Radiative transfer and optical imaging in biological media by low-order transport approximations: the simplified spherical harmonics (SP N ) approach

Time-domain geometrical localization of point-like fluorescence inclusions in turbid media with early photon arrival times

“…As such, analytical solutions are very useful for validation purposes, but are of limited use for imaging complex objects such as mice. Some approaches rely on approximations and Green's functions to compute such predictions [19,20], while others use numerical techniques for partial differential equations to directly solve the forward model [16,[21][22][23]. Algorithms to recover full tomographic maps closer in spirit to the present work are those that exploit early gating of time-domain signals [24][25][26][27][28][29][30][31].…”

Analytical solution of the simplified spherical harmonics equations in spherical turbid media

“…To overcome these shortcomings, the simplified spherical harmonics (SP N ) model has been proposed which is both precise under the aforementioned situations and much less computationally demanding as regards numerical solutions in comparison with the RTE and P N [16]. For this reason, the SP N approximation has proved to be a useful model in recent years in biomedical optics, notably in DOT [15,7,5]. The SP N equations provide a higher order approximation to the RTE than the DE.…”

“…A final note, the simplest way to derive the SP N equations (so-called the formal or heuristic derivation) is to consider a planar symmetry medium [7]. One may then question the validity of the SP N model for curved geometries such as a sphere considered here.…”