Méthodes numériques

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Photon Migration in Tissues

Analytical methods for solving the RTE

The method of rotated reference frames (MRRF) has been proposed in 2004 by Markel. The method was further developed here, here, and here. MRRF is especially convenient for the linearized inverse problem formulation in the slab geometry. This approach to RTE-based image reconstruction was recently implemented with experimental data. Shown below are tomographic reconstructed slices (drawn at different depths, as indicated) of a thin lemon slice suspended in a 1cm-thick optically opaque Intralipid solution. Reconstructions utilize MRRF as the forward model and display the absorptive contrast of the lemon.

Monte-Carlo Methods

We are developing Monte-Carlo methods for the vector radiative transport equation (vRTE), which described propagation of polarized light in multiply-scattering media. While solving the vRTE by Monte-Carlo methods is straightforward, computation of the sensitivity kernels, which are used in the inverse problem of OT, is a much more challenging task. We are using the reciprocity of vRTE Green’s function and the translational invariance of the slab to derive an efficient Monte-Carlo algorithm for computing polarization-gated sensitivity kernels. The images below illustrate vRTE sensitivity kernels for normal (left) and off-normal (right) incidence and detection. In each plot, left column corresponds to polarization-insensitive illumination and detection and the right column corresponds to right-circular incident polarization and detection of the V-component of the Stokes vector on exit. Different rows correspond to different source-detector separations and all distances are shown in units of transport mean free path.