What CTV-to-PTV Margins Should Be Applied for Prostate Irradiation? Four-Dimensional Quantitative Assessment Using Model-Based Deformable Image Registration Techniques

Int. J. Radiation Oncology Biol. Phys., Vol. 72, No. 5, pp. 1416–1425, 2008Copyright � 2008 Elsevier Inc.

Printed in the USA. All rights reserved0360-3016/08/$–see front matter

doi:10.1016/j.ijrobp.2008.03.005

CLINICAL INVESTIGATION Prostate

WHAT CTV-TO-PTV MARGINS SHOULD BE APPLIED FOR PROSTATEIRRADIATION? FOUR-DIMENSIONAL QUANTITATIVE ASSESSMENT USING

MODEL-BASED DEFORMABLE IMAGE REGISTRATION TECHNIQUES

GERT J. MEIJER, PH.D.,* JEROEN DE KLERK, M.SC.,* KARL BZDUSEK, M.SC.,y

HETTY A. VAN DEN BERG, M.D.,* ROGIER JANSSEN, M.SC.,z MICHAEL R. KAUS, PH.D.,y

PATRICK RODRIGUS, M.D.,* AND PETER-PAUL VAN DER TOORN, M.D.*

*Department of Radiotherapy, Catharina Hospital, Eindhoven, The Netherlands; yPhilips Medical Systems, Radiation OncologySystems, Madison, WI; and zDepartment of Radiotherapy, Isala Clinics, Zwolle, The Netherlands

Purpose: To quantify adequate anisotropic clinical target volume (CTV)-to-planning target volume (PTV) marginsfor three different setup strategies used during prostate irradiation: (1) no setup corrections, (2) on-line correctionsdetermined from bony anatomy, and (3) on-line corrections determined from gold markers.Method and Materials: Three radiation oncologists independently delineated the CTV on computed tomographyimages of 30 prostate cancer patients. Eight repeat scans were acquired to allow simulation of the delivered dosedistributions in changing geometry. Different registration approaches were taken to mimic the different setupstrategies. A surface model–based deformable image registration system was used to warp the delivered dose dis-tributions back to the dose in the planning computed tomography scan. On the basis of the geometric extent of theunderdosed areas, a set of anisotropic margins was derived to ensure a minimal dose to the CTVof 95% for 90% ofthe patients.Results: Without setup correction, margins of approximately 11 mm for the corpus of the prostate and 15 mm forthe seminal vesicles were required. These margins could be reduced to 8 and 13 mm when aligning the patient to thebony anatomy and to 3 and 8 mm aligning the patient to implanted gold markers. A larger margin at the apex wasrequired to account for the significant observer variability and steep dose gradients at this location (11 mm usingskin marker registration, 9 mm using bony anatomy registration, and 6 mm using gold marker registration).Conclusions: Novel voxel tracking techniques have enabled us to calculate accumulated dose distributions anddesign accurate three-dimensional CTV-to-PTV margins for prostate irradiation. � 2008 Elsevier Inc.

Prostate, Margins, Image-guided radiotherapy, IGRT, Deformable registration, Dose accumulation.

INTRODUCTION

The planning target volume (PTV) is a geometric concept

that takes into consideration the net effect of all possible geo-

metric variations and is used to ensure that the clinical target

volume (CTV) receives the prescribed dose. These geometric

uncertainties include organ delineation, setup errors, and or-

gan motion that occur throughout the planning and treatment

process. In the past decade, many treatment strategies have

been explored to reduce these uncertainties to maximize the

benefits of conformal therapy and intensity-modulated radio-

therapy (IMRT).

For external beam radiotherapy of the prostate, one of the

first setup and correction strategies was based on the compar-

ison of bony anatomy, visual on portal images, with reference

simulation film or digitally reconstructed radiographs (1, 2).

14

More recently, implanted fiducial markers have been used to

visualize motion of the prostate itself (3, 4). Using that

method, not only setup errors, but also internal motion of

the prostate relative to the bony anatomy, can be identified

(4, 5).

Both on-line and off-line approaches have been proposed

and implemented for both bony anatomy registration and

marker registration (1, 2, 6, 7). Although off-line correction

protocols aim at reducing systematic errors, on-line correc-

tion protocols have the potential to reduce both systematic

and random errors, but at the expense of increasing the treat-

ment time per fraction considerably.

