Diffuse optical tomography using the one-way radiative transfer equation

González-Rodríguez, Pedro; Kim, Arnold D.

doi:10.1364/boe.6.002006

Cited by 8 publications

(8 citation statements)

References 13 publications

(7 reference statements)

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“…All that is required is a "time-stepping" method that advances the solution from z ¼0 to z ¼ z 0 . One such method is used in [20]. In contrast, solving the full RTE requires several iterations which depends on both the optical thickness and the value of the single scattering albedo for a given problem.…”

Section: Methodsmentioning

confidence: 99%

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One-way radiative transfer

González-Rodríguez

Ilan

Kim

2016

Journal of Quantitative Spectroscopy and Radiative Transfer

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a b s t r a c tWe introduce the one-way radiative transfer equation (RTE) for modeling the transmission of a light beam incident normally on a slab composed of a uniform forward-peaked scattering medium. Unlike the RTE, which is formulated as a boundary value problem, the one-way RTE is formulated as an initial value problem. Consequently, the one-way RTE is much easier to solve. We discuss the relation of the one-way RTE to the Fokker-Planck, small-angle, and Fermi pencil beam approximations. Then, we validate the one-way RTE through systematic comparisons with RTE simulations for both the Henyey-Greenstein and screened Rutherford scattering phase functions over a broad range of albedo, anisotropy factor, optical thickness, and refractive index values. We find that the one-way RTE gives very good approximations for a broad range of optical property values for thin to moderately thick media that have moderately to sharply forward-peaked scattering. Specifically, we show that the error made by the one-way RTE decreases monotonically as the anisotropic factor increases and as the albedo increases. On the other hand, the error increases monotonically as the optical thickness increases and the refractive index mismatch at the boundary increases.

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Section: Methodsmentioning

confidence: 99%

“…In this way, the one-way RTE addresses the limitations of the aforementioned approximations. In fact, this approximation has been recently applied to study diffuse optical tomography in biological tissues [20] and shown to be useful. Additionally, the oneway RTE has been derived rigorously using the theory of waves in random media [21].…”

Section: Introductionmentioning

confidence: 99%

One-way radiative transfer

González-Rodríguez

Ilan

Kim

2016

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…Therefore, overall RTE calculations are desirable. As for frequency-domain RTE, several solvers of the inverse problem have been proposed [11,12]. However, image reconstructions based on time-domain RTE are still immature.…”

Section: Introductionmentioning

confidence: 99%

Deep Learning of Diffuse Optical Tomography based on Time-Domain Radiative Transfer Equation

Takamizu¹,

Umemura²,

Yajima³

et al. 2020

Preprint

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Near infrared diffuse optical tomography (DOT) provides an imaging modality for the oxygenation of tissue. In this paper, we propose a novel machine learning algorithm based on time-domain radiative transfer equation. We use temporal profiles of absorption measure for a two-dimensional model of target tissue, which are calculated by solving time-domain radiative transfer equation. Applying a longshort-term memory (LSTM) deep learning method, we find that we can specify positions of cancer cells with high accuracy rates. We demonstrate that the present algorithm can also predict multiple or extended cancer cells.

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“…Although RTE has some analytical solutions [8][9][10] these just hold for simple geometries and cannot be applied to more complex environments, such as an human head or breast models, without making strong assumptions. Apart from classical Monte-Carlo simulations [11,12], new numerical methods have been proposed, some of which are the one-way RTE [13] or hybrid RTE [14]; nevertheless, they are still highly time-consuming for real-time applications.…”

Section: Introductionmentioning

confidence: 99%

Improving Localization of Deep Inclusions in Time-Resolved Diffuse Optical Tomography

et al. 2019

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Time-resolved diffuse optical tomography is a technique used to recover the optical properties of an unknown diffusive medium by solving an ill-posed inverse problem. In time-domain, reconstructions based on datatypes are used for their computational efficiency. In practice, most used datatypes are temporal windows and Fourier transform. Nevertheless, neither theoretical nor numerical studies assessing different datatypes have been clearly expressed. In this paper, we propose an overview and a new process to compute efficiently a long set of temporal windows in order to perform diffuse optical tomography. We did a theoretical comparison of these large set of temporal windows. We also did simulations in a reflectance geometry with a spherical inclusion at different depths. The results are presented in terms of inclusion localization and its absorption coefficient recovery. We show that (1) the new windows computed with the developed method improve inclusion localization for inclusions at deep layers, (2) inclusion absorption quantification is improved at all depths and, (3) in some cases these windows can be equivalent to frequency based reconstruction at GHz order.

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Diffuse optical tomography using the one-way radiative transfer equation

Cited by 8 publications

References 13 publications

One-way radiative transfer

One-way radiative transfer

Deep Learning of Diffuse Optical Tomography based on Time-Domain Radiative Transfer Equation

Improving Localization of Deep Inclusions in Time-Resolved Diffuse Optical Tomography

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