Development of novel light propagation algorithms in turbid media with varying optical heterogeneity

The field of biomedical imaging has experiences a rapid growth in recent years driven by i) theincreased demand for better disease detection and therapy monitoring and ii) the desire tovisualize biology even at the nanoscopic level. This growth has been supported by theimplementation of ad-hoc designed experimental systems and related theoretical andcomputational/numerical support methods. In this dynamic environment, the continuousmedical request for harmless imaging probes and higher resolution, has ultimately pushed theimaging research community towards the developing of novel techniques in the opticalwavelength regime. The high resolution, especially in microscopy, and the flexibility in therealization of optical setups favored the kick-start of optical imaging techniques, which havefinally met their main challenge into the highly scattering of light in biological tissue. Especiallyfor biological samples, the numerous scattering events occurring during the photon propagation process limit the penetration depth and the possibility to perform direct imaging in thicker and not transparent samples. To overcome this limitation, numerous theoretical strategies where proposed to isolate the scattering contribution, minimize the image blurring and reduce the speckled noise due to the random light-path scrambling induced by the complex variation of refractive index in biological tissues. In this thesis, we will examine theoretically and experimentally the scattering process from two opposite points of view, tackling at the same time specific challenges in optical imaging science. We start by examining the light propagation in diffusive biological tissues considering the particular case of the presence of optically transparent regions enclosed in a highly scattering environment. We will point out how, the correct inclusion of this information, can ultimately lead to higher resolution reconstructions and especially aiming at brain tumor neuroimaging. We examined in details the increased accuracy in the forward modelling of the fluorescent emission of spherical tumor distributions in a mouse head, in particular if compared with other currently used techniques. We then examine the extreme case of the three-dimensional imaging of a totally hidden sample, in which the phase has been scrambled by a random scattering layer. By using appropriate numerical methods, we prove the possibility to perform such hiddenreconstructions in a very efficient way, opening the path toward the unexplored field of threedimensional hidden imaging. We present how, the properties described while addressingthese challenges, lead us to the development of a novel alignment-free three-dimensionaltomographic technique that we refer to as Phase-Retrieved Tomography. We have proved thismethod theoretically and used it for the study of the fluorescence distribution in a threedimensional spherical tumor model, the multicellular cancer cell spheroid, one of the most important biological models for the study of such a complex disease. We finally conclude our study, by imaging spherical tumors under two extremely different experimental conditions, improving the depth to resolution ratio of the current state of the art in live microscopic imaging, as defined by Light Sheet Fluorescence Microscopy. Throughout the whole doctoral period, these studies have been stimulating and creating new questions and ideas, which will be discussed in the following and that form the natural continuation of the projects exposed in the present thesis.