Experimental determination and verification of the parameters used in a proton pencil beam algorithm.

We present an experimental procedure for the determination and the verification under practical conditions of physical and computational parameters used in our proton pencil beam algorithm. The calculation of the dose delivered by a single pencil beam relies on a measured spread-out Bragg peak, and the description of its radial spread at depth features simple specific parameters accounting individually for the influence of the beam line as a whole, the beam energy modulation, the compensator, and the patient medium. For determining the experimental values of the physical parameters related to proton scattering, we utilized a simple relation between Gaussian radial spreads and the width of lateral penumbras. The contribution from the beam line has been extracted from lateral penumbra measurements in air: a linear variation with the distance collimator-point has been observed. Analytically predicted radial spreads within the patient were in good agreement with experimental values in water under various reference conditions. Results indicated no significant influence of the beam energy modulation. Using measurements in presence of Plexiglas slabs, a simple assumption on the effective source of scattering due to the compensator has been stated, leading to accurate radial spread calculations. Dose measurements in presence of complexly shaped compensators have been used to assess the performances of the algorithm supplied with the adequate physical parameters. One of these compensators has also been used, together with a reference configuration, for investigating a set of computational parameters decreasing the calculation time while maintaining a high level of accuracy. Faster dose computations have been performed for algorithm evaluation in the presence of geometrical and patient compensators, and have shown good agreement with the measured dose distributions.

A model for the lateral penumbra in water of a 200-MeV proton beam devoted to clinical applications.

An experimental approach for modeling the lateral penumbra of a proton beam has been investigated. Measurements were made with a silicon diode in a water tank. Several geometrical configurations (phantom position, collimator-to-surface distance, collimator diameter, bolus thickness, air gap, etc.) and beam characteristics (range, modulation, etc.) have been studied. The results show that the lateral penumbra is almost independent of the beam modulation and the diameter of the collimator. The use of scaled variables for depth and penumbra allows us to represent the increase in penumbra with depth for any configuration with a second order polynomial function, provided that the penumbra at the entrance of the medium and at the depth of the range are known.