a Finite-Size Pencil Beam Model for Three-Dimensional Photon Dose Calculations.

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 generated in a simulated, semi-infinite water phantom by convolving the photon fluence for a point source with the point dose kernel for Cobalt-60 calculated by the Monte Carlo method. The finite-size pencil beam is calculated once and becomes a new data base with which to build real beams by two-dimensional superposition. Aspects of pencil beam generation have been studied. Beam profile choice and angle correction for beam divergence have negligible effects on the pencil beam dose distribution. Radial and angular sampling rates have a great effect on the dose distribution and appropriate selection of these two rates is important. Error estimation is coupled to the geometry of pencil beam and dose kernel intersections. Two comparisons show the pencil beam method to work quite well. In the first, percent depth doses calculated by pencil beam superposition agree very well with full convolution calculations. In the second, there is good agreement with measured data and differences are attributed to a low energy photon component in the beam which is not modeled. These differences demonstrate the importance of adequately simulating the entire photon spectrum for a real beam. Computation time measurements show the pencil beam method to be a much faster alternate to calculating beams with the full convolution or dSAR methods. The combination of three-dimensional capability and fast computation speed make the finite-size pencil beam model attractive for routine clinical use after further development.