Application of a wavelet-Galerkin method to the forward problem resolution in fluorescence diffuse optical tomography

Area of Science:

• Biomedical Optics
• Computational Imaging
• Mathematical Modeling

Background:

• Fluorescence diffuse optical tomography (FDOT) is crucial for investigating molecular events in therapeutic development.
• Solving the associated Partial Differential Equations (PDEs) with the standard polynomial Finite Element Method (FEM) is computationally intensive.
• There is a need for faster numerical methods to improve the efficiency of FDOT analysis.

Purpose of the Study:

• To develop and present an alternative numerical model for FDOT.
• To accelerate the computation time required for solving the diffusion equation in FDOT.
• To compare the performance of the proposed model against the standard FEM.

Main Methods:

• Formulating the tomography problem as a PDE-based parameter estimation.
• Developing a numerical model using an orthonormal basis of compactly supported wavelets.
• Discretizing PDEs using derivative wavelet product integrals within a fictitious domain approach.

Main Results:

• The proposed wavelet-based model allows for efficient computation of discretized matrices.
• The method enables the inclusion of the studied domain within a regular fictitious domain.
• Validation studies on synthetic data demonstrated the model's feasibility and provided a comparison with standard FEM.

Conclusions:

• The wavelet-based numerical model offers a promising, faster alternative to FEM for FDOT.
• This acceleration can significantly benefit molecular investigations in new therapeutic developments.
• Further validation and application of this method are warranted for clinical and research settings.