Optical imaging of biological tissues

In this thesis, a new time-dependent model for describing light propagation in biological media is proposed. The model is based on the simplified spherical harmonics approximation and is represented by a set of coupled parabolic partial differential equations (TD-pSPN equations). In addition, the model is extended for modeling the time-dependent response of fluorescent agents in biological tissues and the ensuing time-domain propagation of light therein. In a comparison with Monte Carlo simulations, it is shown that the TD-pSPN equations present unique features in its derivation that makes it a more accurate alternative to the diffusion equation (DE). The TD-pSPN model (for orders N > 1) outperforms the DE in the description of the propagation of light in near-nondiffusive media and in all the physical situations where DE fails. Often, only small orders of the SP N approximation are needed to obtain accurate results.;A diffuse optical tomography (DOT) algorithm is also implemented based on the TD-pSPN equations as the forward model using constrained optimization methods. The algorithm uses time-dependent (TD) data directly. Such an approach is benefited from both the accuracy of the SPN models and the richness of TD data. In the calculation of the gradient of the objective function, a time-dependent adjoint differentiation method is introduced that reduces computation time.;Several numerical experiments are performed for small geometry media with embedded inclusions that mimic small animal imaging. In these experiments, the values of the optical coefficients are varied within realistic bounds that are representative of those found in the range of the near-infrared spectrum, including high absorption values. Single and multi-parameter reconstructions (absorption and diffusion coefficients) are performed. The reconstructed images based on the TD-pSPN equations (N > 1) give better estimates of the optical properties of the media than the DE. On the other hand, crosstalk effects and small artifacts appeared in all the cases (more intense in the DE images). Comparatively, the reconstructed images show a lesser influence of these undesirable 'effects than other approaches found in the literature. The results suggest that the DOT algorithm based on the TD-pSPN model is an accurate alternative to the DE for imaging optical properties of biological media.;These results directly benefict the fields of therapeutics and time-domain optical imaging of biological tissues. Particularly, the presented work is a decisive step in the elaboration of an optical scanner for small animal imaging at our lab. Thus, a positive impact in the areas of clinical diagnosis and biomedical research are expected.;Keywords: Light propagation in biological tissues; spectroscopy, fluorescence; time-domain diffuse optical tomography; simplified spherical harmonics equations; constrained optimization methods.