Title:
Experimental validation of the van Herk margin formula for lung radiation therapy.

Abstract:
To validate the van Herk margin formula for lung radiation therapy using realistic dose calculation algorithms and respiratory motion modeling. The robustness of the margin formula against variations in lesion size, peak-to-peak motion amplitude, tissue density, treatment technique, and plan conformity was assessed, along with the margin formula assumption of a homogeneous dose distribution with perfect plan conformity.
3DCRT and IMRT lung treatment plans were generated within the ORBIT treatment planning platform (RaySearch Laboratories, Sweden) on 4DCT datasets of virtual phantoms. Random and systematic respiratory motion induced errors were simulated using deformable registration and dose accumulation tools available within ORBIT for simulated cases of varying lesion sizes, peak-to-peak motion amplitudes, tissue densities, and plan conformities. A detailed comparison between the margin formula dose profile model, the planned dose profiles, and penumbra widths was also conducted to test the assumptions of the margin formula. Finally, a correction to account for imperfect plan conformity was tested as well as a novel application of the margin formula that accounts for the patient-specific motion trajectory.
The van Herk margin formula ensured full clinical target volume coverage for all 3DCRT and IMRT plans of all conformities with the exception of small lesions in soft tissue. No dosimetric trends with respect to plan technique or lesion size were observed for the systematic and random error simulations. However, accumulated plans showed that plan conformity decreased with increasing tumor motion amplitude. When comparing dose profiles assumed in the margin formula model to the treatment plans, discrepancies in the low dose regions were observed for the random and systematic error simulations. However, the margin formula respected, in all experiments, the 95% dose coverage required for planning target volume (PTV) margin derivation, as defined by the ICRU; thus, suitable PTV margins were estimated. The penumbra widths calculated in lung tissue for each plan were found to be very similar to the 6.4 mm value assumed by the margin formula model. The plan conformity correction yielded inconsistent results which were largely affected by image and dose grid resolution while the trajectory modified PTV plans yielded a dosimetric benefit over the standard internal target volumes approach with up to a 5% decrease in the V20 value.
The margin formula showed to be robust against variations in tumor size and motion, treatment technique, plan conformity, as well as low tissue density. This was validated by maintaining coverage of all of the derived PTVs by 95% dose level, as required by the formal definition of the PTV. However, the assumption of perfect plan conformity in the margin formula derivation yields conservative margin estimation. Future modifications to the margin formula will require a correction for plan conformity. Plan conformity can also be improved by using the proposed trajectory modified PTV planning approach. This proves especially beneficial for tumors with a large anterior-posterior component of respiratory motion.