Light Propagation Modeling in a Mie-Scattering Dominated Scintillator

We present an analytical approach to model light propagation in a highly scattering, opaque organic scintillator, as used in the novel positron emission tomography detector concept LiquidO. In this detection scheme, annihilation photons undergo multiple Compton scatterings, each producing a localized light emission. The scintillating medium being opaque, the scintillation light is confined near its emission point, mainly by Mie scattering. Each annihilation photon interaction is characterized by a succession of light balls, collected by a lattice of optical fibers that are read out at both ends. Simulating optical photons using Monte-Carlo (MC) methods, as implemented in Geant4 and Gate, requires substantial computational resources and introduces statistical noise. To address this, we developed an analytical model (AM) to predict the spatial and temporal probability density function of optical photons in a scintillating, scattering and absorbing medium. The model combines isotropic random walk dynamics with a 2-D polynomial parameterization to account for anisotropic scattering, by correcting the transport parameters for a double-lobe Henyey-Greenstein phase function with opposite asymmetry factors and a tunable forward-to-backward lobe ratio. Validated against MC simulations, the model predicts spatial and temporal photon distributions with an average relative deviation of 1.60% for the mean radius per time slice r(t) and 0.42% for the mean time per radial slice tr , while being between 289 and 967 times faster than MC simulations. Its validity spans optical parameters with scattering mean free path of 2-5 mm, asymmetry factor between 0.3-0.7, and forward-to-backward scattering ratio of 0.25-1. The proposed AM can be used to speed up optical simulations, with applications in detector design, event reconstruction, optimization of medium optical properties, and modeling of highly scattering media.