Purpose: C-arm linac-based radiotherapy has seen a recent interest in deliveries with dynamic rotations, principally 4π methods using simultaneous rotations of couch and gantry to reduce doses to organs-at-risk (OARs) and increase conformity. While many methods use heuristics to generate trajectories that avoid OARs combined with arbitrary trajectory restrictions to prevent oversampling, a metric has not yet been developed to succinctly quantify the sampling of the deliverable space with trajectories.
Methods: Evenly spaced sampling points were distributed across a 4π sphere centred on isocentre. Six trajectories which increased sampling of the 4π space were applied, and the minimum arc distance between each sampling point and the nearest point of the trajectory was measured. The distribution of all arc distances was then condensed by taking the mean arc distance to represent the 4π sampling of each trajectory. An open-source treatment planning system, matRad, was used to generate 192 treatment plans to establish the relationship between isodose volumes and trajectory mean arc distance for eight target volumes in four positions and for the six trajectories.
Results: A monotonic relationship between mean arc distance and trajectories that intuitively increased sampling was found. The impact of isodose sparing increases with increased sampling at all levels above 2.0 % of prescription dose. The impact of sparing is exponential, with isodoses between 2.5% and 50% of prescription being reduced most significantly. Reduction of absolute isodose volume with increased 4π sampling is highly dependent on target volume.
Conclusion: Mean arc distance is a representative means of quantifying 4π sampling. Trajectories that increase sampling are useful in decreasing the volume of isodoses relevant for sparing normal tissues. By quantifying this feature, candidate dynamic trajectories can be efficiently compared for sampling. This metric may also have broader applications in radiotherapy when seeking to increase sampling by adding non-axial trajectories.
Funding Support, Disclosures, and Conflict of Interest: All authors acknowledge research support from Brainlab AG, and the Atlantic Canadian Opportunities Agency (ACOA).