Subject Ph. D.

Context. Biophotonics and biomedical optics are major fields of research involved in the development of innovative medical methods and devices [1] enabling non-invasive in vivo characterisation of biological tissues. In this context, CRAN has developed and patented the SpectroLive device, whose industrial and clinical transfer has enabled the acquisition of the richest published spectroscopic database (largest number of samples per diagnostic class) known to date in the field of skin cancer. As part of the clinical implementation of tissue optical spectro-imaging methods for the diagnosis of human skin cancers, the development of reliable methods for estimating the optical parameters (absorption, diffusion) of healthy and pathological tissues in vivo from these spectra is a major challenge and a very active area of research.

Objectives. Radiative transfer models governing light-matter interactions are typically approximated using Monte Carlo methods, in which a large number of photon trajectories are randomly drawn according to laws parameterised by the local optical coefficients of the medium. In the context of skin spectroscopy, multi-layer Monte Carlo (MC) methods are the state of the art in direct simulations [2]. This project considers the associated inverse problem, where we seek to determine the optical parameters from a set Y of spectra (measured under the same conditions). In practice, it is possible to reduce the problem to recovering a small vector of parameters p*, corresponding schematically to the concentrations of the different chromophores present in the medium. The standard variational approach then consists in finding p* as a solution to (1) minimiser par rapport à p > 0 F(p) := L(MC(p), Y) + t * R(p) where L and R are cost functions to be determined, modelling data attachment and regularisation respectively, and t>0 controls the balance between the two terms. Problem (1) can be solved using particle swarm approaches [3]. This thesis aims to study terms L and R that guarantee the robustness of the solutions to (1). In particular, we will focus on the following challenges: A) As standard least squares data fidelity terms are sensitive to spectra heterogeneity and sensor calibration [4], this thesis will consider robust alternatives to normalisation deviations, such as unbalanced optimal transport distances [5]. These innovative approaches will be combined with layer reweighting, as in [2], in order to obtain a fine inverse estimation of multi-layer models. B) Regularisation reduces the set of possible minimizers to a small number of solutions sharing a common prior, defined by the regularisation function R. For example, choosing R(p) as the sum of the coefficients (in absolute value) will favour the appearance of zeros in the solution, i.e. in practice, the total extinction of certain chromophores. Based on prior knowledge of the composition of the different layers of the skin, a biologically informed, multi-layer regularisation term will be developed to ensure the robustness of the estimation (1); C) The first two points will be addressed by focusing on diffuse reflectance data, which is easier to model. The final stage of the project will consist in adapting our approaches to fluorescence measurements, which are crucial in estimating optical properties. The methods developed during the thesis will be evaluated on the SpectroLive data, adapting in particular the algorithm in [3].

References: [1] Blondel et al. (2021) "Spatially-Resolved Multiply-Excited Autofluorescence and Diffuse Reflectance Spectroscopy: SpectroLive Medical Device for Skin In Vivo Optical Biopsy," Electronics, 10(3):243. ?hal-03380396? [2] Colas et al. (2021) ''Proposal for a Skin Layer-Wise Decomposition Model of Spatially-Resolved Diffuse Reflectance Spectra Based on Maximum Depth Photon Distributions: A Numerical Study,'' Photonics, 8(10), 444. ?hal-03377401? [3] Kholodtsova et al. (2014) ''Particle Swarm Optimisation Algorithm for Monte Carlo-based Inverse Problem Solving'', 2014 ICLO, 1-1. ?hal-01078901? [4] Colas et al. (2023) "Photometric and Monte-Carlo modeling unified approach for the calculation of spatially-resolved correction coefficients linking simulated and experimental diffuse reflectance spectra," Optics Express, 31(16), 25954-25969. ?hal-04170118? [5] Peyré et Cututri. (2018) "Computational Optimal Transport : With Applications to Data Science,'' Foundations and Trends in Machine Learning, 11(5-6), 355-607. ?hal-02411770?