Point flux PL-estimators for Monte Carlo dose calculations

At 3D dosimetry planning in radiation therapy, point flux PL-estimators are convenient for Monte Carlo dose calculations in a human body. The method of construction of PL-estimators is based on a property of local optical invariance under spatial shifts of trajectories of the Markov process related to the transport equation. It allows one to receive unbiased estimators, possessing a final variance and a property of continuity of the estimator as a function of a detecting point at each point of continuity of an estimated functional. The algorithm of dose calculation with use of PL-estimators includes the following steps: (a) construction of the main trajectory in the infinite homogeneous water medium; (b) construction of "enclosed" trajectory with smaller number of links, "close" to the main trajectory; (c) construction of a set of similar trajectories (in the case of a heterogeneous medium with various chemical structure); (d) calculation of the contribution to the dose value at each detecting point. The dose calculation time with use of the given algorithm is directly proportional to the number of detecting points.