Application of an inverse kernel concept to Monte Carlo based IMRT

Inverse treatment planning by means of pencil beam algorithms can lead to errors in the calculation of dose in areas without secondary electron equilibrium. Monte Carlo (MC) simulations give accurate results in such areas but result in increased computation times. We present a new, so-called inverse kernel concept that offers MC precision in inverse treatment planning with acceptable computation times and memory consumption. Inverse kernels are matrices that describe the dose contribution from all bixels of a beam to a distinct voxel of the patient phantom. The concept is similar to other generalized pencil-beam concepts, except that inverse kernel elements are precalculated using a single MC simulation and stored as binary trees. In this procedure a modified MC code (XVMC) is applied to trace the photon history for each dose deposition. Iterative optimization is then applied in a second step. The inverse process is separated into (i) a slower MC simulation and (ii) a faster iterative optimization, followed by (iii) the segmentation procedure, and (iv) a final MC dose calculation step including a segment weight reoptimization. Inverse kernel optimization, or IKO, with segmentation and reoptimization steps is demonstrated by means of a lung cancer case. To demonstrate the superiority of an inverse MC system over pencil-beam or collapsed-cone based systems, the final result of the IKO is compared to plans where all segments have been calculated by pencil beam or collapsed cone, respectively. Dose-volume histograms and dose-difference histograms show remarkable differences, which can be attributed to systematic errors in both algorithms. IKO is a precise, nonhybrid, inverse MC treatment planning system which suits current clinical needs, as several optimization steps can follow one single MC-simulation step for a distinct beam setup.