Hybrid model of light propagation in random media based on the time-dependent radiative transfer and diffusion equations

Fujii, Hiroyuki; Okawa, Shinpei; Yamada, Yukio; Hoshi, Yoko

doi:10.1016/j.jqsrt.2014.05.026

Cited by 36 publications

(32 citation statements)

References 27 publications

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“…4(a). It has been confirmed that such a comparison test is possible in our previous study [8,9]. Here, we consider a homogeneous cubic medium with a side of 2.88 cm, where a source is located at the center of the medium, (x s , y s , z s ) =(1.44 cm, 1.44 cm, 1.44 cm) with ρ = 0.56 cm for the detector position.…”

Section: Fluence Ratementioning

confidence: 71%

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

et al. 2016

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Numerical calculation of photon migration in biological tissue using the radiative transfer equation (RTE) has attracted great interests in biomedical optics and imaging. Because biological tissue is a highly forward-peaked scattering medium, renormalization of the phase function in numerical calculation of the RTE is crucial. This paper proposes a simple approach of renormalizing the phase function by the double exponential formula, which was heuristically modified from the original one. Firstly, the validity of the proposed approach was tested by comparing numerical results for an average cosine of the polar scattering angle calculated by the proposed approach with those by the conventional approach in highly forward-peaked scattering. The results show that calculation of the average cosine converged faster using the proposed approach than using the conventional one as a total number of discrete angular directions increases. Next, the accuracy of the numerical solutions of the RTE using the proposed approach was examined by comparing the numerical solutions with the analytical solutions of the RTE in a homogeneous medium with highly forward-peaked scattering. It was found that the proposed approach reduced the errors of the numerical solutions from those using the conventional one especially at a small value of the total number of the directions. This result suggests that the proposed approach has a possibility to

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Section: Fluence Ratementioning

confidence: 71%

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

et al. 2016

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“…Thus, the time dependence of the RTE was ignored. The solution of the RTE can be obtained by the finite difference method or FEM [5][6][7]. The MC simulation statistically approximates the solution of the RTE by tracking the positions and energies of the randomly moving photon packets [31].…”

Section: Light Propagation In Biological Mediummentioning

confidence: 99%

“…By employing the light propagation model described by the radiative transfer equation (RTE) or the photon diffusion equation (PDE) [4][5][6][7], the PA image of the light absorption coefficient can be reconstructed quantitatively. This technique is referred to as quantitative PA tomography (QPAT) [8].…”

Section: Introductionmentioning

confidence: 99%

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

Okawa

Hirasawa

Kubota

et al. 2017

Opt Rev

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Quantitative photoacoustic tomography (QPAT) employing a light propagation model will play an important role in medical diagnoses by quantifying the concentration of hemoglobin or a contrast agent. However, QPAT by the light propagation model with the three-dimensional (3D) radiative transfer equation (RTE) requires a huge computational load in the iterative forward calculations involved in the updating process to reconstruct the absorption coefficient. The approximations of the light propagation improve the efficiency of the image reconstruction for the QPAT. In this study, we compared the 3D/ two-dimensional (2D) photon diffusion equation (PDE) approximating 3D RTE with the Monte Carlo simulation based on 3D RTE. Then, the errors in a 2D PDE-based linearized image reconstruction caused by the approximations were quantitatively demonstrated and discussed in the numerical simulations. It was clearly observed that the approximations affected the reconstructed absorption coefficient. The 2D PDE-based linearized algorithm succeeded in the image reconstruction of the region with a large absorption coefficient in the 3D phantom. The value reconstructed in the phantom experiment agreed with that in the numerical simulation, so that it was validated that the numerical simulation of the image reconstruction predicted the relationship between the true absorption coefficient of the target in the 3D medium and the reconstructed value with the 2D PDE-based linearized algorithm. Moreover, the the true absorption coefficient in 3D medium was estimated from the 2D reconstructed image on the basis of the prediction by the numerical simulation. The estimation was successful in the phantom experiment, although some limitations were revealed.

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“…Many different solutions or approximations for RTE have been proposed [12], such as Monte Carlo [13,14], Diffusion Approximation, calculations using different basis functions [4,6,[15][16][17], Finite-Elementlike methods (FEM) [1,5,7] and combinations of the above [5,8,10,18,19]. In a very simple case a solution has been found based on a -moving'' unity partition of normal distribution, decreasing over time by an exponential factor according to the absorption parameter.…”

Section: Introductionmentioning

confidence: 99%

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

Georgakopoulos

Politopoulos

Georgiou

2018

Journal of Quantitative Spectroscopy and Radiative Transfer

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A new dynamic-system approach to the problem of radiative transfer inside scattering and absorbing media is presented, directly based on first-hand physical principles. This method, the Dynamic Radiative Transfer System (DRTS), employs a dynamical system formality using a global sparse matrix, which characterizes the physical, optical and geometrical properties of the material-volume of interest. The new system state is generated by the above time-independent matrix, using simple matrix-vector multiplication for each subsequent time step. DRTS is capable of calculating accurately the time evolution of photon propagation in media of complex structure and shape. The flexibility of DRTS allows the integration of timedependent sources, boundary conditions, different media and several optical phenomena like reflection and refraction in a unified and consistent way. Various examples of DRTS simulation results are presented for ultra-fast light pulse 3-D propagation, demonstrating greatly reduced computational cost and resource requirements compared to other methods.

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Hybrid model of light propagation in random media based on the time-dependent radiative transfer and diffusion equations

Cited by 36 publications

References 27 publications

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

Renormalization of the highly forward-peaked phase function using the double exponential formula for radiative transfer

Effects of the approximations of light propagation on quantitative photoacoustic tomography using two-dimensional photon diffusion equation and linearization

Time evolution of photon-pulse propagation in scattering and absorbing media: The dynamic radiative transfer system

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