Optimization in interstitial plasmonic photothermal therapy for treatment planning

Gold nanorods have the potential to enhance the treatment efficacy of interstitial photothermal therapy. In order to enhance both the potential efficiency and the safety of such procedures, treatment planning on laser power density, nanoparticle concentration, and exposure time has turned out to be useful in predicting the thermal damage and optimizing treatment outcome. To the best of our knowledge, there is no previous report on the optimization of interstitial plasmonic photothermal therapy (PPTT) for all these free parameters simultaneously. The authors propose to develop a suitable optimization algorithm for interstitial PPTT to optimize these parameters and achieve complete damage to spherical tumors of different sizes with a damage margin width of 1 mm from the tumor boundary embedded deep inside a normal tissue model.

In a numerical tissue model, the standard Pennes bioheat equation and the first-order thermal-chemical rate equation were used to model the temperature and thermal damage distributions, respectively, in spherical tumors that were embedded deep inside a normal tissue and incubated with nanorods. The concentration of nanorods in the normal tissue was set to be about one quarter of that in the tumor. Thermal damage due to varying concentrations of nanorods, laser power density, and exposure time was computed for a series of tumor radii including 2, 3, 4, and 5 mm. An optimization algorithm was developed to determine the optimum laser power density, nanorod concentration, and exposure time for the treatment of such spherical tumors. In this algorithm, a novel objective function was created to enable the optimization of multiple key parameters, including nanoparticle concentration, power density, and exposure time, simultaneously to achieve not only the complete thermal damage to the entire tumor but also the collateral damage to the surrounding normal tissue with a margin width of 1 mm from the tumor boundary. Different weights were assigned sequentially to each free parameter according to the relative importance of the parameters. A thermal damage value of one calculated by Arrhenius damage law, which is more accurate than a threshold temperature typically used for characterizing thermal damage, was used to indicate effective treatment.

The simulation results show that there is a steady increase in the overall temperature as the nanorod concentration increases; however, the uniformity of the temperature distribution changes significantly which in turn affects the thermal damage. Optimization results show that any slight decrease in one free parameter can be compensated by the increase in other free parameters, in which the complete thermal damage of the tumor and the collateral damage to normal tissue with a margin width of 1 mm can be always achieved. This implies the importance of optimization in interstitial PPTT.

The proposed method can optimize laser power density, nanoparticle concentration, and exposure time simultaneously with different weights in interstitial PPTT planning for deep seated tumors. It provides flexibility for a clinician to make appropriate planning for individual patients according to their special needs.