Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

Lehtikangas, Ossi; Tarvainen, Tanja; Kim, A.D.; Arridge, Simon

doi:10.1016/j.jcp.2014.11.025

Cited by 23 publications

(16 citation statements)

References 42 publications

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“…In this study, the diffusion equation was solved using the finite element method [39,40] under the environment of COMSOL Multiphysics 5.2 software [41]. Helmholtz Equation (4) in COMSOL is employed to model the diffusion equation presented in (3) in the steady state.…”

Section: Methodsmentioning

confidence: 99%

Identifying different types of tumors in human brain, breast, and uterus according to their optical properties in the red to near-infrared region

Hamdy

2020

Preprint

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26Optical diagnosis techniques are gaining validity due to their competitive advantages 27 including safety and functionality. These methods probe the tissue using light in the red 28 to near-infrared region that shows relatively high penetration in biological tissues. The 29 reflected light which is controlled by tissue absorption and scattering parameters can 30 provide significant information about its pathology. In the present work, a method for 31 identifying different types of tumors in human brain, breast and uterus based on their 32 absorption and scattering characteristics in the red to near-infrared spectra is proposed. 33The classification method depends on studying the red to near-infrared light diffusion 34 through the examined tissues using Monte-Carlo simulation and finite element solution of 35 the light diffusion equation. The obtained tissue reflectance profiles, optical fluence rate 36 distribution and absorbed faction in each tumor type show different characteristics along 37 the selected wavelengths. The variation in these three features can be considered as an 38 alternative approach of medical diagnosis or can assist with other conventional diagnosis 39 methods. 40 41 42 Brain, breast and uterus are very vital and complex human body organs that have affected 43 by many types of tumors with different characteristics and symptoms. Diagnosing brain 44 tumors can be accomplished using different medical imaging techniques such as 45 magnetic resonance imaging (MRI) and computer tomography (CT) scan or by a 46 neurological exam [1]. While, X-ray mammography, MRI, breast ultrasonography and 48 CT can be used also to diagnose uterus tumors, transvaginal ultrasound and biopsy are 49 the most common utilized techniques [3]. However, many of these techniques have their 50 limitations. Besides, the use of ionizing radiation in the diagnosing process can even 51 develop tumors in the healthy tissues [4]. On the other hand, optical techniques are 52 considered very safe and functional diagnosing tools.53

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Section: Methodsmentioning

confidence: 99%

Identifying different types of tumors in human brain, breast, and uterus according to their optical properties in the red to near-infrared region

Hamdy

2020

Preprint

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“…The equation of a reflection and transmission coefficient for s-polarization and p-polarization [5,6] was used and can be defined as r s = n 1 cos θ inc − n 2 cosθ tra n 1 cosθ inc + n 2 cosθ tra (5) r p = n 2 cos θ inc − n 1 cosθ tra n 1 cosθ tra + n 2 cos θ inc (6) t s = 2n 1 cos θ inc n 1 cosθ inc + n 2 cosθ tra (7) t p = 2n 1 cos θ inc n 1 cosθ tra + n 2 cos θ inc…”

Section: Fresnel's Equation On Reflection and Transmission Coefficientmentioning

confidence: 99%

Analysis of Plasmonic Structure using Finite Element Method

Nasar

Abdul-Kahar

Esa

et al. 2018

JST

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“…Accounting for the boundary conditions arising due to this refractive index mismatch is necessary for accurate modeling of photon propagation [1,2]. It has been observed that not accounting for boundary conditions accurately leads to erroneous modeling of scattered light [3], and 50% or more errors in estimating the optical coefficients of the tissue [1].…”

Section: Introductionmentioning

confidence: 99%

Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging

Jha

Zhu

Arridge

et al. 2018

Biomed. Opt. Express

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We propose a formalism to incorporate boundary conditions in a Neumann-series-based radiative transport equation. The formalism accurately models the reflection of photons at the tissue-external medium interface using Fresnel's equations. The formalism was used to develop a gradient descent-based image reconstruction technique. The proposed methods were implemented for 3D diffuse optical imaging. In computational studies, it was observed that the average root-mean-square error (RMSE) for the output images and the estimated absorption coefficients reduced by 38% and 84%, respectively, when the reflection boundary conditions were incorporated. These results demonstrate the importance of incorporating boundary conditions that model the reflection of photons at the tissue-external medium interface.

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Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index

Cited by 23 publications

References 42 publications

Identifying different types of tumors in human brain, breast, and uterus according to their optical properties in the red to near-infrared region

Identifying different types of tumors in human brain, breast, and uterus according to their optical properties in the red to near-infrared region

Analysis of Plasmonic Structure using Finite Element Method

Incorporating reflection boundary conditions in the Neumann series radiative transport equation: application to photon propagation and reconstruction in diffuse optical imaging

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