RPT 105

Report of the AAPM Task Group No.
105: Issues associated

with clinical implementation of Monte Carlo-based photon
and electron external beam treatment planning
Indrin J. Chettya
University of Michigan, Ann Arbor, Michigan 48109
and University of Nebraska Medical Center, Omaha, Nebraska 68198-7521
Bruce Curran
University of Michigan, Ann Arbor, Michigan 48109
Joanna E. Cygler
Ottawa Hospital Regional Cancer Center, Ottawa, Ontario K1H 1C4, Canada
John J. DeMarco
University of California, Los Angeles, Callifornia 90095
Gary Ezzell
Mayo Clinic Scottsdale, Scottsdale, Arizona 85259
Bruce A. Faddegon
University of California, San Francisco, California 94143
Iwan Kawrakow
National Research Council of Canada, Ottawa, Ontario K1A 0R6, Canada
Paul J. Keall
Stanford University Cancer Center, Stanford, California 94305-5847
Helen Liu
University of Texas MD Anderson Cancer Center, Houston, Texas 77030
C.-M. Charlie Ma
Fox Chase Cancer Center, Philadelphia, Pennsylvania 19111
D. W. O. Rogers
Carleton University, Ottawa, Ontario K1S 5B6, Canada
Jan Seuntjens
McGill University, Montreal, Quebec H3G 1A4, Canada
Daryoush Sheikh-Bagheri
The Regional Cancer Center, Erie, Pennsylvania 16505
Jeffrey V. Siebers
Virginia Commonwealth University, Richmond, Virginia 23298
Received 11 April 2006; revised 11 July 2007; accepted for publication 18 September 2007;
published 27 November 2007
The Monte Carlo MC method has been shown through many research studies to calculate accurate
dose distributions for clinical radiotherapy, particularly in heterogeneous patient tissues where the
effects of electron transport cannot be accurately handled with conventional, deterministic dose
algorithms. Despite its proven accuracy and the potential for improved dose distributions to influ-
ence treatment outcomes, the long calculation times previously associated with MC simulation
rendered this method impractical for routine clinical treatment planning. However, the development
of faster codes optimized for radiotherapy calculations and improvements in computer processor
technology have substantially reduced calculation times to, in some instances, within minutes on a
single processor. These advances have motivated several major treatment planning system vendors
to embark upon the path of MC techniques. Several commercial vendors have already released or
are currently in the process of releasing MC algorithms for photon and/or electron beam treatment
planning. Consequently, the accessibility and use of MC treatment planning algorithms may well
become widespread in the radiotherapy community. With MC simulation, dose is computed sto-
chastically using first principles; this method is therefore quite different from conventional dose
algorithms. Issues such as statistical uncertainties, the use of variance reduction techniques, the
4818 Med. Phys. 34 12, December 2007 0094-2405/2007/3412/4818/36/$23.00 2007 Am. Assoc. Phys. Med. 4818
4819 Chetty et al.: AAPM Task Group Report No. 105: Monte Carlo-based treatment planning 4819
ability to account for geometric details in the accelerator treatment head simulation, and other
features, are all unique components of a MC treatment planning algorithm. Successful implemen-
tation by the clinical physicist of such a system will require an understanding of the basic principles
of MC techniques. The purpose of this report, while providing education and review on the use of
MC simulation in radiotherapy planning, is to set out, for both users and developers, the salient
issues associated with clinical implementation and experimental verification of MC dose algo-
rithms. As the MC method is an emerging technology, this report is not meant to be prescriptive.
Rather, it is intended as a preliminary report to review the tenets of the MC method and to provide
the framework upon which to build a comprehensive program for commissioning and routine
quality assurance of MC-based treatment planning systems. 2007 American Association of
Physicists in Medicine. DOI: 10.1118/1.2795842
Key words: Monte Carlo dose calculation, clinical treatment planning, experimental verification
TABLE OF CONTENTS III.D.7. Cross sections. . . . . . . . . . . . . . . . . . . . . . . 4839

III.E. Experimental verification. . . . . . . . . . . . . . . . . 4839
III.E.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . 4839
I. INTRODUCTION. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4819 III.E.2. Previous work. . . . . . . . . . . . . . . . . . . . . . . 4839
I.A. Motivation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4819 III.E.3. Types of verification experiments. . . . . . . . 4839
I.B. Objectives for the report. . . . . . . . . . . . . . . . . 4820 III.E.4. Verification of the Monte Carlo transport
I.C. Organization of the report. . . . . . . . . . . . . . . . 4820 algorithm in phantom. . . . . . . . . . . . . . . . . 4840
II. THE MONTE CARLO METHOD IN III.E.5. Dose buildup region. . . . . . . . . . . . . . . . . . 4841
RADIOTHERAPY DOSE CALCULATIONS. . . . . 4820 III.E.6. Output ratios. . . . . . . . . . . . . . . . . . . . . . . . 4841
II.A. Definition of the MC method and historical III.E.7. Electron beams. . . . . . . . . . . . . . . . . . . . . . . 4841
background. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4820 III.E.8. Measurement uncertainties. . . . . . . . . . . . . 4842
II.B. Monte Carlo simulation of electron and III.E.9. Example experimental tests. . . . . . . . . . . . . 4842
photon transport. . . . . . . . . . . . . . . . . . . . . . . . 4821 III.E.10. Timing issues. . . . . . . . . . . . . . . . . . . . . . . . 4842
II.B.1. Analog simulations. . . . . . . . . . . . . . . . . . . 4822 IV. CLINICAL IMPLICATIONS OF MONTE
II.B.2. Condensed history simulations. . . . . . . . . . 4822 CARLO-CALCULATED DOSE
II.C. Overview of Monte Carlo-based DISTRIBUTIONS. . . . . . . . . . . . . . . . . . . . . . . . . . . 4843
radiotherapy dose calculations. . . . . . . . . . . . . 4823 IV.A. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4843
II.D. Variance reduction techniques and efficiency IV.B. Clinical examples. . . . . . . . . . . . . . . . . . . . . . . 4844
enhancing methods. . . . . . . . . . . . . . . . . . . . . . 4824 IV.B.1. Photon beam treatment planning. . . . . . . . . 4845
III. MONTE CARLO SIMULATION OF IV.B.2. Electron beam treatment planning. . . . . . . 4845
RADIATION TRANSPORT IN IV.C. Association of Monte Carlo calculated dose
ACCELERATORS AND PATIENTS. . . . . . . . . . . . 4825 distributions with clinical outcome. . . . . . . . . 4846
III.A. Review of current Monte Carlo codes. . . . . . . 4825 V. SUMMARY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4846
III.B. Accelerator treatment head simulation. . . . . . 4826 V.A. Treatment head simulation. . . . . . . . . . . . . . . . 4846
III.B.1. Sensitivity of simulations to electron V.B. Patient simulation. . . . . . . . . . . . . . . . . . . . . . . 4846
beam and other parameters. . . . . . . . . . . . . 4826 V.B.1. Statistical uncertainties. . . . . . . . . . . . . . . . 4846
III.B.2. Electron beam specifics. . . . . . . . . . . . . . . . 4828 V.B.2. Variance reduction techniques, efficiency
III.C. Modeling of the linear accelerator treatment enhancing methods, and other parameters.. 4847
head. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4829 V.B.3. Dose prescriptions. . . . . . . . . . . . . . . . . . . . 4847
III.C.1. General schemes. . . . . . . . . . . . . . . . . . . . . 4829 V.B.4. CT-to-material conversions. . . . . . . . . . . . . 4847
III.C.2. Patient-specific beam modifiers. . . . . . . . . . 4831 V.B.5. Dose-to-water and dose-to-medium. . . . . . 4847
III.C.3. Output ratios. . . . . . . . . . . . . . . . . . . . . . . . 4831 V.C. Experimental verification. . . . . . . . . . . . . . . . . 4847
III.C.4. Dose buildup. . . . . . . . . . . . . . . . . . . . . . . . 4831 V.C.1. Examples of specific tests. . . . . . . . . . . . . . 4847
III.D. Treatment planning: MC-based patient V.C.2. Verification calculations. . . . . . . . . . . . . . . . 4847
calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4832 V.C.3. Measurement uncertainties. . . . . . . . . . . . . 4847
III.D.1. Statistical uncertainties. . . . . . . . . . . . . . . . 4832
III.D.2. Dose prescriptions and monitor unit I. INTRODUCTION
calculation. . . . . . . . . . . . . . . . . . . . . . . . . . 4834 I.A. Motivation
III.D.3. CT-to-material conversions. . . . . . . . . . . . . 4835
III.D.4. Dose-to-water and dose-to-medium. . . . . . 4835 The accuracy of dose calculations is crucial to the quality of
III.D.5. IMRT dose calculation and optimization.. 4837 treatment planning and consequently to the doses delivered
III.D.6. Voxel size effects. . . . . . . . . . . . . . . . . . . . . 4838 to patients undergoing radiation therapy.1 Among other fac-
Medical Physics, Vol. 34, No. 12, December 2007

tors, dose calculations form an integral component in opti- I.C. Organization of the report
mizing the therapeutic gain, i.e., maximizing the dose to the Following the introductory section Sec. I we begin in
tumor for a given normal-tissue dose, for patients treated
Sec. II with a review of the MC method as it applies to
with radiation. Although the clinical benefit of more accurate photon and electron transport. We include in this section an
dose distributions i.e., how the improved dose distributions overview of MC simulation from the accelerator treatment
will affect tumor recurrence, i.e., local control, and normal
head to the patient as well as a discussion of variance reduc-
tissue complications has not been adequately quantified and
tion techniques and efficiency-enhancing methods integral to
requires further investigation, evidence exists that dose dif- MC calculations in radiotherapy. Section III begins with a
ferences on the order of 7% are clinically detectable.2 More- review of the major MC codes being used in clinical appli-
over, several studies have shown that 5% changes in dose
cation and is followed by detailed discussions on accelerator
can result in 10% 20% changes in tumor control probability
treatment head modeling and patient-specific treatment plan-
TCP or up to 20 30% changes in normal tissue complica-
ning. This section concludes with the topic of experimental
tion probabilities NCTP if the prescribed dose falls along
verification, in which guidance is provided on the types of
the steepest region of the dose-effect curves.35 Readers in-
tests needed to verify the accuracy of MC dose calculation
terested in further understanding the need for heterogeneity
algorithms. In Sec. IV we provide a review of recent studies
corrections, among other topics related to dose calculations,
demonstrating the potential clinical impact of MC dose cal-
are encouraged to read the AAPM Report No. 85,1 where a
culations in comparison with conventional algorithms. Fi-
comprehensive review of tissue heterogeneity corrections for
nally, we conclude in Sec. V with a summary of the recom-
megavoltage photon beams is provided.
mendations from this task group report.
In this report we focus our attention on the Monte Carlo
MC method, a dose calculation algorithm known to be very
accurate when used properly for treatment planning in het- II. THE MONTE CARLO METHOD IN
erogeneous patient tissues. The issue of lengthy calculation RADIOTHERAPY DOSE CALCULATIONS
times has traditionally led to the MC method being viewed in
II.A. Definition of the MC method and historical
the medical physics community as a clinically unfeasible ap-
background
proach. However, the development of MC codes optimized
for radiotherapy calculations as well as the availability of Most generally, the MC technique is a statistical method
much faster and affordable computers, have substantially re- for performing numerical integrations. MC simulations are
duced processing times. These significant advances have led employed in many areas of science and technology. Although
to the clinical use of MC algorithms at some treatment cen- a method based on random sampling was discussed as early
ters and the promised availability of MC photon/electron as 1777 by Buffon,6 the MC technique as we know it today
planning modules among several commercial treatment plan- was first developed and named at the end of the second
ning vendors. world war. The motivation was to apply MC techniques to
In light of the above considerations, MC treatment plan- radiation transport, specifically for nuclear weapons.7 The
ning is quickly becoming a reality. An introductory report for driving forces for the initial idea appear to have been Stanis-
the medical physics community on the understanding, imple- law Ulam and John von Neumann who saw the development
mentation, testing, and use of MC algorithms is therefore of ENIAC, the first electronic computer, as an ideal oppor-
warranted. tunity to develop new applications of statistical sampling.
The developments of MC techniques and computers have
been closely intertwined ever since, with an exponential in-
I.B. Objectives for the report
crease of the application of MC simulations since digital
We intend this document to be a preliminary report with computers became widely available in the 1950s and 1960s.
the following objectives: a to provide an educational re- Modeling of particle transport problems is ideally suited
view of the physics of the MC method and how it is applied for the use of MC methods and has been described by Rogers
in external beam radiotherapy dose calculations, b to de- and Bielajew as follows: The Monte Carlo technique for the
scribe the role of the MC method in external beam radio- simulation of the transport of electrons and photons though
therapy treatment planning process: from the interaction of bulk media consists of using knowledge of the probability
electrons in the target of the linear accelerator to the deposi- distributions governing the individual interactions of elec-
tion of dose in the patient tissues, c to describe the issues trons and photons in materials to simulate the random trajec-
associated with MC dose calculation within the patient- tories of individual particles. One keeps track of physical
specific geometry, d to discuss the issues associated with quantities of interest for a large number of histories to pro-
experimental verification of MC algorithms, and e to dis- vide the required information about the average quantities.8
cuss the clinical implications of MC calculated dose distri- As a technique for calculating dose in a patient the underly-
butions. ing physical basis is much simpler in concept than analytic
We expect that areas of concern outlined in this report algorithms because the MC method consists of a straightfor-
will be further investigated and that more detailed reports ward simulation of reality and does not involve complex
providing recommendations on the major issues will be approximations nor models of dose deposition, but only a
forthcoming. knowledge of the physics of the various interactions which

have been well understood for over 50 years in most cases. ing matter via four main processes: incoherent Compton
While some of these interactions may be complex to simu- scattering with atomic electrons, pair production in the
late in detail, the basic ideas of each interaction, e.g., an nuclear or electron electromagnetic field, photoelectric ab-
electron giving off a bremsstrahlung photon, are well under- sorption, and coherent Rayleigh scattering. The first three
stood by medical physicists and, hence, the overall process is collision types transfer energy from the photon radiation field
easy to comprehend. to electrons or positrons. In most cases Compton scattering is
Although MC was used in several particle physics appli- the dominant interaction, although pair production becomes
cations to simulate electron-photon showers in the 1950s, the increasingly important with increasing energy, and may even
seminal paper in the field was that of Berger in 1963,9 in dominate at higher energies in high-Z components of the
which he described the condensed history technique for elec- treatment head of medical linear accelerators.
tron transport. This technique is the basis of all modern When electrons traverse matter, they undergo a large
electron-photon transport MC codes relevant to medical number of elastic interactions and lose energy by two main
physics. The ETRAN code, based on these ideas10 was devel- processes: inelastic collisions with atoms and molecules and
oped by Berger and Seltzer and now forms the basis of elec- radiative interactions. Inelastic collisions result in excitations
tron transport in the MCNP code.11 The release of the EGS4 and ionizations. Ionizations lead to secondary electrons,
MC code system in 198512 served as a catalyst for the appli- sometimes referred to as particles. Radiative energy
cation of the MC method in radiotherapy calculations of dose losses, which occur in the form of bremsstrahlung and posi-
and dosimeter response. The work of Petti et al.,13 Mohan et tron annihilation, transfer energy back to photons and lead to
al.,14 and Udale15 being early examples of the use of the EGS the coupling of the electron and photon radiation fields. One
MC code system12,16,17 to simulate medical linear accelera- therefore speaks of coupled electron-photon showers.
tors. Even without the direct use of MC simulations, the MC The electron-photon macroscopic radiation field can be
method already plays a significant role in radiotherapy treat- described mathematically by a coupled set of integrodiffer-
ment planning since the energy deposition kernels used in ential transport equations. These transport equations are pro-
convolution/superposition algorithms have been calculated hibitively complicated thereby excluding an analytical treat-
using MC techniques. Linear accelerator calibration proto- ment except under severe approximations. The MC
cols e.g., AAPMs TG-5118 use factors derived from MC technique is a solution method that can be applied for any
simulations. MC-based calculations are also used in the de- energy range and underlying geometry and material compo-
sign of treatment head components.19,20 sition.
Although it has only recently become practical, for over A solution of the transport problem of particles in matter,
two decades the application of MC techniques to radiation which is exact within the existing knowledge of the elemen-
treatment planning has been quite clear.21,22 The widely used tary collision processes, can be obtained by an analog MC
23 17
BEAM code system is a pair of EGS4 now EGSnrc user simulation. In an analog simulation all particle interactions
codes for simulating radiation transport in accelerators and in with surrounding atoms and molecules are explicitly simu-
patients represented by CT data sets. These relatively easy to lated, including those of secondary particles created in the
use tools have sparked intense research in MC-based radio- collisions. An analog MC technique is therefore a faithful
therapy treatment planning and have lead to two comprehen- simulation of physical reality on a digital computer: particles
sive reviews of accelerator simulations by Ma and Jiang24 photons for example are born according to distributions
and Verhaegen and Seuntjens.25 Kawrakow and Fippel, describing the source, they travel a certain distance, deter-
among others, have provided the breakthroughs which have mined by a probability distribution, to the site of a collision,
made clinical treatment planning feasible, as discussed in and scatter into another energy and/or direction state, possi-
Sec. III A. The fast MC codes being developed commercially bly creating additional particles. These photons eventually
are almost all based on the results of this collaboration. As die as a result of pair production or photoelectric events or
this report is being written, the first commercial MC systems when they Compton scatter to energies below a predeter-
have already been introduced into routine clinical treatment mined low-energy photon cutoff, often called PCUT. Analog
planning for electrons26 and photons.27 simulations, often referred to as event-by-event or
interaction-by-interaction techniques, are typically used
for the transport of neutral particles. The analog simulation
II.B. Monte Carlo simulation of electron and photon
of charged particle transport is not practical, due to the large
transport
number of interactions they undergo until locally absorbed as
The following material represents a very brief introduc- the energy of the charged particle falls below the predeter-
tion into the MC simulation of electron and photon transport. mined low-energy limit for tracking charged particles, often
For more details the reader is referred to the reviews avail- call ECUT. All general purpose MC codes therefore employ
able in the literature.8,2831 Another source for detailed infor- condensed history schemes for charged particle transport,
mation is the documentation accompanying some of the gen- discussed in more detail in Sec. II B 2.
eral purpose codes, for instance, the EGSnrc,17 MCNP,32 and Within a MC simulation, quantities of interest can be
34
GEANT4 Ref. 33 manuals, and the PENELOPE paper. computed by averaging over a given set of particle showers
In the energy range of interest for external beam radio- also referred to as histories, cases, trajectories, or
therapy megavoltage range, photons interact with surround- tracks. One can calculate both observable measurable

