A proposed alternative to phase-space recycling using the adaptive kernel density estimator method

We have implemented a nonparametric density estimation technique, the adaptive kernel density estimator (AKDE), to generate additional phase space (PS) variables in the vicinity of simulated PS points in Monte Carlo linear accelerator simulation. The method involves the placement of kernels at simulated PS points that have a "window width" that depends on the density of simulated PS points. This method has been tested on known one-dimensional (1-D) and two-dimensional (2-D) probability density functions (PDFs) and has been used to sample (photons only) from PS files generated from accelerator simulations. The original simulated PS vector (x, y, u, v, E) was reduced to a rotationally invariant PS vector (r, theta, alpha, E) that takes advantage of the azimuthal symmetry (phi) above the collimating jaws. The new PS vector (r', theta', alpha', E') is sampled in the vicinity of the sampled PS vector (r, theta, alpha, E). The first step in assessing the accuracy of the method was a correlation analysis among the AKDE generated PS variables compared with correlations among the original PS variables. "In-air" particle fluence distributions between AKDE samples and the original PS distribution showed agreement within 2% (-8.8% to 6.8%) across the entire phase space plane. Central axis energy distributions and angular distributions agreed on average to within 1.5% (range = -1.5% to 6.6%) and 0.1% (range = 0 to 3.0%), respectively. Dose profiles were calculated for field sizes 3 x 3 cm2, 10 x 10 cm2, and 30 x 30 cm2 for AKDE and compared against calculations performed with PS recycling. AKDE calculated depth doses and profiles were within 2% and 2%/1 mm, respectively, of those computed using PS recycling.