. Anderson, and F. H. Sakamoto, “Temperature-modulated photodynamic therapy for the treatment of actinic keratosis on the extremities: a pilot study,” Dermatol. Surg. 40(10), 1094–1102 (2014).
[Crossref] [PubMed]

E. Bay, A. Douplik, and D. Razansk, “Optoacoustic monitoring of cutting efficiency and thermal damage during laser ablation,” Lasers. Med. Sci. 29, 1029–1035 (2014).
[Crossref]

S. Kim and S. Jeong, “Effects of temperature-dependent optical properties on the fluence rate and temperature of biological tissue during low-level laser therapy,” Lasers Med. Sci. 9(4), 637–644 (2014).
[Crossref]

B. S. Hijmansa, A. Grefhorstb, M. H. Oosterveera, and A. K. Groena, “Zonation of glucose and fatty acid metabolism in the liver: mechanism and metabolic consequences,” Biochimie 96, 121–129 (2014).
[Crossref]

A. Miranda, A. P. P López-Cardona, R. Laguna-Barraza, A. Calle, I. López-Vidriero, B. Pintado, and A. Gutiérrez-Adán, “Transcriptome profiling of liver of non-genetic low birth weight and long term health consequences,” BMC Genomics 15(327), 1–12 (2014).
[Crossref]

H. Erkol, A. Demirkiran, N. Uluc, and M. B. Unlu, “Analytical reconstruction of the bioluminescent source with priors,” Opt. Express 22(16), 19758–19773 (2014).
[Crossref] [PubMed]

2013 (7)

H. Erkol and M. B. Unlu, “Virtual source method for diffuse optical imaging,” Appl. Opt. 52, 4933–4970 (2013).
[Crossref] [PubMed]

Y. Lin, Ha. Gao, D. Thayer, A. L. Luk, and G. Gulsen, “Photo-magnetic imaging: resolving optical contrast at MRI resolution,” Phys. Med. Biol. 58, 3551–3562 (2013).
[Crossref] [PubMed]

S. A. Mirnezami, M. R. Jafarabadi, and M. Abrishami, “Temperature distribution simulation of the human eye exposed to laser radiation,” J. Lasers Med. Sci. 4(4), 175–181 (2013).
[PubMed]

S. Sarkar, C. Fan, J. C. Hsiang, and R. M. Dickson, “Modulated fluorophore signal recovery buried within tissue mimicking phantoms,” J. Phys. Chem. A 117, 9501–9509 (2013).
[Crossref] [PubMed]

A. Y. Seteikin, I. V. Krasnikov, E. Drakaki, and M. Makropoulou, “Dynamic model of thermal reaction of biological tissues to laser-induced fluorescence and photodynamic therapy,” J. Biomed. Opt. 18(7), 075002 (2013).
[Crossref] [PubMed]

L. Assis, A. I. Soares-Moretti, T. B. Abrahão, H. P. de Souza, M. R. Hamblin, and N. A. Parizotto, “Low-level laser therapy (808 nm) contributes to muscle regeneration and prevents fibrosis in rat tibialis anterior muscle after cryolesion,” Lasers Med. Sci. 28, 947–955 (2013).
[Crossref]

Y. Xu, D. Sun, Z. Wei, B. Hong, and Y. Yang, “Clinical study on the application of a 2-μm continuous wave laser in transurethral vaporesection of the prostate,” Exp. Ther. Med. 5, 1097–1100 (2013).
[PubMed]

2012 (3)

W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med. 44(2), 158–162 (2012).
[Crossref] [PubMed]

V. V. Barun and A. P. Ivanov, “Temperature regime of biological tissue under photodynamic therapy,” Biofizika 57(1), 120–129 (2012).
[PubMed]

L. R. Braathen, C. A. Morton, N. Basset-Seguin, R. Bissonnette, M. J. Gerritsen, Y. Gilaberte, P. Calzavara-Pinton, A. Sidoroff, H. C. Wulf, and R. M. Szeimies, “Photodynamic therapy for skin field cancerization: an international consensus. International society for photodynamic therapy in dermatology,” J. Eur. Acad. Dermatol. Venereol. 26(9), 1063–1069 (2012).
[Crossref] [PubMed]

2011 (4)

Y. Y. Huang, “Biphasic dose response in low level light therapy an update,” Dose-Response 9(4), 602–618 (2011).
[Crossref]

L. Jiang, W. Zhan, and M. H. Loew, “Modeling static and dynamic thermography of the human breast under elastic deformation,” Phys. Med. Biol. 56, 187–202 (2011).
[Crossref]

F. Nouizi, M. Torregrossa, R. Chabrier, and P. Poulet, “Improvement of absorption and scattering discrimination by selection of sensitive points on temporal profile in diffuse optical tomography,” Opt. Express 19(13), 12843–12854 (2011).
[Crossref] [PubMed]