quantities, such as dose or a particle spectrum, and quantities section of the selected process. The manuals of the popular
that cannot easily be measured such as the fraction of par- general purpose codes17,3234 provide details of the methods
ticles originating from a certain component of the treatment employed for the relevant photon interactions.
head, the dose fraction due to scattered photons, etc. Al- Based on the above discussion it should be clear that an
though there are techniques for scoring quantities at a point analog MC simulation is conceptually quite straightforward.
when using Monte Carlo techniques, in treatment planning
applications, it is usual to score quantities dose mainly av-
eraged over some finite volume or voxel. As the voxel size is II.B.2. Condensed history simulations
increased, for a given statistical uncertainty the total calcu- The condensed history technique was first described com-
lation time will decrease, but the spatial resolution is reduced prehensively in the pioneering work by Berger.9 It is based
see Sec. III D 6 for more discussion. Another important as- on the observation that the vast majority of electron interac-
pect of MC calculations is the presence of statistical uncer- tions lead to very small changes in the electron energy and/or
tainties due to the statistical nature of the method, which is direction. Many such small-effect interactions can there-
discussed in more detail in Sec. III D 1. fore be grouped into relatively few condensed history steps
and their cumulative effect taken into account by sampling
energy, direction, and position changes from appropriate dis-
II.B.1. Analog simulations tributions of grouped single interactions, e.g., multiple scat-
An analog simulation of particle transport consists of four tering, stopping power, etc. Berger defined two main classes
main steps: of condensed history implementations. In a class I scheme all
collisions are subject to grouping. The effect of secondary
1 Select the distance to the next interaction. particle creation above specified threshold energies are taken
2 Transport the particle to the interaction site taking into into account after the fact i.e., independently of the energy
account geometry constraints. actually lost during the step by setting up and transporting
3 Select the interaction type. the appropriate number of secondary particles. In this way
4 Simulate the selected interaction. the correlation between large energy losses and secondary
particle creation is lost. In a class II scheme interactions are
Steps 14 are repeated until the original particle and all
divided into hard sometimes also referred to as cata-
secondary particles leave the geometry or are locally ab-
strophic and soft collisions. Soft collisions are subject to
sorbed. A particle is considered to be locally absorbed when
grouping as in a class I scheme; hard collisions are explicitly
its energy falls below a specified threshold energy.
simulated in an analog manner.
Step 1 is based on the probability, prdr, that a particle
A class II scheme can be described with the same four
interacts in an interval dr at a distance r from its initial
basic steps that make up an analog simulation. The two main
position
differences are that only hard collisions are included and that
prdr = erdr, 1 step 2 is much more difficult because the particles do not
move on straight lines and because it involves the selection
where is the linear attenuation coefficient number of in-
of energy, direction, and position changes from multiple scat-
teractions per unit length. A random distance r distributed
tering distributions. It is also frequently necessary to divide
according to pr can be sampled using the so-called inverse-
the distance between catastrophic interactions into shorter
transform method, which equates the cumulative probability
condensed history steps to guarantee the accuracy of the
of pr with a random number distributed uniformly be-
simulation. As in an analog simulation there is a transport
tween zero and unity
threshold energy. Particle transport thresholds are often the
0
prdr = r =
ln1

. 2
same as the particle production thresholds dividing hard and
soft collisions, but this is not a necessary condition.
A class II MC simulation is illustrated in Fig. 1. The upper
Step 2 involves basic ray tracing, which requires a geom- portion shows a complete electron track including secondary
etry model that can provide the medium and mass density of electrons and photons shown with dashed lines and not in-
a region together with a computation of the distance to the cluding their interactions with energies above the hard col-
next geometry boundary along the particle trajectory. lision thresholds. The lower portion is a magnified view of
Step 3 is similar to step 1 except that now the probability the shaded box. The actual curved path has been simulated
distribution function is discrete, i.e., it involves a fixed num- using four condensed history steps. The filled circles and
ber of final states i, corresponding to an interaction of type i. arrows show the positions and directions at the beginning of
Suppose that the cross section for interaction of type i is the steps. The shaded area around the electron track indicates
denoted by i and the total cross section by = i. A direct the region where the energy of subthreshold secondary par-
application of the inverse-transform method for n interaction ticles is in reality deposited. If this volume is small compared
types yields interaction 1 if 1 / , else interaction 2 if to the calculation resolution i.e., voxel size in the case of
1 + 2 / , else interaction n, if 1 + 2 + + n / . radiotherapy calculations, energy deposition can be consid-
Perhaps the most difficult part is step 4, where one must ered local and modeled using a restricted stopping power
sample energy/direction changes from the differential cross along the electron track. Note that the initial and final posi-

FIG. 1. Illustration of a class II condensed history scheme for electron trans-

port. The upper portion shows a complete electron track including secondary
electrons and photons shown with dashed lines and not including their
interactions with energies above the hard collision thresholds. The lower FIG. 2. Illustration of the components of a typical Varian linear accelerator
portion is a magnified view of the shaded box. treatment head in photon beam mode. Phase space planes for simulating
patient-dependent and patient-independent structures are also represented.
For other manufacturers, component structures such as the jaws, MLC, etc.
may be in different locations, thereby potentially requiring a change in the
tions of a step are not connected in the figure to highlight the placement of the phase space scoring planes.
fact that a condensed history implementation does not pro-
vide information on how the particle goes from A to B the
curved dashed line connecting A and B is a more realistic
II.C. Overview of Monte Carlo-based radiotherapy
representation of the trajectory than a straight line from A to
dose calculations
B. This becomes important when the scoring grid is not the
same as the underlying geometry grid or when a single con- It is possible to carry out a single MC simulation in which
densed history step traverses more than one geometrical re- one starts with the electron exiting from the accelerator
gion as in some of the fast MC codes specialized for use in structure, follows it and its descendants e.g., bremsstrahlung
radiotherapy.3539 This consideration highlights another im- photons, knock-on electrons through the fixed elements of
portant aspect of a condensed history simulation, namely the the head targets or scattering foils, primary collimators,
way the transport is performed in the vicinity of or across monitor chambers, flattening filters, etc., the various beam
boundaries between different regions. The EGSnrc code, for shaping devices which are patient specific jaws, multileaf
instance, utilizes single scattering i.e., analog simulation collimator MLC, applicators, cutouts, wedges, compensa-
within a certain perpendicular distance from an interface.40 tors, and finally the patient as specified by a CT or some
Although this approach is necessary for accurate simulations other data set. This tracking of the initial particle and all of
of certain types of geometries, it is generally not needed for its descendants is referred to as a history. As discussed fur-
typical radiotherapy calculations. ther in Sec. III D 1.1, it is important to include all particles
Although the condensed history technique makes use of associated with a single initiating electron as part of the same
practical MC simulations possible, it introduces the step size history.
as an artificial parameter. Dependencies of the calculated re- Due to significant improvements in the efficiency of pho-
sults on the step size have become known as step-size ton beam treatment head simulations,46 the speed of the com-
artifacts.41 Step-size artifacts were a major factor in the early plete simulation is such that it is feasible to consider per-
years of most general purpose MC codes. Due to significant forming the entire calculation for each patient.47 However,
theoretical developments in the nineties the condensed his- there have been a variety of strategies for dividing such cal-
tory technique is now well understood.42,43 This has lead to culations into several steps. The first step, transporting par-
the development of high accuracy condensed history ticles through the patient-independent elements, can be inef-
implementations40,44 and faster MC codes that can compute ficient without the use of advanced variance reduction
dose distributions with accuracy comparable to traditional techniques see Sec. II D. This is especially true for photon
MC packages in a small fraction of the time.3539,45 beams, since many bremsstrahlung photons generated in the
With charged particle transport one stops tracking the par- target will strike the primary collimator and not contribute to
ticles movement at some low-energy cutoff and the choice the beam reaching the patient. One approach to improve the
of the cutoff can affect the calculation in two important simulation efficiency is to first perform the simulation of the
ways. The higher the value of the cutoff, the faster the cal- patient-independent structures and to store what is called a
culation; this can improve the calculation speed significantly. phase-space file at a plane just below the fixed elements of
On the other hand, unless great care is taken, stopping at too the accelerator head see phase-space plane 1 in Fig. 2. The
high a cutoff energy can distort the dose distribution since phase-space file contains phase-space parameters for all par-
the stopped charged particle might have deposited energy ticles as they cross the scoring plane. The phase-space pa-
some distance from where its trajectory was terminated. rameters consist of the energy, position, direction, charge,
Thus care must be taken in selecting an energy cutoff. and possibly other information such as the region/s of cre-

ation or interaction of particles. The advantage of this ap- Bremsstrahlung splitting and Russian roulette of second-
proach is that this part of the calculation can be reused as ary particles are widely used variance reduction techniques
often as necessary. Particles are then transported through the which are especially useful in simulating an accelerator treat-
patient specific collimation system and are either stored in ment head.23,46 In the various forms of bremsstrahlung split-
another phase-space file at the base of the accelerator see ting, each time an electron is about to produce a bremsstrah-
phase-space plane 2 in Fig. 2 or tracked through the patient lung secondary, a large number of secondary photons with
in the same simulation. Storing a second phase-space may be lower weights are set in motion, the number possibly de-
more efficient when open fields e.g., 10 10 cm2 fields are pending on a variety of factors related to the likelihood of
used for treatment, however, more commonly, when MLCs them being in the field. If the number of photons created is
are used for beam shaping, the latter approach is likely to be selected to minimize those that are not directed toward the
more efficient. patient plane, then there is a further saving in time. Russian
As we will discuss in Sec. III C, the entire phase-space roulette can be played whenever there is little interest in a
data for the accelerator may also be generated using beam particle resulting from a specific class of events. The low
modeling virtual source model approaches which do not interest particles are eliminated with a given probability, but
require direct MC simulation of the accelerator for each to ensure an unbiased result, the weights of the surviving
treatment. One class of virtual source models is based on particles are increased by the inverse of that probability. A
characterizing the results of a MC simulation of the accel- common example is to play Russian roulette with secondary
erator head and another class is based solely on measured electrons created from photon interactions in treatment head
beam data such as depth-dose curves, profiles and output structures. Another variance reduction method, photon forc-
ratios. In either case, the patient-dependent components e.g., ing, may sometimes be used to enhance the production of
the MLC are simulated using either explicit transport meth- electrons in the air downstream of the accelerator. In a pho-
ods or approximate transport methods before detailed trans- ton forcing scheme, the parent photon is forced to interact in
port in the patient. a given geometric region and the weights of the resulting
As with conventional planning methods, experimental particles are adjusted accordingly to maintain an unbiased
verification forms an integral part of the clinical implemen- result.
tation of a MC dose calculation algorithm. MC algorithms Range rejection and increasing the energy at which elec-
will benefit from similar experimental verification proce- tron histories are terminated energy cutoffs are examples of
dures as conventional systems, and as such should follow the methods which, when used correctly, improve efficiency by
commissioning procedures detailed in the AAPM TG-53 decreasing the time per history without significantly chang-
report48 and other relevant publications.49,50 Experimental ing the results. In range rejection, an electrons history is
verification in more complex fields and/or heterogeneous ge- terminated whenever its residual range is so short that it can-
ometries is useful to verify the expected improved accuracy not escape from the current region or reach the region of
associated with MC calculations in these situations. interest. In most implementations this ignores the possible
creation of bremsstrahlung photons while the electron loses
energy which means this is an approximate technique. When
II.D. Variance reduction techniques and efficiency
applied to electrons below a certain energy threshold, this
enhancing methods form of range rejection produces the same results in a re-
duced computing time.23 It is also possible to implement
The efficiency, epsilon , of a MC calculation is defined range rejection in a manner which properly accounts for
as: = 1 / s2T, where s2 is an estimate of the true variance 2 bremsstrahlung production and thus make it an unbiased
of the quantity of interest and T is the CPU time required to variance reduction technique. By stopping tracking of elec-
obtain this variance. Since both Ns2 and T / N are approxi- trons at a higher energy, efficiency can be improved, but this
mately constant, the efficiency is roughly independent of N, may have an effect on the dose distribution if too high a
the number of histories simulated. There are two ways to threshold is used. Playing Russian roulette with particles at
improve the efficiency of a given calculation: either decrease energies below a relatively high transport cutoff or with
s2 for a given T or decrease T for a given N while not chang- range-rejected particles is a comparable variance reduction
ing the variance. Techniques which improve the efficiency by technique for reducing the simulation time. However, its
changing the variance for a given N while not biasing the implementation is typically more difficult and this has fa-
result i.e., not changing the expectation value which is the vored the use of range rejection and high transport cutoffs in
value expected in an infinitely long run are called variance situations where it is easy to demonstrate that the resulting
reduction techniques. Variance reduction techniques often in- error is sufficiently small.
crease the time to simulate a single history and are only There are other variance reduction and efficiency enhanc-
useful if the overall efficiency is improved. A given tech- ing techniques which collectively have allowed substantial
nique may increase the efficiency for some quantities being increases in the speed of a calculation. These methods in-
scored and decrease it for others. In contrast to variance re- clude the reuse of particle tracks,37 and other adaptations of
duction techniques, there are a variety of ways to speed up a particle track reuse, such as the simultaneous transport of
given calculation by making an approximation which may or particle sets STOPS approach of Kawrakow,36 which is a
may not affect the final result in a significant way. variance reduction technique. For a more comprehensive re-

