Medical Dosimetry, Vol. 28, No. 2, pp. 107–112, 2003
Copyright © 2003 American Association of Medical Dosimetrists
Printed in the USA. All rights reserved
0958-3947/03/$–see front matter
doi:10.1016/S0958-3947(02)00245-5
RADIOTHERAPY DOSE CALCULATIONS IN THE PRESENCE OF HIP
PROSTHESES
PAUL J. KEALL, JEFFREY V. SIEBERS, ROBERT JERAJ, and RADHE MOHAN
Department of Radiation Oncology, Medical College of Virginia, Richmond, VA;
Joz̆ef Stefan Institute, University of Ljubljana, Slovenia; and
University of Wisconsin, Madison, WI
(Accepted 12 June 2002)
Abstract—The high density and atomic number of hip prostheses for patients undergoing pelvic radiotherapy
challenge our ability to accurately calculate dose. A new clinical dose calculation algorithm, Monte Carlo, will
allow accurate calculation of the radiation transport both within and beyond hip prostheses. The aim of this
research was to investigate, for both phantom and patient geometries, the capability of various dose calculation
algorithms to yield accurate treatment plans. Dose distributions in phantom and patient geometries with high
atomic number prostheses were calculated using Monte Carlo, superposition, pencil beam, and no-heterogeneity
correction algorithms. The phantom dose distributions were analyzed by depth dose and dose profile curves. The
patient dose distributions were analyzed by isodose curves, dose-volume histograms (DVHs) and tumor control
probability/normal tissue complication probability (TCP/NTCP) calculations. Monte Carlo calculations predicted the dose enhancement and reduction at the proximal and distal prosthesis interfaces respectively, whereas
superposition and pencil beam calculations did not. However, further from the prosthesis, the differences
between the dose calculation algorithms diminished. Treatment plans calculated with superposition showed
similar isodose curves, DVHs, and TCP/NTCP as the Monte Carlo plans, except in the bladder, where Monte
Carlo predicted a slightly lower dose. Treatment plans calculated with either the pencil beam method or with no
heterogeneity correction differed significantly from the Monte Carlo plans. © 2003 American Association of
Medical Dosimetrists.
Key Words:
Dose calculation, Hip prosthesis, Monte Carlo, Superposition, Pencil beam.
femoral heads.1 Hollow prostheses tend to be larger.
Only solid prostheses were considered here.
The aim of this work was to compare dose distributions in the vicinity of hip prosthesis materials in both
phantom and patient geometries as calculated by the
Monte Carlo, superposition, and pencil beam algorithms.
The clinical significance of the dose distribution differences in the patient geometry was investigated.
CT imaging of hip prostheses causes streak artifacts
due to aliasing.16 –19 These artifacts reduce the diagnostic
quality of the images and provide erroneous density
information needed for dose calculation. However, the
effects of image reconstruction on target delineation and
dose calculation are beyond the scope of this article.
INTRODUCTION
The high density and atomic number of hip prostheses
relative to water yield challenges for radiotherapy dose
calculation when beams pass through these structures.
Several authors have quantitatively calculated or measured the effects of such prostheses or high atomic number interfaces on dose distributions.1–12 This topic has
created enough attention to warrant the formation of an
American Association of Physicists in Medicine
(AAPM) Task Group to examine the subject of management of patients with inserted high-Z materials.13
Sauer12 performed Monte Carlo and superposition calculations for phantom geometries; however, a comparison of both simple and advanced dose calculation algorithms in a patient computed tomography (CT) geometry
has not been performed.
Most hip prostheses are made from cobalt-chrome
alloys,14 because they are considered to have the best
combination of corrosion resistance, fatigue resistance,
and mechanical strength.15 However, both titanium and
stainless steel hip prostheses are also available.1 The
prostheses vary in size and may have solid or hollow
METHODS AND MATERIALS
Calculations using various dose calculation algorithms were performed in phantom and patient geometries containing high atomic number and density materials. The phantom calculations were performed to study
the dosimetric effects of the prostheses under well-defined conditions. The patient calculations were performed to study the clinical significance of the resultant
dose distributions obtained under realistic conditions.
Three dose calculation algorithms were used: Monte
Carlo, superposition, and pencil beam. For reference,
Reprint requests to: Paul J. Keall, Ph.D., Department of Radiation Oncology, PO Box 980058, Medical College of Virginia, Richmond, VA 23298. E-mail: [email protected]
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calculations with no heterogeneity correction were also
performed.
Dose calculation methods
The Monte Carlo method was chosen because of its
recognition as the most accurate dose calculation method
available. The superposition method was selected, because it is the most accurate broadly available algorithm,
and the pencil beam method was selected because of its
status as one of the most widely used correction methods.
The Monte Carlo code used was EGS420 with usercodes
BEAM21 and DOSXYZ.22 The energy cutoffs were AE
! ECUT ! 700 keV and AP ! PCUT ! 10 keV.
