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Research Papers

Computational Simulation of Temperature Elevations in Tumors Using Monte Carlo Method and Comparison to Experimental Measurements in Laser Photothermal Therapy

[+] Author and Article Information
Liang Zhu

e-mail: zliang@umbc.edu
Department of Mechanical Engineering,
University of Maryland Baltimore County,
1000 Hilltop Circle,
Baltimore, MD 21250

1Corresponding author.

Contributed by the Bioengineering Division of ASME for publication in the Journal of Biomechanical Engineering. Manuscript received May 31, 2013; final manuscript received August 27, 2013; accepted manuscript posted September 12, 2013; published online October 10, 2013. Assoc. Editor: Ram Devireddy.

J Biomech Eng 135(12), 121007 (Oct 10, 2013) (11 pages) Paper No: BIO-13-1251; doi: 10.1115/1.4025388 History: Received May 31, 2013; Revised August 27, 2013; Accepted September 12, 2013

Accurate simulation of temperature distribution in tumors induced by gold nanorods during laser photothermal therapy relies on precise measurements of thermal, optical, and physiological properties of the tumor with or without nanorods present. In this study, a computational Monte Carlo simulation algorithm is developed to simulate photon propagation in a spherical tumor to calculate laser energy absorption in the tumor and examine the effects of the absorption (μa) and scattering (μs) coefficients of tumors on the generated heating pattern in the tumor. The laser-generated energy deposition distribution is then incorporated into a 3D finite-element model of prostatic tumors embedded in a mouse body to simulate temperature elevations during laser photothermal therapy using gold nanorods. The simulated temperature elevations are compared with measured temperatures in PC3 prostatic tumors in our previous in vivo experimental studies to extract the optical properties of PC3 tumors containing different concentrations of gold nanorods. It has been shown that the total laser energy deposited in the tumor is dominated by μa, while both μa and μs shift the distribution of the energy deposition in the tumor. Three sets of μa and μs are extracted, representing the corresponding optical properties of PC3 tumors containing different concentrations of nanorods to laser irradiance at 808 nm wavelength. With the injection of 0.1 cc of a 250 optical density (OD) nanorod solution, the total laser energy absorption rate is increased by 30% from the case of injecting 0.1 cc of a 50 OD nanorod solution, and by 125% from the control case without nanorod injection. Based on the simulated temperature elevations in the tumor, it is likely that after heating for 15 min, permanent thermal damage occurs in the tumor injected with the 250 OD nanorod solution, while thermal damage to the control tumor and the one injected with the 50 OD nanorod solution may be incomplete.

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Figures

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Fig. 1

Possible path trajectories for incident photons on the tumor top surface

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Fig. 3

The generated mouse model and the two embedded tumors. The thermocouple paths are illustrated in the spherical tumor as solid and dash lines.

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Fig. 2

The left panel shows the subregions of the top surface of a spherical tumor irradiated by a laser spot of 7 mm in diameter. The right panel illustrates individual grid elements which are 0.2 × 0.2 × 0.2 mm3 in volume in the tumor region.

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Fig. 4

The effect of the absorption coefficient on the SAR distribution in the spherical tumor while the scattering coefficient μs is kept unchanged as 3 cm−1

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Fig. 5

The effect of the scattering coefficient on the SAR distribution in the spherical tumor while the absorption coefficient μa is kept unchanged as 1.5 cm−1

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Fig. 6

The obtained objective function values for various combinations of the absorption and scattering coefficients in the 250 OD injection case. The objective function is the smallest when μa = 1.1 cm−1 and μs = 7 cm−1.

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Fig. 7

Experimental (symbols) and theoretical (lines) temperature distribution profiles in the tumors during laser photothermal therapy in the 250 OD injection case. Temperature mappings are along two tumor paths shown on the right bottom of the figure.

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Fig. 8

Panel (a) gives the SAR contour map along the centerline in the mouse model, including the mouse body and the tumor. An enlarged SAR distribution in the tumor in the 250 OD injection case is shown in panel (b). The top view of the SAR distribution in the 3D structure of the mouse model is illustrated in panel (c).

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Fig. 9

The temperature contours inside the tumor based on the obtained optical properties of the tumor. (a) No nanorod injection, (b) the tumor is injected with 0.1 cc of the 50 OD nanorod solution, and (c) the tumor is injected with 0.1 cc of the 250 OD nanorod solution.

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