Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

Konovalov, Alexander; Vlasov, Vitaly V.; Lyubimov, V. V.

doi:10.1016/j.ijleo.2013.04.111

Cited by 8 publications

(10 citation statements)

References 26 publications

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“…In our further consideration we will follow in part an approach presented many years ago by Dr. Vladimir Lyubimov 63 . Lyubimov dealt with the photon average trajectory method ‐ an approximate method of DOT and FMT, which solves the inverse problem in real time 63‐66 . It reduces the problem to the inversion of the integral equation with integration over the photon average trajectory.…”

Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%

“…First, to simplify analytical computation assume that t s = 0. Second, make use of our results we earlier presented in Reference 66 where Robin boundary condition (6) is compared with the zero Dirichlet boundary condition. For early arriving photons, the two conditions were found to give almost equal statistical characteristics of photon trajectory distributions, such as banana‐shaped zones, photon average trajectories and root‐mean‐square deviations of photons from them.…”

Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%

“…In view of disagreement between results, critical are the times t d already on the trailing edge of the TPSF. This means that for the Green function G e ( r − r ′ , t − t ′ ) in Equation (14) we can use not the awkward expressions of the Robin boundary condition, 66 but the much simpler expressions of the Dirichlet condition. So, for half‐space {( x, y, z ) : z ≥ 0} we obtain

\begin{matrix} lefttrue \\ G^{e} (r - {boldr}^{'}, t - t^{'}) = {([], 4 italicπD c ((), t - t^{'}))}^{- 3 / 2} \exp [- μ_{a} c (t - t^{'})] \\ \times \{\exp [- \frac{{((), x - x^{'})}^{2} + {((), y - y^{'})}^{2} + {((), z - z^{'})}^{2}}{4 D c (t - t^{'})}] - \exp [- \frac{{((), x - x^{'})}^{2} + {((), y - y^{'})}^{2} + {((), z + z^{'})}^{2}}{4 D c (t - t^{'})}]\}, \end{matrix}

and for half‐plane {( x, y ) : y ≥ 0} we obtain

\begin{matrix} lefttrue \\ G^{e} (r - {boldr}^{'}, t - t^{'}) = {([], 4 italicπD c ((), t - t^{'}))}^{- 1} \exp [- μ_{a} c (t...)] \end{matrix}

…”

Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%

“…We studied feasibility of their reconstruction for sizes 0.5, 0.2, and 0.1 mm. Distances between inclusions were taken to be equal to their diameter in order to create the periodical spatial structures and be able to evaluate the modulation transfer coefficient and therefore the spatial resolution 52,64‐66 . Probing depths were 3, 6, and 9 mm.…”

Section: Numerical Experiments On Fluorescent Image Reconstructionmentioning

confidence: 99%

“…63 Lyubimov dealt with the photon average trajectory method -an approximate method of DOT and FMT, which solves the inverse problem in real time. [63][64][65][66] It reduces the problem to the inversion of the integral equation with integration over the photon average trajectory. Unfortunately, its resolution is far behind the resolution of traditional reconstruction methods based on the inversion of an equation of type (2) with integration over the entire space.…”

Section: Fundamental Equation Of Ep-fmtmentioning

confidence: 99%

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Early‐photon reflectance fluorescence molecular tomography for small animal imaging: Mathematical model and numerical experiment

Konovalov

Vlasov

Uglov

2020

Numer Methods Biomed Eng

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The paper presents an original approach to time‐domain reflectance fluorescence molecular tomography (FMT) of small animals. It is based on the use of early arriving photons and state‐of‐the‐art compressed‐sensing‐like reconstruction algorithms and aims to improve the spatial resolution of fluorescent images. We deduce the fundamental equation that models the imaging operator and derive analytical representations for the sensitivity functions which are responsible for the reconstruction of the fluorophore absorption coefficient. The idea of fluorescence lifetime tomography with our approach is also discussed. We conduct a numerical experiment on 3D reconstruction of box phantoms with spherical fluorescent inclusions of small diameters. For modeling measurement data and constructing the sensitivity matrix we assume a virtual fluorescence tomograph with a scanning fiber probe that illuminates and collects light in reflectance geometry. It provides for large source‐receiver separations which correspond to the macroscopic regime. Two compressed‐sensing‐like reconstruction algorithms are used to solve the inverse problem. These are the algebraic reconstruction technique with total variation regularization and our modification of the fast iterative shrinkage‐thresholding algorithm. Results of our numerical experiment show that our approach is capable of achieving as good spatial resolution as 0.2 mm and even better at depths to 9 mm inclusive.

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Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%

Section: Mathematical Model Of the Ep‐fmt Forward Problemmentioning

confidence: 99%