Y. Feng and D. Fuentes, “Model-based planning and real-time predictive control for laserinduced thermal therapy,” Int. J. Hyperthermia 27(8), 751–761 (2011).
[Crossref] [PubMed]

2010 (5)

A. Liemert and A. Kienle, “Light diffusion in N-layered turbid media: frequency and time domains,” J Biomed. Opt. 15, 025002 (2010).
[Crossref] [PubMed]

A. Liemert and A. Kienle, “Light diffusion in a turbid cylinder. I. Homogeneous Case,” Opt. Express 18, 9456–9473 (2010).
[Crossref] [PubMed]

A. Zhang, D. Piao, C. F. Bunting, and B. W. Pogue, “Photon diffusion in a homogeneous medium bounded externally or internally by an infinetely long circular cylindrical applicator. I. Steady-state theory,” J. Opt. Soc. Am. A 27, 648–662 (2010).
[Crossref]

B. Zhao and Y. Y. He, “Recent advances in the prevention and treatment of skin cancer using photodynamic therapy,” Expert. Rev. Anticancer Ther. 10(11), 1797–1809 (2010).
[Crossref] [PubMed]

J. Yang, A. C. Chen, Q. Wu, S. Jiang, X. Liu, L. Xiong, and Y. Xia, “The influence of temperature on 5–aminolevulinic acid-based photodynamic reaction in keratinocytes in vitro,” Photodermatol. Photoimmunol. Photomed. 26(2), 83–91. (2010).
[Crossref] [PubMed]

2009 (3)

T. Bach, N. Huck, F. Wezel, A. Häcker, A. J. Gross, and M. S. Michel, “70 vs 120 W thulium:yttrium-aluminium-garnet 2-μm continuous-wave laser for the treatment of benign prostatic hyperplasia: a systematic ex-vivo evaluation,” BJU Int. 106, 368–372 (2009).
[Crossref]

A. M. Elliott, J. Schwartz, J. Wang, A. M. Shetty, C. Bourgoyne, D. P. ONeal, J. D. Hazle, and R. J. Stafford, “Quantitative comparison of delta P1 versus optical diffusion approximations for modeling near-infrared gold nanoshell heating,” Med. Phys. 36, 1351–1358 (2009).
[Crossref] [PubMed]

S. K. Cheong, S. Krishnan, and S. H. Cho, “Modeling of plasmonic heating from individual gold nanoshells for near-infrared laser-induced thermal therapy,” Med. Phys. 36, 4664–4671 (2009).
[Crossref] [PubMed]

2008 (3)

M. Jaunicha, S. Rajea, K. Kimb, K. Mitraa, and Z. Guob, “Bio-heat transfer analysis during short pulse laser irradiation of tissues,” Int. J. Heat Mass Transfer 51, 5511–5521 (2008).
[Crossref]

G. Wendt-Nordahl, S. Huckele, P. Honeck, P. Alken, T. Knoll, M. S. Michel, and A. Häcker, “Systematic evaluation of a recently introduced 2-μm continuou-wave thulium laser for vaporesection of the prostate,” J. Endourol. 22(5), 1041–1045 (2008).
[Crossref] [PubMed]

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–743 (2008).
[Crossref] [PubMed]

2007 (4)

M. N. Rylander, Y. Feng, J. Bass, and K. R. Diller, “Heat shock protein expression and injury optimization for laser therapy design,” Laser Surg. Med. 39, 731–746 (2007).
[Crossref]

R. K. Banerjee, L. Zhu, P. Gopalakrishnan, and M. J. Kazmierczak, “Influence of laser parameters on selective retinal treatment using single-phase heat transfer analyses,” Med. Phys. 34(5), 1828–1841 (2007).
[Crossref] [PubMed]

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).
[Crossref] [PubMed]

E. Neufeld, N. Chavannes, T. Samaras, and N. Kuster, “Novel conformal technique to reduce staircasing artifacts at material boundaries for FDTD modeling of the bioheat equation,” IEEE Trans. Biomed. Eng. 52(4), 4371–4381 (2007).

2006 (3)

G. Wang, H. Shen, W. Cong, S. Zhao, and G. Wei, “Temperature-modulated bioluminescence tomography,” Opt. Express 14(17), 7852–7871 (2006).
[Crossref] [PubMed]

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).
[Crossref] [PubMed]

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcioğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[Crossref]

2005 (3)

A. Kienle, “Light diffusion through a turbid parallelepiped,” J. Opt. Soc. Am. A 22, 1883–1888 (2005).
[Crossref]

J. J. Zhao, J. Zhang, N. Kang, and F. Yang, “A two level finite difference scheme for one dimensional Pennes bioheat equation,” Appl. Math. Comput. 171(1), 320–331 (2005).
[Crossref]

R. Zhang, W. Verkruysse, G. Aguilar, and J. S. Nelson, “Comparison of diffusion approximation and Monte Carlo based finite element models for simulating thermal responses to laser irradiation in discrete vessels,” Phys. Med. Biol. 50(5), 4075–4086 (2005).
[Crossref] [PubMed]

