A theoretical framework to predict the most likely ion path in particle imaging

In this work, a generic rigorous Bayesian formalism is introduced to predict the most likely path of any ion crossing a medium between two detection points. The path is predicted based on a combination of the particle scattering in the material and measurements of its initial and final position, direction and energy. The path estimate's precision is compared to the Monte Carlo simulated path. Every ion from hydrogen to carbon is simulated in two scenarios to estimate the accuracy achievable: one where the range is fixed and one where the initial velocity is fixed. In the scenario where the range is kept constant, the maximal root-mean-square error between the estimated path and the Monte Carlo path drops significantly between the proton path estimate (0.50 mm) and the helium path estimate (0.18 mm), but less so up to the carbon path estimate (0.09 mm). In the scenario where the initial velocity is kept constant, helium have systematically the minimal root-mean-square error throughout the path. As a result, helium is found to be the optimal particle for ion imaging.