4Spots and beamletsBeam beamlets or pencil beams (defined by the resolution of the calculation grid)The dose from each beamlet is evaluated (at the vertices of the calculation grid)The spot dose is calculated (as the sum of the dose contributions of the corresponding beamlets, weighted for the position of each beamlet within the spot)
5Sx and Sy depend on zspot depends on the density and on zbeamlet
6Optimisation: a closer look Desired dose at point i: piDose delivered at point i: di = aij xj(sum over all sources j)Objective function: Fobj = (di - pi)2(sum over target points)+ contribution due to the violation of dose-limit constraints (for targets and organs)+ contribution due to the violation of dose-volume constraints (for organs)
8Strategy in the optimisation Pre-optimisation Reasonable initial ‘guess’ for the weights Convergence two consecutive iterationsyield improvement below 5%Main optimisation Full implementation of a methodyield improvement below 0.1%
9Toy exampleA phantom has been created with three important structures: one target and two organs; some inhomogeneity has been introduced (an additional structure simulating the presence of a bone)Pixel size: 2.5mmSpot advance in y (scanning direction): 2.5mmSpot advance in x: 5mmCut-off for dose contributions: 3 standard deviations
20ConclusionsAs far as the dose distribution is concerned, three optimisation methods (CG, SA, and PSI) yield results which seem to be in good agreement. Very similar dose distributions may be obtained on the basis of very different weight distributions.The use of raw (unfiltered) weights does not seem to create cold/hot spots within the irradiated volume. It remains to be seen whether, in some occasions, filtering will be called for.
21Under consideration…Other forms of the objective function to be tried?Strategy in the optimisation: an improvement of about 25% was found in the execution time in case that the target dose is firstly optimised (with vanishing dose everywhere else)Other optimisation methods to be tried?