view of variance reduction and efficiency enhancing tech- allelization of MC techniques over multiple computers to
niques, readers are referred to a chapter by Rogers and provide more reasonable turn-around times for simulation in
Bielajew51 and the papers by Rogers et al.23 and Kawrakow clinical research.6163 Specific to radiation therapy, there
et al.46,52 Other useful references on the influence of variance have been a variety of MC codes developed to improve the
reduction methods in the context of phantom and patient calculation efficiency, especially in the patient simulation.
treatment planning are provided in the articles by Ma et al.53 The PEREGRINE system North American Scientific: Nomos
and Kawrakow and Fippel.45 Division was developed at the Lawrence Livermore Na-
In summary, variance reduction techniques are an impor- tional Laboratory and has been benchmarked against
tant requirement for the use of MC calculations in the clini- measurements.27 The PEREGRINE electron transport algorithm
cal setting; without them, calculation times would still be too is a modified version of the EGS4 condensed history imple-
long for use in most situations. However, inappropriate use mentation. PEREGRINE uses the random hinge approach64 for
of a variance reduction technique can reduce calculation ef- electron transport mechanics. Several efficiency enhancing
ficiency, thus increasing calculation time. In principle vari- and variance reduction techniques are implemented in PER-
ance reduction techniques, implemented correctly, do not al- EGRINE, including source particle reuse, range rejection, Rus-
ter the physics and thereby produce unbiased results. Other sian roulette and photon splitting. Parallelizing the calcula-
efficiency improving techniques can significantly alter the tion on several computer processors is also implemented to
accuracy of the calculation if applied inappropriately. Im- reduce the overall dose calculation time. The system de-
proper implementations can lead to unpredictable results in couples the scoring zones from the transport geometry.
either case. Source modeling in PEREGRINE is achieved by performing a
It is incumbent upon the medical physicist to understand, full MC simulation of the accelerator head using the BEAM
at a minimum, those techniques that the user can adjust in a code23 and using the output to create a source model65 from
clinical MC algorithm. In addition, tests must be done to which source particles are regenerated above the patient-
show correct implementation of those techniques over the dependent beam modifiers. PEREGRINE uses several approxi-
range of clinical situations. Vendors should provide adequate mations when transporting the beam through the patient spe-
documentation for users to understand the techniques em- cific beam modifiers, followed by transport through a
ployed and how the implementation was validated. patients CT data set.66 The PEREGRINE system was the first
MC algorithm to receive FDA 510-K approval and repre-
III. MONTE CARLO SIMULATION OF RADIATION sents the first commercially available photon beam treatment
TRANSPORT IN ACCELERATORS AND planning system in the United States.
PATIENTS Several commercial MC implementations currently avail-
able or under development are based on the Voxel Monte
III.A. Review of current Monte Carlo codes
Carlo VMC series of codes. The initial version37 of VMC was
A large number of general purpose MC algorithms have only applicable to electron beams and involved several ap-
been developed for simulating the transport of electrons and proximations in the modeling of the underlying interaction
photons. Perhaps the most widely used of these in medical processes. Improved treatment of multiple elastic scattering67
physics is the EGS code system.12,16,17,40,44 There are several was incorporated in 1996, PENELOPEs random hinge method
other comparable general purpose systems used in medical in 1997,68 and all remaining approximations removed in
physics such as the ITS Refs. 54 and 55 and MCNP 2000.45 A photon transport algorithm was added in 1998,35
systems11,32 both of which have incorporated the electron which included precalculated interaction densities in each
transport algorithms from ETRAN Refs. 10 and 56 which voxel similar to approaches developed previously.69,70 The
was developed at NIST by Berger and Seltzer following the resulting code was named XVMC. In 1999, a series of ad-
condensed history techniques proposed by Berger.9 Other vanced variance reduction techniques were developed and
newer general purpose systems include PENELOPE Ref. 34 incorporated into XVMC which brought an additional factor
and GEANT4.33 The EGS and ITS/ETRAN and MCNP systems are of 59 increase in simulation speed. Treatment planning ap-
roughly of the same efficiency for calculations in very simple plications and experimental verification of VMC-based sys-
geometries when no variance reduction techniques are used, tems have been reported in several articles.7175 Separate ver-
whereas the other systems tend to be considerably slower. An sions of the VMC code were subsequently developed by
important special purpose code is the EGS user code, Fippel XVMC Refs. 45 and 76 and Kawrakow VMC++36.
23,5760
BEAM. The BEAM code is optimized to simulate the XVMC is being incorporated into the Monaco CMS, Pre-
treatment head of radiotherapy accelerators and includes a cisePlan Elekta, and iPlan BrainLab treatment planning
number of variance reduction techniques to enhance the ef- systems. VMC++ includes additional refinements in the phys-
ficiency of the simulation.46 Comprehensive reviews of MC ics models, such as the exact KawrakowBielajew multiple
simulation of radiotherapy beams from linear accelerators scattering formalism,77 including relativistic spin effects,17
are available elsewhere.24,25 and the STOPS method mentioned in Sec. II D. VMC++ is
While the accuracy of these general-purpose codes can be the basis for the first commercial electron MC algorithm
roughly the same as long as they are carefully used, these from Nucletron and is being incorporated into the Master-
codes are considered too slow for routine treatment planning plan Nucletron and Eclipse Varian treatment planning
purposes. Several groups have published on the use of par- systems for photon beam dose calculations. The VMC/XVMC/

VMC++ code systems have also been integrated into several An MCNP Monte Carlo N-particle-based code, RT_MCNP
MC-based research systems including those at the University Ref. 86 has been in use for treatment planning research at
of Tubingen, McGill University, and the Virginia Common- UCLA. There have been a series of publications related to
wealth University. the use of RT_MCNP for a variety of applications, from radio-
Another MC code that has reached commercial imple- surgery to IMRT planning using a micromultileaf
mentation is the Macro Monte Carlo MMC method38,78 for collimator.8691 Finally, treatment planning studies using the
9294 95
electron beam treatment planning. MMC uses the MC tech- GEANT, PENELOPE, gamma electron positron transport
96,97
nique, but is very different from the standard simulation of system GEPTS, and ORANGE Ref. 98 MCNP-based
radiation transport. MMC uses a precalculated database from MC codes have also been reported.
EGSnrc simulations of electron transport through small In an effort to quantify the speed and accuracy for the
spheres of varying sizes and materials and follows a random phantom component of the calculations by the various MC
walk through the CT phantom based on these precalculated codes being used for research and/or clinical planning pur-
values. The commercial implementation of MMC, eMC, poses, Rogers and Mohan99 proposed what came to be
Eclipse, Varian makes use of some precalculated known as the ICCR benchmark. The tests and geometries for
accelerator-specific information; however, fluence intensities the ICCR benchmark comparisons were as follows:99 a
arising from the various subsources are fitted to the users speed test: phantom of dimensions 30.5 30.5 30 cm with
measured data.79 More details on the performance of the 5 mm3 voxels filled either randomly with one of 4 materi-
eMC system for clinical electron dose calculations is avail- als water, aluminum, lung, and graphite or with water
able elsewhere.80 alone, 6 MV photons spectrum from a point source at 100
There are several institutions currently engaged in devel- cm SSD and collimated to 10 10 cm2 at the phantom sur-
oping MC radiotherapy applications for clinical and/or re- face, b accuracy test: heterogeneous phantom as defined in
search related purposes. MCDOSE Ref. 53 and 81 is among a with 5 5 2 mm voxels 2 mm along the depth axis,
the first of these types of systems. MCDOSE is based on EGS4 18 MV photons spectrum from a point source at 100 cm
and includes fundamental changes in some aspects of the SSD and collimated to 1.5 1.5 cm2 at the phantom surface.
electron transport in order to improve speed. MCDOSE has Beam spectra268 were provided for these comparisons in or-
been shown to give results very similar to EGS4.53 It performs der to standardize the beam model used in the dose calcula-
particle tracking through the beam modifiers in conjunction tions. Statistical uncertainties were to be reported as the rela-
with the patient calculation and has built-in capability to tive uncertainty in the dose for voxels with a dose greater
handle various models of the incident beam. The speed ups than some arbitrary lower limit, such as 50% of the maxi-
have been obtained by using various techniques bremsstrah- mum dose.99 Results for the ICCR benchmark are summa-
lung splitting, photon forcing, track repetition,37 and range rized in Table I. Some timing results have been added re-
rejection. cently. Timing values have been scaled to that on a single
The MCV Monte Carlo Vista 82 code is used for clinical Intel P-IV 3.0 GHz processor.
IMRT planning and verification61 as well as for a variety of The reader should be aware that the timing results re-
research related applications. MCV interfaces photon-electron ported in Table I are susceptible to large variations on the
MC dose algorithms to the Pinnacle Philips Radiation On- order of at least 20% due to variations in compilers,
cology Systems, Madison, WI commercial planning system, memory size, cache, etc.99 Timing comparisons for more
and calculations are performed in a parallel environment us- clinically relevant treatment plans are presented in Sec.
ing multiple Unix-based processors.82 Treatment head simu- III E 4. These results have been reported by medical physi-
lation is accomplished using a modified version of the BEAM cists using commercial MC systems for treatment planning.
code, with calculations divided into two stages, based on the
patient-dependent83 and patient-independent component III.B. Accelerator treatment head simulation
structures.82 Patient and phantom calculations within MCV
are completed using DOSXYZnrc,58 VMC++ described III.B.1. Sensitivity of simulations to electron beam
above, or MCVRTP, a C++ MC code developed by Philips and other parameters
that uses many of the algorithms of EGS4.82 MCV utilizes In general one does not know all the details of the clinical
variance reduction techniques inherent to the subcodes it accelerator. For example, the characteristics of the incident
uses, and achieves speed by use of multiple processors.82 electron beam are only known approximately. Knowledge of
Another major research code is the dose planning the sensitivity of MC simulation results to input parameters,
method39 DPM code system developed initially for perform- such as the position, direction, and energy of the initial elec-
ing electron beam dose calculations in a voxelized geometry. tron beam exiting the accelerator and to details of the geom-
DPM utilizes the KawrakowBielajew multiple scattering etry of the treatment head, is important. A sensitivity analysis
formalism77 and the random hinge approach for transport is indispensable in determining which source and geometry
mechanics.64 Particles do not stop at boundaries39 as is the parameters to adjust and by how much in order to improve
case with other fast codes. DPM has been integrated into the agreement with user-specific measurements.
University of Michigans in-house treatment planning system Factors influencing the characteristics of a photon beam
UMPlan and is currently being used for a variety of photon are the energy, spatial, and angular distributions of the elec-
beam treatment planning studies.84,85 trons incident on the target or exiting the waveguide, and

TABLE I. Summary of timing and accuracy results from the ICCR benchmark. Timing comparisons were
performed using 6 MV photons, 10 10 cm2 field size, and those for the accuracy test, using 18 MV photons
and a 1.5 1.5 cm2 field size, as detailed in the ICCR benchmark Ref. 99. All times have been scaled to the
time it would take running on a single, Pentium IV, 3 GHz processor. Readers should be aware that the timing
results, as well as the method used to scale the times, are subject to large uncertainties due to differences in
compilers, memory size, cache size, etc.
Monte Carlo code Time estimate % mean difference relative to ESG4/PRESTA/DOSXYZ

min
ESG4/PRESTA/DOSXYZ 43 0, benchmark calculation

VMC++ 0.9 1
XVMC 1.1a 1
MCDOSE modified ESG4/PRESTA 1.6 1
MCV modified ESG4/PRESTA 22 1
DPM modified DPM 7.3b 1
MCNPX 60c Maximum difference of 8% at Al/lung interface
on average 1% agreement
PEREGRINE 43d 1
GEANT4 4.6.1 193e 1 for homogeneous water and water/air interfaces
a
Results not originally part of the ICCR benchmark study, from Ref. 76.
b
Results not originally part of the ICCR benchmark study, reported independently by author I.J.C. for the
modified version of DPM developed for clinical planning calculations.
c
Timing results not originally part of the ICCR benchmark study, reported independently by author J.J.D.
Calculations were performed using the *F8 energy deposition tally.
d
Timing and accuracy results not originally part of the ICCR benchmark study, reported independently by
author D.S.-B.
e
Timing and accuracy results not originally part of the ICCR benchmark study. Estimated independently by
author Seuntjens based on Poon and Verhaegen Ref. 94 and ICCR type speed-test dose calculations Ref. 270.
Timing results are for the standard physics model; the low-energy and the PENELOPE model lead to a factor of
2 more CPU time. The accuracy result reported is derived from the interface perturbation studies in Poon and
Verhaegen Ref. 94, applies to 1.25 MeV monoenergetic photon beams and represents the difference with
EGSnrc using PRESTA-II electron step algorithm and exact boundary crossing. For a water/Pb interface and
1.25 MeV photons, the maximum difference with EGSnrc increases to 6% Ref. 94.
the dimensions, materials, and densities of all the compo- beam energies from accelerators produced by different
nents interacting with the beam the target, primary collima- manufacturers Varian, Siemens, and Elekta. The electron
tor, flattening filters, monitor chamber, collimating devices, beam radial intensity distribution was found to influence the
such as blocks or MLCs, and beam modifying devices such off-axis ratios to a great extent. The greater the width of the
as wedges. Several investigators have reported on the sen- electron-beam radial intensity distribution, the relatively
sitivity of megavoltage beam simulations to the electron more intense is the photon beam on the central axis.102 Fig-
beam striking the target and other treatment head ure 3 shows the influence of the electron-on-target energy
parameters.19,100103 Faddegon et al.,19 in simulating Siemens and radial intensity FWHM on 40 40 cm2 field profile
accelerators, showed that the key parameters are the mean doses from Tzedakis et al.103 The calculated profiles are ob-
energy and focal spot size of the electron beam incident on served to be quite sensitive to these parameters. The central
the exit window, the material composition and thickness pro- axis depth dose curves are also strongly influenced by the
file of the exit window, target, flattening filter, primary col- electron-on-target energy.102 However, the central-axis
limator, and the position of the primary collimator relative to depth-dose curves are quite insensitive to variation in the
the target. Bieda et al.101 showed that the accelerator simu- radial intensity distribution of the electron beam striking the
lation for 20 MeV Varian-produced electron beams was target, because the dose along the central axis is deposited
very sensitive to the distance between the scattering foils primarily by particles in the vicinity of the central axis. The
and, to a lesser extent, to the width of the shaped secondary divergence of the electron beam incident on the target also
scattering foil. Changes to the primary or secondary foil needs to be considered as it may affect large field profiles.
thickness were found to significantly alter the falloff and Regarding the influence of individual treatment head
bremsstrahlung components of the depth-dose curve.101 components, SheikhBagheri and Rogers102 see Table II
Sheikh-Bagheri and Rogers102 performed calculations of in- showed that even small changes 0.01 cm in the primary
air off-axis ratios and depth-dose curves and compared collimators upstream opening can affect in-air off-axis ratios
these with measurements to derive estimates for the param- by restricting the number of bremsstrahlung photons contrib-
eters of the electron beam incident on the target, and to study uting to the scattered photon fluence reaching off-axis points
the effects of some mechanical parameters, such as target downstream. Dose profiles are quite sensitive to the compo-
width, primary collimator opening, flattening filter material, sition and density of the flattening filter as noted in Fig. 4,
and density. Their study102 included several different photon where two different flattening filter materials were used for

chamber is being taken into account. The ion chamber and

mirror are, however, potentially important structures in elec-
tron beam simulations. The collimating jaws have no signifi-
cant effect on the energy and angular photon
distributions.14,107,108 Changing the composition of the sec-
ondary collimators from pure tungsten to an alloy containing
50% tungsten by weight does not significantly affect the cal-
culated dose.102
Even in those cases for which the beam model includes an
explicit simulation of the accelerator head, end users of MC
treatment planning algorithms will probably have little con-
trol over parameters affecting the treatment head simulation.
It will be incumbent upon vendors to provide accurate beam
models verified by measurements for treatment planning
purposes. Vendors and developers should be aware of poten-
tial difficulties associated with accurate specification of the
treatment head component structures. Such issues include
difficulty in obtaining proprietary information from accelera-
tor manufacturers, incorrect proprietary information pro-
vided by the manufacturers,101,102,104 undocumented accel-
erator updates, and large uncertainties in important
parameters needed for accurate simulation, such as the
electron-on-target energy. Accelerator vendors are encour-
aged to make accurate, detailed information of their accel-
erators accessible in formats easy to implement in MC simu-
lation, as established for instance by Siemens.109
III.B.2. Electron beam specifics

Simulation of the passage of electron beams through the
treatment heads of accelerators has figured prominently in
MC radiotherapy calculations for many years. The first ap-
plication of the BEAM code23 was to simulate electron beams
for a wide range of accelerators. A variety of publications
have demonstrated the accuracy of this technique for com-
puting dose distributions and output ratios.24,110,111 Recent
work has established the methodology to achieve high accu-
FIG. 3. a The lateral dose-profile curves as a function of the FWHM of the racy in matching calculated and measured dose distributions
radial intensity distribution for a monoenergetic, 6 MV, electron beam. The
measured profile and five calculated dose profile curves are presented; each
for even the largest fields, including asymmetries and the
curve is normalized to the central axis. b The influence of electron energy bremsstrahlung tail.112
on dose-profile curves. The energy was varied from monoenergetic 5.4 to The procedure for simulating the electron beam treatment
6.6 MeV. For clarity only four calculated and measured profiles are pre- head is quite similar to that of x rays. The components gen-
sented; each curve is normalized to the central axis. The FWHM of the
radial intensity distribution was 0.3 cm FWHM in all cases. Reprinted from erally important for electron beam therapy treatment head
Tzedakis et al. Ref. 103 with permission. simulations are shown in Table III. Photon beam components
are also presented for comparison. For electrons, accelerators
from the major vendors use a pair of scattering foils to flatten
the calculations.102,104 The careful specification of the geom- the beam with minimal bremsstrahlung contamination. A
etry and materials within the MC code is an important con- low-scatter monitor chamber may be employed and the mir-
sideration. This includes verification of the input of the com- ror may be retracted from the beam. The jaw position is
ponent geometric specifications, for example, by using the generally fixed for a given applicator and energy such that
listing files available with the BEAM Ref. 23 system. More- the relative output ratio depends only on the custom insert.
over, for complicated components, such as the flattening fil- The critical parameters for electron beam simulation are
ter, independent attenuation calculations of these structures, different than those for x rays. Sensitivity analyses provide
using monoenergetic photons, may be helpful to verify their quantitative evidence of these differences.100,101,113 Due to
thickness profiles.105,106 Attenuation of the photon beam by the sensitivity of the beam range to the primary electron
the monitor ion chamber and the field mirror is negligible energy a 0.2 MeV change in electron energy corresponds
and these structures are often omitted from MC simulations with a 1 mm change in beam range, the incident electron
of photon beams, except when backscatter to the monitor energy is the primary tuning parameter for electron beam

