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 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 most likely path (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. 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. Our MLP does not require any parameter. The method assumes the imaged object to be homogeneous, as most conventional MLPs, but makes no assumption about the kind of material as opposed to most conventional MLP expressions which generally assume water. 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. Our results indicate that this might improve spatial resolution in proton CT images of objects which are significantly different from water, e.g.~the lungs. We validate our MLP method numerically and find excellent agreement with conventional MLP methods.