2004 (2)

G. Shafirstein, W. Bäumler, M. Lapidoth, S. Ferguson, P. E. North, and M. Waner, “A new mathematical approach to the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment of port-wine stains,” Lasers Surg. Med. 34, 335–347 (2004).
[Crossref] [PubMed]

Z. S. Deng and J. Liu, “Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics,” Comput. Biol. Med. 34(6), 495–521 (2004).
[Crossref] [PubMed]

2002 (2)

G. Brix, M. Seebass, G. Hellwiga, and J. Griebela, “Estimation of heat transfer and temperature rise in partial-body regions during MR procedures: an analytical approach with respect to safety considerations,” Magn. Reson. Imaging 20(1), 65–76 (2002).
[Crossref] [PubMed]

F. Martelli, A. Sassaroli, Y. Yamada, and G. Zaccanti, “Analytical approximate solutions of the timedomain diffusion equation in layered slabs,” J. Opt. Soc. Am. A. 19, 71–80 (2002).
[Crossref]

2001 (1)

S. H. Diaz, G. Aguilar, E. J. Lavernia, and B. J. F. Wong, “Modeling the thermal response of porcine cartilage to laser irradiation,” IEEE J. Sel. Top. Quantum Electron. 7, 944–951 (2001).
[Crossref]

2000 (1)

M. E. Kowalski and J. M. Jin, “Determination of electromagnetic phased-array driving signals for hyperthermia based on a steady-state temperature criterion,” IEEE Trans. Microw. Theory Techn. 48(11), 1864–1873 (2000).
[Crossref]

1999 (2)

J. Liu, X. Chen, and L. X. Xu, “New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating,” IEEE Trans. Biomed. Eng. 46(4), 420–428 (1999).
[Crossref] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).
[Crossref]

1998 (1)

1997 (2)

D. Contini, F. Martelli, and G. Zaccanti, “Photon migration through a turbid slab described by a model based on diffusion approximation I. Theory,” Appl. Opt. 36, 4587–4599 (1997).
[Crossref] [PubMed]

A. Kienle and M. S. Patterson, “Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium,” J. Opt. Soc. Am. A. 14, 246–254 (1997).
[Crossref]

1994 (3)

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. 91, 4887–4891 (1994).
[Crossref] [PubMed]

B. W. Pogue and M. S. Patterson, “Frequency-domain optical absorption spectroscopy of finite tissue volumes using diffusion theory,” Phys. Med. Biol. 39, 1157–1180 (1994).
[Crossref] [PubMed]

D. R. Wyman and W. M. Whelan, “Basic optothermal diffusion theory for interstitial laser photocoagulation,” Med. Phys. 21, 1651–1656 (1994).
[Crossref] [PubMed]

1993 (3)

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).
[Crossref]

S. R. Arridge, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[Crossref] [PubMed]

G. L. LeCarpentier, M. Motamedi, L. P. McMath, S. Rastegar, and A. J. Welch, “Continuous wave laser ablation of tissue: analysis of thermal and mechanical events,” IEEE Trans. Biomed. Eng. 40(2), 188–200 (1993).
[Crossref] [PubMed]

1992 (2)

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[Crossref] [PubMed]

T. J. Farrel, M. S. Patterson, and B. C. Wilson, “A diffusion theory model of specially resolved steady state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo,” Med. Phys. 19, 879–888 (1992).
[Crossref]

1991 (1)

M. S. Patterson and S. J. Madsen, “Diffusion equation representation of photon migration in tissue,” IEEE MTT-S Digest 2, 905–908 (1991).

1990 (1)

1984 (1)

H. Arkin, L. X. Xu, and K. R. Holmes, “Recent developments in modeling heat transfer in blood perfused tissues,” Phys. Med. Biol. 41(2), 97–107 (1984).

1948 (1)

H. H. Pennes, “Analysis of tissue and arterial blood temperatures in resting forearm,” J. Appl. Psychol. 1, 93–122 (1948).

Abrahão, T. B.

L. Assis, A. I. Soares-Moretti, T. B. Abrahão, H. P. de Souza, M. R. Hamblin, and N. A. Parizotto, “Low-level laser therapy (808 nm) contributes to muscle regeneration and prevents fibrosis in rat tibialis anterior muscle after cryolesion,” Lasers Med. Sci. 28, 947–955 (2013).
[Crossref]

Abrishami, M.

S. A. Mirnezami, M. R. Jafarabadi, and M. Abrishami, “Temperature distribution simulation of the human eye exposed to laser radiation,” J. Lasers Med. Sci. 4(4), 175–181 (2013).
[PubMed]

Aguilar, G.

