Calculation of high-resolution and spatially variant photon energy

Calculation of high-resolution and spatially variant photon energy

Calculation of high-resolution and spatially variant photon
energy deposition kernels
Jessie Huang1,2, Nathan Childress3, and Stephen Kry1,2
(1) The University of Texas MD Cancer Center, Houston, TX (2) The University of Texas Health Science Center Houston, Graduate
School of Biomedical Sciences (3) Mobius Medical Systems, LP, Houston, TX

Introduction
Commercial implementations of the convolution/superposition (C/S) method
make several approximations, which can lead to dose calculation inaccuracies.
For instance, the energy deposition kernel (EDK) used is spatially invariant; that
is, a single polyenergetic kernel is used for the entire dose calculation,
reflecting the beam spectrum at a single location (e.g. dmax on CAX). This
approximation ignores spectral changes with depth, field size, and off-axis
distance. Furthermore, for heterogenous media, density scaling is applied to
kernels calculated in water. This simplification has been shown to lead to
inaccuracies at material interfaces (e.g. water/air)1 and underestimation of dose
downstream of metals2.These dose calculation inaccuracies can cause errors in
certain clinical situations, e.g. sites with stark heterogeneities (dental fillings
and metal implants, lung/tissue interfaces in thoracic RT).Since the
implementation of spatially variant kernels has the potential to improve dose
calculation accuracy in a variety of clinical situations, the purpose of this study
was to generate high-resolution, material-specific, and spatially variant
polyenergetic kernels based on the beam spectrum of 6MV photon beam from
a Varian Clinac 2100.

High-resolution kernels

Polyenergetic kernels

Material-specific kernels

Methods: Primary energy spectra of a 6MV photon beam from a Varian

Methods: The EDKnrc user code was used to calculate material-

2100 Clinac linear accelerator were calculated using the BEAMnrc Monte
Carlo system4. Our BEAMnrc accelerator model has been validated in previous
studies5 and consists of the target, primary collimator, flattening filter and
moveable upper (Y) and lower (X) jaws. Using this accelerator model, particle
phase space data were generated for various scoring planes in a water
phantom for different field sizes. This phase space data was then used to
calculate the energy spectrum of the beam based on the primary fluence only,
and then these beam spectra were used as weighting factors for combining the
high-resolution monoenergetic water kernels into spatially variant
polyenergetic kernels.

specific kernels, except the simulation geometry consisted of various
ICRU materials6 (lung, bone, titanium, silver, and gold) rather than water.

Results: Table 2 summarizes the results for the material-specific
kernels. Notably, the density-weighted effective lateral distance, which
indicates how far primary particles travel in the lateral direction (i.e.
perpendicular to the direction of the incident photon), is different for
different materials and does not simply increase for materials of increasing
density. This can also been seen in Figure 3, which shows the angular
dose distribution for different material-specific kernels.

Results: Table 1 summarizes the results for the polyenergetic kernels.

Figure 3: Normalized

Based on the beam spectra generated in this study (Figure 2), the mean
energy of the spectrum, as well as the effective distances of the polyenergetic
kernels, is most dependent on depth. Although depth appears to be the
dominant factor, there were spectral differences as well as noticeable
differences in the polyenergetic kernels themselves due to field size and offaxis distance. These differences were more pronounced at shallower depths.

dose D() deposited in
cones inside the first radial
shell (r = 0.05 cm) plotted
as a function of the
bounding polar angle for
material-specific kernels
simulated with 300 keV
incident photons. Expected
values of the polar angle
<> > are given in degrees.