Although these setup correction protocols can reduce geo-

metric treatment uncertainties, it is not straight forward to de-

rive appropriate CTV-to-PTV margins. Stroom et al. (8) and

Reprint requests to: Gert J. Meijer, Ph.D., Department of Radio-therapy, The Catharina Hospital, Postbus 1350, Eindhoven 5602 ZA,The Netherlands. Tel: (+31) 40-239-6400; Fax: (+31) 40-239-8499;E-mail: [email protected]

Conflict of interest: M. Kaus and K. Bzdusek are employees ofPhilips Medical Systems; no conflicts of interest for rest of authors.

Acknowledgments—The authors thank Fanny van Gorkum-vanAarle, Marjon Janssen-Reinders and Tamara Scheenstra for their ef-forts in the data acquisition, and Professor Gunther Cornelissen forfruitful discussions on statistical analysis.

Received Dec 14, 2007, and in revised form March 3, 2008.Accepted for publication March 3, 2008.

16

mailto:[email protected]

CTV to PTV margins for prostate irradiation d G. J. MEIJER et al. 1417

van Herk et al. (9) derived recipes expressing the margin as

a function of the systematic and random errors:

M ¼ aSþ bs (1)

where S is the standard deviation of the overall systematic er-

ror, and s, the standard deviation of the overall random error;

both errors were assumed to be normally distributed. On the

basis of a coverage probability simulation, Stroom et al. (8)

concluded that an a of 2.0 and b of 0.7 would result in a mar-

gin to cover 99% of the CTV with a dose of 95%. These

values are comparable to a simplified outcome of the margin

recipe using dose population statistics by van Herk et al. (a =

2.5 and b = 0.7), yielding a minimal dose to the CTV of 95%

for 90% of the patient population.

An important shortcoming of these margin recipes is their

lack of adequately incorporating both rotational and morpho-

logic errors. It is just these errors that become essential after

eliminating the translational errors and, for this reason, mar-

gin recipes might have only limited validity when trying to

establish adequate CTV-to-PTV margins when using setup

correction protocols.

The aim of this study was to assess the appropriate CTV-

to-PTV margins for 90% of the patient population by quan-

titatively simulating the total treatment dose using anatomic

data obtained from repeat computed tomography (CT)

scans during the course of therapy. The accumulated dose

distribution was calculated using a surface-based deform-

able image registration method (10). By aligning the repeat

CT data sets either to the external markers, the bony anat-

omy, or the internal markers, three different setup strategies

were simulated. Furthermore, intensity-modulated radio-

therapy (IMRT) plans were generated and evaluated for

independent CTV delineations to assess the effect of inter-

observer variability in target delineation. The approach has

two fundamental advantages. First, the use of a deformable

dose accumulation algorithm fully accounts for transla-

tional, rotational, and morphologic variations. Second, in

contrast to existing attempts, no Gaussian distributions

need to be assumed to model geometric uncertainties, be-

cause the actual data in the repeat scans will be real samples

in the treatment simulation.

METHODS AND MATERIALS

CT dataA total of 30 prostate cancer patients with four implanted gold

markers were used in this simulation study. For each patient, nine

CT scans of the pelvic region (one treatment planning and eight re-

peat CT scans) were acquired with a 16-slice helical scanner (Bril-

liance Big Bore CT Scanner, Philips Medical Systems, Cleveland,

OH) using a slice thickness of 1.5 mm. The repeat scans were ac-

quired immediately before eight treatment sessions regularly spread

over the entire treatment course. The patients were instructed to void

their bladder 1 h before treatment (and before the CT scan) and drink

300 mL afterward.

Delineation of CTV and organs at riskThree experienced radiation oncologists independently delin-

eated the CTV in a three-dimensional (3D) manner. In this proce-

dure, we assumed only microscopic tumor involvement in the first

2 cm of the seminal vesicles corresponding to the pathologic fea-

tures of intermediate-risk tumors (11, 12). First, two spheres with

a radius of 2 cm were centered at the central part of the interfaces

between the prostate and each of the seminal vesicles. Second, the

CTVs were delineated slice by slice by each observer. In this pro-

cess, the spheres were used as a guideline to indicate the boundaries

of the seminal vesicles. Finally, a template CTV mesh with 962 no-

des (or vertices) was automatically fit to the delineated contours.

