Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method.

Area of Science:

• Biomedical Optics
• Computational Physics
• Medical Imaging

Background:

• Accurate photon transport modeling is crucial for optical tomography.
• The radiative transfer equation (RTE) is the most accurate forward model but faces numerical challenges.
• Existing methods struggle with robust and efficient high-dimensional implementations.

Purpose of the Study:

• To develop a robust and efficient numerical method for solving the RTE in high dimensions.
• To improve the accuracy of photon transport prediction for biomedical optical tomography.
• To validate the proposed method against established simulation techniques.

Main Methods:

• Combined the discrete ordinate method (DOM) with a streamline diffusion modified continuous Galerkin method.
• Employed a phase function normalization technique to reduce DOM instability.
• Compared numerical solutions with Monte Carlo (MC) simulations using various sources and optical properties.

Main Results:

• The proposed method accurately solves the RTE for photon transport.
• Photon densities computed by the RTE method showed good agreement with MC simulations (within ~5% in deeper regions).
• The method demonstrated robustness across different source types and optical properties.

Conclusions:

• The finite element method-RTE implementation provides an accurate forward model for optical tomography.
• This method overcomes previous numerical limitations in solving the RTE.
• The findings support the use of this approach for enhanced accuracy in biomedical imaging.