  Purpose: Multiple Coulomb scattering (MCS) poses a challenge in proton CT
(pCT) image reconstruction. The assumption of straight paths is replaced with
Bayesian models of the most likely path (MLP). Current MLP-based pCT
reconstruction approaches assume a water scattering environment. We propose an
MLP formalism based on accurate determination of scattering moments in
inhomogeneous media. Methods: Scattering power relative to water (RScP) was
calculated for a range of human tissues and investigated against relative
stopping power (RStP). Monte Carlo simulation was used to compare the new
inhomogeneous MLP formalism to the water approach in a slab geometry and a
human head phantom. An MLP-Spline-Hybrid method was investigated for improved
computational efficiency. Results: A piecewise-linear correlation between RStP
and RScP was shown, which may assist in iterative pCT reconstruction. The
inhomogeneous formalism predicted Monte Carlo proton paths through a water cube
with thick bone inserts to within 1.0 mm for beams ranging from 210 to 230 MeV
incident energy. Improvement in accuracy over the conventional MLP ranged from
5% for a 230 MeV beam to 17% for 210 MeV. There was no noticeable gain in
accuracy when predicting 200 MeV proton paths through a clinically relevant
human head phantom. The MLP-Spline-Hybrid method reduced computation time by
half while suffering negligible loss of accuracy. Conclusions: We have
presented an MLP formalism that accounts for material composition. In most
clinical cases a water scattering environment can be assumed, however in
certain cases of significant heterogeneity the proposed algorithm may improve
proton path estimation.
