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Finite element approximation of the Fokker-Planck equation for diffuse optical tomography |
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| Authors: | O Lehtikangas V Kolehmainen SR Arridge |
| Institution: | a Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland b Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK c Sunnybrook Research Institute, Sunnybrook Health Sciences Centre, 2075 Bayview Ave., Toronto, ON, Canada M4N 3M5 d Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142, New Zealand |
| Abstract: | In diffuse optical tomography, light transport theory is used to describe photon propagation inside turbid medium. A commonly used simplification for the radiative transport equation is the diffusion approximation due to computational feasibility. However, it is known that the diffusion approximation is not valid close to the sources and boundary and in low-scattering regions. Fokker-Planck equation describes light propagation when scattering is forward-peaked. In this article a numerical solution of the Fokker-Planck equation using finite element method is developed. Approach is validated against Monte Carlo simulation and compared with the diffusion approximation. The results show that the Fokker-Planck equation gives equal or better results than the diffusion approximation on the boundary of a homogeneous medium and in turbid medium containing a low-scattering region when scattering is forward-peaked. |
| Keywords: | Diffuse optical tomography Finite element method Fokker-Planck equation Inverse problems |
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