TABLE II. A summary of the findings of Sheikh-Bagheri and Rogers Ref. 102.
Parameter in the linac model Impact on in-air off-axis factors Impact on central-axis depth dose values
Mean energy of the incident electron intensity Decrease with increasing primary electron energy, A 0.2 MeV change in mean energy
distribution assumed Gaussian e.g., 0.105 0.007/ MeV at 15 cm off-axis for a causes an observable change 2% or 3
Siemens KD 6 MV beam. A 0.2 MeV mean energy with 0.7% or 1 dose uncertainty.
change produces an observable effect.
Gaussian width of the incident electron Show little or no dependence, e.g., widening of the Show weak dependence in the dose
energy distribution FWHM from 0% to 20% resulted in no change, for a buildup region and at large depths, e.g.,
Siemens KD 6 MV beam. Asymmetrical energy an asymmetric Gaussian with 14% FWHM
distribution has a small effect, e.g., an asymmetric on the LHS of the peak and 3% FWHM
Gaussian with 14% FWHM on the LHS of the peak and on the RHS of the peak increases buildup
3% FWHM on the RHS of the peak causes a change of dose by up to 1.5% for a Siemens KD
2% for a Siemens KD 18 MV beam. 18 MV beam.
Gaussian width of the incident electron radial Decrease quadratically with increasing Gaussian Little or no observable effect
intensity distribution width, e.g., a change in FWHM from 0.01 to 0.15 cm considering statistical uncertainties.
leads to 7% decrease at 15 cm off-axis for a Varian 18
MV beam.
Divergence of the incident electron beam Show little or no effect up to 0.5; at 1 show a No observable effect up to a few
at a given intensity distribution FWHM decrease of 1% at 15 cm off axis at 100 cm SSD, for degrees considering statistical uncertainties
an 18 MV Varian beam. 1% or 1.
Radius of the upstream opening of the primary Sensitive to small changes, e.g., varying the upstream No observable effect.
collimator opening by 0.01 cm produces a 1% change at 15 cm
off-axis for a Varian 18 MV beam.
Density and material of the flattening filter Show strong dependence, e.g., reducing tungsten Not reported.
density by 1 g cm3 causes a 6% reduction at 15 cm
off axis for a Varian 15 MV beam. Using the incorrect
material has a very large effect, primarily because of
the density change.
simulations. However, electron distributions are very sensi- distributions and parameters to adjust include angle of the
tive to all the materials in the beam, especially the scattering incident beam and the lateral position of shaped scattering
foils and may also be affected by the monitor chamber if it foils and the monitor chamber.
has thick walls. Hence, accurate geometric descriptions of all
components in the beam path are required for the simulation III.C. Modeling of the linear accelerator treatment
of electron beams. Asymmetries are evident in electron dose head
III.C.1. General schemes
A beam model in the context of MC treatment planning is
any algorithm that delivers the location, direction, and en-
ergy of particles to the patient dose-calculating algorithm.
The direct MC simulation of a beam is one form of a beam
model but for clarity we refer to it as a beam simulation
rather than as a beam model. Accurate beam modeling is an
important prerequisite for accurate dose calculation within
the patient. Beam models use one of three possible ap-
TABLE III. Components in the treatment head and other beam modifying
devices for x ray and electron beams.
X rays Electrons
FIG. 4. MC calculated profiles in a water phantom modified DPM, Univer- Exit window and target Exit window and primary scattering foil
sity of Michigan/UMPlan for a 15 MV 10 10 cm2 at 10 cm depth in Primary collimator Primary collimator
water. Input for the profile calculations were the phase space simulations of Flattening filter Secondary scattering foil may be present
the Varian 21-EX treatment head, performed using BEAMnrc, with two
Monitor chamber Monitor chamber low scatter
different material compositions specified for the flattening filter. Open
circles represent the MC profile with a copper flattening filter Mirror Mirror
= 8.933 g / cm3 and open triangles that with the tungsten filter Asymmetric jaws and MLC Jaw position fixed for each applicator
= 19.30 g / cm3. Ion chamber measurements are shown in the solid line. Wedge, blocks, graticule Applicator with insert
Calculations and measurements are each normalized to the central axis Ref. Bolus Bolus, shielding on or below patient surface
104.

proposed by Ma et al.,114 is based on the development of

multiple-source models with parameters derived from the
original simulated phase-space data.65,88,93,114,116120 In a
multiple-source model, source particles are grouped by the
location of their last interaction prior to being scored at the
phase-space plane, resulting in subsources representing the
major components of the treatment head. Fluence distribu-
tions for each subsource may be reconstructed from the
phase-space data in the form of correlated histogram
distributions,65,93,114 thereby approximately retaining correla-
tion of the particles position, energy and direction. Although
the development of accurate multiple-source models is also
reliant upon simulation parameters and geometric and mate-
rial specifications of the component structures, sub-sources
may be adjusted without redoing the simulations, based
on measurements to optimize agreement between calcula-
tions and measured data, An example of such an approach
consists of adjusting the spatial or energy boundaries of the
planar fluence and energy distributions for each subsource to
produce agreement with measured dose profiles and depth-
dose curves, respectively, for a range of square field shapes,
FIG. 5. The three routes for accelerator beam model specification: a starting with fluence distributions reconstructed from phase-
solid linedirect use of phase-space information from simulation of the
accelerator treatment head, b dashed linemultiple virtual source mod-
space data for one field size.117,121 For instance, one changes
els derived from the phase-space information with or without enhancements the range of energies sampled from the discrete energy dis-
from measured data, and c dotted linedevelopment of other models de- tribution as a function of radius, to provide a match with
rived from measurements measurement-driven models. measurements, without having to redo the entire treatment
head simulation. This method has been extended to MC-
based commissioning of electron beams.111,121 Models devel-
proaches see Fig. 5: i direct use of phase-space informa- oped for reference accelerators were used to accurately com-
tion from the accelerator treatment head simulation, ii de- mission within 2% / 2 mm of measurements in the high
velopment of virtual, multiple-source models reconstructed dose/high gradient profile regions electron beams from other
from the treatment head simulation with or without enhance- machines of similar design by adjusting a few parameters in
ment from measurements, or iii development of other mod- the model. Implementation of photon and electron beam
els derived exclusively from measurements measurement- multiple-source models has been reported for a variety of
driven models. accelerator manufacturers including, Varian,122,123
73,124,125 73,86,88
While the utilization of direct phase-space information Siemens, Elekta, Novalis BrainLab,87,89 and
126
provides details on the physical interactions within the treat- Cyberknife.
ment head, it may not be practical for routine clinical A possibly more practical approach to beam modeling in-
application.65,93,114116 Some of the limitations include: a volves derivation of the model parameters from a standard
generation and quality assurance of phase-space information set of measurements. The advantage of such measurement-
requires MC simulation expertise, b accurate phase-space driven models is that they may be developed without depen-
simulation is dependent upon accurate input parameters dence on the details of the accelerator treatment head. Flu-
such as the incident electron energy as well as detailed ence distributions in measurement-driven models may be
geometric and material specifications of the accelerator com- developed starting with analytical models whose parameters
ponents, which may be subject to inaccuracies, as well as are optimized based on minimization of the differences be-
proprietary issues, c storage requirements are large tween calculations and measurements.100,125,127131 Informa-
typical MC simulation may require up to 109 phase-space tion for the model can be deconvolved from measured
particles for multiple photon beams,115 which may amount to data.100,127 Similar methods have been reported for beam-
tens or hundreds of gigabytes of computer disk space for an model specification using conventional dose calculation al-
accelerator with two photon energies and five electron ener- gorithms with good agreement established between calcula-
gies with five different applicator sizes,117 and d due to the tions and measurements in water phantoms.132135 The same
much slower pace of speed increase in hard drives and net- beam modeling criteria for conventional dose algorithms
works compared to CPU speed development, reading the should also be applicable to the MC method although differ-
phase-space data can be a bottleneck in the calculation. It is ences in the technical details such as source parameterization
therefore clear that a more concise, accurate characterization and software implementation are expected. The use of
of radiation interactions in the treatment head is necessary measurement-driven beam models eliminates the need for
for performing routine clinical MC dose calculation. phase-space simulation and, as the model parameters are de-
Another method for beam model specification, initially rived from measurements, may provide an added level of

confidence in the accuracy of the model in homogeneous flattening filter and primary collimator, typically 3% 8% of
phantoms. Moreover, specification of beam models is similar the energy fluence in a 10 10 cm2 field. The primary
to that with conventional dose algorithms, and does not re- source is a narrow sharp source normally a few millimeters
quire expertise with MC accelerator simulation. However, in diameter, while the extrafocal sources tend to be much
rigorous verification of measurement-driven models in het- broader, more diffuse and bell-shaped in nature.142,143 The
erogeneous phantoms is necessary to validate the empiri- output ratio is affected by the size and geometry of these
cally derived fluence distributions. It has been shown that, sources. The collimators jaws and MLCs block the extrafo-
in addition to the use of measurements in water phantoms, cal source when the field size is sufficiently small 3
test cases in heterogeneous phantoms under conditions of 3 cm2 and for smaller fields the primary source starts
electronic disequilibrium may be necessary to determine the being blocked by the collimators. The combination of ex-
correct energy spectrum unambiguously.136 trafocal source and primary source cutoffs cause the output
ratios to fall off sharply at small field sizes.143,144 Accurate
III.C.2. Patient-specific beam modifiers source modeling of small fields is especially important in
IMRT planning where multiple, small field, off-axis seg-
Transport through the patient-dependent components
ments are often used.61,87,145 For medium sized fields 10
such as the field-defining collimators and the MLC may be
10 cm2 20 20 cm2, output ratios are more likely af-
classified into one of the following three schemes, which we
fected by the extrafocal sources as the collimators are large
will term: a explicit transport, b explicit-approximate
enough to expose the entire primary source, however, small
transport, and c pseudo-explicit transport. In an explicit
enough to eclipse the extrafocal sources. In large fields, be-
transport scheme, all particles with appropriate energy cut-
yond 20 20 cm2, the extrafocal sources are nearly com-
off values are transported using MC techniques through the
pletely exposedthe increase in output ratios in these situa-
components; all details of the design geometry such as
tions is primarily a result of phantom scatter, lack of
rounded leaf ends, interleaf spacing, etc. for a MLC should
backscatter from the collimator jaws to the monitor chamber,
be included in the geometry modeling.72,115,137 With explicit-
and stray radiation from the treatment head.146,147 Depending
approximate transport, approximations are employed in the
on the location of the jaws relative to the transmission cham-
MC photon/electron tracking scheme to improve the effi-
ber which varies among the different linear accelerator
ciency of the calculation.83,87,138,139 An example is the ap-
types, radiation backscattered from the jaws into the cham-
proach of Siebers et al.,83 in which only first Compton scat-
ber can also have an effect on the output ratios. Relative to
tered photons are transported through the MLC. The method
large field sizes 40 40 cm2, backscattered radiation in-
of Tyagi et al.139 includes simulation through the detailed
creases by 2% 3% at small field sizes 3 3 cm2 for 15
MLC geometry accounting for all Compton scattered pho-
MV photons on a Varian 21EX linear accelerator, for ex-
tons, however, ignores the secondary electrons, i.e., assumes
ample. Studies for photon beam MC algorithms have shown
they deposit their energies locally. In a pseudo-explicit trans-
calculated output ratios to be within 1.5% of measurements
port scheme, beam fluence distributions are reconstructed
over a range of field sizes when accounting for backscattered
from the phase-space simulation to develop subsources for
radiation.27,139,148,149 MC calculated electron beam output ra-
characterizing components, such as the field defining
tios for field size-specific applicators have also been re-
jaws,93,120 electron applicators,114 and the MLC.88 Although
ported to agree with measurements within 1% 2%.26,110
the need for time-intensive, explicit transport is obviated
with the use of multiple subsources, the ability to incorporate
detailed geometric characteristics of components like the III.C.4. Dose buildup
MLC may be difficult with this approach. Appropriate
There has been considerable discussion on discrepancies
benchmarking must be performed by developers and vendors
between MC calculations and measurements in the dose
to evaluate the tradeoffs between speed and accuracy related
buildup region. Hartmann-Siantar et al.27 observed MC dose
to the use of various beam model approaches in MC-based
deficits of up to 5 mm distance-to-agreement versus mea-
modeling of patient-specific beam modifiers.
surements and attributed these discrepancies to a source of
electrons in the accelerator head not fully accounted for in
III.C.3. Output ratios the treatment head simulation with BEAM. It has been shown
The output ratio or relative output factor is the ratio of that arbitrarily increasing the electron contamination by a
dose per monitor unit in a phantom for an arbitrary field size significant amount removes the discrepancy.27,88,125 As the
to that for a reference collimator setting, the latter usually result of further investigation, Ding150 concluded that the dis-
10 10 cm2 at a SAD or SSD of 100 cm for a depth of 10 crepancy could not be explained by the electron source hy-
cm for x-ray beams.140 Output ratios over the range of clini- pothesis and postulated that contaminant neutrons emerging
cally useful field sizes are heavily influenced by the amount from the treatment head might be the cause. However, Ding
of head scattered radiation impinging on the phantom.140,141 et al.151 subsequently refuted this neutron hypothesis by
Radiation generated by clinical accelerators can be charac- measuring minimal neutron component in the dose buildup
terized by a primary photon source generated through the region. Abdel-Rahman et al.,152 who performed MC calcula-
bremsstrahlung process, and other extrafocal sources ac- tions using EGSnrc and a comprehensive set of measure-
counting for scattered photons arising primarily from the ments with multiple detectors, again found significant differ-

ences between measurements and calculations in the buildup deposition in the phantom. Using an already calculated
region for 18 MV photons even when completely simulating phase-space file, the statistical uncertainty in the dose calcu-
the response of the detectors. They ruled out the following lated in a phantom by reusing the particles from the phase-
possible causes of the discrepancy: a an unknown electron space file i.e., assuming they are independent and ignoring
source in the accelerator head simulation, b contaminating correlations between them, will approach the finite, latent
neutrons, c inaccurate cross section data, and d gamma, variance associated with the phase space data, regardless of
p reactions. They also showed that explicit modeling of trip- the number of times the phase space is reused. The use of
let production interactions influences the dose buildup for an source models derived from phase space simulation will tend
18 MV beam. However, work by Kawrakow153 showed that to smooth out point fluctuations in the phase space.114 How-
a more accurate triplet production model does not remove ever, if the latent variance is large enough to introduce sys-
the discrepancies. Benchmarking of the NRCC accelerator tematic bias then this will be propagated in the reconstructed
photon beams has shown agreement well within 1%, for field phase space source model. Beam models derived exclu-
sizes up to 10 10 cm2, at all depths154; it should be noted sively from measurements, on the other hand, are analogous
that the NRCC accelerator 20 MV photons uses a sweeping to those generated using conventional analytical
beam technique154 as opposed to a flattening filter to flatten algorithmslatent variance as defined above is not a con-
the beam. These comparisons explicitly accounted for cern for such models, but other systematic uncertainties in
stopping-power ratio variation with depth. the beam model will be present. In estimating the statistical
More recently, Kawrakow,155 in performing detailed ion uncertainty in the patient dose calculation, it is necessary to
chamber simulations using the EGSnrc code system, showed account for the latent variance from the phase-space calcula-
that the relationship between measured ionization and dose tion as well as the random uncertainty from the patient cal-
for relative photon beam dosimetry depends on details of the culation. To make this possible in practice, more work is
chamber design, including cavity length, mass density of the needed to develop tools to assess the role of latent variance
wall material, size of the central electrode, and cavity radius, in patient dose calculations. Should latent variance be a sig-
in addition to the beam quality and field size. When the nificant factor in the total uncertainty, more independent
correct ionization-to-dose relationship was used with the ex- phase-space particles need to be used in the patient simula-
perimental data155 and a variety of other improvements in the tions. It must be emphasized that all beam models are subject
head simulations were made e.g., using a larger diameter to systematic uncertainties, which are analogous to those in-
primary collimator opening and including the effects of extra troduced by the latent variance. For measurement-driven
shielding upstream of the jaws or MLC,156 correcting a bug models, these uncertainties will be related to inaccuracies in
in the JAWS component of the BEAMnrc code, including an the measurement data. Both types of models are subject to
angular spread in the incident electron beam and several systematic uncertainties due to inadequacies in the model
small effects in the simulation153, the discrepancies in the itself.
build-up region were reduced to an acceptable level. Chibani There are two common methods for calculating statistical
and Ma showed that resolving inaccuracies in the modeling uncertainties: the batch method and the history-by-history
of the primary collimator for a Varian 18 MV accelerator as method. In the batch method, the estimate of uncertainty
well as including virtual sources for the lead shield and mir- standard error of the mean, sx of a scored quantity, X, is
ror frame, resulted in significantly better agreement between given by

calculations and measurements in the dose buildup region.156 n
Other sources of inaccuracy associated with detectors for
dose buildup measurements are presented in Sec. III E 3.3.

