Introduction

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.

References1. 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).

Calculation of high-resolution and spatially variant photon energy deposition kernelsJessie 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

Polyenergetic kernels

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

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.

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

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 off-

axis distance. These differences were more pronounced at shallower depths.

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 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).

Contact: [email protected]

High-resolution kernels

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.

(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.

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.

Conclusions• 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 off-axis 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.

• 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).

Material-specific kernels

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

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.

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.

Figure 3: Normalized 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.

SupportThe investigation was supported by PHS grant CA10953 awarded by the NCI, DHHS.