Radiative Transfer Equation

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Simon R Arridge - One of the best experts on this subject based on the ideXlab platform.

  • Utilizing the Radiative Transfer Equation in optical tomography
    Piers Online, 2020
    Co-Authors: Tanja Tarvainen, Jp Kaipio, Marko Vauhkonen, Ville Kolehmainen, Simon R Arridge
    Abstract:

    We propose a method which utilizes the Radiative Transfer Equation in optical tomography. In this approach, the Radiative Transfer Equation is used as light propagation model in those regions in which the assumptions of the diffusion theory are not valid and the diffusion approximation is used elsewhere. Both the Radiative Transfer Equation and the diffusion approximation are numerically solved with a finite element method. In the finite element solution of the Radiative Transfer Equation, both the spatial and angular discretizations are implemented in piecewise linear bases.

  • utilising the Radiative Transfer Equation in quantitative photoacoustic tomography
    Proceedings of SPIE, 2017
    Co-Authors: Tanja Tarvainen, Aki Pulkkinen, Simon R Arridge
    Abstract:

    Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating optical parameters inside tissue from photoacoustic images. This optical parameter estimation problem is an ill-posed inverse problem, and thus it is sensitive to measurement and modelling errors. Therefore, light propagation in quantitative photoacoustic tomography needs to be accurately modelled. A widely accepted model for light propagation in biological tissue is the Radiative Transfer Equation. In this work, the Radiative Transfer Equation is utilised in quantitative photoacoustic tomography. Estimating absorption and scattering distributions in quantitative photoacoustic tomography using various illuminations is investigated.

  • Image reconstruction in quantitative photoacoustic tomography using the Radiative Transfer Equation and the diffusion approximation
    Opto-Acoustic Methods and Applications, 2013
    Co-Authors: Tanja Tarvainen, Jp Kaipio, Aki Pulkkinen, Simon R Arridge
    Abstract:

    Quantitative photoacoustic tomography is an emerging imaging technique aiming at estimating the distribution of optical parameters inside tissue from photoacoustic image which is formed by combining optical information and ultrasound propagation. In this paper reconstruction of absorption and scattering distributions using the Radiative Transfer Equation and the diffusion approximation as forward models for light propagation is investigated. Data is simulated using Monte Carlo method and different size target domains are considered. The results show that the Radiative Transfer Equation can estimate both absorption and scattering distributions with good accuracy. Furthermore, in the simulated test cases, the diffusion approximation can produce as good estimates for absorption as the Radiative Transfer Equation.

  • Förster resonance energy Transfer imaging in vivo with approximated Radiative Transfer Equation.
    Appl Opt, 2011
    Co-Authors: Simon R Arridge
    Abstract:

    We describe a new light transport model, which was applied to three-dimensional lifetime imaging of Förster resonance energy Transfer in mice in vivo. The model is an approximation to the Radiative Transfer Equation and combines light diffusion and ray optics. This approximation is well adopted to wide-field time-gated intensity-based data acquisition. Reconstructed image data are presented and compared with results obtained by using the telegraph Equation approximation. The new approach provides improved recovery of absorption and scattering parameters while returning similar values for the fluorescence parameters.

  • gauss newton reconstruction method for optical tomography using the finite element solution of the Radiative Transfer Equation
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2008
    Co-Authors: Tanja Tarvainen, Marko Vauhkonen, Simon R Arridge
    Abstract:

    Abstract The Radiative Transfer Equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain Radiative Transfer Equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss–Newton algorithm. The Radiative Transfer Equation is numerically solved with a finite element method in which both the spatial and angular discretizations are implemented in piecewise linear bases. Furthermore, the streamline diffusion modification is utilized to improve the numerical stability. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the Radiative Transfer Equation can be utilized in optical tomography and it can produce good quality images even in the presence of low-scattering regions.

Tanja Tarvainen - One of the best experts on this subject based on the ideXlab platform.

