
A PENCIL BEAM KERNEL MODEL FOR FLATTENING FILTERFREE XRAY BEAM
Mehmet Ertuğrul Ertürk, Cemil Kocar, Salih Gürdall, Mehmet Tombakoğlu
Pages: 186190
DOI: 10.21175/RadProc.2017.38
Abstract 
References 
Full Text (PDF)
Fast and accurate dose computation is an important requirement for algorithms that are often used in optimization schemes. Decreasing the number of variables and parameters and the amount of tabulated data can reduce computation time. Flattening FilterFree (FFF) beams provide reduced profile shape variations with depth relative to flattened beams. Therefore, the pencil beam kernel of a FFF beam must exhibit the reduced variation with depth when compared to the kernel of flattened beams. In this paper, a kernel with a minimal number of parameters is derived for the FFF beams. Moreover, some of the parameters are defined as depth independent. A finitesize pencil beam dose calculation model was used for kernel generation. The grid size for the dose calculation was set to 2.5 mm. During the kernel generation, the parameters (preexponential constants and exponential constants) of the kernel were determined in such a way that the difference between the computed and measured profiles is minimized by the global gamma analysis technique. The criteria for this technique were 1 % dose difference at distance of 1 mm with a 10 % threshold. Profiles for each field (5 x 5 cm2, 10 x 10 cm2, and 20 x 20 cm2) at five standard depths (dmax, 5 cm, 10 cm, 20 cm, and 30 cm), a total of 15 profiles, were used to generate the kernels. The multiobjective, nonderivative, unconstrained, nonlinear optimization method in the programming package MATLAB (Mathworks, Natick, MA) optimization toolbox was used to generate kernel parameters. Commissioning of the model was performed for the static fields and the intensitymodulated radiation therapy (IMRT) fields. In static fields and dynamic IMRT fields, more than 95 % of data points satisfied the criteria defined in the global gamma analysis with 3 % and 3 mm. There was a good agreement between modelled and measured data in both cases. It is demonstrated that the pencil beam model developed in this study could be used for FFF xray beams. Pencil beam kernel parameters do not need to be defined at each depth.
 A. Boyer and E. Mok, “A photon dose distribution model employing convolution calculations,” Med. Phys.,vol. 12,no. 2, pp. 169 – 177, Mar. 1985.
DOI: 10.1118/1.595772 PMid: 4000072
 A. L. Boyer, “Shortening the calculation time of photon dose distributions in an inhomogeneous medium,” Med. Phys.,vol. 11,no. 4, pp. 552 – 554, Jul. 1984.
DOI: 10.1118/1.595526 PMid: 6482848
 R. Mohan and C. S. Chui, “Use of fast Fourier transforms in calculating dose distributions for irregularly shaped fields for threedimensional treatment planning,” Med. Phys., vol. 14, no. 1, pp. 70 – 77, Jan. 1987.
DOI: 10.1118/1.596097 PMid: 3104741
 A. Ahnesjö, M. Saxner and A. Trepp, “A pencil beam model for photon dose calculation,” Med. Phys., vol. 19, no. 2, pp. 263 – 273, Mar. 1992.
DOI: 10.1118/1.596856 PMid: 1584117
 C. S. Chui and R. Mohan, “Extraction of pencil beam kernels by the deconvolution method,” Med. Phys., vol. 15, no. 2, pp. 138 – 144, Mar. 1988.
DOI: 10.1118/1.596267 PMid: 3386581
 C. P. Ceberg, B. E. Bjärngard and T. C. Zhu, “Experimental determination of the dose kernel in highenergy xray beams,” Med. Phy., vol. 23, no. 4, pp. 505 – 511, Apr. 1996.
DOI: 10.1118/1.597807 PMid: 9157261
 L. Dong et al., “A pencilbeam photon dose algorithm for stereotactic radiosurgery using a miniature multileaf collimator,” Med. Phys., vol. 25, no. 6, pp. 841 – 850, Jun. 1998.
DOI: 10.1118/1.598294 PMid: 9650171
 U. Jeleń et al., “A finite size pencil beam for IMRT dose optimization,” Phys. Med. Biol., vol. 50, no. 8, pp. 1747 – 1766, Apr. 2005.
DOI: 10.1088/00319155/50/8/009 PMid: 15815094
 U. Jeleń and M. Alber, “A finite size pencil beam algorithm for IMRT dose optimization: density corrections,” Phys. Med. Biol., vol. 52, no. 3, pp. 617 – 633, Jan. 2007.
DOI: 10.1088/00319155/52/3/006 PMid: 17228109
 J. C. Lagarias et al., “Convergence properties of the NelderMead Simplex Method in low dimensions,” SIAM Journal of Optimization, vol. 9, no. 1, pp. 112 – 147, Dec. 1998.
DOI: 10.1137/S1052623496303470
 D. A. Low and J. F. Dempsey, “Evaluation of the gamma dose distribution comparison method,” Med. Phys., vol. 30, no. 9, pp. 2455 – 2464, Sep. 2003.
DOI: 10.1118/1.1598711 PMid: 14528967
 T. Bortfeld, W. Schlegel and B. Rhein, “Decomposition of pencil beam kernels for fast dose calculations in threedimensional treatment planning,” Med. Phys., vol. 20, no. 2, pp. 311 – 318, Mar. 1993.
DOI: 10.1118/1.597070 PMid: 8497215
 D. W. Rogers, B. A. Faddegon, G. X. Ding, C. M. Ma, J. We, T. R. Mackie, “BEAM: A Monte Carlo code to simulate radiotherapy treatment units,” Med. Phys., vol. 22, no. 5, pp. 503 – 524, May 1995.
DOI: 10.1118/1.597552 PMid: 7643786
 J. D. Azcona et al., “Experimental pencil beam kernels derivation for 3D dose calculation in flattening filter free modulated fields,” Phys. Med. Biol., vol. 61, no. 1, pp. 50 – 66, Jan. 2016.
DOI: 10.1088/00319155/61/1/50 PMid: 26611490
 W. Ulmer, D. Harder, “A Triple Gaussian Pencil Beam Model for Photon Beam Treatment Planning,” Z. Med. Phys., vol. 5, no. 1, pp. 25 – 30, Jan. 1995.
DOI: 10.1016/S09393889(15)707580
