Analytical calculation of the mean time spent by photons inside an absorptive inclusion embedded in a highly scattering medium

Chernomordik, Victor; Hattery, David; Gannot, Israel; Zaccanti, Giovanni; Gandjbakhche, Amir

doi:10.1117/1.1481900

Cited by 10 publications

(6 citation statements)

References 14 publications

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“…The time steps may be discrete or continuous (Weiss et al 1998). Random walk theory is particularly suited to modelling time-domain measurements (Chernomordik et al 2000) and has been used, for example, to determine the time spent by photons in a scattering inclusion (Chernomordik et al 2002a) and to quantify the optical properties of a breast tumour (Chernomordik et al 2002b). Recently, an extension to the technique has been developed for modelling media with anisotropic optical properties (see section 3.3.6), maintaining the cubic lattice but allowing the transition properties along different axes to differ (Dagdug et al 2003).…”

Section: Statistical Modelling Techniquesmentioning

confidence: 99%

Recent advances in diffuse optical imaging

2005

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We review the current state-of-the-art of diffuse optical imaging, which is an emerging technique for functional imaging of biological tissue. It involves generating images using measurements of visible or near-infrared light scattered across large (greater than several centimetres) thicknesses of tissue. We discuss recent advances in experimental methods and instrumentation, and examine new theoretical techniques applied to modelling and image reconstruction. We review recent work on in vivo applications including imaging the breast and brain, and examine future challenges.

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Section: Statistical Modelling Techniquesmentioning

confidence: 99%

Recent advances in diffuse optical imaging

2005

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“…The exponential correction factor for nonlocalized absorptive inclusions was recently verified by a set of Monte Carlo simulations and phantom measurements of the mean time spent by photons inside an inclusion (⌬t). 39 Increased scattering inside an inclusion results in an additional time delay, 16,17…”

Section: ͑4͒mentioning

confidence: 99%

Quantification of optical properties of a breast tumor using random walk theory

Chernomordik¹,

Hattery

Grosenick

et al. 2002

J. Biomed. Opt.

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For the first time we use a random walk methodology based on time-dependent contrast functions to quantify the optical properties of breast tumors (invasive ductal carcinoma) of two patients. Previously this theoretical approach was successfully applied for analysis of embedded objects in several phantoms. Data analysis was performed on distributions of times of flight for photons transmitted through the breast which were recorded in vivo using a time-domain scanning mammograph at 670 and 785 nm. The size of the tumors, their optical properties, and those of the surrounding tissue were reconstructed at both wavelengths. The tumors showed increased absorption and scattering. From the absorption coefficients at both wavelengths blood oxygen saturation was estimated for the tumors and the surrounding tissue.

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“…Despite that human tissues are turbid media, transport of near-infrared photons in them are reasonably well described by the diffusion equation. Being motivated by the studies on absorption of photons diffusing in turbid media, [1][2][3][4][5][6][7][8][9][10][11] Krapivsky and Redner 12 recently considered trapping of diffusing particles by dilute static absorbers randomly and uniformly distributed in a spherical cavity. They assumed that a particle touching the cavity wall exits the cavity and never comes back, and they modelled this by considering the wall as a perfectly absorbing boundary for diffusing particles.…”

Section: Introductionmentioning

confidence: 99%

Trapping of diffusing particles by small absorbers localized in a spherical region

Berezhkovskii

Dagdug

Bezrukov

2019

The Journal of Chemical Physics

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We study trapping of particles diffusing in a spherical cavity with an absorbing wall containing small static spherical absorbers localized in a spherical region in the center of the cavity. The focus is on the competition between the absorbers and the cavity wall for diffusing particles. Assuming that the absorbers and, initially, the particles are uniformly distributed in the central region, we derive an expression for the particle trapping probability by the cavity wall. The expression gives this probability as a function of two dimensionless parameters: the transparency parameter, characterizing the efficiency of the particle trapping by the absorbers, and the ratio of the absorber-containing region radius to that of the cavity. This work is a generalization of a recent study by Krapivsky and Redner [J. Chem. Phys. 147, 214903 (2017)] who considered the case where the absorber-containing region occupies the entire cavity. The expression for the particle trapping probability is derived in the framework of a steady-state approach which, in our opinion, is much simpler than the time-dependent approach used in the above-mentioned study.

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Analytical calculation of the mean time spent by photons inside an absorptive inclusion embedded in a highly scattering medium

Cited by 10 publications

References 14 publications

Recent advances in diffuse optical imaging

Recent advances in diffuse optical imaging

Quantification of optical properties of a breast tumor using random walk theory

Trapping of diffusing particles by small absorbers localized in a spherical region

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