Dual coupled radiative transfer equation and diffusion approximation for the solution of the forward problem in fluorescence molecular imaging

Dimitris Gorpas; Stefan Andersson-Engels

doi:10.1117/12.907811

13 February 2012 Dual coupled radiative transfer equation and diffusion approximation for the solution of the forward problem in fluorescence molecular imaging

Dimitris Gorpas, Stefan Andersson-Engels

Author Affiliations +

Proceedings Volume 8225, Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues X; 822522 (2012) https://doi.org/10.1117/12.907811
Event: SPIE BiOS, 2012, San Francisco, California, United States

Abstract

The solution of the forward problem in fluorescence molecular imaging is among the most important premises for the successful confrontation of the inverse reconstruction problem. To date, the most typical approach has been the application of the diffusion approximation as the forward model. This model is basically a first order angular approximation for the radiative transfer equation, and thus it presents certain limitations. The scope of this manuscript is to present the dual coupled radiative transfer equation and diffusion approximation model for the solution of the forward problem in fluorescence molecular imaging. The integro-differential equations of its weak formalism were solved via the finite elements method. Algorithmic blocks with cubature rules and analytical solutions of the multiple integrals have been constructed for the solution. Furthermore, specialized mapping matrices have been developed to assembly the finite elements matrix. As a radiative transfer equation based model, the integration over the angular discretization was implemented analytically, while quadrature rules were applied whenever required. Finally, this model was evaluated on numerous virtual phantoms and its relative accuracy, with respect to the radiative transfer equation, was over 95%, when the widely applied diffusion approximation presented almost 85% corresponding relative accuracy for the fluorescence emission.

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Dimitris Gorpas and Stefan Andersson-Engels "Dual coupled radiative transfer equation and diffusion approximation for the solution of the forward problem in fluorescence molecular imaging", Proc. SPIE 8225, Imaging, Manipulation, and Analysis of Biomolecules, Cells, and Tissues X, 822522 (13 February 2012); https://doi.org/10.1117/12.907811

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