R. Zhang, W. Verkruysse, G. Aguilar, and J. S. Nelson, “Comparison of diffusion approximation and Monte Carlo based finite element models for simulating thermal responses to laser irradiation in discrete vessels,” Phys. Med. Biol. 50(5), 4075–4086 (2005).
[Crossref] [PubMed]

S. H. Diaz, G. Aguilar, E. J. Lavernia, and B. J. F. Wong, “Modeling the thermal response of porcine cartilage to laser irradiation,” IEEE J. Sel. Top. Quantum Electron. 7, 944–951 (2001).
[Crossref]

Alken, P.

G. Wendt-Nordahl, S. Huckele, P. Honeck, P. Alken, T. Knoll, M. S. Michel, and A. Häcker, “Systematic evaluation of a recently introduced 2-μm continuou-wave thulium laser for vaporesection of the prostate,” J. Endourol. 22(5), 1041–1045 (2008).
[Crossref] [PubMed]

Anderson, R. R.

A. Willey, R. R. Anderson, and F. H. Sakamoto, “Temperature-modulated photodynamic therapy for the treatment of actinic keratosis on the extremities: a pilot study,” Dermatol. Surg. 40(10), 1094–1102 (2014).
[Crossref] [PubMed]

Arkin, H.

H. Arkin, L. X. Xu, and K. R. Holmes, “Recent developments in modeling heat transfer in blood perfused tissues,” Phys. Med. Biol. 41(2), 97–107 (1984).

Arora, R. P.

W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med. 44(2), 158–162 (2012).
[Crossref] [PubMed]

Arridge, S. R.

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).
[Crossref] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Problems 15, 41–93 (1999).
[Crossref]

S. R. Arridge, “A finite element approach for modelling photon transport in tissue,” Med. Phys. 20, 299–309 (1993).
[Crossref] [PubMed]

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).
[Crossref]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[Crossref] [PubMed]

Assis, L.

L. Assis, A. I. Soares-Moretti, T. B. Abrahão, H. P. de Souza, M. R. Hamblin, and N. A. Parizotto, “Low-level laser therapy (808 nm) contributes to muscle regeneration and prevents fibrosis in rat tibialis anterior muscle after cryolesion,” Lasers Med. Sci. 28, 947–955 (2013).
[Crossref]

Bach, T.

T. Bach, N. Huck, F. Wezel, A. Häcker, A. J. Gross, and M. S. Michel, “70 vs 120 W thulium:yttrium-aluminium-garnet 2-μm continuous-wave laser for the treatment of benign prostatic hyperplasia: a systematic ex-vivo evaluation,” BJU Int. 106, 368–372 (2009).
[Crossref]

Banerjee, R. K.

R. K. Banerjee, L. Zhu, P. Gopalakrishnan, and M. J. Kazmierczak, “Influence of laser parameters on selective retinal treatment using single-phase heat transfer analyses,” Med. Phys. 34(5), 1828–1841 (2007).
[Crossref] [PubMed]

Barun, V. V.

V. V. Barun and A. P. Ivanov, “Temperature regime of biological tissue under photodynamic therapy,” Biofizika 57(1), 120–129 (2012).
[PubMed]

Bass, J.

M. N. Rylander, Y. Feng, J. Bass, and K. R. Diller, “Heat shock protein expression and injury optimization for laser therapy design,” Laser Surg. Med. 39, 731–746 (2007).
[Crossref]

Basset-Seguin, N.

L. R. Braathen, C. A. Morton, N. Basset-Seguin, R. Bissonnette, M. J. Gerritsen, Y. Gilaberte, P. Calzavara-Pinton, A. Sidoroff, H. C. Wulf, and R. M. Szeimies, “Photodynamic therapy for skin field cancerization: an international consensus. International society for photodynamic therapy in dermatology,” J. Eur. Acad. Dermatol. Venereol. 26(9), 1063–1069 (2012).
[Crossref] [PubMed]

Bäumler, W.

G. Shafirstein, W. Bäumler, M. Lapidoth, S. Ferguson, P. E. North, and M. Waner, “A new mathematical approach to the diffusion approximation theory for selective photothermolysis modeling and its implication in laser treatment of port-wine stains,” Lasers Surg. Med. 34, 335–347 (2004).
[Crossref] [PubMed]

Bay, E.

E. Bay, A. Douplik, and D. Razansk, “Optoacoustic monitoring of cutting efficiency and thermal damage during laser ablation,” Lasers. Med. Sci. 29, 1029–1035 (2014).
[Crossref]

Bianco, S. D.

F. Martelli, A. Sassaroli, S. D. Bianco, and G. Zaccanti, “Solution of the time-dependent diffusion equation for a three-layer medium: application to study photon migration through a simplified adult head model,” Phys. Med. Biol. 52, 2827–2843 (2007).
[Crossref] [PubMed]

Birgul, O.

M. B. Unlu, O. Birgul, R. Shafiha, G. Gulsen, and O. Nalcioğlu, “Diffuse optical tomographic reconstruction using multifrequency data,” J. Biomed. Opt. 11, 054008 (2006).
[Crossref]

Bissonnette, R.