i=1
Xi X2
sx = , 3a
nn 1
III.D. Treatment planning: MC-based patient where n is the number of independent batches, Xi is the
calculations scored quantity such as dose in batch i, and X is the mean
III.D.1. Statistical uncertainties value of X over all the batches. The sample size is therefore
III.D.1.a. Latent variance and statistical estimators. For given by the number of batches, where each batch is a cal-
a finite number of independent simulated histories N, the culation of the same quantity carried out with independent
dose calculated using the MC method is subject to statistical phase-space file inputs and random number sequences. In the
uncertainty. By invoking the central limit theorem,157 one history-by-history method, Xi represents the scored quantity
can show that the statistical uncertainty in dose is propor- in history i rather than batch i so that the standard error of
tional to 1 / N, in the limit of infinite large N. There are the mean can be recast in a mathematically equivalent form
generally two sources of statistical uncertainty in MC calcu- as follows:

lations of patient dosethose resulting from the simulation
i=1 X2i i=1 Xi
N N 2
of the accelerator treatment head and those arising from fluc- 1
tuations in the phantom/patient dose calculation. Sempau et sx = , 3b
N1 N N
al.95 coined the term, latent variance to describe the uncer-
tainty due to statistical fluctuations in the phase-space as where N is the number of primary independent histories, Xi
opposed to the uncertainty due to the random nature of dose the contribution to the scored quantity by independent his-

tory, i. An issue evident with the batch approach Eq. 3a is some volume, such as a planning target volume or some dose
that the sample size, n, is given by the number of batches. As volume, such as the volume receiving greater than X% of the
n is usually small on the order of ten or less there is statis- treatment dose, can be computed from the square root of the
tical fluctuation in the uncertainty itself. Advantages of the average variance of each constituent voxel. For example, the
history-by-history method have been detailed elsewhere.158 fractional uncertainty in the average dose for voxels with
An important consideration when calculating uncertain- dose values greater than 50% of the maximum dose,
ties is to take into account the correlation between a primary FD0.5Dmax as suggested by Kawrakow, and Rogers and
particle and all its secondaries, especially in the case of Mohan99 could be used

bremsstrahlung splitting where a large number of photons
may all come from a single electron. Thus, to be strictly
correct, these secondaries must be treated as part of the same
history. If this correlation is not taken into account one can
FD0.5Dmax =
1

s Di
KD0.5Dmax D0.5Dmax Di
2
, 4
underestimate the uncertainty in a dose calculation, as the

where Di is the dose estimate in the ith voxel, sDi is its
secondaries will be treated as independent particles thereby
reducing the uncertainty erroneously. Another important case uncertainty, and the summation runs over the K voxels with
dose greater than 50% of Dmax. For clarity in communica-
of correlation is when a single particle is being used several
tion, this report recommends that quantities, such as
times as a source particle. In this situation it is important to
recycle the particles, i.e., use them multiple times, all at once FD0.5Dmax or FPTV or FPRV for doses to the specific vol-
and treat them as part of the same history. If one were to umes, planning target volume PTV or planning risk volume
restart the phase-space file multiple times, one would lose PRV, be adopted as a standard method of reporting statis-
the correlation between particles which are all part of the tical uncertainties in dose averaged over the relevant volume.
same history. These secondaries would then be treated as The use of uncertainties to voxels, such as the maximum
dose should be avoided. In situations where doses in single
independent particles causing the uncertainty to be underes-
voxels are important, such as the maximum dose to a serial
timated. A more comprehensive review of the implications of
organ like the spinal cord, users are reminded to also con-
recycling and restarting phase-space particles is provided in
sider the statistical uncertainty of that dose voxel.162 In such
the paper by Walters et al.158
instances, it may be necessary to simulate a large enough
III.D.1.b. Influence of statistical uncertainties on dose dis-
number of histories so that sDi is very small.162 This will
tributions. For radiation therapy dose distributions, sDi
ensure that the absolute uncertainty in the highest dose voxel
Di, where sDi is an estimate of the standard error of the
will also be small. The statistical precision required for dose
mean standard deviation/ N of the dose in voxel i and Di
estimates in single voxels should be decided upon with guid-
is the dose in that voxel.159161 The fractional or relative ance from the clinician. Users should also note that for a
uncertainty in dose, FDi = sDi / Di 1 / Di. In other words, the constant number of source particles, the statistical uncer-
fractional uncertainty in dose in a voxel decreases as the dose tainty also depends upon the size of the dose voxel. Reduc-
increases. This relationship provides a useful rule of thumb ing the volume to achieve a point-like voxel will require
when viewing dose distributions since it implies that the rela- increasing the number of particles simulated to achieve con-
tive uncertainty in the dose in high-dose regions will be stant statistical precision.
smaller than in low-dose regions, even though the absolute To varying degrees, statistical uncertainties affect all mea-
uncertainty is usually larger. sures of the dose distribution, including output ratios, iso-
From Eq. 3b we see that the uncertainty is roughly pro- dose profiles, dose-volume histograms, dose response param-
portional to 1 / N. Since, the simulation time T N, it can be eters such as equivalent uniform dose and TCP/NTCP. In a
seen that achieving absolute precision sD = 0 with MC uniform dose distribution, the dose metrics most sensitive to
simulation requires an infinite calculation time. Fortunately, statistical uncertainties are the maximum and minimum dose
absolute precision is not required in dose calculation results. voxels. These extreme values are by definition the voxels
This section concerns the precision required for MC simula- that have the greatest deviation from the mean dose. If one
tion and the impact of a lack of precision on MC dose dis- desires a region of uniform dose e.g., within the PTV, that
tribution quantities. dose will not be uniform using a MC-based calculation, due
Radiation therapy dose distributions contain many voxels to statistical fluctuations between adjacent dose voxels. The
in which the dose is computed for example, a cubic volume reported minimum and maximum dose voxels will differ
with sides of 10 cm contains 15 625 voxels with sides of 0.4 from the mean of the idealized dose distribution by up to
cm. Since the subvolume receiving a therapeutic dose can several standard deviations if many voxels are present in the
be highly variable, a standardized method to specify the sta- distribution.45,163 For example, in a uniform dose distribution
tistical uncertainty for such a distribution is necessary. Al- with 15 625 voxels computed with MC algorithms, due to
though the statistical uncertainty can be specified for a single statistical fluctuations, there is a 63% probability that the
voxel in a dose distribution such as that at the isocenter or at dose in at least one voxel differs from the mean by more than
the maximum dose voxel, Dmax, as described below, these four standard deviations.45 With regard to dose prescriptions,
voxels are poor measures for the uncertainty of a MC com- the specification of the maximum dose to a single voxel
puted plan. Alternatively, the statistical uncertainty over when there is a desired volume of uniform dose e.g., the

PTV, will result in an underdosage to this volume. Simi- creases more than the systematic component increases.
larly, dose prescription to the minimum dose voxel will result Kawrakow presented a series of tests to evaluate the suitabil-
in an overdose to the relevant volume. Isodose contours are ity of MC dose distribution denoising algorithms.167 These
also sensitive to statistical noise. For well-defined fields, tests are based on the fact that one can determine the cor-
such as rectangular fields used in beam commissioning, even rect dose distribution by simulating many histories for a
1% 1s statistical uncertainty causes observable jitter in iso- very high precision and then comparing the denoised distri-
dose contours. For patient fields that have irregular shapes, bution from a simulation with a much smaller number of
the acceptable amount of statistical uncertainty for isodose histories to the high precision results. The tests include:
viewing is a matter of personal preference and should be visual inspection of isodose contours,
agreed upon by the planner and the physician. It has been evaluating root-mean-square difference between dose
suggested that 2% statistical uncertainty on the Dmax voxel is distributions,
adequate for isodose evaluation.160 When viewing statistical evaluating the maximum dose difference,
jitter in MC isodose distributions, the physicist should re- comparisons of dose-volume histograms with and with-
mind observers that overall dose delivery accuracy is limited out denoising, and
to within a few percent; therefore there is uncertainty in the comparing the fraction of voxels failing an x% / y mm
actual location of an isodose surface even when dose is com- test.
puted with non-MC algorithms. From this point of view, the
planning team can use MC isodose jitter as a mechanism to Denoising methods reduce the number of particles and,
open the dialog on realistic dose uncertainty in actual treat- hence, the calculation time required to achieve a given un-
ment delivery. certainty by a factor of 310. Denoising techniques require
Integrated dose quantities, such as dose volume histo- proper validation under the full range of clinical circum-
grams DVHs are less sensitive to statistical stances before they are used with MC dose algorithms.
uncertainty.159165 DVHs computed with the MC method rep-
resent the actual DVH that computed with a hypothetical III.D.2. Dose prescriptions and monitor unit
0% statistical uncertainty simulation, convolved with a sta- calculation
tistical uncertainty distribution. With this realization, Sem-
The stochastic nature of the MC method raises questions
pau and Bielajew159 and Jiang et al.165 reported that the ef-
for prescribing dose. It is common clinical practice to pre-
fect of the statistical noise on DVHs could be removed by
scribe dose to a single voxel or to base the dose prescription
deconvolving the uncertainty from the DVH, allowing sub-
on the maximum or minimum dose voxels. However, as dis-
stantial decrease in the required number of histories used,
cussed above Sec. III D 1.2, in an approximately uniform
depending on the complexity of the DVH. In general, the
dose distribution, the outliers the maximum and minimum
blurring effect due to statistical noise is greatest for steep
dose voxels are subject to the largest statistical fluctuation
DVHs, such as those for PTVs, while shallow DVHs, such as and even other single voxel doses may lack the precision for
those for critical structures are less affected. monitor unit calculations. Standard treatment planning analy-
The sensitivity of quantities such as TCP and NTCP to sis methods using isodose distributions and dose-volume his-
statistical noise depends upon the parameters used by the tograms rely on dose averaged over a volume. It is logical to
model164 and on the magnitude of the noise. Kawrakow161 extend this practice to the prescription of dose, thereby
has shown for general dose-based cost functions that the un- avoiding precision issues in doses calculated in small vol-
certainty in the cost function decreases more rapidly than the umes. For example, dose may be prescribed to an isodose
individual dose uncertainties when the plan is close to opti- surface, to a region of uniform dose averaged over many
mum as expressed by the cost function. This implies that voxels about the isocenter, or to a single point on a dose
during IMRT optimization, where plan updates are based volume histogram. The practice is emerging to calibrate the
upon evaluation of such cost functions, larger statistical un- calculated dose distribution by performing a calculation in
certainty might be acceptable. the standard geometry where the accelerator is set to deliver
A method to reduce the effect of statistical uncertainties in a given dose per monitor unit, e.g., 1 cGy/MU at a given
MC dose distributions is to postprocess the dose distribution. voxel. In this case, the dose at the calibration point may be
These methods have been termed denoising or smoothing calculated to high precision by averaging over a large num-
techniques. Various methods related to digital filtering,166,167 ber of voxels in a uniform dose region.
wavelet thresholding,168,169 adaptive anisotropic diffusion,170 The issue of monitor unit calculations to specific single
and denoising based on a minimization problem171 have been voxels within the target volume e.g., the isocenter for rou-
proposed. A detailed comparison of these methods is pre- tine clinical planning may be confounded by large statistical
sented in the article by El Naqa et al.172 Denoising is an fluctuations in the doses to individual voxels. Although the
approximate, efficiency enhancing method i.e., it is not a treatment planning practice is quickly moving toward
variance reduction technique since it can introduce system- volume-based dose prescriptions, particularly for IMRT plan-
atic bias into the calculation. Nonetheless, denoising tech- ning, the ability to perform second MU checks for plan veri-
niques are useful as they can reduce the overall systematic fication purposes is an important component of the standard
+ random uncertainty when the random component de- practice. Until more efficient solutions are available, MU cal-

culations based on single-voxel-dose prescriptions should be To ensure proper correspondence between HU and mate-
performed with very high precision. That said, this task rials or material interaction coefficients, correspondence
group encourages a shift in paradigm from point-based to- between these quantities must be established during the CT
ward volume-based dose prescriptions, which we feel will and treatment planning system commissioning process. To
soon become the standard method for prescribing doses in ensure appropriate material specifications, it may be desir-
radiotherapy planning. The task group strongly discourages able to have several conversion tables, whose selection is
vendors from using the Dmax or Dmin dose voxels or other based upon knowledge of the particular patients character-
single voxel doses for dose prescription and monitor unit istics. Use of multiple calibration curves reduces the volume
calculations in their MC-based treatment planning systems. of inappropriate tissues specified in given regions, such as
Current users of MC algorithms are encouraged to find ways lung tissue within a prostate gland, however. Although the
of circumventing point-based dose prescriptions if their sys- importance of exact material specification has been estab-
tems are not flexible enough to allow otherwise. To obviate lished in other studies,178 more work in this area of research
the concerns of dose prescription based on a single voxel, relevant to clinical treatment planning is necessary. Other
one institution author J.E.C., Ottawa Hospital has devel- information about the patient may also be helpful. For ex-
oped the following work around method for MC-based ample, in a patient with a hip implant, it may be impossible
electron beam calculations: A dose distribution is calculated to distinguish if the implant is titanium, steel, or a composite
using 100 MU; this dose distribution in absolute terms is based solely on the CT numbers. In this case, material as-
equivalent to a relative isodose distribution normalized to the signment based on knowledge of the material implanted in
standard calibration conditions 10 10 applicator, 100 cm the patient would be beneficial. A recent evaluation of the
SSD, dmax depth. For dose prescription, the physician influence of material compositions on dose distributions178
chooses the isodose line that encompasses the target. The showed dose errors of up to 10% for 6 and 15 MV photons,
dose prescription point is then positioned on this isodose line and 30% for 18 MeV electrons due to media and/or mass
along the central axis of the beam, and the treatment MUs density misassignment, when comparing dose distributions
are determined. A second calculation is performed as a check between a known phantom and a CT-imaged phantom with
of the MUs and the final dose distribution. compositions and densities assigned by a conversion process.
For multiple 3D-CRT or IMRT fields, the procedure for The use of conversion techniques based purely on mass den-
generating monitor units is similar to that for single fields. sity e.g., assuming the only patient material is water, but
For example, a given isodose line such as the 95% line can with varying density, as employed in conventional algo-
be selected for dose prescription and, for a given field, the rithms, is discouraged with MC simulation because most of
dose contribution to a single voxel e.g., the projected field these methods ignore dependencies of particle interactions
cax point along this line is determined from the treatment on the materials, which can lead to notable discrepancies in
plan. For a calibrated MC algorithm, the absolute dose con- high atomic number materials.176
tribution from the given field in this voxel on the selected CT number artifacts caused by issues such as beam hard-
isodose line will be computed in units of cGy/MU, from ening in the CT scanning process or by high density struc-
which the monitor units for the beam can be calculated. A tures, such as dental fillings are potentially important in MC
complete formalism for MU calculations for the different dose calculation. Other artifacts may arise, for example,
types of treatment deliveries has been provided by Ma et when the CT scanner encounters a sharp edge, such as the
al.173 surface of a rectangular solid phantom, where a blurred edge
may result after image reconstruction. In one observed case,
the resultant contour showed 3 mm of additional phantom,
III.D.3. CT-to-material conversions causing the MC-calculated percentage depth dose curves to
For conventional algorithms, electron densities extracted be shifted 3 mm toward the surface.269 Such issues are of
from the CT image are used to scale the influence of primary relevance to both MC- and non-MC-based algorithms and
and, ideally, also secondary radiation interactions. MC algo- will need to be taken into consideration in order to perform
rithms utilize material density and the material atomic com- accurate dose calculations in the dose buildup region.
position when performing particle transport. The differing As with any dose algorithm, testing should be performed
atomic compositions of patient materials e.g., soft tissue, to evaluate the effect of artifacts on the accuracy of the MC
bone, lung, air result in different cross sections for the vari- dose calculation.179,180 It must be emphasized that the accu-
ous radiation interactions. While material compositions can- racy of CT-number to material conversions affects all dose
not be determined solely from a single energy CT, they can calculation algorithms, both MC- and non-MC-based meth-
be indirectly approximated by estimating the mass density ods.
from the electron density followed by assigning a material to
each voxel.37,86,174176 For some MC codes, explicit material
specification is circumvented by directly relating the CT
III.D.4. Dose-to-water and dose-to-medium
Hounsfield HU numbers to material interaction coeffi-
cients, based upon parameterization of materials representa- Historically, radiotherapy dose measurements and calcu-
tive of the patient,37 for example those tabulated in ICRU lations have been performed in, or specified in terms of the
Report No. 46.177 absorbed dose to water Dw. With MC-based algorithms,

FIG. 6. MC-based MCV system dose-to-medium Dm

and dose-to-water Dw results for a typical head and
neck IMRT treatment plan: a Dm, b Dw, and c
DVH comparison. Reprinted from Dogan et al. Ref.
181 with permission.
particle transport simulations occur in materials representa- simulation. Figure 6 shows the dose and DVH differences
tive of patient media; dose is therefore specified to the pa- between plans calculated with Dw and Dm for a typical head
tient medium Dm. For tissues with densities near and neck IMRT treatment plan.181
1.0 g / cm3, the difference between Dw and Dm for megavolt- To use MC simulation in the current clinical practice so as
age photon beams is small 1% 2%, however, for higher to be able to compare Dm with historical Dw results, requires
density materials, such as cortical bone, the difference can be a conversion of Dm to Dw for dose prescriptions, isodose
as large as 15%,176 since the stopping powers of water and coverage, dose-volume histograms, and any other dose re-
these higher-density materials differ more significantly. lated metrics. In this context, the converted Dw represents the
Therefore, there is a systematic difference between the dose dose to a small volume of water embedded in the actual
computed using conventional analytical algorithms and MC medium. Whether one should eventually use Dm in place of