Methods: The EGSnrc user-code2 EDKnrc was used to calculate
monoenergetic photon kernels at twice the radial (48 spheres) and three times
the angular (144 cones) resolution used by Mackie et al. (1988)3. 22 energies
ranging from 100keV to 40 MeV were simulated. For each kernel, we
calculated the total energy fraction (Ftot), primary energy fraction (Fprim,), and

Figure 2: Energy spectra of the primary
fluence of a Varian Clinac 2100 6MV
photon beam for (a) various depths and a
10x10 field, (b) various field sizes at a
depth of 1.5 cm, and (c) various off-axis
distances for a 20x20 field at a depth of
1.5 cm (using annular scoring planes).

effective distance along the direction of the incident photon (z), lateral direction
(y), and radial direction (r), as illustrated below. The effective distances were
calculated using equation (1) where d is the pertinent distance (z, r, or y) and
prim is the primary EDK of the i,j th voxel.

Table 2: Density-weighted effective depth of penetration (z), effective radial
distance (r), and effective lateral distance (y) for material-specific kernels for 300keV
monoenergetic photons and a 6 MeV polyenergetic beam spectrum. In parenthesis
is the % difference w.r.t the water kernel.

(1)

Results: Our high-resolution kernels showed good agreement with the
original Mackie kernels based on the metrics calculated to characterize the
kernels. This good agreement validates that our simulations were performed
correctly (Figure 1). However, we did observe differences near the interaction
site for the lower energies (<500 keV), most likely due to improvements in electron transport in the EGSnrc code4. Conclusions Table 1: Effective depth of penetration (z), effective radial distance (r), and effective lateral distance (y) for polyenergetic kernels calculated using the energy spectrum of the primary photon beam at various locations in a water phantom. The mean energy of the spectrum is also listed. In parenthesis is the % difference w.r.t the polyenergetic kernel at d=1.5 cm for a 10x10 field (i.e. the reference spectrum). Our high-resolution water kernels show good agreement with Mackie kernels. However, this good agreement along with the fact that the kernels appear to be smoothly varying functions leads us to believe that they will not appreciably increase the accuracy of dose calculations, with the possible exception of near material interfaces. For our polyenergetic kernels, we found that depth was the most important factor, but that spectral differences due to field size and offaxis distance were not negligible. For our material-specific kernels, we found that density scaling is generally a good approximation for lung, but not for higher density, higher effective Z materials such as bone and metals. Use of density scaling for these higher Z materials will lead to underestimation of lateral scatter and dose calculation inaccuracies downstream of such materials. Figure 1: Comparison of our high-resolution water kernels and Mackie et al. (1988) kernels averaged over selected angular intervals for (a) 1MeV and (b) 10MeV incident photons. References 1. M. K. Woo and J. R. Cunningham, Med Phys 17 (2), 187-194 (1990). 2.S. Spirydovich, L. Papiez, M. Langer, G. Sandison and V. Thai, Radiother Oncol 81 (3), 309-314 (2006). 3. D. W. O. Rogers, I. Kawrakow, J. P. Seuntjens, B. R. B. Walters, and E. Mainegra-Hing, Technical Report PIRS-702(RevB), National Research Council of Canada, Ottowa, Canada (2003). 4.I. Kawrakow, E. Mainegra-Hing, D.W.O Rogers, F. Tessier, and B. R. B. Walters. Technical Report PIRS-701. National Research Council of Canada, Ottowa, Canada (2011). 5.T. R. Mackie, A. F. Bielajew, D. W. Rogers and J. J. Battista, Phys Med Biol 33 (1), 1-20 (1988). 6.D. W. O. Rogers, B. Walters, and I. Kawrakow, NRCC Report PIRS-0509(A)revK, National Research Council of Canada, Ottawa, Canada (2009). 7.O. N. Vassiliev, U. Titt, S. F. Kry, F. Ponisch, M. T. Gillin and R. Mohan, Med Phys 33 (4), 820-827 (2006). 8.ICRU, ICRU Report 37, ICRU, Washington D.C. (1984). Support The investigation was supported by PHS grant CA10953 awarded by the NCI, DHHS. Based on our data, we expect the use of material-specific kernels and spatially variant polyenergetic kernels to improve dose accuracy for many clinical situations (e.g., downstream of metal implants, in the penumbra region, in peripheral organs at risk, etc). Contact: [email protected]

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