A reconstruction approach for proton computed tomography by modeling the integral depth dose of the scanning proton pencil beam

Purpose To present a proton computed tomography (pCT) reconstruction approach that models the integral depth dose (IDD) of the clinical scanning proton beam into beamlets. Using a multilayer ionization chamber (MLIC) as the imager, the proposed pCT system and the reconstruction approach can minimize extra ambient neutron dose and simplify the beamline design by eliminating an additional collimator to confine the proton beam. Methods Monte Carlo simulation was applied to digitally simulate the IDDs of the exiting proton beams detected by the MLIC. A forward model was developed to model each IDD into a weighted sum of percentage depth doses of the constituent beamlets separated laterally by 1 mm. The water equivalent path lengths (WEPLs) of the beamlets were determined by iteratively minimizing the squared L2-norm between the forward projected and simulated IDDs. The final WEPL values were reconstructed to pCT images, that is, proton stopping power ratio (SPR) maps, through simultaneous algebraic reconstruction technique with total variation regularization. The reconstruction process was tested with a digital cylindrical water-based phantom and an ICRP adult reference computational phantom. The mean of SPR within regions of interest (ROIs) and the WEPL along a 4 mm-wide beam (WEPL4mm${\rm{WEP}}{{\rm{L}}_{4{\rm{mm}}}}$) were compared with the reference values. The spatial resolution was analyzed at the edge of a cortical insert of the cylindrical phantom. Results The percentage deviations from reference SPR were within +/- 1% in all selected ROIs. The mean absolute error of the reconstructed SPR was 0.33%, 0.19%, and 0.27% for the cylindrical phantom, the adult phantom at the head and lung region, respectively. The corresponding percentage deviations from reference WEPL4mm${\rm{WEP}}{{\rm{L}}_{4{\rm{mm}}}}$ were 0.48 +/- 0.64%, 0.28 +/- 0.48%, and 0.22 +/- 0.49%. The full width at half maximum of the line spread function (LSF) derived from the radial edge spread function (ESF) of a cortical insert was 0.13 cm. The frequency at 10% of the modulation transfer function (MTF) was 6.38 cm(-1). The mean signal-to-noise ratio (SNR) of all the inserts was 2.45. The mean imaging dose was 0.29 and 0.25 cGy at the head and lung region of the adult phantom, respectively. Conclusion A new pCT reconstruction approach was developed by modeling the IDDs of the uncollimated scanning proton beams in the pencil beam geometry. SPR accuracy within +/- 1%, spatial resolution of better than 2 mm at 10% MTF, and imaging dose at the magnitude of mGy were achieved. Potential side effects caused by neutron dose were eliminated by removing the extra beam collimator.