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.
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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]