Modélisation et représentation dans l'espace des phénomènes photoniques inélastiques en biophotonique

This master's thesis focuses on mathematical modelling to address the spatiality of Raman spectroscopy and fluorescence signals to assist instrumentation and diagnostics. Firstly, this thesis presents a simulation technique adapted to a broad spectrum of photon-matter interaction based on the Monte Carlo path tracing resolution for discrete domains. The developed algorithm, the hidden path of photons, notably supports linear phenomena, namely absorption and spontaneous emission, elastic and inelastic scattering (Raman), reflections, refractions and fluorescence. The model was designed with the objective of being adapted to the complexity of biological environments, of interactions and of geometries. The discrete representation of space is performed by Marching Cube and the set of phenomena is simulated simultaneously, for several discrete wavelengths, in order to support the interactions between the phenomena (crosstalk) and to produce a physically exact solution. The solution has been implemented in a general-purpose processing on graphics processing units format by adaptation of the 3D pipeline. The presented algorithm also addresses methods to limit the use of memory in order to present a non-prohibitive solution to Raman diffusion and fluorescence at several wavelengths. In addition, the proposed solution integrates a camera, a visualization of fluence and a 3D visualization of photons to be adapted to the field of biophysics. Finally, the algorithms developed are validated by the prediction of known results on a theoretical and empirical basis. The simulator represents a theoretical method for calibrating optical measuring instruments and determining the spatial range of a signal. Secondly, this thesis proposes dimensionality reduction methods to optimize the automated recognition of data volumes related to optical modalities in biomedical contexts. Two optical modalities are more specifically targeted, namely Raman microscopy and optical coherence tomography. In the first case, a tool performing chemometrics analysis was developed to reproduce histologic staining images with traditional microscopy. The algorithm has been proposed for samples fixed on aluminium microscope slides. By evaluating the contribution of the measured signal on an empty slide, algorithm seeks to evaluate the drop in concentration of the compounds of interest, making analogy to the gradual transparency in histology, thus offering a more faithful representation.