Technical Note: A direct ray-tracing method to compute integral depth dose in pencil beam proton radiography with a multilayer ionization chamber.

PURPOSE: To introduce a fast ray-tracing algorithm in pencil proton radiography (PR) with a multilayer ionization chamber (MLIC) for in vivo range error mapping.

METHODS: Pencil beam PR was obtained by delivering spots uniformly positioned in a square (45 × 45 mm(2) field-of-view) of 9 × 9 spots capable of crossing the phantoms (210 MeV). The exit beam was collected by a MLIC to sample the integral depth dose (IDDMLIC). PRs of an electron-density and of a head phantom were acquired by moving the couch to obtain multiple 45 × 45 mm(2) frames. To map the corresponding range errors, the two-dimensional set of IDDMLIC was compared with (i) the integral depth dose computed by the treatment planning system (TPS) by both analytic (IDDTPS) and Monte Carlo (IDDMC) algorithms in a volume of water simulating the MLIC at the CT, and (ii) the integral depth dose directly computed by a simple ray-tracing algorithm (IDDdirect) through the same CT data. The exact spatial position of the spot pattern was numerically adjusted testing different in-plane positions and selecting the one that minimized the range differences between IDDdirect and IDDMLIC.

RESULTS: Range error mapping was feasible by both the TPS and the ray-tracing methods, but very sensitive to even small misalignments. In homogeneous regions, the range errors computed by the direct ray-tracing algorithm matched the results obtained by both the analytic and the Monte Carlo algorithms. In both phantoms, lateral heterogeneities were better modeled by the ray-tracing and the Monte Carlo algorithms than by the analytic TPS computation. Accordingly, when the pencil beam crossed lateral heterogeneities, the range errors mapped by the direct algorithm matched better the Monte Carlo maps than those obtained by the analytic algorithm. Finally, the simplicity of the ray-tracing algorithm allowed to implement a prototype procedure for automated spatial alignment.

CONCLUSIONS: The ray-tracing algorithm can reliably replace the TPS method in MLIC PR for in vivo range verification and it can be a key component to develop software tools for spatial alignment and correction of CT calibration.