L. R. Braathen, C. A. Morton, N. Basset-Seguin, R. Bissonnette, M. J. Gerritsen, Y. Gilaberte, P. Calzavara-Pinton, A. Sidoroff, H. C. Wulf, and R. M. Szeimies, “Photodynamic therapy for skin field cancerization: an international consensus. International society for photodynamic therapy in dermatology,” J. Eur. Acad. Dermatol. Venereol. 26(9), 1063–1069 (2012).
[Crossref] [PubMed]

Boas, D. A.

S. A. Walker, D. A. Boas, and E. Gratton, “Photon density waves scattered from cylindrical inhomogeneities: theory and experiments,” Appl. Opt. 37, 1935–1944 (1998).
[Crossref]

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. 91, 4887–4891 (1994).
[Crossref] [PubMed]

Bourgoyne, C.

A. M. Elliott, J. Schwartz, J. Wang, A. M. Shetty, C. Bourgoyne, D. P. ONeal, J. D. Hazle, and R. J. Stafford, “Quantitative comparison of delta P1 versus optical diffusion approximations for modeling near-infrared gold nanoshell heating,” Med. Phys. 36, 1351–1358 (2009).
[Crossref] [PubMed]

Braathen, L. R.

L. R. Braathen, C. A. Morton, N. Basset-Seguin, R. Bissonnette, M. J. Gerritsen, Y. Gilaberte, P. Calzavara-Pinton, A. Sidoroff, H. C. Wulf, and R. M. Szeimies, “Photodynamic therapy for skin field cancerization: an international consensus. International society for photodynamic therapy in dermatology,” J. Eur. Acad. Dermatol. Venereol. 26(9), 1063–1069 (2012).
[Crossref] [PubMed]

Brix, G.

G. Brix, M. Seebass, G. Hellwiga, and J. Griebela, “Estimation of heat transfer and temperature rise in partial-body regions during MR procedures: an analytical approach with respect to safety considerations,” Magn. Reson. Imaging 20(1), 65–76 (2002).
[Crossref] [PubMed]

Bunting, C. F.

Calle, A.

A. Miranda, A. P. P López-Cardona, R. Laguna-Barraza, A. Calle, I. López-Vidriero, B. Pintado, and A. Gutiérrez-Adán, “Transcriptome profiling of liver of non-genetic low birth weight and long term health consequences,” BMC Genomics 15(327), 1–12 (2014).
[Crossref]

Calzavara-Pinton, P.

L. R. Braathen, C. A. Morton, N. Basset-Seguin, R. Bissonnette, M. J. Gerritsen, Y. Gilaberte, P. Calzavara-Pinton, A. Sidoroff, H. C. Wulf, and R. M. Szeimies, “Photodynamic therapy for skin field cancerization: an international consensus. International society for photodynamic therapy in dermatology,” J. Eur. Acad. Dermatol. Venereol. 26(9), 1063–1069 (2012).
[Crossref] [PubMed]

Carpenter, C. M.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–743 (2008).
[Crossref] [PubMed]

Chabrier, R.

Chances, B.

D. A. Boas, M. A. O’leary, B. Chances, and A. G. Yodh, “Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications,” Proc. Natl. Acad. Sci. 91, 4887–4891 (1994).
[Crossref] [PubMed]

Chavannes, N.

E. Neufeld, N. Chavannes, T. Samaras, and N. Kuster, “Novel conformal technique to reduce staircasing artifacts at material boundaries for FDTD modeling of the bioheat equation,” IEEE Trans. Biomed. Eng. 52(4), 4371–4381 (2007).

Chen, A. C.

J. Yang, A. C. Chen, Q. Wu, S. Jiang, X. Liu, L. Xiong, and Y. Xia, “The influence of temperature on 5–aminolevulinic acid-based photodynamic reaction in keratinocytes in vitro,” Photodermatol. Photoimmunol. Photomed. 26(2), 83–91. (2010).
[Crossref] [PubMed]

Chen, X.

J. Liu, X. Chen, and L. X. Xu, “New thermal wave aspects on burn evaluation of skin subjected to instantaneous heating,” IEEE Trans. Biomed. Eng. 46(4), 420–428 (1999).
[Crossref] [PubMed]

Cheong, S. K.

S. K. Cheong, S. Krishnan, and S. H. Cho, “Modeling of plasmonic heating from individual gold nanoshells for near-infrared laser-induced thermal therapy,” Med. Phys. 36, 4664–4671 (2009).
[Crossref] [PubMed]

Cho, S. H.

S. K. Cheong, S. Krishnan, and S. H. Cho, “Modeling of plasmonic heating from individual gold nanoshells for near-infrared laser-induced thermal therapy,” Med. Phys. 36, 4664–4671 (2009).
[Crossref] [PubMed]

Choi, B.

