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Analytical solutions for diffuse fluorescence spectroscopy/imaging in biological tissues. Part II: comparison and
Kalyan Ram Ayyalasomayajula1, Phaneendra K Yalavarthy
1Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore, India.
Summary
Analytical solutions for diffuse fluorescence spectroscopy/imaging closely match numerical models. Extrapolated boundary conditions (EBCs) improve accuracy for mean time of flight calculations, enabling bulk optical property determination.
Area of Science:
- Biomedical optics
- Diffusion theory
- Fluorescence spectroscopy and imaging
Background:
- Coupled diffusion equations are fundamental in diffuse fluorescence spectroscopy/imaging.
- Finite element method (FEM) is a standard numerical approach for solving these equations.
- Analytical solutions offer a potentially faster alternative for regular geometries.
Purpose of the Study:
- Compare analytical solutions with FEM numerical models for diffuse fluorescence spectroscopy/imaging.
- Evaluate the impact of boundary conditions (zero vs. extrapolated) on analytical solution accuracy.
- Assess the capability of analytical solutions to determine bulk optical properties using a realistic breast model.
Main Methods:
- Developed and applied analytical solutions for coupled diffusion equations in regular geometries.
- Utilized the finite element method for established numerical modeling.
- Performed comparative analysis between analytical solutions (with zero and extrapolated boundary conditions) and numerical solutions.
- Conducted a numerical experiment with a realistic breast model to extract bulk optical properties.
Main Results:
- Analytical solutions demonstrated close agreement with FEM numerical solutions.
- Analytical solutions employing extrapolated boundary conditions (EBCs) yielded more accurate mean time of flight data compared to those using zero boundary conditions.
- The study successfully determined bulk optical properties using analytical solutions within a realistic breast model simulation.
Conclusions:
- Analytical solutions are a viable and accurate alternative to numerical methods for diffuse fluorescence spectroscopy/imaging in regular geometries.
- Extrapolated boundary conditions significantly enhance the accuracy of analytical solutions, particularly for time-resolved measurements.
- Analytical solutions hold promise for non-invasive determination of tissue optical properties, aiding in diagnostic applications.