This template mesh was constructed from the CTV contours of an

arbitrary patient with a left–right symmetric CTV and average-

size seminal vesicles. In the fitting process, care was taken that

the nodes were evenly distributed over the CTV and that each cluster

of nodes always represented the same particular surface area of the

CTV (Fig. 1). This enabled us to perform population statistics be-

cause the mesh of each prostate of each patient and observer had

the same topology.

A similar procedure was used to generate a mesh of the rectum.

First, the rectum was delineated by a single observer at the trans-

verse slices of the CT scan. Second, a template rectum mesh was

fit around the contours.

IMRT planningInitially, the five-field IMRT plans were generated with no CTV-

to-PTV margin for each delineated CTV. The aim was to generate

a very conformal dose distribution. In a standard prostate IMRT

plan, a high-dose gradient is often mainly desired at the prostate in-

terface with the rectum; however, in this study, it was important to

Fig. 1. ‘‘Patchwork’’ clinical target volume meshes of prostate and seminal vesicles for 3 patients, in which surface patches(i.e., spatially connected regions of mesh nodes) were encoded with one color. Graph qualitatively illustrates that each nodecorresponds to approximately same surface location from one organ to another, allowing us to perform population statisticson a node-by-node basis.

1418 I. J. Radiation Oncology d Biology d Physics Volume 72, Number 5, 2008

create an instant dose decline at each location at the exterior border

of the PTV. Clearly, these plans were expected to yield bad target

coverage, but it was exactly the amount of underdosed areas that

guided us to find the appropriate margins in the second phase.

The IMRT plans were generated in two steps. First, for each PTV

(i.e., the CTV in this exercise), a 2-mm, thin, ring-shaped structure

was created 3 mm separated from the PTV in the left–right and ante-

roposterior directions. The plans were fluence-based optimized us-

ing four objectives ranked in decreasing weights: (1) a minimal

dose to the PTV (or CTV in this exercise) of 80 Gy with a weight

of 100; (2) a maximal dose to the ring structure of 76 Gy with

a weight of 20; (3) a maximal equivalent uniform dose (n = 0.13)

to the rectum of 54 Gy with a weight of 5; and (4) a maximal

dose to the PTV of 86 Gy with a weight of 1. The outcome of this

optimization was a very conformal plan in all directions with an

80-Gy target coverage of $99%. However, the conformality came

at the price of a rather high dose maximum in the PTV. The high-

dose regions would not necessarily be present in the clinical case

and, when considering a worst case scenario for the dose to each

voxel of the PTV, these high-dose regions were not wanted in our

treatment simulation: a low dose to a voxel moving outside the

PTV can be compensated by a high dose when this voxel has moved

to the center of the PTV. Therefore, in the second step, all high-dose

values in the PTV were artificially cut down to 80 Gy. The complete

procedure yielded an ideal, although perhaps physically unachiev-

able, dose distribution (extremely homogeneous within the PTV

with an instant dose decline at all borders) that was designed to

not underestimate the needed CTV-to-PTV margin for each surface

element of the CTV in the later analysis.

Treatment simulationThe aim of the treatment simulation was to quantify the dosimet-

ric outcome of a given setup protocol. Three setup protocols were

investigated in this study:

1. A skin marker protocol: a no-correction setup protocol in which

the patient’s skin markers were aligned to the laser system in the

treatment room, followed by a table height adjustment to repro-

duce the table-to-isocenter distance from treatment planning.

2. A bony anatomy protocol: an on-line correction protocol in

which, before treatment, the patient setup was verified and cor-

rected for using the 3D bony anatomy.

3. A gold marker protocol: an on-line correction protocol in which,

before treatment, the patient setup was verified and corrected for

using the 3D position of internal gold markers.

These various setup protocols were individually simulated by reg-

istering the repeat data sets to the planning CT at the external lead

markers, bony anatomy, and internal gold markers, respectively.

The latter two registrations were automatically performed using

a mutual information-based registration algorithm after the data

sets were cropped to a large volume encompassing the symphysis

and sacrum or a small volume just encompassing the markers.

