Quantitative photo-acoustic Imaging based on data normalisation : application to the reconstruction of the opto-mechanical properties of the intervertebral disc

The inverse problem in quantitative photoacoustic imaging (QPAI), particularly in optical inversion, presents significant challenges for accurate image reconstruction due to the nonlinearity of photoacoustic signal. In this study, we introduce a novel reconstruction strategy specifically tailored for imaging the intervertebral disc (IVD), a biphasic tissue primarily composed of water and collagen. This work offers two key contributions: (1) the development of a new model-based optical inversion method that leverages the ratio of multi-wavelength photoacoustic measurements to define the cost function-circumventing the need for prior knowledge of the Grüneisen parameter, which is typically difficult to estimate; and (2) a first demonstration of QPAI's potential to non-invasively probe the biochemical composition of the IVD, particularly its water-to-collagen ratio. A non-linear model-based reconstruction approach was implemented, using the adjoint variables method to express gradients, and Monte Carlo simulations to solve the Radiative Transfer equation for both the forward and adjoint problems. Several scenarios were investigated, and a method was proposed that does not rely on prior knowledge of the Grüneisen coefficient. A numerical study was conducted using a digitised pig's disc and opto-mechanical properties sourced from the literature, under measurement configurations compatible with experimental setups. The results show that the derived ratio-based cost function in the model-based optical inversion scheme significantly enhances the reconstructions quality, particularly when combined with appropriate regularisation, thereby validating the feasibility and robustness of the approach. Tridimensional reconstructions of the two chromophores content in the IVD, performed under the highly restricted configuration of a single illumination, were obtained with less than 5% error, along with the reconstruction of the Grüneisen coefficient with less than 15% error, up to 2 cm in depth (noiseless synthetic data) with the proposed method, with only three different wavelength measurements required.