Dw directly in clinical prescriptions remains the subject of

debate.182 Arguments in favor of using Dw for dose specifi-
cations include:
Historical clinical experience has been derived based on
Dw, hence, Dw allows direct compliance with previous
clinical experience and with conventional dose algo-
rithms. Doses reported in clinical trials are based on Dw,
hence, therapeutic and normal tissue tolerance doses are
based on Dw.
Accelerator and ionization chamber calibration proto-
cols are Dw based.
Tumor cells embedded within a medium are more
water-like than medium-like, e.g., a tumor cell embed-
ded in a bone matrix.
Arguments in favor of using Dm for dose specification

include:
Dm or the dose to the tissues of interest is the quantity FIG. 7. Mass collision stopping power divided by the mass collision stop-
ping power of water as a function of density normalized to water. A com-
inherently computed by MC dose algorithms. This may parison of the fit function to the ICRU data Ref. 177 for body tissues for
be of more clinical relevance than the doses on which electron energies of 5, 15, and 30 MeV is shown. The few points outside the
historical clinical experience is based, which are ap- curve are materials like urinary stones, which are considered to have negli-
gible effects. Reprinted from Kawrakow et al. Ref. 37 with permission.
proximate estimates of the true dose in the first place.
Converting Dm back to Dw may involve additional com-
plexity and introduce additional dose uncertainty.
The difference between Dm and Dw for tissue equivalent ization of the mass collision stopping power as a function of
materials is rather small and is likely to have minimal tissue density for different electron beam energies.37 The fit
impact in clinical practice. is shown to be in good agreement with ICRU data177 for
It is known that, due to organ and target motion, the body tissues. The advantage of this approach is that it cir-
dose actually delivered in the course of a treatment may cumvents the potential misassignment of media at material
be significantly different from the planned dose. Con- boundaries37 which arises when the human tissue mass den-
version of Monte Carlo computed doses to Dw may sity range is divided into bins representing different tissues,
analogously necessitate discussions on conversion to especially when the number of material bins is small.184
dose to a static patient, should 4D planning and de- Until further studies indicate clinical justification for se-
livery techniques become routinely used in the clinic.183 lecting Dm or Dw, it is the consensus of this task group that
MC dose results should: a explicitly indicate the material to
The conversion of Dm to Dw or vice versa requires an which the dose is computed and b allow conversion be-
application of BraggGray cavity theory: Dw = DmS / m w
, tween Dm and Dw using one of the methods discussed above,
where S / m is the unrestricted water-to-medium mass col-
w
or other methods as developed in future investigations.
lision stopping power averaged over the energy spectra of
primary electrons at the point of interest. One method to
accomplish this conversion176 is to utilize the fact that for III.D.5. IMRT dose calculation and optimization
patient-like materials, S / mw
is approximately invariant A strength of the MC method is its ability to accurately
throughout a photon radiation therapy field within 1%, compute dose for complex dose delivery scenarios such as
hence, S / m
w
can be used as a post-processing step to con- encountered in IMRT. IMRT often involves large intensity
vert Dm to Dw. However, this requires that a sufficient num- gradients and is usually delivered using a sequence of small
ber of materials be specified so that the material-dependent static or dynamically shaped MLC segments. Under these
dose conversion approximates a continuous function.184 circumstances, the assumptions used in conventional algo-
Rather than postprocessing the dose conversion, one can rithms regarding scatter equilibrium and output ratio varia-
multiply the energy deposited by primary and secondary tion with field size often break down.185 Additionally, in
electrons on each electron energy-loss step by the factor IMRT a significant fraction of dose to structures of interest
L / m
w
, the ratio of the restricted mass collision stopping particularly dose limiting critical structures is due to radia-
powers of water to local medium for the current energy of tion scattered from or transmitted through the MLC.186 MC
the electron. This is done in the MC transport code, thereby simulation circumvents these limitations since it makes no
directly obtaining Dw. Alternatively, material interaction data assumptions regarding radiation equilibrium and can trans-
may be evaluated over continuously parameterized space port particles through the detailed MLC leaf
with cross sections and stopping powers for specific materi- geometry87,137,187 to include MLC leakage radiation, even for
als scaled relative to water.35,37 Figure 7 shows a parameter- dynamic MLC leaf sequences.138,188,189

In using MC calculation in IMRT, a consideration is the MC-based IMRT plan optimization is limited by the clini-
method used to incorporate the MLC into the dose calcula- cal availability of MC calculation as a whole and the large
tion. Intensity modulation has been incorporated into MC calculation time required to perform the multiple IMRT dose
simulation using the conventional planning systems inten- calculations required for optimization. MC simulation during
sity matrix,190 independently generated fluence modification optimization allows the optimizer to account for heterogene-
matrices,87,92,191,192 or direct transport through the MLC.61,189 ity induced dose perturbations, as well as for MLC leakage
Note that errors introduced by fluence approximations used and scattered radiation. Inaccurate dose algorithms used dur-
during the MC dose calculation will be propagated through ing optimization can result in convergence errors195 in which
to the prediction of the patients dose. Thus, when a fluence the optimized fluence pattern differs from that corresponding
matrix approach is used for MC dose calculations, differ- to the optimal dose distribution.
ences with respect to a conventional algorithms heterogene- Studies demonstrating the use of the MC method in IMRT
ity correction will be detected, but fluence prediction errors optimization include the work of Laub et al.,197 who utilized
may go undetected, particularly if the same fluence matrix is a MC algorithm to evaluate the cost function during optimi-
used both for the conventional and MC calculations. How- zation but a pencil beam to compute the cost function deriva-
ever, when MC simulation is used to transport directly tives used by the optimizer. Jeraj et al.,195 reported on con-
through the detailed MLC geometry, these fluence errors vergence and systematic errors in the IMRT inverse planning
should be detected. Accounting for geometric details in the process for lung cancer resulting from the use of
MLC geometry, such as interleaf leakage is possible using a convolution/superposition and pencil beam algorithms, ver-
fluence matrix approach, however, will require a very high sus the Monte Carlo method. A similar study for treatment
resolution calculation matrix, which may be a limiting factor. planning of head and neck cancers was published by Dogan
Moreover, the energies of the scattered particles through the et al.198 Another study by Siebers et al.199 demonstrated the
MLC using such an approach will be approximate. Whether use of correction-based schemes to produce convergence of
or not modeling the intricate details of the MLC versus doses computed by conventional algorithms with MC calcu-
more approximate fluence matrix approaches will lead to lations. Bergman et al.200 reported on the use of an EGSnrc-
clinically significant differences in IMRT treatment planning based MC beamlet dose distribution matrix for IMRT plan-
is not a fully resolved issue. More treatment planning studies ning using a direct aperture optimization algorithm. The goal
in this area of research are necessary to better understand the of their work was to assess the improvement in accuracy
associated clinical implications. over conventional algorithms in using MC methods for both
Application of the MC method for IMRT QA has been the final dose calculation as well as in the inverse planning
demonstrated by several research groups61,87,139,190,192194 us- process.200 Combining these methods with statistical smooth-
ing MC simulation to recompute dose distributions opti- ing and denoising techniques,166172 after comprehensive
mized with the conventional dose planning algorithm. When benchmarking, may allow introduction of MC-based IMRT
using MC calculations as the reference plan and ignoring optimization into routine clinical practice, particularly since
statistical fluctuations, dose differences between conven- it has been shown that cost functions converge faster than
tional and MC algorithms can be considered systematic.195 individual dose uncertainties.161 For a review of other stud-
Ma et al.191 found dose errors in excess of 5% and 20% ies, the reader is referred to the article by Verhaegen and
relative to the prescribed dose in targets and critical struc- Seuntjens.25
tures respectively due to patient heterogeneities, in compar-
ing MC calculations employing an independent fluence ma-
trix with a pencil-beam model. In comparing MC III.D.6. Voxel size effects
calculations with a conventional planning systems pencil- As is the case with any dose calculation algorithm, calcu-
beam model intensity matrix for head and neck and lung lated dose is affected by the size of the scoring voxel. For
cases, Wang et al.190 found a 20% lower V95 volume receiv- MC calculations, typical values in the scoring dimension are
ing at least 95% of the target dose for a lung plan, and a 9% voxel sides of 25 mm for field sizes greater than 3
lower D95 dose delivered to at least 95% of the target vol- 3 cm2 and 12 mm for field sizes less than 3 3 cm2. For
ume for a head and neck plan. Average agreement among all calculations where geometric details of the MLC are in-
head/neck and lung cases in this study, however, was quite cluded in the modeling, scoring voxel sizes no larger than
good.190 Regarding the transport of particles through the 12 mm will be necessary to diminish volume averaging of
MLC, Siebers and Mohan61 showed fluence-based IMRT dose from inter- and intraleaf leakage. As with conventional
dose underestimates of 4.5% in V95 and heterogeneity-based algorithms, MC-based IMRT calculations should be per-
dose overestimates of 5% in V15 in the same treatment plan. formed using voxel sizes of 23 mm or less in the high
In intercomparing MC codes, Reynaert et al.196 reported de- gradient regions.201,202 In addition to affecting the spatial
viations of up to 10% in DVHs between PEREGRINE and resolution, the statistical uncertainty will be influenced by
BEAMnrc calculations. These discrepancies were attributed the voxel size; reducing the voxel size will increase the rela-
to differences in modeling of the Elekta SLi-plus MLC, not tive uncertainty for a fixed number of source particles be-
caused by the particle transport in the patient. This study cause fewer particles deposit dose in the smaller volume.
further illustrates the importance of careful modeling of the Increasing the voxel size and, hence, volume will reduce
details of the MLC in IMRT treatment planning. the relative uncertainty but may introduce errors due to re-

duced spatial resolution. An example of the influence of rithms, such as the convolution and MC methods, can be
volume-averaging effects resulting from the use of larger used to produce more accurate results. More recently, Arn-
voxel sizes 0.5 cm on each side in MC electron calcula- field et al.213 found large differences up to 10% between
tions is discussed in Sec. III E 3.5. collapsed cone convolution and MC PEREGRINE calcula-
tions in an 8 cm lung-equivalent slab embedded within solid
III.D.7. Cross sections water and irradiated by a 4 4 cm2, 18 MV photon beam.
Their work included film and ion chamber detectors and
The uncertainties in photon interaction cross section data
showed that MC calculations were in good agreement with
in the energy range from 5 keV to a few MeV is of the order
measurements.213
of 1% 2%.203 Although many MC codes use the incoherent-
With respect to patient planning, studies91,115,214219 have
scattering-factor approximation which assumes scattering of
pointed out major differences between MC calculation and
photons from stationary, free electrons, this approximation
conventional methods, such as the 3D pencil beam and
is found to be accurate in the mega-voltage energy regime,
convolution/superposition algorithms. Over the past ten
where the energy of the incident photon is much higher than
years, there has been a growing interest in the use of the MC
that of the electron K-shell binding energy.204 An excellent
method in clinical treatment applications with many institu-
review of the cross sections for bremsstrahlung production
tions around the world actively involved in the development
and electron-impact ionization has been provided by
and testing of such systems. Many experiments in homoge-
Seltzer.205 It is shown that, in general, calculated cross sec-
neous and heterogeneous
tions for the various electron interaction processes are in
phantoms26,27,71,75,82,84,86,93,96,115,119,194,213,220225 have been
agreement with measurements within the combined experi-
directed toward verification of MC algorithms for clinical
mental and theoretical uncertainties.205 It is felt that cross
planning applications. The interested reader is referred to
section and electron data in the megavoltage energy range
these and other related publications for a comprehensive re-
are sufficiently accurate,206 assuming that sampling of these
view of the various types of experimental testing of MC
cross sections is done accurately within a given code. These
treatment planning algorithms.
same effects will be present in doses computed with the
convolution/superposition algorithm.
III.E.3. Types of verification experiments
III.E. Experimental verification Experimental verification of a MC algorithm should in-
III.E.1. Introduction clude testing to assess the accuracy of: a the beam model
be it measurement-driven or based on treatment head simu-
In this report experimental verification of the MC algo-
lation and b the radiation transport algorithm in homoge-
rithm deals with how accurately the algorithm performs un-
neous and heterogeneous phantoms. The former is part of
der different test conditions within a phantom. As with any
routine commissioning of dose calculation algorithms,
algorithm, verification and testing is a necessary step to en-
whereas the latter is likely to have significantly more in-
sure safety of use in the clinical setting. It is the consensus of
volvement from developers and vendors.
this task group that verification of a MC algorithm should be
III.E.3.a. The beam model. The purpose of verification
similar to that of any model-based dose calculation algo-
of the beam treatment head model is to ensure that param-
rithm, such as convolution/superposition. The clinical com-
eters, such as the incident beam energy if used are correctly
missioning and acceptance testing of dose calculation algo-
tuned to produce dose distributions in agreement with
rithms has been reported.4850 Additional testing to confirm
measurement. Such verification is the same as that for any
the accuracy of the MC algorithm in situations of electronic
dose algorithm and may best be performed with measure-
disequilibrium will be helpful. Quantification of benchmark
ments in a homogeneous water phantom. These tests
cases such as the ICCR benchmark99 should be performed
should include the acquisition of depth and profile doses in a
by either the user, or the vendor. The intent of this section is
water phantom for a range of field sizes, as is routinely per-
to provide some examples of additional types of testing that
formed for conventional algorithmic verification, and docu-
may be included to assure the accuracy of the MC algorithm.
mented in the AAPM TG-53 report.4850 In addition, the use
The specification of required measurements for acceptance
of measured in-air off axis ratios may be useful for bench-
testing and commissioning of the MC algorithm and the cri-
marking the beam model. Calculated in-air off-axis ratios
teria for algorithmic agreement with measurements is beyond
have been shown to be very sensitive to the incident electron
the scope of this report.
beam parameters e.g., mean energy, intensity distribution,
etc., as well as the dimensions and densities of other struc-
III.E.2. Previous work tures, such as the primary collimator and flattening filter.102
Toward the goal of verification of dose calculation algo- The multileaf collimator (MLC). Experiments to bench-
rithms, there have been a variety of studies related to mea- mark the MLC transport have ranged from arbitrarily shaped
surements in heterogeneous media. These investigations see, AP fields designed to verify overall penumbral and transmis-
for example, Refs. 207212 have usually focused on estab- sion dose88 to more complicated MLC shapes designed to
lishing limitations of conventional dose algorithms in hetero- test modeling of detailed effects, such as transport through
geneous media and on how the use of physics-based algo- the rounded leaf ends,83,87,226 tongue-and-groove

effect,27,72,83,87,137 and intra/interleaf transmission.27,72,83,87,137

The complexity of MLC verification experiments will de-
pend on the usage of the MC algorithm in the clinical setting.
For the purposes of 3D conformal radiotherapy 3D-CRT,
the shaped field cases provided in Fig. A31 of the AAPM
TG-53 Ref. 48 report are good examples of tests designed
to test overall MLC transmission and penumbral effects. In
the context of 3D-CRT planning, the accurate modeling of
details of the MLC and the influence of these effects on leaf
transmission and penumbra may be of reduced clinical im-
portance to the target doses for an appropriate CTV-to-PTV
margin as these issues affect the dose at the field edges and
outside the field.227 For IMRT, it is now well established that
the accurate modeling of MLC transmission and penumbra is
critical.61,227 A stringent test of the ability of the MLC model
to accurately handle intra/interleaf transmission is presented
in Fig. 8a, for a Varian, Millenium 120-leaf MLC. In this
example, the calculated MLC leakage radiation is compared
with film measurements in a direction perpendicular to the
leaf motion.83 Figure 8b shows a comparison between MC
calculations and film measurements for a MLC picket
fence shape where the field is blocked by even numbered
MLC leaves with odd numbered leaves retracted behind the
jaws.83 This test is useful in evaluating how accurately the
tongue-and-groove effect is handled.
In designing a test suite for verification of the MLC trans-
port accuracy, the clinical physicist should give special con-
sideration to the detailed specifications of the MLC, particu-
larly if the MC model is to be used for IMRT planning.
These details include: density and composition of the MLC
leaves, rounded leaf-end dimensions, intra/interleaf gaps, and
tongue-and-groove dimensions. Discrepancies between MC
calculations and measurements deemed significant by the
physicist should be reported to the vendor; modification of
FIG. 8. a Measured solid line and calculated dashed line MLC leakage
the relevant parameters influencing the model accuracy, such radiation perpendicular to the direction of MLC leaf motion for a 10
as the MLC geometric model should be performed by the 10 cm2 MLC-blocked field for 6 and 18 MV beams. Dose calculation and
vendor to establish acceptable agreement between calcula- measurement for the 6 MV beams occurred at 5 cm depth, 95 cm SSD, and
the 18 MV data at 10 cm depth, 90 cm SSD. One should note that the dose
tions and measurements.
due to leakage radiation under the closed leafs typically accounts for 2%
Other beam modifying devices. The accuracy of MC 3% of the open field dose. The discrepancy noted for the 18 MV compari-
simulation of beam modifying devices, such as wedges and son is roughly 0.1% of the open field dose and is most likely to a small
blocks may be benchmarked using methods similar to that difference in the MLC density used in the calculations Ref. 83. Reprinted
from Siebers et al. Ref. 83 with permission. b Measured solid line and
for conventional algorithms.48 A publication on the experi- calculated dashed line doses for 6 and 18 MV 10 10 cm2 field a
mental verification of the PEREGRINE MC system27 included blocked by even numbered MLC leaves with odd numbered MLC leaves
the acquisition of large wedged field profiles 40 20 cm2 retracted behind the jaws. One should note that the dose due to leakage
at various depths see Fig. 13 of Hartmann-Siantar et al.27. radiation under the closed leafs typically accounts for 2% 3% of the open
field dose. Reprinted from Siebers et al. Ref. 83 with permission.
The purpose of large field testing is to ensure that radiation
transport through the wedge or other beam modifying de-
vice is in acceptable agreement with measurements across
the entire physical range of the device. Unacceptable differ-
ences between calculations and measurements should be re- stances of electronic disequilibrium, verification of the MC
ported to the vendorappropriate action should be taken by algorithm should include testing under these types of condi-
the vendor to help resolve these differences. tions to confirm the expected accuracy. Although reports,
such as the AAPM TG-53 Ref. 48 and others,49,50 recom-
mend testing in heterogeneous phantoms, issues related to
III.E.4. Verification of the Monte Carlo transport electronic disequilibrium are generally excluded. This task
algorithm in phantom group strongly encourages that verification testing of the MC
Given the improvement in the accuracy of MC simulation algorithm include experiments emphasizing electronic dis-
over conventional algorithms, particularly under circum- equilibrium effects, in addition to standard tests in heteroge-