Only translations were performed to mimic the on-line couch-cor-

rection at the treatment unit. The registration of the skin marker pro-

tocol was done manually by shifting the image around until visual

overlap of the lead markers was established. In contrast to the setup

procedure at the treatment room, no adjustment to reproduce the

fixed table-to-isocenter distances needed to be performed, because

the CT table top was always at a fixed height as a result of the pro-

tocolized scanning procedure. Because of the limited number of re-

peat scans (eight), we were unable to adequately simulate off-line

protocols, although we realize that bony landmark registration, in

particular, is often related to a shrinking action level protocol or

a no-action level protocol.

Dose accumulationIn this study, the too-tight nonclinical plans (of the previously de-

scribed optimization process) were delivered in eight fractions, such

that each fraction was associated with a repeat CT and a registration

corresponding to a one-setup protocol. For each fraction, the dose

was recomputed, taking into account the actual patient setup and

anatomy. A surface model-based deformable image registration

technique according to Kaus et al. (10) was used to register each

voxel of the repeat CT scans to the corresponding voxel of the plan-

ning CT scan. The dose accumulation system (Pinnacle3 treatment

planning research software, version 8.1r) started by propagating

and adapting the 3D triangular surface mesh of the organs of interest

(discussed in the next paragraph) for each repeat scan. The corre-

sponding mesh points were considered to be surrogates for identical

tissue voxels, as was justified by Kaus et al. (10) when evaluating

the accuracy of anatomic correspondence for anatomic landmarks

identified by clinical experts. The deformation of a particular loca-

tion on the surface was measured from a vertex of the mesh in

each repeat CT scan to the corresponding vertex of the mesh in

the planning CT scan. The set of all corresponding mesh vertices de-

fined a prescribed surface displacement. An elastic body spline de-

formation model was used to interpolate the surface deformation to

the entire volume to derive a volumetric displacement vector field.

The summation of the deformed dose distributions over all fractions

yielded the accumulated dose distribution.

As the meshes were propagated (i.e., copied) to the repeat scans,

the world coordinates of the meshes were maintained and subse-

quently linked to the corresponding repeat CT scans. It turned out

to be convenient to propagate the organs in the data sets that were

registered to the internal gold markers. Thus, no translations needed

to be performed to put the CTV and rectum in place. After the prop-

agation, the meshes were edited three dimensionally to correct for

the shape changes and rotations of the organs at the repeat CT scans.

For the CTV, minor rotations typically needed to be performed in

combination with a small adjustment of the orientation of the sem-

inal vesicles. A rather extreme example that required substantial ed-

iting of the CTV at the seminal vesicles is shown in Fig. 2. The

rectum only needed to be adjusted for the variation in rectal filling.

Only one of the delineated CTV meshes was propagated and adap-

ted, because, owing to the smooth nature of the image deformation

model, the displacement vector fields in the simulation were ex-

pected not to be dependent on the observer variability of the CTV

in the planning CT scan. If, in the simulation, the skin marker or

bony anatomy registration parameters were applied to the repeat

CT scans, the meshes moved correspondingly.

3D dose analysisFor each patient, three independent expert observers manually de-

lineated the CTV, and, for each of these CTVs, an IMRT plan was

created. Because adequate dose coverage was defined as a minimally

delivered dose to the CTV of 95%, meshes were created of the 95%

isodose surfaces for both the planned and the accumulated dose dis-

tribution for each setup protocol. Ignoring observer variability, the

target coverage can be directly analyzed by examining each CTV

with a corresponding 95% isodose surface. However, we sought

to analyze the 95% isodose surface with respect to the ground truth,

i.e. the average delineation of an infinite number of observers. Be-

cause we had only three observers, it might seem reasonable to

take the arithmetic mean of the three delineated CTVs as a reference.


Fig. 2. Axial and sagittal images of (Left) planning CT scan and (Right) repeat CT scan of patient with large deformationsof seminal vesicles. Clinical target volume meshes of planning CT scan (black) and repeat CT scan (white) projected onboth data sets. Dashed lines indicate intersection of axial and sagittal planes. Centimeter ruler displayed at right in eachimage.

