Energy-adaptive calculation of the most likely path in proton CT

This note addresses an issue faced by every proton computed tomography (CT) reconstruction software: the modelling and the parametrisation of the multiple Coulomb scattering power for the estimation of the most likely path (MLP) of each proton. The conventional approach uses a polynomial model parameterised as a function of depth for a given initial beam energy. This makes it cumbersome to implement a software that works for proton CT data acquired with an arbitrary beam energy or with energy modulation during acquisition. We propose a simple way to parametrise the scattering power based on the measured proton CT list-mode data only and derive a compact expression for the MLP based on a conventional MLP model. Our MLP does not require any parameter. The method assumes the imaged object to be homogeneous, as most conventional MLPs, but requires no information about the material as opposed to most conventional MLP expressions which often assume water to infer energy loss. Instead, our MLP automatically adapts itself to the energy-loss which actually occurred in the object and which is one of the measurements required for proton CT reconstruction. We validate our MLP method numerically and find excellent agreement with conventional MLP methods.