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 highresolution, material-specific, and spatially variant polyenergetic kernels based
on the beam spectrum of 6MV photon beam from a Varian Clinac 2100.
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
system4.
Carlo
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
dose D(θ) deposited in
cones inside the first radial
shell (r = 0.05 cm) plotted
as a function of the
bounding polar angle θ for
material-specific kernels
simulated with 300 keV
incident photons. Expected
values of the polar angle
<θ> are given in degrees.
kernels, is most dependent on depth. Although depth appears to be the
dominant factor, there were spectral differences as well as noticeable
High-resolution kernels
differences in the polyenergetic kernels themselves due to field size and offaxis distance. These differences were more pronounced at shallower depths.
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 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 εprim is the
primary EDK of the i,j th voxel.
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).
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.
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• 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).
Support
The investigation was supported by PHS grant CA10953 awarded by the NCI, DHHS.
Contact: jyhuang@mdanderson.org