K. M. Kelly, W. J. Moy, A. J. Moy, B. S. Lertsakdadet, J. J. Moy, E. Nguyen, A. Nguyen, K. E. Osann, and B. Choi, “Talaporfin sodium-mediated photodynamic therapy alone and in combination with pulsed dye laser on cutaneous vasculature,” J. Invest. Dermatol. 135(1), 302–306 (2015).
[Crossref]

W. J. Moy, S. J. Patel, B. S. Lertsakdadet, R. P. Arora, K. M. Nielsen, K. M. Kelly, and B. Choi, “Preclinical in vivo evaluation of NPe6-mediated photodynamic therapy on normal vasculature,” Lasers Surg. Med. 44(2), 158–162 (2012).
[Crossref] [PubMed]

Cong, W.

Contini, D.

Cope, M.

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[Crossref] [PubMed]

Danish, S. F.

S. Sinha, E. Hargreaves, N. V. Patel, and S. F. Danish, “Assessment of irrigation dynamics in magnetic-resonance guided laser induced thermal therapy (MRgLITT),” Lasers Surg. Med. 47, 273–280 (2015).
[Crossref] [PubMed]

Darne, C.

C. Darne, Y. Lu, and E. M. Sevick-Muraca, “Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update,” Phys. Med. Biol. 59(1), R1–R64 (2014).
[Crossref]

Davis, S. C.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–743 (2008).
[Crossref] [PubMed]

de Souza, H. P.

L. Assis, A. I. Soares-Moretti, T. B. Abrahão, H. P. de Souza, M. R. Hamblin, and N. A. Parizotto, “Low-level laser therapy (808 nm) contributes to muscle regeneration and prevents fibrosis in rat tibialis anterior muscle after cryolesion,” Lasers Med. Sci. 28, 947–955 (2013).
[Crossref]

Debaty, G.

G. Debaty, M. Maignan, S. Ruckly, and J-F Timsit, “Impact of intra-arrest therapeutic hypothermia on outcome of prehospital cardiac arrest: response to comment by Saigal and Sharma,” Intensive Care Med. 41(1), 172–173 (2015).
[Crossref]

Dehghani, H.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–743 (2008).
[Crossref] [PubMed]

Delpy, D. T.

M. Schweiger, S. R. Arridge, and D. T. Delpy, “Application of the finite element method for the forward and inverse model in optical tomography,” J. Mat. Imaging Vis. 3, 263–283 (1993).
[Crossref]

S. R. Arridge, M. Cope, and D. T. Delpy, “The theoretical basis for the determination of optical pathlengths in tissue: temporal and frequency analysis,” Phys. Med. Biol. 37, 1531–1560 (1992).
[Crossref] [PubMed]

Demirkiran, A.

Deng, Z. S.

Z. S. Deng and J. Liu, “Mathematical modeling of temperature mapping over skin surface and its implementation in thermal disease diagnostics,” Comput. Biol. Med. 34(6), 495–521 (2004).
[Crossref] [PubMed]

Diaz, S. H.

S. H. Diaz, G. Aguilar, E. J. Lavernia, and B. J. F. Wong, “Modeling the thermal response of porcine cartilage to laser irradiation,” IEEE J. Sel. Top. Quantum Electron. 7, 944–951 (2001).
[Crossref]

Dickson, R. M.

S. Sarkar, C. Fan, J. C. Hsiang, and R. M. Dickson, “Modulated fluorophore signal recovery buried within tissue mimicking phantoms,” J. Phys. Chem. A 117, 9501–9509 (2013).
[Crossref] [PubMed]

Diller, K. R.

M. N. Rylander, Y. Feng, J. Bass, and K. R. Diller, “Heat shock protein expression and injury optimization for laser therapy design,” Laser Surg. Med. 39, 731–746 (2007).
[Crossref]

Douiri, A.

J. Sikora, A. Zacharopoulos, A. Douiri, M. Schweiger, L. Horesh, S. R. Arridge, and J. Ripoll, “Diffuse photon propagation in multilayered geometries,” Phys. Med. Biol. 51, 497–516 (2006).
[Crossref] [PubMed]

Douplik, A.

E. Bay, A. Douplik, and D. Razansk, “Optoacoustic monitoring of cutting efficiency and thermal damage during laser ablation,” Lasers. Med. Sci. 29, 1029–1035 (2014).
[Crossref]

Drakaki, E.

A. Y. Seteikin, I. V. Krasnikov, E. Drakaki, and M. Makropoulou, “Dynamic model of thermal reaction of biological tissues to laser-induced fluorescence and photodynamic therapy,” J. Biomed. Opt. 18(7), 075002 (2013).
[Crossref] [PubMed]

Eames, M. E.

H. Dehghani, M. E. Eames, P. K. Yalavarthy, S. C. Davis, S. Srinivasan, C. M. Carpenter, B. W. Pogue, and K. D. Paulsen, “Near infrared optical tomography using NIRFAST: algorithm for numerical model and image reconstruction,” Commun. Numer. Methods Eng. 25, 711–743 (2008).
[Crossref] [PubMed]

Eiichi, S.

