Purpose: To propose a pencil beam (PB) dose calculation algorithm for volumetric modulated arc therapy (VMAT) that can reduce dose discrepancies due to angular under-sampling issue and improve the computational efficiency.
Methods: 6 MV 1x1 mm² pencil beams were simulated and calculated on ArcCheck phantom under EGSnrc environment. Monte Carlo generated PB kernels were collected in Polar system for each bixel in a 40x40 cm² grid. These kernels were fine-tuned based on a squared field dose from a commercial treatment planning system (TPS, Pinnacle³) and then fitted using multiple Gaussians. Fluence for VMAT arc was calculated using detectors’ eye view with leaf end, tongue and groove, and transmission factors corrected. Dose in Polar system for an arc can be calculated by a summation of convolutions of the corresponding PB fitting kernels and fluence for each bixel using fast Fourier transforms. Dose was converted to Cartesian system and compared with the dose from TPS using gamma analysis. Ten VMAT arcs were studied to evaluate the robustness of the algorithm.
Results: The average gamma passing rate between the calculated and TPS dose was 96%(2%/2mm) and 98%(3%/3mm). With a 2x2x2 mm³ calculation grid, the proposed algorithm can provide a comparable computational efficiency(~150s) as TPS for common arcs and a shorter computational time for arcs with large fields using a PC equipped with a quad-core CPU.
Conclusion: We proposed a Polar coordinate based pencil beam algorithm that can be implemented for VMAT dose calculation. It improves the computational efficiency of VMAT dose calculation since the convolution is applied to Polar system, whereas the convolution in the traditional discretized algorithm needs to be done for each discretized apertures with small angular separations. This algorithm can also reduce dose discrepancies due to angular under-sampling issue, which improves the accuracy of VMAT dose calculation.