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

Abstract

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 (μ(a)) and scattering (μ(s)) 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 μ(a), while both μ(a) and μ(s) shift the distribution of the energy deposition in the tumor. Three sets of μ(a) and μ(s) 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.

Development of a computational simulation tool to design a protocol for treating prostate tumours using transurethral laser photothermal therapy

“…We equipped the laser catheter with a water cooling system to protect the urethral boundaries from overheating, see Figure 1. We also injected the prostate tumour with 0.1 mL of the 250 OD (optical density) gold nanorod solution used in our previous experiments [21,22,25].…”

“…Since the incident laser beam is a rectangular area of A ¼ 0.5 cm 2 , the total incident laser power can then be calculated as I 0 ¼ 3.5 W. The anisotropic factor g is equal to 0.9 [33]. In our previous study we explained how the optical properties were extracted via comparing the theoretically predicted temperature profiles in the tumour to those measured in the in vivo experiments [25]. Table 1 gives a summary of the radiation properties of a PC3 tumour injected with 0.1 mL of 250 OD nanorod solution, and the prostate tissue without nanorods [25].…”

“…We proposed inserting a laser catheter into the prostatic urethra and a laser at 808 nm wavelength incident on the prostatic urethral surface, penetrating into the deep tissue with a targeted tumour embedded in the prostate. The tumour was injected with 0.1 mL of a gold nanorod solution, as in our previous studies [21,25]. The previously extracted optical properties of the prostatic tissue with or without gold nanorods were then used in a Monte Carlo simulation for predicting laser photon propagation in a multi-region tissue domain [25].…”

“…The tumour was injected with 0.1 mL of a gold nanorod solution, as in our previous studies [21,25]. The previously extracted optical properties of the prostatic tissue with or without gold nanorods were then used in a Monte Carlo simulation for predicting laser photon propagation in a multi-region tissue domain [25]. Mathematical formulation, finite element modelling of the heat transfer process, and possible thermal responses to heating were simulated, leading to thermal damage assessments and treatment protocol designs.…”

“…That was also the first time showing the relatively uniform deposition of nanorods in tumours after their injection. Based on the measured temperature fields of the tumours, the radiation properties of PC3 tumours containing the gold nanorods were extracted for future theoretical simulations [25]. Unfortunately, the temperature elevations measured in the tumours implanted on the skin surface of the mice may be quite different from when the tumour is located inside the prostate, leading to different heating protocols being required to achieve the same thermal dosage.…”