Motion as a perturbation: Measurement-guided dose estimates to moving patient voxels during modulated arc deliveries

Abstract

To present a framework for measurement-guided VMAT dose reconstruction to moving patient voxels from a known motion kernel and the static phantom data, and to validate this perturbation-based approach with the proof-of-principle experiments. As described previously, the VMAT 3D dose to a static patient can be estimated by applying a phantom measurement-guided perturbation to the treatment planning system (TPS)-calculated dose grid. The fraction dose to any voxel in the presence of motion, assuming the motion kernel is known, can be derived in a similar fashion by applying a measurement-guided motion perturbation. The dose to the diodes in a helical phantom is recorded at 50 ms intervals and is transformed into a series of time-resolved high-density volumetric dose grids. A moving voxel is propagated through this 4D dose space and the fraction dose to that voxel in the phantom is accumulated. The ratio of this motion-perturbed, reconstructed dose to the TPS dose in the phantom serves as a perturbation factor, applied to the TPS fraction dose to the similarly situated voxel in the patient. This approach was validated by the ion chamber and film measurements on four phantoms of different shape and structure: homogeneous and inhomogeneous cylinders, a homogeneous cube, and an anthropomorphic thoracic phantom. A 2D motion stage was used to simulate the motion. The stage position was synchronized with the beam start time with the respiratory gating simulator. The motion patterns were designed such that the motion speed was in the upper range of the expected tumor motion (1-1.4 cm∕s) and the range exceeded the normally observed limits (up to 5.7 cm). The conformal arc plans for X or Y motion (in the IEC 61217 coordinate system) consisted of manually created narrow (3 cm) rectangular strips moving in-phase (tracking) or phase-shifted by 90° (crossing) with respect to the phantom motion. The XY motion was tested with the computer-derived VMAT MLC sequences. For all phantoms and plans, time-resolved (10 Hz) ion chamber dose was collected. In addition, coronal (XY) films were exposed in the cube phantom to a VMAT beam with two different starting phases, and compared to the reconstructed motion-perturbed dose planes. For the X or Y motions with the moving strip and geometrical phantoms, the maximum difference between perturbation-reconstructed and ion chamber doses did not exceed 1.9%, and the average for any motion pattern∕starting phase did not exceed 1.3%. For the VMAT plans on the cubic and thoracic phantoms, one point exhibited a 3.5% error, while the remaining five were all within 1.1%. Across all the measurements (N = 22), the average disagreement was 0.5 ± 1.3% (1 SD). The films exhibited γ(3%∕3 mm) passing rates ≥90%. The dose to an arbitrary moving voxel in a patient can be estimated with acceptable accuracy for a VMAT delivery, by performing a single QA measurement with a cylindrical phantom and applying two consecutive perturbations to the TPS-calculated patient dose. The first one accounts for the differences between the planned and delivered static doses, while the second one corrects for the motion.