Hybrid forward-peaked-scattering-diffusion approximations for light propagation in turbid media with low-scattering regions

Abstract Coupled light transport models which use forward-peaked scattering approximations of the radiative transport equation and the diffusion approximation to model light propagation in tissues are introduced. The forward-peaked Fokker–Planck–Eddington approximations are used in those parts of the domain in which the diffusion approximation is not valid, such as close to the source and boundary, and in low-scattering regions. The diffusion approximation is used elsewhere. The models are coupled through boundary conditions and the resulting system of equations is solved using a finite element method. The proposed coupled Fokker–Planck-diffusion and Fokker–Planck–Eddington-diffusion models are tested with simulations, and compared with the radiative transport equation, diffusion approximation and coupled radiative transport-diffusion model. The results show that the new coupled models give almost as accurate results as the radiative transport equation with reduced computational load.

[1]  C. Lancellotti,et al.  On the accuracy of generalized Fokker-Planck transport equations in tissue optics. , 2009, Applied optics.

[2]  Simon R Arridge,et al.  Methods in diffuse optical imaging , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[3]  M. Moscoso,et al.  Beam propagation in sharply peaked forward scattering media. , 2004, Journal of the Optical Society of America. A, Optics, image science, and vision.

[4]  M. Schweiger,et al.  The finite element model for the propagation of light in scattering media: a direct method for domains with nonscattering regions. , 2000, Medical physics.

[5]  R. Cubeddu,et al.  Optical Tomography , 1998, Technical Digest. 1998 EQEC. European Quantum Electronics Conference (Cat. No.98TH8326).

[6]  Edward W. Larsen,et al.  Generalized Fokker-Planck Approximations of Particle Transport with Highly Forward-Peaked Scattering , 2001 .

[7]  Guillaume Bal,et al.  Mathematical Modelling and Numerical Analysis Coupling of Transport and Diffusion Models in Linear Transport Theory , 2022 .

[8]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[9]  Jari P. Kaipio,et al.  Finite element model for the coupled radiative transfer equation and diffusion approximation , 2006 .

[10]  Stephen J. Wright,et al.  Reconstruction in optical tomography using the PN approximations , 2006 .

[11]  G. Habetler,et al.  Uniform asymptotic expansions in transport theory with small mean free paths, and the diffusion approximation , 1975 .

[12]  Guillaume Bal,et al.  Inverse transport theory and applications , 2009 .

[13]  Guido Kanschat.  A Robust Finite Element Discretization for Radiative Transfer Problems with Scattering , 2007 .

[14]  Pedro González-Rodríguez,et al.  Comparison of light scattering models for diffuse optical tomography. , 2009, Optics express.

[15]  S. Arridge.  Optical tomography in medical imaging , 1999 .

[16]  Arnold D Kim,et al.  Correcting the diffusion approximation at the boundary. , 2011, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  S. Jacques,et al.  Hybrid model of Monte Carlo simulation and diffusion theory for light reflectance by turbid media. , 1993, Journal of the Optical Society of America. A, Optics, image science, and vision.

[18]  G. C. Pomraning.  THE FOKKER-PLANCK OPERATOR AS AN ASYMPTOTIC LIMIT , 1992 .

[19]  Arridge,et al.  Optical tomography in the presence of void regions , 2000, Journal of the Optical Society of America. A, Optics, image science, and vision.

[20]  M S Patterson,et al.  Determination of the optical properties of two-layer turbid media by use of a frequency-domain hybrid monte carlo diffusion model. , 2001, Applied optics.

[21]  Ville Kolehmainen,et al.  Hybrid radiative-transfer-diffusion model for optical tomography. , 2005, Applied optics.

[22]  R. Alcouffe,et al.  Comparison of finite-difference transport and diffusion calculations for photon migration in homogeneous and heterogeneous tissues. , 1998, Physics in medicine and biology.

[23]  Simon R. Arridge,et al.  Image reconstruction in diffuse optical tomography using the coupled radiative transport–diffusion model , 2011 .

[24]  Erkki Somersalo,et al.  Estimation of optical absorption in anisotropic background , 2002 .

[25]  M. Schweiger,et al.  The finite element method for the propagation of light in scattering media: boundary and source conditions. , 1995, Medical physics.

[26]  J. Keller,et al.  Asymptotic solution of neutron transport problems for small mean free paths , 1974 .

[27]  Arnold D Kim,et al.  Light propagation in biological tissue , 2003, SPIE BiOS.

[28]  Simon R. Arridge,et al.  Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements , 2011, J. Comput. Phys..

[29]  Dario Fasino,et al.  An inverse Robin problem for Laplace's equation: theoretical results and numerical methods , 1999 .

[30]  Pedro González-Rodríguez,et al.  Light propagation in tissues with forward-peaked and large-angle scattering. , 2008, Applied optics.

[31]  S R Arridge,et al.  Recent advances in diffuse optical imaging , 2005, Physics in medicine and biology.

[32]  Edgar Olbrant,et al.  Generalized Fokker-Planck Theory for Electron and Photon Transport in Biological Tissues: Application to Radiotherapy , 2010, Comput. Math. Methods Medicine.

[33]  S. Arridge,et al.  Optical tomography: forward and inverse problems , 2009, 0907.2586.

[34]  William Thomlinson,et al.  Quantitative measurement of regional lung gas volume by synchrotron radiation computed tomography , 2005, Physics in medicine and biology.

[35]  Dimitris Gorpas,et al.  A three-dimensional finite elements approach for the coupled radiative transfer equation and diffusion approximation modeling in fluorescence imaging , 2010 .

[36]  Antonio Laganà,et al.  A massively parallel approach to the quasiclassical reactive scattering , 1992 .

[37]  L. Zou,et al.  Several Theorems for the Trace of Self-conjugate Quaternion Matrix , 2008 .

[38]  L. C. Henyey,et al.  Diffuse radiation in the Galaxy , 1940 .

[39]  M S Patterson,et al.  Monte carlo diffusion hybrid model for photon migration in a two-layer turbid medium in the frequency domain. , 2000, Applied optics.

[40]  Akira Ishimaru,et al.  Wave propagation and scattering in random media , 1997 .

[41]  S. Arridge,et al.  Coupled radiative transfer equation and diffusion approximation model for photon migration in turbid medium with low-scattering and non-scattering regions , 2005, Physics in medicine and biology.

[42]  A. Welch,et al.  A review of the optical properties of biological tissues , 1990 .

[43]  Simon R. Arridge,et al.  Finite element approximation of the Fokker–Planck equation for diffuse optical tomography , 2010 .

[44]  Lihong V. Wang,et al.  Biomedical Optics: Principles and Imaging , 2007 .

[45]  E. Okada,et al.  Hybrid Monte Carlo-diffusion method for light propagation in tissue with a low-scattering region. , 2003, Applied optics.

[46]  Weimin Han,et al.  On a family of differential approximations of the radiative transfer equation , 2012, Journal of Mathematical Chemistry.