Numerical simulation of nanoparticles assisted laser photothermal therapy: a comparison of the P1-approximation and discrete ordinate methods

Photothermal therapy (PTT) with combined use of laser radiation and photon absorber nanoparticles is a promising technique to treat cancer. Treatment planning and devising appropriate protocols for cancer photo thermal therapy require the computational simulation of coupled physical phenomena, such as radiation, conduction, and blood perfusion. The P1-approximation is a numerical method to solve radiation heat transfer which features the advantage of being computationally fast and, therefore, desirable for PTT simulations. However, the method is known to become inaccurate under certain conditions. In this study, the P1-approximation and the accurate discrete ordinate method were applied to solve a set of test problems idealized to portray conditions encountered in PTT. The test problems were one-dimensional, and the radiation scattering was assumed as isotropic. Tissues composed by layers with different properties were considered, including cases in which gold nanoparticles were embedded in the tissue to increase photon absorption. For the problems considered here, the P1-approximation and discrete ordinate method results presented quite good agreement for the time-dependent temperature distribution, which is the quantity of interest in PTT.