Several simplifications used in clinical implementations of the convolution/superposition (C/S) method, specifically, density scaling of water kernels for heterogeneous media and use of a single polyenergetic kernel, lead to dose calculation inaccuracies. Although these weaknesses of the C/S method are known, it is not well known which of these simplifications has the largest effect on dose calculation accuracy in clinical situations. The purpose of this study was to generate and characterize high-resolution, polyenergetic, and material-specific energy deposition kernels (EDKs), as well as to investigate the dosimetric impact of implementing spatially variant polyenergetic and material-specific kernels in a collapsed cone C/S algorithm.
High-resolution, monoenergetic water EDKs and various material-specific EDKs were simulated using the EGSnrc Monte Carlo code. Polyenergetic kernels, reflecting the primary spectrum of a clinical 6 MV photon beam at different locations in a water phantom, were calculated for different depths, field sizes, and off-axis distances. To investigate the dosimetric impact of implementing spatially variant polyenergetic kernels, depth dose curves in water were calculated using two different implementations of the collapsed cone C/S method. The first method uses a single polyenergetic kernel, while the second method fully takes into account spectral changes in the convolution calculation. To investigate the dosimetric impact of implementing material-specific kernels, depth dose curves were calculated for a simplified titanium implant geometry using both a traditional C/S implementation that performs density scaling of water kernels and a novel implementation using material-specific kernels.
For our high-resolution kernels, we found good agreement with the Mackieet al. kernels, with some differences near the interaction site for low photon energies (<500 keV). For our spatially variant polyenergetic kernels, we found that depth was the most dominant factor affecting the pattern of energy deposition; however, the effects of field size and off-axis distance were not negligible. For the material-specific kernels, we found that as the density of the material increased, more energy was deposited laterally by charged particles, as opposed to in the forward direction. Thus, density scaling of water kernels becomes a worse approximation as the density and the effective atomic number of the material differ more from water. Implementation of spatially variant, polyenergetic kernels increased the percent depth dose value at 25 cm depth by 2.1%–5.8% depending on the field size, while implementation of titanium kernels gave 4.9% higher dose upstream of the metal cavity (i.e., higher backscatter dose) and 8.2% lower dose downstream of the cavity.
Of the various kernel refinements investigated, inclusion of depth-dependent and metal-specific kernels into the C/S method has the greatest potential to improve dose calculation accuracy. Implementation of spatially variant polyenergetic kernels resulted in a harder depth dose curve and thus has the potential to affect beam modeling parameters obtained in the commissioning process. For metal implants, the C/S algorithms generally underestimate the dose upstream and overestimate the dose downstream of the implant. Implementation of a metal-specific kernel mitigated both of these errors.
This work was supported by Public Health Service Grant Nos. CA 10953 and CA 081647, awarded by the National Cancer Institute, Department of Health and Human Services. One of the authors, Jessie Huang, would like to acknowledge financial support from the Graduate School of Biological Sciences, UT Health Science Center at Houston. The authors would like to thank Kathryn Carnes for her assistance in editing this paper and Oleg Vassiliev for his help with the Monte Carlo system.
II. METHODS AND MATERIALS
II.A. Calculation of high-resolution kernels
II.B. Calculation of polyenergetic kernels
II.C. Calculation of material-specific kernels
II.D. Investigation of “pocket of material” kernels
II.E. Calculation of energy deposition kernel metrics
II.F. Investigation of dosimetric impact of kernel hardening and material-specific kernels
III.A. Calculation of high-resolution kernels
III.B. Calculation of polyenergetic kernels
III.C. Calculation of material-specific kernels
III.D. Investigation of “pocket of material” kernels
III.E. Investigation of dosimetric impact of kernel hardening and material-specific kernels
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