Light transport in biological tissue based on the simplified spherical harmonics equations

Klose, Alexander D.; Larsen, Edward W.

doi:10.1016/j.jcp.2006.07.007

Cited by 250 publications

(298 citation statements)

References 44 publications

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“…Although more complex mathematical models like the diffusion equation (Patterson et al, 1989) have been applied to model the light propagation in tissue, for the low number of sources and detectors and therefore the low complexity initially used in many fNIRS systems, the MBLL law is well suited. Systems working in time domain (TD) and frequency domain (FD) have traditionally used more complex mathematical frameworks based on derivations of the diffusion equation in complex geometries (Arridge et al, 1992) or even direct derivations of the Boltzmann radiative transfer equation (Klose and Larsen, 2006) to model how light travels through highly scattering tissue. These models allow calculating not only the optical properties of bulk tissue but also to reconstruct chromophore concentrations in a three-dimensional space.…”

Section: Multivariate Methods Of Typementioning

confidence: 99%

A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology

Scholkmann¹,

Kleiser²,

Metz³

et al. 2014

NeuroImage

1,523

1,394

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This year marks the 20th anniversary of functional near-infrared spectroscopy and imaging (fNIRS/fNIRI). As the vast majority of commercial instruments developed until now are based on continuous wave technology, the aim of this publication is to review the current state of instrumentation and methodology of continuous wave fNIRI. For this purpose we provide an overview of the commercially available instruments and address instrumental aspects such as light sources, detectors and sensor arrangements. Methodological aspects, algorithms to calculate the concentrations of oxy-and deoxyhemoglobin and approaches for data analysis are also reviewed. From the single-location measurements of the early years, instrumentation has progressed to imaging initially in two dimensions (topography) and then three (tomography). The methods of analysis have also changed tremendously, from the simple modified Beer-Lambert law to sophisticated image reconstruction and data analysis methods used today. Due to these advances, fNIRI has become a modality that is widely used in neuroscience research and several manufacturers provide commercial instrumentation. It seems likely that fNIRI will become a clinical tool in the foreseeable future, which will enable diagnosis in single subjects. This year marks the 20th anniversary of functional near-infrared spectroscopy and imaging (fNIRS/fNIRI). As the vast majority of commercial instruments developed until now are based on continuous wave technology, the aim of this publication is to review the current state of instrumentation and methodology of continuous wave fNIRI. For this purpose we provide an overview of the commercially available instruments and address instrumental aspects such as light sources, detectors and sensor arrangements. Methodological aspects, algorithms to calculate the concentrations of oxy-and deoxyhemoglobin and approaches for data analysis are also reviewed. From the single-location measurements of the early years, instrumentation has progressed to imaging initially in two dimensions (topography) and then three (tomography). The methods of analysis have also changed tremendously, from the simple modified Beer-Lambert law to sophisticated image reconstruction and data analysis methods used today. Due to these advances, fNIRI has become a modality that is widely used in neuroscience research and several manufacturers provide commercial instrumentation. It seems likely that fNIRI will become a clinical tool in the foreseeable future, which will enable diagnosis in single subjects. Contents

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Section: Multivariate Methods Of Typementioning

confidence: 99%

A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology

Scholkmann¹,

Kleiser²,

Metz³

et al. 2014

NeuroImage

1,523

1,394

View full text Add to dashboard Cite

show abstract

“…Using the Schwarz inequality and the Sobolev continuous embedding theorems, it follows that there exists a constant C 0 > 0 (depending only on a and b) such that 12) where…”

Section: Weak Variational Formulationmentioning

confidence: 99%

“…One of the most popular regularization methods is due to Tikhonov [18]. The method replaces the problem (4.11) by the following unconstrained optimization problem 12) where the typical cost functional J λ is…”

Section: Discretized Inverse Problem Tikhonov Regularization and Newmentioning

confidence: 99%

“…The principle of the optical tomography is to use multiple movable light sources and detectors attached to the tissue surface, such as human tissue, to collect information on light attenuation and to reconstruct the internal absorption and scattering distributions. The time-dependent diffusion transport equations have been studied by several authors in the recent years; see [12,13,14,17]. The radiative transfer transport equation (also derived from the Boltzmann equation) has been used successfully as a standard model for describing light transport in scattering media, see [11,13,14,17].…”

Section: Introductionmentioning

confidence: 99%

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An inverse problem for one-dimensional diffusion equation in optical tomography

Addam¹

2017

B Soc Paran Mat

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In this paper, we study the one-dimensional inverse problem for the diffusion equation based optical tomography. The objective of the present work is a mathematical and numerical analysis concerning one-dimensional inverse problem. In the first stage, the forward diffusion equation with boundary conditions is solved using an intermediate elliptic equation. We give the existence and the uniqueness results of the solution. An approximation of the photon density in frequency-domain is proposed using a Splines Galerkin method. In the second stage, we give theoretical results such as the stability and lipschitz-continuity of the forward solution and the Fréchet differentiability of the Dirichlet-to-Neumann nonlinear map with respect to the optical parameters. The Fréchet derivative is used to linearize the considered inverse problem. The Newton method based on the regularization technique will allow us to compute the approximate solutions of the inverse problem. Several test examples are used to verify high accuracy, effectiveness and good resolution properties for smooth and discontinuous optical property solutions.

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“…MLT involves NIR light stimulation to make energy-stored nanophosphors emit luminescence photons. A light propagation model is needed to describe interactions of light photons with scattering and absorbing media, which is essential for MLT image reconstruction [25,26]. For biological samples, the diffusion approximation model, a computationally-efficient approximation to the radiative transport equation (RTE), would break down with small sample size, strong absorbers, near sources, and across boundaries [27,28].…”

Section: Photon Transport Modelmentioning

confidence: 99%

X-ray micro-modulated luminescence tomography (XMLT)

Cong¹,

Liu²,

Wang³

et al. 2014

Opt. Express

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Imaging depth of optical microscopy has been fundamentally limited to millimeter or sub-millimeter due to strong scattering of light in a biological sample. X-ray microscopy can resolve spatial details of few microns deep inside a sample but contrast resolution is inadequate to depict heterogeneous features at cellular or sub-cellular levels. To enhance and enrich biological contrast at large imaging depth, various nanoparticles are introduced and become essential to basic research and molecular medicine. Nanoparticles can be functionalized as imaging probes, similar to fluorescent and bioluminescent proteins. LiGa 5 O 8 :Cr 3+ nanoparticles were recently synthesized to facilitate luminescence energy storage with x-ray pre-excitation and subsequently stimulated luminescence emission by visible/near-infrared (NIR) light. In this paper, we propose an x-ray micromodulated luminescence tomography (XMLT, or MLT to be more general) approach to quantify a nanophosphor distribution in a thick biological sample with high resolution. Our numerical simulation studies demonstrate the feasibility of the proposed approach.

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Light transport in biological tissue based on the simplified spherical harmonics equations

Cited by 250 publications

References 44 publications

A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology

A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology

An inverse problem for one-dimensional diffusion equation in optical tomography

X-ray micro-modulated luminescence tomography (XMLT)

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