Validation of the Monte Carlo codes with both other
Monte Carlo results and experimental results has been
performed.23,24 To allow comparison between Monte
Carlo and other dose calculation algorithms, the Monte
Carlo dose-to-material values (except in the prostheses
itself) were converted to dose-to-water using the method
of Siebers et al.25 The superposition calculations used
Pinnacle3’s (ADAC Laboratories, Milpitas, CA) collapsed-cone convolution24 algorithm. The physical density of the prosthesis (rather than the relative electron
density) was used as specified in the Pinnacle3 Physics
Guide. The pencil beam code was developed in-house,
based on that of Mohan and Chui.26 The pencil beam
algorithm physics employed is similar to that of the ratio
of tissue-air-ratios (RTAR) method described in Metcalfe et al.27
Phantom calculations
A 2 " 2 " 2-cm3 block of iron (! ! 8.0, Z ! 26)
or titanium (! ! 4.5, Z ! 22) centered on the beam axis
at 4-cm depth was inserted into a 40 " 40 " 40-cm3
water phantom by adding CT numbers corresponding to
the correct density in the CT image set. (The CT number
was determined using the material density and the CTto-density conversion table.) The phantom is shown in
Fig. 1. Because of comparable densities and effective
atomic numbers, the calculations with the iron represent
those of cobalt-chrome prostheses and yield similar dosimetric results. The voxel size for the calculations was
0.4 " 0.4 " 0.2 cm3.
A 6-MV 100 cm SSD 10 " 10-cm2 field was
incident on the phantom. Sibata et al.1 showed that the
perturbations of the high-Z prostheses were slightly more
pronounced for 6 MV than 18 MV; thus, 6-MV calculations are presented here.
From the dose distributions calculated, central-axis
depth dose curves and profiles through the center of
metal block (5-cm depth) were extracted.
Patient calculations
Due to the CT image reconstruction limitations for
the high-density and atomic number prosthesis materials
described above, it was not possible to use an artifactfree CT image set of a patient with a hip prosthesis. Thus,
Fig. 1. Geometry used for the phantom calculations.
a 28-mm diameter sphere with a density of 8.0 g cm#3,
representing the head of a typical hip prosthesis,14 was
inserted into the right femoral head of an existing CT
image set of a patient, replacing the normal hip. The
subsequent dose calculations used the existing treatment
plan for the patient, including the same number of monitor units for each field. This treatment plan was composed of 18-MV isocentric fields in the standard 4-field
box configuration. The voxel size for the calculations
was 0.4 " 0.4 " 0.4 cm3.
The analysis of the dose distributions obtained by
the various algorithms used isodose distribution comparison, DVH comparison, and radiobiological indice calculation. The TCP calculation method is described elsewhere28 using a "50 value (the percent increase in TCP
per percent increase in dose at TCP ! 50%) of 1.0 for a
prostate tumor.29 The NTCPs for the rectum and prostate
were calculated using the Lyman model,30 values tabulated in Burman et al.,31 and data taken from Emami et
al.32
RESULTS
Phantom calculations
Depth dose curves for the phantom geometry using
the different calculation methodologies are shown in Fig.
2. Neither the superposition nor pencil beam methods
predict the increase in electron backscattering (and to a
lesser extent, photon backscattering) from the high
atomic number material. Note that the magnitude of this
backscattering is dependent on the beam energy and the
prosthesis composition and density. The finite voxel size
underestimates the true interface dose, because converting a CT grid to a dose calculation grid is an averaging
process. Because of this, smoother density interfaces
exist in the dose calculation grid than in the CT grid.
Dose calculations for hip prostheses ● P.J. KEALL et al.
109
Fig. 2. Central axis depth dose curves in a water phantom with a 2 " 2 " 2 cm3 titanium block (top) and an iron block (bottom)
placed at 4-cm depth. The calculation methods were Monte Carlo, superposition, pencil beam, and no-heterogeneity correction.
The plot on the right is zoomed in on the prosthesis.
Fig. 2 shows that immediately beyond the prosthesis, the superposition and pencil beam methods predict a
higher dose than that calculated by Monte Carlo. Further
from the prosthesis, the differences between the algorithms decrease.
The increased mass scattering power of the prosthesis relative to that of water causes the dose increase at the
proximal edge of the prosthesis. This increased lateral
electron scattering within the prosthesis means that fewer
electrons cross the distal prosthesis/water interface, causing the rebuild-up near the distal edge of the prosthesis.
Neither the superposition nor the pencil beam method
accounts for rebuild-up in electron fluence past the prosthesis. It is interesting to note that with the addition of an
opposed field, the total magnitude of the dose enhancement will be reduced.
Monte Carlo is the only algorithm that explicitly
accounts for the effect of different atomic composition of
the prosthesis relative to water. The higher atomic number causes the photon spectrum to be attenuated more by
photoelectric and pair production interactions and less by
Compton interactions than an equivalent mass of water.
The different interaction probabilities within the prosthe-
sis mean that relatively fewer scattered photons per unit
mass exit the prosthesis. From this phenomenon, we
would expect superposition and pencil beam methods to
predict a higher dose than Monte Carlo outside the prosthesis. The differing atomic number of the prosthesis
with respect to water also changes the spectrum of the
photons transmitted through the prosthesis, further affecting dose downstream of the prosthesis.