plate Roos and cylindrical ion chambers IC-10, Scan-

ditronix in both 6 and 18 MV photon beams. Similar differ-
ences were found between a cylindrical ion chamber and a
parallel plate chamber P11 and a stereotactic diode Scan-
ditronix by Yokoyama et al.232 who measured dose buildup
regions for IMRT fields. Based on the available literature, it
is therefore recommended that dose buildups be carefully
measured with either a parallel plate chamber, an extrapola-
tion chamber, or with methods such as TLD extrapolation.233
Diode detectors may also be considered for dose buildup
measurements234 but should be cross referenced with other
detectors, such as parallel plate ion chambers. As pointed out
by Kawrakow155 see Sec. III C 4, the relationship between
FIG. 9. Measured percent depth ionization and Monte Carlo calculated per- the measured ionization and dose is sensitive to details of the
cent depth dose in the dose buildup region in water with the IC-10 cylindri-
ion chamber design and needs to be accounted for in dose
cal ionization chamber and the Roos parallel-plate ionization chamber in
water for a 10 10 cm2 field and SSD of 100 cm, for an 18 MV x-ray buildup measurements.
beam. For the IC-10 ion chamber, the effective point of measurement was
1.8 mm upstream from the chamber center. Reprinted from Abdel-Rahman
III.E.6. Output ratios
et al. Ref. 152 with permission.
MC calculations of output should be performed in a
measurement-like geometry, usually consisting of a central
neous phantoms as documented in other reports.4850 This axis point dose estimate at a fixed depth dmax, 10 cm or
type of testing is needed to exploit the advantages of MC- other in a water phantom for square field sizes defined by
based simulation to its full potential. the collimating jaws. If the backscattered radiation into the
Verification measurements in slab phantoms with embed- monitor chamber is correctly modeled, it is possible to cal-
ded low density inserts and irradiated by high energy pho- culate output ratios to within 1% 2% agreement with mea-
tons are useful in assessing the transport accuracy under con- surements over a range of square field sizes, with sides from
ditions of electronic disequilibrium.84,213,220 Effects of 3 to 40 cm.146 In addition, comprehensive verification of out-
penumbral broadening of the dose distribution resulting from put ratios should include testing for small segmental fields
lateral electron transport may be evaluated using such located off-axis, which are commonly used in IMRT plan-
phantoms.84,213,220 ning. Output ratios should be verified against measurements
Dose measurements at various locations depths and off- of specially designed IMRT fields, such as junction narrow
axis distances both within and outside a high-density hetero- slit fields, in which the effects of small field dosimetry are
geneity provide a benchmark to evaluate the perturbation of magnified. Examples of such fields have been
the photon and electron fluence due to the presence of the reported.83,87,145,187
heterogeneity.225 Dosimetric effects at interfaces e.g., due to
backscattering at bone/tissue interfaces53,225, transport III.E.7. Electron beams
within the heterogeneity, and the doses outside the heteroge-
Careful experimental verification is especially necessary
neity may all be assessed with careful positioning of mea-
for electrons because the tolerance of parameters, such as the
surement devices within the heterogeneous phantom.
electron energy and the treatment head structure constituents
Experimental verification should also be performed in
are much tighter than for photons. Accurate measurements
more clinically relevant situations. Examples of such geom-
are a prerequisite to accurate simulation. Care must be taken
etries include thorax phantoms,228 and mediastinal229 and
in measurement of the central axis depth-dose curve used to
tumor-like phantoms.229,230
define the beam energy. Profiles in large fields need to be
Verification experiments for algorithmic verification have
included to determine geometry details such as the distance
also included the use of anthropomorphic Rando phantoms,
between the scattering foils, the thickness of these foils, and
where TLDs are most often used for the measurements.225,231
the lateral position of shaped scattering foils, if present. Mea-
With anthropomorphic phantoms, calculated patient treat-
surement of dose profiles in the bremsstrahlung tail are help-
ment plans may be verified under a range of clinical circum-
ful to validate the photon component of the beam model.112
stances. However, measurements must be carried out care-
Comparison to measured output ratios and dose distributions
fully with appropriate experimental techniques, theoretical
over the full clinical range of field sizes and SSDs is neces-
interpretation, and reproducibility.
sary for each applicator and beam energy, to rigorously vali-
date the dose calculation. Further measurements, such as
III.E.5. Dose buildup region dose measured in an anthropomorphic phantom,221 should be
It is challenging to make accurate measurements in the performed to validate the beam model for the specific MC-
dose buildup region. A recent study by Abdel-Rahman et based application.
al.152 showed significant differences see Fig. 9 in the dose Comprehensive verification for electron beam MC simu-
buildup region 1 cm between the response of a parallel lation should include measurements in heterogeneous phan-

particularly in nonuniform dose regions. It is important to

take into account point of measurement effects, variations in
stopping power ratios for ion chambers, and beam quality
dependence in general for other detectors e.g., the well
known over-response of film in regions of low mean photon
energy, polarity effects, ion recombination effects, and
chamber perturbation effects. Specific detectors may be re-
quired for accurate measurements under specific conditions;
for example, properly constructed parallel plate chambers
may be favored over ion chambers for measurements in the
dose buildup region or at material interfaces. Uncertainties
due to improper detector positioning must also be quantified
as these measurements are often performed in regions of
high dose gradients.
When using modern IMRT techniques there can be strong
perturbation effects or corrections needed with ion chamber
and other detector measurements. However, as with other
algorithms, detector perturbations are generally not ac-
counted for in verification of MC-based treatment planning
algorithms. MC methods may be used to model the physical
details of the detectors to provide a better understanding of
measurements performed under nonequilibrium conditions.
These approaches are available to developers of MC tech-
niques but further advancement and investigation of this
technology is necessary before specific recommendations
FIG. 10. Trachea and spine phantom: measured and Monte Carlo Master- can be made. Measurements form the basis for benchmark-
plan, Nucletron, based on VMC++ calculated crossplane dose profiles at ing the accuracy of dose calculation algorithms in clinical
various depths for: a 9 and b 20 MeV. SSD= 100 cm, 10 10 cm2 ap- radiotherapy. It is therefore important that the uncertainties
plicator. Monte Carlo simulations were performed with
50 000 histories/ cm2 and a voxel size of 0.49 cm. 100 MU were used for in the measuring techniques be accounted for.
the calculations. The relative uncertainty in the calculations is about 1%
1.5%. The phantom geometry is shown in the inset. Differences between III.E.9. Example experimental tests
measurements and calculations in this example were attributed to the vol-
ume averaging effects of a large voxel size 0.5 cm Ref. 26. Reprinted Example tests for verification of MC dose algorithms are
from Cygler et al. Ref. 26 with permission. provided in Table IV. These tests, intended as a supplement
to those provided in the AAPM TG 53 report,48 aim to evalu-
toms, such as those reported in the Electron Collaborative ate the various components of the MC algorithm.
Working Group report235 and its update.236 Cygler et al.26
performed experimental benchmarks using a variety of het-
III.E.10. Timing issues
erogeneous phantoms, including a 1D slab geometry with an
aluminum slab insert, a 2D geometry with cortical bone- The issue of calculation time is of considerable impor-
equivalent inserts ribs geometry, a 3D cylindrical geom- tance in the clinical treatment planning process. To provide a
etry with an air insert, and a complex trachea and spine perspective on this subject, users of commercial MC dose
equivalent geometry. Figure 10 shows the example trachea algorithms were asked to submit calculation times for photon
and spine phantom used in their study.26 Differences between and electron treatment plans. The treatment plans ranged in
measurements and calculations in this example were shown complexity from simple AP beams to dynamically delivered
to be due to the volume averaging effects of a large voxel IMRT plans. These results are summarized in Table V. As
size 0.5 cm.26 The MC calculations are found to under- noted in Table V, photon beam calculations with PEREGRINE
estimate the measurements because the large voxel size av- are approximately a factor of 23 times slower than those for
erages the density distribution in the vicinity of the hetero- conventional planning systems. However, these times will be
geneity, effectively reducing the calculated dose across the reduced using faster, currently available processors
low-density heterogeneity.26 2 GHz versus 800 MHz. Electron beam calculations with
Careful measurements in such heterogeneous phantoms VMC++ Nucletron are roughly equivalent in processing
will provide rigorous benchmark data for verification of the times to conventional systems. The timing comparisons pro-
MC algorithm, and as such should be strongly considered for vide good justification of the fact that significant processing
testing purposes. times are no longer a concern for routine clinical MC dose
calculation. MC calculations for a plan with one beam take
III.E.8. Measurement uncertainties the same time as that for a plan with multiple beams of
Making dose measurements is fraught with problems if approximately the same field size, for the same statistical
the aim is to verify calculations at the 2% or better level, uncertainty to the PTV. This is because the statistical uncer-

TABLE IV. Partial listing of example specific tests, phantom designs, and detector measurements for Monte Carlo treatment planning systems. These tests are
intended as a supplement to those detailed in the AAPM TG-53 Ref. 48 and other related publications Refs. 49 and 50 for algorithmic verification. Note
that extreme care should be taken when performing many of these measurements as they are, in some instances, highly sensitive to the measurement setup
conditions.
Test description Reason Phantom design
Water depth doses and profilesemphasis on To evaluate the beam Depth doses and profiles at
large open field sizes, 30 30 cm2 model accuracytest is sensitive to multiple depths measured in
2D planar dose perpendicular to the beam cax structures like the flattening filter a water phantom using a cylindrical
for large open fields and other parameters, such as the ion chamber. 2D planar dose at multiple depths
electron-on-target energy. in solid water using film.
2D planar dose perpendicular to the beam cax To evaluate the accuracy of the MLC 2D planar dose at multiple depths
of large MLC-shaped fields see Fig. A31 of model, leaf-tip penumbra in solid water using film.
the AAPM TG 53 reporta and leaf transmission. Dose profiles under closed MLC leaves
Dose profiles under the closed MLC leaves, measured with film or small volume
perpendicular to the direction of motion see Fig. 7.b detector diode, TLD, pinpoint chamber,
diamond detector.
Small field 1 1 cm2 4 4 cm2 depth doses To evaluate the transport Depth doses in a layered phantom
in low density media; larger field sizes should algorithm accuracyuse of see Fig. 8 and Fig. 1 of Rice et al.c
also be tested. high energies 10 MV consisting of solid water and low density
Penumbral broadening; lateral dose spreading and low density media emphasizes material lung equivalent or cork
in lung assessed over a range of field sizes electronic disequilibrium effects. measured with small volume detector
2 2 30 30 cm2. diode, TLD, pinpoint chamber, diamond
detector, at multiple point depths or with film.
Beam is directed perpendicularly to the slabs.
2D penumbral measurements with film in planes
perpendicular to the beam cax at depths above, below,
and within the low density slab in the layered phantom.
Beam should also be directed parallel to the slabs to
evaluate interface effects.d
Depth doses in high density media over a range To evaluate the transport algorithm Depth doses in a layered phantom consisting of solid
of field sizes, 3 3 30 30 cm2. accuracy in high density media, such water and high density material cortical bone
as cortical-bone equivalent slabs. equivalent measured with small volume detector diode,
TLD, pinpoint chamber, diamond detector for smaller
field sizes, or with film.
Point doses in the vicinity of tissue interfaces tissue/ To evaluate the algorithmic See, for example, Fig. 1 of Ref. 230. Dose measured
lung and tissue/bone, over a range of field sizes, 3 3 accuracy in with film or with small volume detector, where possible,
30 30 cm2. the perturbed dose field at tissue at incremental depths, for example, 0.2, 0.5, 1.0, 2.0, and
interfaces. 5.0 cm anterior/posterior to the medial and proximal
tissue/lung equivalent and tissue/bone-equivalent
interfaces.
Dose evaluation in clinical treatment planning, for To assess the accuracy of dose Dose measured with small
simple, intermediate and complex static treatment plans calculation to points located within volume detectors within
as well as IMRT plans, in anthropomorphic phantoms. structures of different inserts of different materials,
densities and receiving different ranging from air to cortical
doses based on the treatment plan. bone-equivalent. Plans designed should
include simple, intermediate, complex static and IMRT
beam arrangements. Anthropomorphic phantoms should
be CT-imaged for planning purposes.
a
See Ref. 48.
b
See Ref. 83.
c
See Ref. 229.
d
See Ref. 222.
tainty is determined by the number of particles passing gorithm, we are confronted with the following clinical ques-
through a volume, and this number can be held constant tion: What is the effect of more accurate MC dose
when performing a MC plan with multiple beams. This is a distributions on patient clinical outcome? To answer this
distinct advantage over conventional algorithms where com- question, we will need to investigate the correlation of MC
putational time scales linearly with the number of beams. calculated dose distributions with clinical outcome in terms
IV. CLINICAL IMPLICATIONS OF MONTE of tumor control and normal tissue toxicity.
CARLO-CALCULATED DOSE DISTRIBUTIONS To date the evidence directly correlating the improved
accuracy of MC-calculated dose distributions with clinical
IV.A. Introduction outcome is scant. Investigations by De Jaeger et al.,237
In spite of our confidence in the improved dose calcula- which included convolution but not MC calculations,
tion accuracy with a suitably commissioned clinical MC al- Chetty et al.,238 and Lindsay et al.239 are among the first

TABLE V. Summary of timing results for clinical treatment plans from currently available commercial Monte Carlo systems. Data for photon beams were
provided by author G.E., performed using the PEREGRINE Nomos division, North American Scientific system and those for electrons by author J.E.C.,
conducted with Nucletron. The 1 relative statistical uncertainty was approximately 2% in the maximum dose voxel for the Nomos calculations and roughly
1% 1.5% in the average depth dose along the central axis for the Nucletron electron beam calculations. Eclipse calculations were reported with an
uncertainty of 1% 2% in the mean dose of all voxels receiving more than 50% of the maximum dose within the body of the contour. Readers should be
cautioned that the timing results are subject to large uncertainties due to differences in compilers, memory size, cache size, etc.
Monte Carlo code/configuration Description of treatment plan Time estimate

min
PEREGRINE Nomos, North American Scientific 16 AP beam, 6 MV photons, 10 10 cm2 in a water 48

processors 8-dual, Pentium III, 800 MHz phantom, cubic voxels with 2 mm sides
5 field, 6 MV CRT prostate plan, 7 11 cm2, cubic 89
voxels with 2.4 mm sides
5 field, 6 MV prostate plan with modulation delivered 71
with DMLC exposed field 4 8 cm2, cubic voxels
with 2.4 mm sides
Masterplan VMC++, Nucletron, single CPU Pentium IV AP beam, 6 MeV electrons, 10 10 cm applicator, 4.2
XEON, 2.2 GHz water phantom, cubic voxels with 4.9 mm sides
AP beam, 17 MeV electrons, 10 10 cm applicator, 8.2
water phantom, cubic voxels with 4.9 mm sides
AP beam, 20 MeV electrons, 15 15 cm applicator, 21
water phantom, cubic voxels with 3.9 mm sides
Breast boost treatment plan: 2 fields, 11 MeV electrons, 8.6 both fields
3 3 cm cutouts, cubic voxels with 5.4 mm sides
eMC MMC, Eclipse, Varian single CPU Pentium IV AP beam, 6, 12, 18 MeV electrons, 10 10 cm 3, 4, 4 6, 12, 18 MeV, respectively
XEON, 2.4 GHz applicator, water phantom, cubic voxels with 5.0 mm
sides
studies evaluating the influence of improved dose distribu- IV.B. Clinical examples
tions on outcome observed in patients treated with lung can-
cer. The study by De Jaeger et al.,237 in which lung cancer
treatment plans were retrospectively recalculated using a In reviewing the literature on clinical treatment planning,
convolution/superposition CS-based algorithm initially one should keep in mind that the dose differences found
calculated with an equivalent-path-length EPL algorithm, between MC-based and conventional algorithms will be
showed clinically significant differences between calculated highly dependent on the beam arrangements, field sizes,
and observed incidences of radiation pneumonitis. They beam energies, tumor size, and location. This is particularly
demonstrated that the calculated incidence of radiation pneu- true in anatomical sites where the target is situated near tis-
monitis correlated better with observed incidence when using
sues with widely varying densities, such as the lung and
dose distributions calculated with CS rather than EPL
head/neck. For example, due to electron transport issues, dif-
algorithms.237 Although this study was carried out using a CS
algorithm, it provides strong support that the dose-response ferences found in a lung CRT treatment plan using small
relationships determined with correction-based algorithms field sizes and 15 MV photons may be much larger than
will be different than those computed with model-based those found with a standard AP/PA lung plan, using large
methods.237 With the sometimes large differences observed field sizes and 6 MV photon beams. The reader should there-
between the doses calculated with CS and MC algorithms,240 fore be advised that, although there is a general consensus on
the MC method is likely to add a higher degree of accuracy the importance of the MC method in sites such as the lung,
to the dose-effect relationships, and will be instrumental in the dosimetry in many of the reported studies is based on
putting these relationships on a more solid footing. specific conditions. The following literature review will fo-
There is clearly a need for more studies addressing the cus on treatment planning in the lung and head and neck
clinical impact of MC-calculated dose distributions. The use since differences between MC-based and conventional algo-
of retrospective data may provide a useful means to perform
rithms are likely to be smaller in other external beam treat-
such studies. Retrospective dose assessments of already ex-
ment sites. This does not include the potential for improve-
isting local tumor control and normal tissue complications,
using doses recalculated with MC algorithms, may give an ment in dose estimates in any site from accurate simulation
early indication of the clinical utility of the MC method, and of beam modifiers, in particular, the MLC for delivering
may also help physicians determine how to use the new MC- IMRT. More studies using MC-based dose calculation tech-
calculated doses.206 Retrospective analyses should eventually niques in clinical treatment planning are warranted to better
show us how to make use of this information in a prospective quantify the dosimetric and clinical benefits of these algo-
way.206 rithms.

