Delta-P1 model implementation for numerical simulation of photothermal cancer therapy in three-dimensional heterogeneous tissues

Photothermal therapy (PTT) stands as a promising avenue for cancer treatment. Metallic nanoparticles (NPs) absorb near-infrared light, inducing localized heating for tumor cell apoptosis. Predicting spatial temperature information in preclinical models is crucial due to cell death sensitivity to temperature changes. Heat transfer models, rely on the radiative transport equation (RTE), where its approximation is essential for this purpose. Existing models for the radiative transport equation, such as the Beer-Lambert law, the diffusion approximation, the discrete ordinates method, and Monte Carlo (MC) simulations, are widely used in the context of PTT. However, each of them has limitations. This study focuses on the δP1 model, wich is an extension of the diffusion approximation. Unlike standard diffusion approximation (SDA), the δP1 model treats forward and scattered light independently, preserving accuracy over a wider range of optical properties, including media with plasmonic NPs. The δP1 model equations are discretized and solved by the Finite Element Method (FEM) . Its numerical results for fluence rate in a heterogeneous geometry with nanoshells is compared to MC simulations and the standard diffusion approximation. This study validates and applies the model to the simulation of light transport in photothermal therapy in general two-dimensional geometries. Results demonstrate the δP1 shows a significant improvement over the SDA in heat transfer simulations in heterogeneous tissues geometries. This underscores its potential as a valuable tool for optimizing photothermal therapy preclinical models.