S. Eiichi, K. Hiroyasu, F. Hirosuke, F. Motoki, K. Tadashi, O. Yasutaka, Y. Susumu, T. Ryosuke, M. Tsuyoshi, and S. Michiyasu, “Diverse effects of hypothermia therapy in patients with severe traumatic brain injury based on the computed tomography classification of the traumatic coma data bank,” J. Neurotrauma 32(5), 353–361 (2015).
[Crossref]

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A. M. Elliott, J. Schwartz, J. Wang, A. M. Shetty, C. Bourgoyne, D. P. ONeal, J. D. Hazle, and R. J. Stafford, “Quantitative comparison of delta P1 versus optical diffusion approximations for modeling near-infrared gold nanoshell heating,” Med. Phys. 36, 1351–1358 (2009).
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Figures (7)

Fig. 1
Fig. 1 The schematic representing the geometry of a homogeneous medium with a δ function source located at r = ri.
Fig. 2
Fig. 2 The schematic of the interface used in the experiment. The laser beam is collimated using a GRIN lens and delivered to the homogeneous phantom from a hole prepared at the side of the custom built RF coil. The total power is distributed to three point light sources and simulation results for individual sources are superimposed.
Fig. 3
Fig. 3 The experimental, analytical, and FEM based temperature maps for the phantom. The first and second rows show the linear, T(°C), and logarithmic, ln(T), scaled temperature maps, respectively. For the simulated temperature, the light sources are positioned at 1/μ′s mm under the illumination site as imposed by the diffusion approximation. The simulation results are obtained 18 seconds after the beginning of the laser heating while the experimental data is acquired between 12 s and 24 s. Some artifacts are observable in the experimental data particularly towards the edges.
Fig. 4
Fig. 4 The temperature profiles (a) linear, (b) logarithmic carried out along the x-axis on the temperature maps presented in Fig. 3. For the simulated temperature, the light sources are positioned at 1/μ′s mm under the illumination site as imposed by the diffusion approximation. The simulation results are obtained 18 seconds after the beginning of the laser heating while the experimental data is acquired between 12 s and 24 s. All three methods are in good agreement above the MRT noise level, 0.1 °C (green dotted line).
Fig. 5
Fig. 5 The temporal temperature profiles obtained between 0 s and 400 s at (a) x = 5 mm and (b) x = 12 mm. The temperature near the boundary (x = 12 mm) reaches a plateau much quicker due to heat convection.
Fig. 6
Fig. 6 The temperature maps for the chicken breast tissue obtained experimentally, analytically, and numerically (FEM), respectively. The simulation results are obtained 42 seconds after the beginning of the laser heating while the experimental data is acquired between 36 s and 48 s. The cross-section of the chicken breast sample is approximated by a 28 mm diameter circle indicated by the green dash-line.
Fig. 7
Fig. 7 The temperature profiles for chicken breast tissue (a) linear, (b) logarithmic carried out along the x-axis on the temperature maps presented in Fig. 6. The simulation results are obtained 42 seconds after the beginning of the laser heating while the experimental data is acquired between 36 s and 48 s. All three methods are in good agreement above the MRT noise level, 0.15 °C (green dotted line).

Tables (1)

Tables Icon

Table 1 Agar phantom parameters used in the experiment.

Equations (35)