Due to the complicated dosimetric issues associated with

treatment planning in the lung, more studies and compari-
sons using the MC method are encouraged. The utilization of
advanced techniques, such as extracranial stereotactic radio-
therapy using 1024 Gy fractions,247 for the treatment of
early stage lung cancer, may increase the importance of ac-
curate dosimetry and the clinical importance of MC calcu-
lated doses. One of the important next steps must be to
evaluate how the improved MC dose distributions will clini-
cally impact outcome for tumors and normal tissues.
FIG. 11. Opposed, oblique field treatment plan 15 MV photons showing IV.B.1.b. Head and neck There have been numerous
the 100% isodose coverage for MC modified DPM, University of Michigan/ studies on MC head and neck CRT and IMRT
UMPlan in the solid line, and an equivalent path length EPL, University of
Michigan/UMPlan algorithm in the dashed line. The PTV is demarcated in
planning.190,192,193,214,248250 These studies have shown in
white. general that dose differences between convolution and MC
algorithms are dosimetrically insignificant. However, it has
also been shown that dose differences for tumors located in
An excellent review of MC-based dose calculation meth- the presence of air cavities can be significant due to inaccu-
ods in clinical planning for various treatment sites, including rate calculation of the photon/electron energy fluence inside
the breast and prostate is provided in the article by Reynaert and around air cavities using Batho and ETAR methods214 as
et al.241 well as a collapsed cone convolution algorithm.250,251
IV.B.1.c. Other treatment sites Readers are encouraged
to review articles published on MC-based treatment planning
IV.B.1. Photon beam treatment planning in other anatomical sites, which include: brain,89,91,219,252254
IV.B.1.a. Lung Perhaps the strongest motivation for the breast,216,255 and prostate.193,214,216,256,257
need for MC dose calculation comes from treatment plan-
ning for lung cancer. This is because electron transport is-
IV.B.2. Electron beam treatment planning
sues, not accounted for accurately with conventional algo-
rithms, are exacerbated in the low density tissues. A There have been numerous studies on the use of MC cal-
consequence of electronic disequilibrium in the lung is the culations in electron beam treatment plan-
underdosage of the PTV, as shown in Fig. 11. The penumbral ning.26,111,115,121,258262 In some instances, significant differ-
widening in the dose distribution as a result of the increased ences between pencil beam dose distributions and MC cal-
electron scattering in the lung is illustrated for a conformal culations have been demonstrated, particularly in regions in
lung plan in Fig. 12. Depending on the location and size of or near air cavities and lung or bone tissues.115,263 Large
the tumor, and the beam energy, underdosage of the PTV in differences have also been observed for small irregular
lung planning may be significant. In addition to the target fields, beams with oblique incidence, and for extended SSD
coverage, dose to normal tissues, particularly the normal treatments.115,263 The use of the MC method represents a
lung, may be equally affected. Numerous lung planning stud- significant improvement in accuracy for electron beam dose
ies have shown sometimes substantial differences 10% calculation compared with conventional algorithms. Electron
20% between conventional and MC MC calculations require far fewer primary histories to
algorithms.117,190,192,214,216,242246 achieve a given uncertainty on the dose being calculated be-
cause electrons deposit their energy in a more continuous
manner, in a smaller volume and mostly starting from the
same location the patient surface. This timing advantage
has allowed the development of commercial electron beam
MC algorithms which are time efficient taking on the order
of minutes per plan even on a single processor.26
From phantom and routine patient planning calculations
based on experience with a commercial electron beam MC
algorithm VMC++, currently Nucletron, Cygler et al.26 have
reported that MC-generated monitor unit MU values may
differ from the homogeneous water phantom values by as
much as 10%, depending on surface irregularities and inho-
FIG. 12. Isodose distributions for a 3D conformal lung plan 15 MV pho- mogeneities present in the irradiated volume. This situation
tons calculated using an equivalent path length EPL, University of is frequently encountered for head and neck sites, especially
Michigan/UMPlan algorithm on the left and a MC calculation modified in the region of the nasal cavities. In such cases, surface
DPM, UMPlan on the right. A distinct penumbral broadening in the MC-
irregularities and missing tissue lateral to the air cavity ne-
based dose distribution on the right is observed due to the increased elec-
tron scattering in the lung tissue. This effect is not as pronounced in the cessitate larger MUs to deliver the same prescribed dose ver-
EPL-calculated dose distribution. sus flat surface anatomies. As is the case with photon beams,

it is important that the statistical uncertainties in the single suggests that even small differences in dose distributions, as
voxel MU calculations be reported. a result of inaccurate dose calculation, are likely to affect
local control and survival for patients with NSCLC. Further
studies of MC dose distributions in the lung and in other
IV.C. Association of Monte Carlo calculated dose
sites, such as the head/neck, are necessary and are encour-
distributions with clinical outcome
aged in order to unequivocally evaluate the clinical utility of
As with other changes to the therapy treatment process, MC-calculated doses.
with the implementation of a new dose calculation algorithm
such as the MC method, users should correlate doses and V. SUMMARY
prescriptions with respect to previous clinical experience.
Chetty et al.238 studied dose-effect relationships for tu- We wish to reiterate that, from a clinical implementation
mor and normal tissues by recalculating dose distributions standpoint, the MC method should be treated as would any
retrospectively using the MC method for patients treated on a conventional dose algorithm. Proper implementation will re-
nonsmall cell lung cancer NSCLC dose escalation quire the clinical physicist to understand, on some level, the
protocol264original plans were generated using an EPL al- fundamentals of the algorithm as well as the possible pitfalls
gorithm. Follow-up data was evaluated from CT scans taken associated with its clinical implementation, much as one
six months to two years postradiation therapy. Follow-up CT would for any dose algorithm. In addition to providing an
scans were fused with initial treatment planning scans and educational review of the MC dose calculation method, we
the original and replanned dose distributions were mapped have identified issues that will need to be considered by de-
onto the anatomy to establish associations between dose and velopers, vendors, and end users of MC-based techniques,
regions of local recurrence and normal lung damage ultimately to ensure that patient dose calculations are ef-
radiation-induced pneumonitis.238 Preliminary results of fected safely.
this study showed that the originally planned PTVs are In conclusion, we present a summary of some of the is-
sometimes significantly underdosed with MC calculations sues which are important in the implementation and clinical
compared with the EPL algorithm.238 For normal lung tissue, use of MC dose calculation algorithms. The recommenda-
the correlation of dose with normal tissue complications was tions summarized here are not meant to be prescriptive;
also found to differ, but also showed that beam model differ- rather they are intended as a preliminary guide for medical
ences not related to the dose calculation algorithm in the physicists to ensure thoughtful and safe implementation of
patient are important and must be considered for an unbi- clinical MC algorithms. We anticipate that many of the areas
ased comparison of dose calculated by different of concern will be studied in further detail in future, more
algorithms.136,238,241,265 specific task group reports.
Lindsay et al.239 performed retrospective MC-based recal-
culations of a large group of lung cancer treatment plans and V.A. Treatment head simulation
showed significant differences in dose indices V20, maxi- a Vendors of MC-based dose calculation systems should
mum lung dose and mean GTV dose between plans without be responsible for providing the necessary guidance
heterogeneity correction and MC calculations. Moreover, and assistance with the beam modeling and bench-
correlations between V20 and observed radiation pneumoni- marking process. Such guidance includes the tuning of
tis in this study were found to be different between plans parameters such as the electron energy, or the adjust-
without heterogeneity correction and MC-based treatment ment of model parameters in measurement-driven
plans.239 models to ensure that the beam model meets the re-
Despite the preliminary and somewhat anecdotal nature quired specifications.
of the evidence thus far, observations suggest that more ac- b In reporting statistical uncertainties in the calculated
curate dose calculations will reveal inadequate target cover- patient dose, vendors should properly account for latent
age or hot spots in certain areas of organs at risk that could variance in the beam model if the model is based on
lead to differences in outcome. Complete MC recalculations treatment head simulation. Further, if the latent vari-
of delivered dose distributions that include the effects of ance is a significant contributor to the total variance the
other factors, such as organ motion and patient setup errors, number of phase-space particles in the beam simulation
will be required to refine these correlation studies. In addi- should be increased.
tion, it should be noted that the efficacy of radiation therapy
is also dependent upon individual patient response.
The clinical evidence thus far, albeit preliminary and ret- V.B. Patient simulation
rospective, provides support that dose delivery based on MC
treatment plans, particularly for lung cancer, have the poten- V.B.1. Statistical uncertainties
tial to result in clinically significant changes. Kong et al.266 We recommend that quantities, such as FD0.5Dmax, or
have shown that dose significantly impacts local control and FPTV, or FPRV for doses to the specific volumes, PTV or PRV
overall survival for NSCLC; local control was found to in- respectively, be adopted as a standard method of reporting
crease at a rate of 1.3% per gray above the conventional dose fractional statistical uncertainties in dose averaged over the
fractionation scheme 6369 Gy in 2.0 Gy fractions. This relevant volume. The sole use of dose uncertainties to indi-

vidual voxels, such as the maximum dose voxel, Dmax, III D 4, or other methods as developed in future investiga-
should be avoided. Additionally, reporting of single voxel tions. It is strongly encouraged that appropriate documenta-
doses or doses over patient subvolumes should be accompa- tion on the dose-to-water conversion method used by the
nied by their respective statistical uncertainties. In situations software be provided to the user.
where doses in individual voxels are important, such as Dmax
to a serial organ like the spinal cord, it may be necessary to V.C. Experimental verification
simulate a large enough number of histories so that sDmax is V.C.1. Examples of specific tests
very small. This will ensure that the absolute uncertainty in
Dmax will also be small. The required statistical precision In addition to the standard testing necessary for conven-
required for individual voxel dose estimates should be de- tional dose algorithms, it is strongly recommended that ad-
cided upon with guidance from the clinical team. ditional tests e.g., as suggested in Sec. III E 3 be included
to evaluate the accuracy of MC calculations under situations
where the MC method is known to perform better than con-
V.B.2. Variance reduction techniques, efficiency
ventional algorithms.
enhancing methods, and other parameters
Users should understand the influence on the dose accu- V.C.2. Verification calculations
racy of variance reduction implementations and approximate
methods used to improve the calculation efficiency, as well MC verification calculations should be performed under
as any other accessible parameters of importance to the MC the same conditions as the experiments. Phantoms used
dose algorithm. Appropriate documentation on the methods should be CT-imaged for planning purposes. Statistical un-
used and their influence should be made available to the user. certainties for verification plans should be reported and in-
More studies on the influence of efficiency enhancing meth- cluded in the comparison of calculations with measurements.
ods in clinical treatment planning are warranted, as it is More studies of the influence of detector perturbations using
likely that the tradeoffs between speed and accuracy will not MC calculations are encouraged.
be the same in different anatomical sites.267 Where possible,
vendors should provide users with the flexibility to adjust V.C.3. Measurement uncertainties
parameter inputs for these efficiency enhancement tech- It is important for the user to understand the limitations of
niques but implement default values which are conservative, the various measurement devices as they are used in different
i.e., accurate in all situations. situations. It is recommended that realistic measurement un-
certainties be assessed and included when evaluating MC
V.B.3. Dose prescriptions verification calculations against measurements.
Although the implementation of MC treatment planning
Vendors are strongly discouraged from using single voxel
will require clinical physicists to once again understand a
point doses for dose prescription and monitor unit calcula-
new technology, one should view this in a positive light.
tions in their MC-based treatment planning systems. Rather,
Properly implemented MC algorithms will provide dose cal-
doses should be prescribed to volumes larger than a single
culation with sufficient accuracy in at least a single instance
voxel, such as the volume contained by an isodose surface.
of the patient geometry such that dose calculation is no
Current users of MC-based planning systems are encouraged
longer a source of meaningful uncertainty in the radiotherapy
to find ways of circumventing point-based dose prescriptions
planning process. In addition, although the details are some-
if their systems are not flexible enough to allow otherwise.
times complex, the underlying idea of simulating the actual
transport of individual particles is simpler to understand than
V.B.4. CT-to-material conversions many other algorithms because it is based on actual physical
The use of conversion techniques based purely on mass processes familiar to the medical physicist. Finally, this may
density i.e., assuming the only patient material is water, but well be the last new dose calculation algorithm that medical
with varying density, as employed in conventional algo- physicists will need to learn since MC techniques provide the
rithms, is discouraged with MC simulation because these highest level of accuracy for dose calculations in radio-
methods ignore dependencies of particle interactions on the therapy treatment planning.
materials, which can lead to notable discrepancies in high
atomic number materials. The conversions should include the ACKNOWLEDGMENTS
use of both mass density and the atomic compositions of the
I.J.C. acknowledges the support of his colleagues, in par-
materials. Appropriate documentation on the CT number-to-
ticular, Dick Fraass, Daniel McShan, and Randy Ten Haken,
material conversion method used by the software should be
at the University of Michigan, Department of Radiation On-
accessible to the user.
cology. Thanks to Neelam Tyagi and Mihaela Rosu for their
help with compiling references. We are grateful to Lesley
V.B.5. Dose-to-water and dose-to-medium Buckley, Dan La Russa, and Randy Taylor of Carleton Uni-
MC dose results should: a explicitly indicate the mate- versity for commenting on early versions of the manuscript.
rial to which the dose is computed, b allow conversion I.J.C. is thankful to Alex Bielajew for helpful discussions on
between Dm and Dw using the methods discussed in Sec. various topics in this report. I.J.C. acknowledges the support

21
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23
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Report of the AAPM Task Group No.

105: Issues associated

TABLE OF CONTENTS III.D.7. Cross sections. . . . . . . . . . . . . . . . . . . . . . . 4839

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Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

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FIG. 1. Illustration of a class II condensed history scheme for electron trans-

Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

Monte Carlo code Time estimate % mean difference relative to ESG4/PRESTA/DOSXYZ

ESG4/PRESTA/DOSXYZ 43 0, benchmark calculation

Medical Physics, Vol. 34, No. 12, December 2007

chamber is being taken into account. The ion chamber and

III.B.2. Electron beam specifics

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Medical Physics, Vol. 34, No. 12, December 2007

proposed by Ma et al.,114 is based on the development of

Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

underestimate the uncertainty in a dose calculation, as the

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Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

FIG. 6. MC-based MCV system dose-to-medium Dm

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Dw directly in clinical prescriptions remains the subject of

Arguments in favor of using Dm for dose specification

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Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

effect,27,72,83,87,137 and intra/interleaf transmission.27,72,83,87,137

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plate Roos and cylindrical ion chambers IC-10, Scan-

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particularly in nonuniform dose regions. It is important to

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Test description Reason Phantom design

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Monte Carlo code/configuration Description of treatment plan Time estimate

PEREGRINE Nomos, North American Scientific 16 AP beam, 6 MV photons, 10 10 cm2 in a water 48

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Due to the complicated dosimetric issues associated with

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Medical Physics, Vol. 34, No. 12, December 2007

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rays, Med. Phys. 30, 533543 2003. 45, 30093023 2000.

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Medical Physics, Vol. 34, No. 12, December 2007

Medical Physics, Vol. 34, No. 12, December 2007

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