Determination of the initial beam parameters in Monte Carlo linac simulation

For Monte Carlo linac simulations and patient dose calculations, it is important to accurately determine the phase space parameters of the initial electron beam incident on the target. These parameters, such as mean energy and radial intensity distribution, have traditionally been determined by matching the calculated dose distributions with the measured dose distributions through a trial and error process. This process is very time consuming and requires a lot of Monte Carlo simulation experience and computational resources. In this paper, we propose an easy, efficient, and accurate method for the determination of the initial beam parameters. We hypothesize that (1) for one type of linacs, the geometry and material of major components of the treatment head are the same; the only difference is the phase space parameters of the initial electron beam incident on the target, and (2) most linacs belong to a limited number of linac types. For each type of linacs, Monte Carlo treatment planning system (MC-TPS) vendors simulate the treatment head and calculate the three-dimensional (3D) dose distribution in water phantom for a grid of initial beam energies and radii. The simulation results (phase space files and dose distribution files) are then stored in a data library. When a MC-TPS user tries to model their linac which belongs to the same type, a standard set of measured dose data is submitted and compared with the calculated dose distributions to determine the optimal combination of initial beam energy and radius. We have applied this method to the 6 MV beam of a Varian 21EX linac. The linac was simulated using EGSNRC/BEAM code and the dose in water phantom was calculated using EGSNRC/DOSXYZ. We have also studied issues related to the proposed method. Several common cost functions were tested for comparing measured and calculated dose distributions, including χ², mean absolute error, dose difference at the penumbra edge point, slope of the dose difference of the lateral profile, and the newly proposed κ_α factor (defined as the fraction of the voxels with absolute dose difference less than α%). It was found that the use of the slope of the lateral profile difference or the difference of the penumbra edge points may lead to inaccurate determination of the initial beam parameters. We also found that in general the cost function value is very sensitive to the simulation statistical uncertainty, and there is a tradeoff between uncertainty and specificity. Due to the existence of statistical uncertainty in simulated dose distributions, it is practically impossible to determine the best energy/radius combination; we have to accept a group of energy/radius combinations. We have also investigated the minimum required data set for accurate determination of the initial beam parameters. We found that the percent depth dose curves along or only a lateral profile at certain depth for a large field size is not sufficient and the minimum data set should include several lateral profiles at various depths as well as the central axis percent depth dose curve for a large field size.