Monte Carlo evaluation of kerma at a point for photon transport problems

Estimation of collision kerma at a geometric point arising from scattered photons is a potentially important application of Monte Carlo simulation, especially in the presence of steep flux gradients. We examine the usual method of extracting point-kerma estimates from randomly generated photon trajectories which consists of tallying the energy lost by photon collisions occurring in the vicinity of the point of interest. Several other methods derived from the equivalence of track length per unit volume and flux are evaluated as to accuracy and efficiency. Finally, a next-flight estimator is discussed in which the expected contribution of each simulated photon collision to kerma at the point of interest is calculated regardless of proximity of the collision to the point. All of these techniques are shown to involve a trade-off between statistical precision and spatial resolution: increasing the number of contributing collisions requires averaging kerma over a larger volume. Based upon both analytic models and realistic Monte Carlo simulations, use of next-flight and track-length estimators is shown to improve simulation efficiencies by factors of 2 to 20 compared to analog scoring. Practical guidelines as to choice of estimator and successful implementation are presented.