Calculating 1/β2p2 for most likely path estimates for protons and helium ions using an analytical model. (September 2021) - Kaser, Stefanie; Bergauer, Thomas; Hirtl, Albert; Irmler, Christian; Pitters, Florian; Ulrich-Pur, Felix
Highlights: Kinematic terms for protons and helium ions were calculated with an analytical model. The terms were used to calculate most likely path estimates for ion CT. Comparisons with path estimates based on Monte Carlo simulations were made. Average RMS between both path estimates and real ion path were analyzed. Abstract: In ion computed tomography, limited spatial resolution can be related to the non-straight path of ions resulting from multiple Coulomb scattering in the object to be imaged. By including sophisticated path estimates such as most likely path (MLP) or optimized cubic spline into the image reconstruction algorithm, the achieved spatial resolution can be substantially improved compared to assuming a simple straight line path only. The typically used implementation of the MLP is a matrix-based approach employing Bayesian statistics and modelling multiple Coulomb scattering as Gaussian distribution. For the elements of the scattering matrices, the term 1 / β ( w ) 2 p ( w ) 2, depending on the momentum and velocity of an ion within a phantom depth w, has to be known and integrated along the depth w . Usually, this term is extracted from a Monte Carlo simulation and approximated by a polynomial fit to solve the integral. In the present study, an existing analytical model for ion ranges and stopping powers was used to calculate 1 / β ( w ) 2 p ( w ) 2 and the scattering matrices for the MLP and was tested for protons and helium ions. The model was investigated for 10 cm to 40 cm water targets and initial energies ranging from 150 MeV to 300 MeV for protons and 150 MeV/u to 300 MeV/u for helium ions. In all cases, the calculated value obtained for 1 / β ( w ) 2 p ( w ) 2 was compared to a GATE simulation. The difference between root-mean-square errors of MLP estimates using calculated and simulated 1 / β ( w ) 2 p ( w ) 2 values were found to be smaller than 3 μm for all investigated water targets and energies.