The optical inverse problem in quantitative photoacoustic tomography

Photoacoustic tomography relies on the generation of ultrasound due to optical absorption to produce high resolution images with rich optical absorption-based contrast. In quantitative photoacoustic tomography, the aim is to estimate the concentration of the chromophores and thus provide functional information in addition to the structural images. This is a challenging task due to the unknown and spatially and spectrally varying light fluence within the tissue, which causes the photoacoustic images to be nonlinearly related to the chromophore concentrations. This thesis approaches this problem from two perspectives: Firstly, the conditions under which two linear quantification methods, linear spectroscopic inversion (SI) and independent component analysis (ICA), provide accurate results are investigated. Secondly, the statistical independence between the chromophores is used to improve the robustness and hence the usefulness of nonlinear model-based inversion methods in experimental settings. Using simulated images of a mouse brain, SI was shown to estimate the blood oxygenation within 5% error for a large range of imaging depths (0-9mm) and oxygenation levels (60-100%) if a large number of evenly spread wavelengths (>17) from the range 670-1000nm were used. Based on simulated and experimental images of tissue mimicking phantoms, ICA was shown to estimate the relative concentrations more accurately than SI when the spectral matrix is ill-conditioned and when the absorption of vessel-like features is approximately 0.5mm-1, under the assumption that the chromophores are statistically independent and a first order fluence correction has been applied. To reduce the sensitivity of model-based inversion to model-mismatch, a measure of the statistical independence between the chromophores was included in the error functional in addition to the least-squares data error. By minimising the new error functional using a gradient-based optimisation algorithm, more accurate quantification was obtained for both simulated and experimentally acquired phantom images in the presence of experimental uncertainties