The finite element method for the propagation of light in scattering media: Boundary and source conditions

Abstract. Obtaining absolute chromophore concentrations from photoacoustic images obtained at multiple wavelengths is a nontrivial aspect of photoacoustic imaging but is essential for accurate functional and molecular imaging. This topic, known as quantitative photoacoustic imaging, is reviewed here. The inverse problems involved are described, their nature (nonlinear and ill-posed) is discussed, proposed solution techniques and their limitations are explained, and the remaining unsolved challenges are introduced.

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“…(14) may be solved by standard numerical methods such as finite elements. 31,32 For a homogeneous medium, the solution to Eq. (14) is given by…”

Section: Diffusion Approximationmentioning

confidence: 99%

Quantitative spectroscopic photoacoustic imaging: a review

et al. 2012

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“…A compromise between these two is the extrapolated boundary condition (EBC), where an extrapolated boundary is introduced at a certain distance d ext from the real physical boundary, and the DBC is then applied at this extrapolated boundary. Comparing with Monte Carlo simulations and experimental results, the RBC and EBC give much better agreement than the DBC (Okada et al, 1996;Schweiger et al, 1995).…”

Section: Boundary and Source Conditionsmentioning

confidence: 90%

Diffuse Optical Imaging

Nissilä

Noponen

Heino

et al.

Advances in Electromagnetic Fields in Living Systems

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Diffuse optical imaging is a functional medical imaging modality which takes advantage of the relatively low attenuation of near-infrared light to probe the internal optical properties of tissue. The optical properties are affected by parameters related to physiology such as the concentrations of oxy-and deoxyhemoglobin. Instrumentation that is used for optical imaging is generally able to measure changes in the attenuation of light at several wavelengths, and in the case of time-and frequency-domain instrumentation, the time-of-flight of the photons in tissue.Light propagation in tissue is generally dominated by scattering. Models for photon transport in tissue are generally based on either stochastic approaches or approximations derived from the radiative transfer equation. If a numerical forward model which describes the physical situation with sufficient accuracy exists, inversion methods may be used to determine the internal optical properties based on boundary measurements.Optical imaging has applications in, e.g., functional brain imaging, breast cancer detection, and muscle imaging. It has the important advantages of transportable instrumentation, relatively high tolerance for external electromagnetic interference, non-invasiveness, and applicability for neonatal studies. The methods are not yet in clinical use, and further research is needed to improve the reliability of the experimental techniques, and the accuracy of the models used. In this chapter, we describe the interaction between light and tissue, light propagation models and inversion methods used in optical tomography, and instrumentation and experimental techniques used in optical imaging. The main applications of optical imaging are described in detail, with results from recent literature.

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“…Its application to the inverse problem was first introduced by Schweiger et al (1992). Fast methods for deriving measurement operators are described by , and boundary conditions for a diffuse source are discussed by Schweiger et al (1995). Furthermore, provided an analysis wherein the noise properties of a Monte-Carlo model were accurately predicted by a deterministic diffusion approximation.…”

Section: (B) Solution Methods For Photon Transport Modelsmentioning

confidence: 99%

Image reconstruction in optical tomography

Arridge

Schweiger

1997

Phil. Trans. R. Soc. Lond. B

139

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SUMMARYOptical tomography is a new medical imaging modality that is at the threshold of realization. A large amount of clinical work has shown the very real benefits that such a method could provide. At the same time a considerable effort has been put into theoretical studies of its probable success. At present there exist gaps between these two realms. In this paper we review some general approaches to inverse problems to set the context for optical tomography, defining both the terms for ard problem and in erse problem. An essential requirement is to treat the problem in a nonlinear fashion, by using an iterative method. This in turn requires a convenient method of evaluating the forward problem, and its derivatives and variance. Photon transport models are described and methods for obtaining analytical and numerical solutions for the most commonly used ones are reviewed. The inverse problem is approached by classical gradientbased solution methods. In order to develop practical implementations of these methods, we discuss the important topic of photon measurement densit functions, which represent the derivative of the forward problem. We show some results that represent the most complex and realistic simulations of optical tomography yet developed. We suggest, in particular, that both time-resolved, and intensity-modulated systems can reconstruct variations in both optical absorption and scattering, but that unmodulated, nontime-resolved systems are prone to severe artefact. We believe that optical tomography reconstruction methods can now be reliably applied to a wide variety of real clinical data. The expected resolution of the method is poor, meaning that it is unlikely that the type of high-resolution images seen in computed tomography or medical resonance imaging can ever be obtained. Nevertheless we strongly expect the functional nature of these images to have a high degree of clinical significance.

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The finite element method for the propagation of light in scattering media: Boundary and source conditions

Cited by 554 publications

References 0 publications

Quantitative spectroscopic photoacoustic imaging: a review

Quantitative spectroscopic photoacoustic imaging: a review

Diffuse Optical Imaging

Image reconstruction in optical tomography

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