A finite-size pencil beam model for photon dose calculations in three dimensions

A three-dimensional dose computation model employing a finite-size, diverging, pencil beam has been developed and is demonstrated for Cobalt-60 gamma rays. The square cross-section pencil beam is simulated in a semi-infinite water phantom by convolving the pencil beam photon fluence with the Monte Carlo point dose kernel for Cobalt-60. This finite-size pencil beam is calculated one time and becomes a new data base with which to build larger beams by two-dimensional superposition. The pencil beam fluence profile, angle correction for beam divergence, the Mayneord inverse square correction, radial and angular sampling rates, error propagation, and computation time have been investigated and are reported. Radial and angular sampling rates have a great effect on accuracy and their appropriate selection is important. Percent depth doses calculated by finite-size pencil beam superposition are within 1% of values calculated by full convolution and the agreement with values from the literature is within 6%. The latter disagreement is shown to be due to a low-energy photon component which is not modeled in other calculations. Computation time measurements show the pencil beam method to be faster than full convolution and one implementation of the differential-scatter-air-ratio (dSAR) method.