A comprehensive study of the most likely path formalism for proton-computed tomography

We investigate some generalizations of the most likely path formalism developed for proton-computed tomography. The stochastic path of a proton inside a homogeneous medium is replaced by a deterministic smooth path that maximizes the probability of the proton passing through the points on this curve, given measured entrance and exit parameters for each individual proton. We study various factors that influence this curve and the associated error envelopes. These factors are the influence of the energy loss, a logarithmic correction factor in the small angle Coulomb scattering and the importance of path length versus material thickness. We develop a method for further constraining the possible proton paths by including energy information in the derivation of the most likely path, utilizing an infinite-dimensional constrained functional analysis method. It is shown that while there is an additional uncertainty on the most likely path that is difficult to determine experimentally, the associated error envelopes are smaller, resulting in possibly slightly improved spatial resolution for proton-computed tomography.