Comparison of Monte Carlo and diffusion approximation simulations in optical tomography

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Perustieteiden korkeakoulu | Master's thesis
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Date

2023-08-22

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Major/Subject

Mathematics

Mcode

SCI3054

Degree programme

Master’s Programme in Mathematics and Operations Research

Language

en

Pages

v + 80

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Abstract

Optical tomography is a non-invasive, low-cost alternative to traditional radiological techniques. However, its poor resolution is its main disadvantage. Consequently, reconstructing the scattering coefficient μs and especially the absorption coefficient μa at high accuracy has been an important problem in optical tomography, especially in the field of medical imaging. This is important as the capability to produce an accurate reconstruction can improve the quality of the generated images. In order to do so, one needs to first study how to simulate light propagation inside the illuminated domain in a manner that is accurate and efficient. The aim of this thesis is to compare the outward photon flux predictions by two well-known simulation methods; Monte Carlo (MC) for the radiative transfer equation (RTE) and its diffusion approximation (DA), and study if they produce comparable results. We investigate this under three possible cases: a case where the domain is a homogeneous strongly scattering disk under a homogeneous inward photon flux, a case where the domain is a homogeneous strongly scattering disk under a general inward photon flux and lastly, a case where the domain is a strongly scattering disk with an annular non-scattering region. For the last case, the non-scattering region is modelled in the DA by certain non-local boundary conditions. Our main point of investigation is to see how the absorption coefficient μa, the scattering coefficient μs, the absorption coefficient for the annular non-scattering region μ ̃a and the width non-scattering region affect the discrepancy between MC and the DA. By default, the scattering coefficient for the annular non-scattering region is set to zero. The effect of these parameters on the predicted outward photon flux for both MC and the DA can also be used to check how well they can be detected on the boundary of the illuminated domain. The general conclusion is that MC and the DA produce similar outward photon flux predictions if enough photon packets are used for the MC simulations and the inward flux of photons does not have quick spatial variations.

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Supervisor

Hyvönen, Nuutti

Thesis advisor

Hyvönen, Nuutti

Keywords

optical tomography, Diffusion Approximation (DA), Monte Carlo (MC), radiative transfer equation (RTE), inward flux, outward flux

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https://urn.fi/URN:NBN:fi:aalto-202309035545

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[dipl] Perustieteiden korkeakoulu / SCI