  • Utilizing the Radiative Transfer Equation in optical tomography
    Piers Online, 2020
    Co-Authors: Tanja Tarvainen, Jp Kaipio, Marko Vauhkonen, Ville Kolehmainen, Simon R Arridge
    Abstract:

    We propose a method which utilizes the Radiative Transfer Equation in optical tomography. In this approach, the Radiative Transfer Equation is used as light propagation model in those regions in which the assumptions of the diffusion theory are not valid and the diffusion approximation is used elsewhere. Both the Radiative Transfer Equation and the diffusion approximation are numerically solved with a finite element method. In the finite element solution of the Radiative Transfer Equation, both the spatial and angular discretizations are implemented in piecewise linear bases.

  • utilising the Radiative Transfer Equation in quantitative photoacoustic tomography
    Proceedings of SPIE, 2017
    Co-Authors: Tanja Tarvainen, Aki Pulkkinen, Simon R Arridge
    Abstract:

    Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating optical parameters inside tissue from photoacoustic images. This optical parameter estimation problem is an ill-posed inverse problem, and thus it is sensitive to measurement and modelling errors. Therefore, light propagation in quantitative photoacoustic tomography needs to be accurately modelled. A widely accepted model for light propagation in biological tissue is the Radiative Transfer Equation. In this work, the Radiative Transfer Equation is utilised in quantitative photoacoustic tomography. Estimating absorption and scattering distributions in quantitative photoacoustic tomography using various illuminations is investigated.

  • Approximating the time-domain Radiative Transfer Equation using truncated Fourier series
    Diffuse Optical Imaging IV, 2013
    Co-Authors: Aki Pulkkinen, Tanja Tarvainen
    Abstract:

    The Radiative Transfer Equation describes propagation of light in scattering media. It is widely used model, with applications in medical imaging, astronomy and atmospheric sciences to name a few. Simulating the Radiative Transfer Equation in time-domain is, however, time consuming. In this work truncated Fourier series approximation is used to approximate the solution of the time-domain Radiative Transfer Equation. Method is validated by comparison to direct temporal integration of the Radiative Transfer Equation and time-domain Monte Carlo. Computational speedup is observed using the truncated Fourier series approximation in comparison to the direct temporal integration approach. Different simulation errors associated with the truncated Fourier series approximation and direct time-domain integration approaches are briefly demonstrated.

  • Image reconstruction in quantitative photoacoustic tomography using the Radiative Transfer Equation and the diffusion approximation
    Opto-Acoustic Methods and Applications, 2013
    Co-Authors: Tanja Tarvainen, Jp Kaipio, Aki Pulkkinen, Simon R Arridge
    Abstract:

    Quantitative photoacoustic tomography is an emerging imaging technique aiming at estimating the distribution of optical parameters inside tissue from photoacoustic image which is formed by combining optical information and ultrasound propagation. In this paper reconstruction of absorption and scattering distributions using the Radiative Transfer Equation and the diffusion approximation as forward models for light propagation is investigated. Data is simulated using Monte Carlo method and different size target domains are considered. The results show that the Radiative Transfer Equation can estimate both absorption and scattering distributions with good accuracy. Furthermore, in the simulated test cases, the diffusion approximation can produce as good estimates for absorption as the Radiative Transfer Equation.

  • gauss newton reconstruction method for optical tomography using the finite element solution of the Radiative Transfer Equation
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2008
    Co-Authors: Tanja Tarvainen, Marko Vauhkonen, Simon R Arridge
    Abstract:

    Abstract The Radiative Transfer Equation can be utilized in optical tomography in situations in which the more commonly applied diffusion approximation is not valid. In this paper, an image reconstruction method based on a frequency domain Radiative Transfer Equation is developed. The approach is based on a total variation output regularized least squares method which is solved with a Gauss–Newton algorithm. The Radiative Transfer Equation is numerically solved with a finite element method in which both the spatial and angular discretizations are implemented in piecewise linear bases. Furthermore, the streamline diffusion modification is utilized to improve the numerical stability. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the Radiative Transfer Equation can be utilized in optical tomography and it can produce good quality images even in the presence of low-scattering regions.

Hedzer A Ferwerda - One of the best experts on this subject based on the ideXlab platform.

J M Zhao - One of the best experts on this subject based on the ideXlab platform.

