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

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.

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

Nanotechnology using gold nanoshells or nanorods is a newly developed hyperthermia approach and has been tested in the past several years in cancer treatment.1–2 Gold nanorods have a diameter of ∼10 nm and an aspect ratio of approximately four. By varying the geometric ratio, the nanostructures can be tuned to have strong absorption and scattering to a specific laser wavelength. Designing an optimal treatment protocol of laser photothermal therapy requires understanding of gold nanorod deposition inside the tumor after injection, its resulted specific absorption rate (SAR) distribution, and the ultimate temperature field in the tumor during the treatment. Recent microCT studies by our group have suggested that the gold nanorod solution injected into PC3 prostatic tumors results in an almost uniform distribution of the gold nanorods in the tumors.3 The Monte Carlo method has been used in the past to determine the heating pattern (SAR) of laser-tissue thermal interaction.4 However, the accuracy of the theoretical simulation of the temperature fields in tumors relies on precise measurements of the optical properties of the tumors with nanorods presence.

Visualization and Quantification of Gold Nanorods Distribution in Prostatic Tumors Using MicroCT Imaging

One uncertainty in use of gold nanorods for laser photothermal therapy is the non-uniform spreading of gold nanorods in tissue after either systemic delivery or intratumoral injections. High concentration of gold nanorods in certain areas influences the resulted optical absorption of the laser and thermal damage to tumors. This also provides challenges in designing optimal heating protocols via modeling thermal transport in laser photothermal therapy. For successful cancer treatment, the tissue should be heated with minimum thermal dosage to induce tumor cell damage, while minimizing overheating in the surrounding healthy tissues. Thus, one of the main challenges for reliable cancer therapy is to precisely control loading and distribution of gold nanorods in the tumour tissue. The critical mass transport processes are the distribution of gold nanorods after injection to the tumor and the redistribution of gold nanorods during laser treatment. Since tumors are opaque, nanostructure distribution in tissue is often studied either by theoretical modeling approaches1, or via dye enhanced imaging on superficial layers of tumors.2 It is important to find a technique which can directly visualize and analyze three-dimensional nanostructure distribution of tumors. Three-dimensional reconstructions of tumors with the ability to trace gold nanorod spreading have the potential for precise theoretical simulation of temperature fields. Previous studies showed that computer tomography (CT) scan is a promising technique to be utilized to characterize the distribution of intratumorally injected magnetic nanoparticles in tumors 3.