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D Φ ( r ) + μ a Φ ( r ) = S ( r )
ρ c T ( r , t ) t = [ k T ( r , t ) ] + E ( r )
2 Φ ( r ) + μ a D Φ ( r ) = γ D δ ( r , r )
Φ ( r , θ ) = m = [ A m ( β ) J m ( β r ) + B m ( β ) Y m ( β r ) ] [ C m ( β ) cos ( m θ ) + D m ( β ) sin ( m θ ) ]
Φ ( r , θ ) = m = [ a m ( β ) J m ( β r ) + b m ( β ) Y m ( β r ) ] cos ( m θ )
Φ < ( r , θ ) = m = a m ( β ) J m ( β r ) cos ( m θ )
Φ > ( r , θ ) = m = [ b m ( β ) J m ( β r ) + c m ( β ) Y m ( β r ) ] cos ( m θ )
Φ ( R , θ ) + 2 ξ D Φ ( r , θ ) r | r = R = 0
Φ < ( r , θ ) | r = r i = Φ > ( r , θ ) | r = r i .
m = { 1 r d d r [ r d d r G m ( β r ) ] cos ( m θ ) + 1 r 2 d 2 d θ 2 [ cos ( m θ ) ] G m ( β r ) μ a D G m ( β r ) cos ( m θ ) } = γ D δ ( r , r i )
m = r i ε r i + ε [ d d r ( r d G m ( β r ) d r ) ] d r 0 2 π cos ( m θ ) cos ( n θ ) d θ = 1 D γ r i ε r i + ε 0 2 π δ ( r , r i ) cos ( n θ ) r d r d θ .
d G m ( β r ) d r | r = r i + ε d G m ( β r ) d r | r = r i ε = γ π D r i cos ( m θ i )
b m ( β ) J m ( β R ) + c m ( β ) Y m ( β R ) = 2 ξ D [ b m ( β ) d J m ( β r ) d r + c m ( β ) d Y m ( β r ) d r ] | r = R ,
b m ( β ) J m ( β r i ) + c m ( β ) Y m ( β r i ) = a m ( β ) J m ( β r i )
[ b m ( β ) d J m ( β r ) d r + c m ( β ) d Y m ( β r ) d r a m ( β ) d J m ( β r ) d r ] | r = r i = γ π D r i cos ( m θ i ) .
a m ( β ) = γ cos ( m θ i ) 2 D [ 2 D β ξ R J m 1 ( β R ) + ( R 2 D m ξ ) J m ( β R ) ] × { J m ( β r i ) [ 2 D β ξ R Y m 1 ( β R ) + ( R 2 D m ξ ) Y m ( β R ) ] + Y m ( β r i ) [ 2 D β ξ R J m 1 ( β R ) ( R 2 D m ξ ) J m ( β R ) ] } ,
b m ( β ) = γ R D β ξ [ Y m 1 ( β R ) Y m + 1 ( β R ) ] + Y m ( β R ) 2 D [ 2 D β ξ R J m 1 ( β R ) + ( R 2 D m ξ ) J m ( β R ) ] × J m ( β r i ) cos ( m θ i )
c m ( β ) = γ 2 D J m ( β r i ) cos ( m θ i ) ,
Φ ( r , θ ) = m = { a m ( β ) J m ( β r ) cos ( m θ ) if r r i ( b m ( β ) J m ( β r ) + c m ( β ) Y m ( β r ) ) cos ( m θ ) if r r i .
k T ( r ) t = h ( T s T ( r ) )
ρ c T ˜ ( r , t ) t = [ k T ˜ ( r , t ) ] .
T ˜ ( t , r , θ ) = { exp ( k ρ c λ 2 t ) , J p ( λ r ) , cos ( p θ ) } .
k T ˜ ( R ) t = h T ˜ ( R )
J p ( λ r ) | r = R k h d J p ( λ r ) d r | r = R = 0 .
T ˜ ( r , θ , t ) = p = l = 0 T p , l exp ( k ρ c λ l 2 t ) J p ( λ l r ) cos ( p θ )
T ( r , θ , 0 ) = T s
T ˜ ( r , θ , 0 ) = 0 .
μ a Φ ( r , θ ) ρ c = p = l = 0 ω ( t ) J p ( λ l r ) cos ( p θ ) .
Ω ( t ) = exp ( k ρ c λ l 2 t ) 0 t exp ( k ρ c λ l 2 t ) ω ( t ) d t .
Ω ( t ) = ρ c k λ l 2 ω [ 1 exp ( k ρ c λ l 2 t ) ] .
μ a ρ c m = Λ m ( β r ) cos ( m θ ) = p = l = 0 ω J p ( λ l r ) cos ( p θ )
Λ m ( β r ) = { a m ( β ) J m ( β r ) if r r i b m ( β ) J m ( β r ) + c m ( β ) Y m ( β r ) if R r r i .
ω m , l = μ a ρ c m = 0 R Λ m ( β r ) J m ( λ l r ) r d r 0 2 π cos ( m θ ) cos ( p θ ) d θ 0 R J p 2 ( λ l r ) r d r 0 2 π cos 2 ( p θ ) d θ .
ω m , l = μ a ρ c { a m ( β ) r i [ β J m 1 ( β r i ) J m ( r i λ l ) λ l J m ( β r i ) J m 1 ( r i λ l ) ] + b m ( β ) r i [ β J m 1 ( β r i ) J m ( r i λ l ) λ l J m ( β r i ) J m 1 ( r i λ l ) ] β R J m 1 ( R β ) J m ( R λ l ) + R λ l J m ( R β ) J m 1 ( R λ l ) + c m ( β ) r i [ β Y m 1 ( β r i ) J m ( r i λ l ) λ l Y m ( β r i ) J m 1 ( r i λ l ) ] β R Y m 1 ( R β ) J m ( R λ l ) + R λ l Y m ( R β ) J m 1 ( R λ l ) } × 1 1 2 R ( β 2 λ l 2 ) { R [ J m 1 ( R λ l ) 2 + J m ( R λ l ) 2 ] 2 m J m 1 ( R λ l ) J m ( R λ l ) λ l }
T ( r , θ , t ) = T s + m = l = 0 ρ c k λ l 2 ω m , l J m ( λ l r ) cos ( m θ ) [ 1 exp ( k ρ c λ l 2 t ) ] .

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