  • a second order Radiative Transfer Equation and its solution by meshless method with application to strongly inhomogeneous media
    Journal of Computational Physics, 2013
    Co-Authors: J M Zhao
    Abstract:

    A new second order form of Radiative Transfer Equation (named MSORTE) is proposed, which overcomes the singularity problem of a previously proposed second order Radiative Transfer Equation [J.E. Morel, B.T. Adams, T. Noh, J.M. McGhee, T.M. Evans, T.J. Urbatsch, Spatial discretizations for self-adjoint forms of the Radiative Transfer Equations, J. Comput. Phys. 214 (1) (2006) 12-40 (where it was termed SAAI), J.M. Zhao, L.H. Liu, Second order Radiative Transfer Equation and its properties of numerical solution using finite element method, Numer. Heat Transfer B 51 (2007) 391-409] in dealing with inhomogeneous media where some locations have very small/zero extinction coefficient. The MSORTE contains a naturally introduced diffusion (or second order) term which provides better numerical property than the classic first order Radiative Transfer Equation (RTE). The stability and convergence characteristics of the MSORTE discretized by central difference scheme is analyzed theoretically, and the better numerical stability of the second order form Radiative Transfer Equations than the RTE when discretized by the central difference type method is proved. A collocation meshless method is developed based on the MSORTE to solve Radiative Transfer in inhomogeneous media. Several critical test cases are taken to verify the performance of the presented method. The collocation meshless method based on the MSORTE is demonstrated to be capable of stably and accurately solve Radiative Transfer in strongly inhomogeneous media, media with void region and even with discontinuous extinction coefficient.

  • second order Radiative Transfer Equation and its properties of numerical solution using the finite element method
    Numerical Heat Transfer Part B-fundamentals, 2007
    Co-Authors: J M Zhao
    Abstract:

    The original Radiative Transfer Equation is a first-order integrodifferential Equation, which can be taken as a convection-dominated Equation. The presence of the convection term may cause nonphysical oscillation of solutions. This type of instability can occur in many numerical methods, including the finite-difference method and the finite-element method, if no special stability treatment is used. To overcome this problem, a second-order Radiative Transfer Equation is derived, which is a diffusion-type Equation similar to the heat conduction Equation for an anisotropic medium. The consistency of the second-order Radiative Transfer Equation with the original Radiative Transfer Equation is demonstrated. The perturbation characteristics of error are analyzed and compared for both the first- and second-order Equations. Good numerical properties are found for the second-order Radiative Transfer Equation. To show the properties of the numerical solution, the standard Galerkin finite-element method is employed ...

J Freimanis - One of the best experts on this subject based on the ideXlab platform.

  • Cylindrically symmetric eigenfunctions of polarized Radiative Transfer Equation
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2019
    Co-Authors: J Freimanis
    Abstract:

    Abstract The general expressions for cylindrically symmetric eigenfunctions of polarized Radiative Transfer Equation in homogeneous space obeying Euclidean geometry are derived and proved. The medium is assumed to be statistically homogeneously filled with polydisperse particles, the effective medium (host medium together with particles) is assumed to be isotropic, and birefringence (both linear and circular) is assumed to be negligible.

  • Polarized Radiative Transfer Equation in some curvilinear coordinate systems
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2014
    Co-Authors: J Freimanis
    Abstract:

    Abstract The differential operator for polarized Radiative Transfer Equation in homogeneous space obeying Euclidean geometry is explicitly written down for several orthogonal curvilinear coordinate systems of astrophysical interest. The medium is assumed to be statistically homogeneously filled with polydisperse particles, and birefringence in the effective medium is assumed to be negligible.

  • on vector Radiative Transfer Equation in curvilinear coordinate systems
    Journal of Quantitative Spectroscopy & Radiative Transfer, 2011
    Co-Authors: J Freimanis
    Abstract:

    Abstract The differential operator of polarized Radiative Transfer Equation is examined in case of homogeneous medium in Euclidean three-dimensional space with arbitrary curvilinear coordinate system defined in it. This study shows that an apparent rotation of polarization plane along the light ray with respect to the chosen reference plane for Stokes parameters generally takes place, due to purely geometric reasons. Analytic expressions for the differential operator of Transfer Equation dependent on the components of metric tensor and their derivatives are found, and the derivation of differential operator of polarized Radiative Transfer Equation has been made a standard procedure. Considerable simplifications take place if the coordinate system is orthogonal.