A polar-coordinate-based pencil beam algorithm for VMAT dose computation with high-resolution gantry angle sampling

Abstract

Purpose: Most commercially available treatment planning systems (TPSs) approximate the continuous delivery of volumetric modulated arc therapy (VMAT) plans with a series of discretized static beams for treatment planning, which can make VMAT dose computation extremely inefficient. In this study, we developed a polar-coordinate-based pencil beam (PB) algorithm for efficient VMAT dose computation with high-resolution gantry angle sampling that can improve the computational efficiency and reduce the dose discrepancy due to the angular under-sampling effect.

Methods and materials: 6 MV $1\times 1m{m}^2$ pencil beams were simulated on a uniform cylindrical phantom under an EGSnrc Monte Carlo (MC) environment. The MC-generated PB kernels were collected in the polar coordinate system for each bixel on a $40\times 40c{m}^2$ fluence map and subsequently fitted via a series of Gaussians. The fluence was calculated using a detectors' eye view with off-axis and MLC transmission factors corrected. Doses of VMAT arc on the phantom were computed by summing the convolution results between the corresponding PB kernels and fluence for each bixel in the polar coordinate system. The convolution was performed using fast Fourier transform to expedite the computing speed. The calculated doses were converted to the Cartesian coordinate system and compared with the reference dose computed by a collapsed cone convolution (CCC) algorithm of the TPS. A heterogeneous phantom was created to study the heterogeneity corrections using the proposed algorithm. Ten VMAT arcs were included to evaluate the algorithm performance. Gamma analysis and computation complexity theory were used to measure the dosimetric accuracy and computational efficiency, respectively.

Results: The dosimetric comparisons on the homogeneous phantom between the proposed PB algorithm and the CCC algorithm for 10 VMAT arcs demonstrate that the proposed algorithm can achieve a dosimetric accuracy comparable to that of the CCC algorithm with average gamma passing rates of 96% (2%/2mm) and 98% (3%/3mm). In addition, the proposed algorithm can provide better computational efficiency for VMAT dose computation using a PC equipped with a 4-core processor, compared to the CCC algorithm utilizing a dual 10-core server. Moreover, the computation complexity theory reveals that the proposed algorithm has a great advantage with regard to computational efficiency for VMAT dose computation on homogeneous medium, especially when a fine angular sampling rate is applied. This can support a reduction in dose errors from the angular under-sampling effect by using a finer angular sampling rate, while still preserving a practical computing speed. For dose calculation on the heterogeneous phantom, the proposed algorithm with heterogeneity corrections can still offer a reasonable dosimetric accuracy with comparable computational efficiency to that of the CCC algorithm.

Conclusions: We proposed a novel polar-coordinate-based pencil beam algorithm for VMAT dose computation that enables a better computational efficiency while maintaining clinically acceptable dosimetric accuracy and reducing dose error caused by the angular under-sampling effect. It also provides a flexible VMAT dose computation structure that allows adjustable sampling rates and direct dose computation in regions of interest, which makes the algorithm potentially useful for clinical applications such as independent dose verification for VMAT patient-specific QA.

Keywords: VMAT; dose calculation algorithm; fast Fourier transform; pencil beam model; polar coordinate system.