New nonlocal forward model for diffuse optical tomography.

Area of Science:

• Biomedical Optics
• Computational Imaging
• Medical Physics

Background:

• Diffuse optical tomography (DOT) uses a diffusion equation (DE) forward model, typically solved with the finite element method (FEM).
• Accurate light propagation modeling is crucial for DOT image reconstruction.
• Existing methods face computational challenges in speed and scalability.

Purpose of the Study:

• Introduce a novel nonlocal diffusion equation (NDE) as a forward model for DOT.
• Develop and evaluate an efficient graph-based numerical method (GNM) for NDE discretization.
• Compare the numerical accuracy and image reconstruction performance of NDE against the conventional DE.

Main Methods:

• Implemented a nonlocal diffusion equation (NDE) forward model.
• Utilized a graph-based numerical method (GNM) for NDE discretization.
• Conducted experiments on a homogeneous slab to compare NDE and DE accuracy against analytical solutions.
• Evaluated inverse problem performance (image reconstruction) using both NDE and DE.

Main Results:

• The NDE forward model demonstrated quantitative accuracy comparable to the DE.
• The GNM for NDE achieved up to 64% faster computation times compared to FEM for DE.
• The GNM implementation is adaptable to different dimensional geometries.

Conclusions:

• The proposed NDE with GNM offers a computationally efficient and accurate alternative for DOT forward modeling.
• This approach has potential applications in other diffusion-equation-based imaging techniques like diffuse correlation spectroscopy.
• NDE provides a promising direction for accelerating DOT image reconstruction.