A finite element approach for modeling photon transport in tissue

Area of Science:

• Medical Physics
• Biophotonics
• Computational Modeling

Background:

• Optical radiation is crucial for medical diagnosis and treatment.
• Accurate models of radiation propagation in tissue are essential for interpreting procedures.
• The diffusion approximation to the radiative transfer equation is widely used for scattering-dominated tissues.

Purpose of the Study:

• To introduce a finite element method (FEM) for modeling photon transport in tissue.
• To compute photon density within an object and photon flux at its boundary.
• To validate the FEM model against analytical solutions and Monte Carlo simulations.

Main Methods:

• Developed a finite element method (FEM) based on the diffusion approximation of the radiative transfer equation.
• Applied the FEM to a 2D circle with homogeneous scattering and absorption properties, simulating a line source.
• Analyzed the convergence of FEM results with increasing mesh resolution.

Main Results:

• The FEM accurately calculates photon density and boundary flux over time.
• FEM results demonstrate convergence to the analytical Green's function solution.
• The model shows high agreement with results from the Monte Carlo method.
• FEM offers significant speed advantages over Monte Carlo methods.

Conclusions:

• The finite element method provides a fast, flexible, and accurate computational tool for modeling photon transport in biological tissues.
• This FEM approach is suitable for applications in near-infrared spectroscopy and imaging.
• The method enables calculation of both internal photon density and boundary flux, offering comprehensive insights.