Lateral dose profile curves for the different calculation methodologies are shown in Fig. 3. Neither the
superposition nor the pencil beam method predicts the
increase in dose, due to an increased scattering of electrons in the metal and the resulting higher dose adjacent
to the prosthesis.
Patient calculations
Isodose plans for the prosthesis geometry as calculated by the Monte Carlo, superposition, and pencil beam
algorithms are shown in Fig. 4. Dosimetric differences in
the vicinity of the prosthesis are seen. Also of note is the
60-Gy line through the rectum, which for the pencil
beam calculation remains straight, whereas the Monte
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Volume 28, Number 2, 2003
Fig. 4. Isodose plans for the prosthesis geometry as calculated
by (a) Monte Carlo, (b) superposition (c) pencil beam, and (d)
no-heterogeneity correction. The 40-, 60-, and 70-Gy isodose
lines are shown.
similar, although the NTCPs calculated by superposition
are higher than those of Monte Carlo, and the pencil
beam NTCPs are higher still. The predicted outcome
values in Table 1 are not surprising, based on the DVHs
of Fig. 5.
DISCUSSION
Fig. 3. Dose profile curves at 5-cm depth in a water phantom
with a 2 " 2 " 2 cm3 titanium block (top) and an iron block
(bottom) placed at 4-cm depth. The calculation methods were
Monte Carlo, superposition, pencil beam, and no-heterogeneity
correction.
Carlo and superposition 50-Gy lines curve slightly inward through the rectum. This difference is due to the
pencil beam algorithm’s inability to account for the electronic disequilibrium in the lower density media.
The difference in the 3D dose distributions can be
represented by DVHs, as shown in Fig. 5. This figure
shows that for the prostate, rectum, and bladder, the
pencil beam calculations were consistently higher than
the superposition calculations, which in turn were generally slightly higher than the Monte Carlo calculations.
The higher pencil beam results for the prostate and
bladder are consistent with the phantom calculation results. Pencil beam-predicted dose differences in the rectum are due to the lack of accounting for electronic
disequilibrium in the lower density media rather than the
effect of the prosthesis.
The differences in the 3D dose distributions can be
quantitatively represented by a single value if predicted
clinical outcome is used. The TCPs and NTCPs of the
rectum and bladder are given in Table 1. This table
shows that the TCPs calculated by the 3 algorithms are
The accuracy of the dose calculation algorithms in
the vicinity of hip prosthesis materials is proportional to
their complexity of physical process modeling. The limitation of superposition at interfaces with different
atomic numbers is observed near hip prostheses. An
improvement could be the addition of kernels generated
in different media as suggested by Papanikolaou and
Mackie,33,34 or the corrections of Sauer.12 However,
further than a few millimeters from the boundary, superposition results do not significantly differ from those of
Monte Carlo.
The pencil beam method does not predict dose well
near the interface. However, beyond the interface, the
dose difference between pencil beam and Monte Carlo
calculations decreases. These results are consistent with
those of Sibata et al.,1 who showed that the equivalent
path length correction method yields acceptable dosimetric results at a distance of 5 cm or greater from the
prosthesis.
The Monte Carlo, pencil beam, and superposition
dose calculation methods were significantly more accurate than the no-heterogeneity correction method.
Dose distribution results for a patient plan with a
hip prosthesis showed the pencil beam method calculating a higher dose than superposition. In general, the
superposition dose was slightly higher than that of Monte
Carlo.
It should be noted that the calculations performed
here used high CT numbers (up to 8000). Often, the CT
Dose calculations for hip prostheses ● P.J. KEALL et al.
111
Table 1. Radiobiological indices as predicted by Monte
Carlo, superposition, pencil beam, and no-heterogeneity
correction for a steel prosthesis
Calculation Method
Monte Carlo
Superposition
Pencil beam
No correction
TCP
NTCP Rectum
NTCP Bladder
87
87
90
89
14
15
21
18
11
15
18
18
lation algorithm that can account for dose variations at
interfaces with different atomic numbers. The Monte
Carlo and superposition methods both accounted for the
electronic disequilibrium present in the lower density
rectum. The pencil beam method does not account for
electronic disequilibrium. For the prostate case, the prosthesis was a sufficient distance from the target so that
interface effects did not affect the dose to the target.
However, this may be a problem for other sites, such as
paraspinal treatments, where surgical rods have been
inserted close to the vertebrae and tumor.
Acknowledgments—The authors acknowledge the financial support of
NIH Grant CA 74158-02 and the Grant-in-Aid Program for Faculty of
Virginia Commonwealth University. The authors thank Dr. Bruce
Libby for assistance with the phase space calculations, and the radiation
physics group at MCV for their helpful advice. The authors also thank
Devon Farnsworth for revising this manuscript.
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Fig. 5. Dose-volume histograms for the (a) prostate, (b) rectum,
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pencil beam, and no-heterogeneity correction.
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