Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

Mohan, P. Surya; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon

doi:10.1016/j.jcp.2011.06.004

Cited by 42 publications

(14 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Solving RTE requires long computational time and large storage capacities [57]. Therefore, the light propagation in a turbid medium can be described under general assumptions [58].…”

Section: Light Propagation In the Human Headmentioning

confidence: 99%

Diffuse optical tomography in the human brain: A briefly review from the neurophysiology to its applications

Hernández‐Martín

González–Mora

2020

Brain Science Advances

View full text Add to dashboard Cite

The present work describes the use of noninvasive diffuse optical tomography (DOT) technology to measure hemodynamic changes, providing relevant information which helps to understand the basis of neurophysiology in the human brain. Advantages such as portability, direct measurements of hemoglobin state, temporal resolution, non‐restricted movements as occurs in magnetic resonance imaging (MRI) devices mean that DOT technology can be used in research and clinical fields. In this review we covered the neurophysiology, physical principles underlying optical imaging during tissue‐light interactions, and technology commonly used during the construction of a DOT device including the source‐detector requirements to improve the image quality. DOT provides 3D cerebral activation images due to complex mathematical models which describe the light propagation inside the tissue head. Moreover, we describe briefly the use of Bayesian methods for raw DOT data filtering as an alternative to linear filters widely used in signal processing, avoiding common problems such as the filter selection or a false interpretation of the results which is sometimes due to the interference of background physiological noise with neural activity.

show abstract

“…Solving RTE requires long computational time and large storage capacities [57]. Therefore, the light propagation in a turbid medium can be described under general assumptions [58].…”

Section: Light Propagation In the Human Headmentioning

confidence: 99%

Diffuse optical tomography in the human brain: A briefly review from the neurophysiology to its applications

Hernández‐Martín

González–Mora

2020

Brain Science Advances

View full text Add to dashboard Cite

show abstract

“…These functions serve as an easy to use interface for anyone who wants to run Monte Carlo simulations for their problem but are not comfortable with technical programming. The simulation code is based on our earlier Monte Carlo software that has previously been utilised in simulating light propagation for example in [20,23,[47][48][49][50][51]. A summary of other Monte Carlo simulation software that have MATLAB interface can be found in Ref.…”

Section: Introductionmentioning

confidence: 99%

ValoMC: a Monte Carlo software and MATLAB toolbox for simulating light transport in biological tissue

Leino¹,

Pulkkinen²,

Tarvainen³

2019

OSA Continuum

Self Cite

View full text Add to dashboard Cite

A Monte Carlo method for photon transport has gained wide popularity in biomedical optics for studying light behaviour in tissue. Nowadays, typical computation times range from a few minutes to hours. Although various implementations of the Monte Carlo algorithm exist, there is only a limited number of free software available. In addition, these packages may require substantial learning efforts. To address these issues, we present a new Monte Carlo software with a user-friendly interface. The simulation geometry is defined using an unstructured (triangular or tetrahedral) mesh. The program solves the photon fluence in the computation domain and the exitance at the domain boundary. It is capable of simulating complex measurement geometries with spatially varying optical parameter distributions and supports several types of light sources as well as intensity modulated light. Furthermore, attention is given to ease of use and fast problem set up with a MATLAB (The MathWorks Inc., Natick, MA) interface. The simulation code is written in C++ and parallelized using OpenMP. The simulation code has been validated against analytical and numerical solutions of radiative transfer equation and other Monte Carlo software in good agreement. The software is available for download from the homepage https://inverselight.github.io/ValoMC/ and the source code from GitHub https://github.com/InverseLight/ValoMC.

show abstract

“…Although this calculation could be transformed into two independent low-dimensional integrals, the tensor product of these two integral-related matrices still needs to be performed. 1 In addition to using linear basis functions, Surya Mohan et al 22 also investigated the use of spherical harmonic functions to approximate the angular components of the solution. However, this formulation still required computation of the high-dimensional integral and tensor product of the matrices (e.g., when considering the three-dimensional (3-D) space and two-dimensional unit sphere in angular space, a five-dimensional integral was calculated in general).…”

Section: Introductionmentioning

confidence: 99%

Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method

Long

Intes

et al. 2016

J. Biomed. Opt

View full text Add to dashboard Cite

Optical tomography has a wide range of biomedical applications. Accurate prediction of photon transport in media is critical, as it directly affects the accuracy of the reconstructions. The radiative transfer equation (RTE) is the most accurate deterministic forward model, yet it has not been widely employed in practice due to the challenges in robust and efficient numerical implementations in high dimensions. Herein, we propose a method that combines the discrete ordinate method (DOM) with a streamline diffusion modified continuous Galerkin method to numerically solve RTE. Additionally, a phase function normalization technique was employed to dramatically reduce the instability of the DOM with fewer discrete angular points. To illustrate the accuracy and robustness of our method, the computed solutions to RTE were compared with Monte Carlo (MC) simulations when two types of sources (ideal pencil beam and Gaussian beam) and multiple optical properties were tested. Results show that with standard optical properties of human tissue, photon densities obtained using RTE are, on average, around 5% of those predicted by MC simulations in the entire/deeper region. These results suggest that this implementation of the finite element method-RTE is an accurate forward model for optical tomography in human tissues.

show abstract

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

Cited by 42 publications

References 35 publications

Diffuse optical tomography in the human brain: A briefly review from the neurophysiology to its applications

Diffuse optical tomography in the human brain: A briefly review from the neurophysiology to its applications

ValoMC: a Monte Carlo software and MATLAB toolbox for simulating light transport in biological tissue

Radiative transfer equation modeling by streamline diffusion modified continuous Galerkin method

Contact Info

Product

Resources

About