UCL Discovery
UCL home » Library Services » Electronic resources » UCL Discovery

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

Lehtikangas, O; Tarvainen, T; Kim, AD; Arridge, SR; (2015) Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index. Journal of Computational Physics , 282 pp. 345-359. 10.1016/j.jcp.2014.11.025. Green open access

[thumbnail of Lehtikangas_Finite_element_approximation.pdf]
Preview
Text
Lehtikangas_Finite_element_approximation.pdf

Download (4MB) | Preview

Abstract

The radiative transport equation can be used as a light transport model in a medium with scattering particles, such as biological tissues. In the radiative transport equation, the refractive index is assumed to be constant within the medium. However, in biomedical media, changes in the refractive index can occur between different tissue types. In this work, light propagation in a medium with piece-wise constant refractive index is considered. Light propagation in each sub-domain with a constant refractive index is modeled using the radiative transport equation and the equations are coupled using boundary conditions describing Fresnel reflection and refraction phenomena on the interfaces between the sub-domains. The resulting coupled system of radiative transport equations is numerically solved using a finite element method. The approach is tested with simulations. The results show that this coupled system describes light propagation accurately through comparison with the Monte Carlo method. It is also shown that neglecting the internal changes of the refractive index can lead to erroneous boundary measurements of scattered light.

Type: Article
Title: Finite element approximation of the radiative transport equation in a medium with piece-wise constant refractive index
Open access status: An open access version is available from UCL Discovery
DOI: 10.1016/j.jcp.2014.11.025
Publisher version: http://dx.doi.org/ 10.1016/j.jcp.2014.11.025
Language: English
Additional information: Copyright ©2014 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Keywords: Radiative transport equation, Refractive index, Finite element method
UCL classification: UCL
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: https://discovery.ucl.ac.uk/id/eprint/1488000
Downloads since deposit
76Downloads
Download activity - last month
Download activity - last 12 months
Downloads by country - last 12 months

Archive Staff Only

View Item View Item