Schweiger, Martin; (1995) Application of the Finite Element Method in Infrared Image Reconstruction of Scattering Media. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The main objective of this work was the development of a mathematical model for light propagation in a scattering medium, to be applied to a near infrared image (NIRI) reconstruction system. The model calculates the photon density within the medium, and the photon current through its surface by solving the diffusion equation numerically with the finite element method (FEM). Its main advantage, compared to other photon transport models, lies in the combination of speed and the ability to handle complex geometries and inhomogeneous absorption and scattering properties. The model includes mesh generators, FEM solvers, and processing and analysing tools. The solvers allow for the simulation of various boundary conditions and different data acquisition techniques, such as steady-state, time-of-flight and intensity modulated systems. The image reconstruction algorithm generates a spatially resolved map of the absorption and scattering parameters within the tissue from a set of measurements obtained at the boundary, where the measurement type may be one or several moments of the temporal point spread function, obtained by a time-of-flight system, or the phase shift and modulation depth obtained by a frequency domain system. The reconstruction iteratively minimises an error function which describes the difference between the true data and the ones generated with the FEM model for a given parameter distribution. Both 2D and 3D versions of the model haven been developed, although due to the high demand in computing resources only 2D reconstructions have been performed to date. Apart from the incorporation into the reconstruction algorithm, the FEM model on its own is also valuable to investigate the dependence of boundary measurements upon the optical properties of the medium, and the quantification of perturbations caused by scattering and absorbing inhomogeneities. Its ability to simulate the light distribution in highly complex geometries such as a human head makes it a useful tool for quantifying the measurements of near infrared spectroscopy (NIRS) systems.

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