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

Abhinav K Jha; Yansong Zhu; Simon Arridge; Dean F Wong; Arman Rahmim

doi:10.1364/BOE.9.001389

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

Biomed Opt Express. 2018 Mar 1;9(4):1389-1407. doi: 10.1364/BOE.9.001389. eCollection 2018 Apr 1.

Authors

Abhinav K Jha^#^{1

2

3}, Yansong Zhu^#^{1

4}, Simon Arridge⁵, Dean F Wong^{1

6

7

8}, Arman Rahmim^{1

4}

Affiliations

¹ Department of Radiology and Radiological Sciences, Johns Hopkins University, Baltimore, MD, USA.
² Department of Biomedical Engineering, Washington University in St. Louis, St. Louis, MO, USA.
³ Mallinckrodt Institute of Radiology, Washington University in St. Louis, St. Louis, MO, USA.
⁴ Department of Electrical and Computer Engineering, Johns Hopkins University, Baltimore, MD, USA.
⁵ Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK.
⁶ Department of Neuroscience, Johns Hopkins University, Baltimore, MD, USA.
⁷ Department of Psychiatry and Behavioral Sciences, Johns Hopkins University, Baltimore, MD, USA.
⁸ Department of Neurology, Johns Hopkins University, Baltimore, MD, USA.

^# Contributed equally.

Abstract

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.

Keywords: (170.3660) Light propagation in tissues; (170.3880) Medical and biological imaging.

Grants and funding

R24 MH106083/MH/NIMH NIH HHS/United States