However, because the shape of the 95% isodose surface correlates to

the shape of the corresponding CTV, a weight correction for this

sample in the calculation of the mean should be applied. The vertex

coordinates of the ground truth could then be approximated by

a weighted average over the vertices of the three delineated CTVs:

CTVground truthi ¼ 1ffiffiffi

6p � ffiffiffi

6p� 2�

, CTVi þX3

jsi

CTVj

!(2)

where the index i refers to the observer delineating the CTV in the

IMRT plan (see Appendix). For each vertex of this ground truth,

we calculated a signed Euclidean distance to the nearest point at

a specific isodose surface. A negative distance indicates that this

point was outside the CTV, and a positive distance reflected an

underdosed area with respect to this dose level. This yielded a distri-

bution of 90 distances (three observers� 30 patients) per setup pro-

tocol for each vertex.

For each setup protocol, the margin maps were constructed in

a two-step process. First, nine simulation results (10%) were selected

that were considered outliers at a ‘‘global’’ level in the sense of the

extent of a specific underdosed area. In this process, one set of 692

vertices (i.e., one virtual treatment course) is taken as one data point.

These treatment courses were discarded from additional analysis to

derive an adequate margin map for the remaining 90% of the patient

population. The margin maps were constructed by locally taking the

signed maximum of the remaining 81 distances for each vertex.

Validation of margin mapsFrom the margin maps, we derived ellipsoidal expansion kernels

for both the corpus of the prostate and seminal vesicles. Because the

shape of the dose distribution of a zero-margin plan is different from

the dose distribution of a nonzero-margin treatment plan, a second

simulation run was performed to validate adequate target coverage

for each protocol.

RESULTS

A visual example showing sagittal reconstructions of

a treatment simulation of a skin marker (no-correction) pro-

tocol (Fig. 3) demonstrated that the planned 100% isodose

line almost coincided with the CTV contour (Fig. 3, top

left). The distance between the CTV surface and the 95% iso-

dose level typically varied between 2 and 5 mm. The dose in

Fractions 1–8 was recalculated using the imaged setup and

anatomy. The skin markers (lead wires) at the surface of

the patient of each repeat CT scan were aligned with the

skin markers of the planning CT scan. Because of the large

rectum filling during planning CT acquisition, a systematic

posterior shift of the CTV with respect to the ‘‘delivered’’

dose distributions was observed in the repeat CT scans.

This was reflected in the lower left image displaying the

dose accumulated from each warped fraction projected onto

the dose grid of the planning CT.

For each setup protocol, the local margins were assessed

according to the 95% isodose surfaces in the 90 (3 � 30) ac-

cumulated dose distributions and the ground truth CTVs. This

was accomplished in a two-step procedure. First, the nine sim-

ulation runs (10%) that resulted in the most outlying


underdosing of the ground truth CTV were manually selected

and excluded from additional analysis. For different setup

protocols, different simulation results were sometimes con-

sidered to be the most outlying. One outlying simulation result

was caused by a 1-cm underestimation of the apical border of

the CTV in relation to the other delineations. Other outlying

simulation results were, for example, related to an extreme

systematic change in orientation of the seminal vesicles be-

cause of an empty rectum at the planning CT scan (Fig. 2).

In the second step, the distances between each vertex of the

estimate of the ground truth CTV and the 95% isodose sur-

face were calculated and ranked for each setup protocol. In

Fig. 4a, the maximal distance between each CTV node and

the 95% isodose surface was calculated and plotted at the

(earlier defined) template CTV. For example, the black tip

in the seminal vesicles of the skin marker protocol indicates

that in one of the simulations of the remaining 90% of the pa-

tients, the distance between the estimate of the ground truth

and the 95% isodose was 1.5 cm. In the other 80 ([90 �0.9] � 1) simulations, the underdosage was less. Or re-

versely, a CTV-to-PTV margin of 1.5 cm for the seminal ves-

icles would have counterbalanced the errors causing these

underdosages in at least 90% of the patients. Smaller margins

were required for the corpus of the prostate (#8 mm),

although at the apex and dorsal side of the prostate, an

11-mm margin was required.

Daily setup correction using the pelvic bony anatomy led to

slightly reduced margins (Fig. 4b). A substantial margin re-

duction was observed when applying daily setup corrections

using gold marker implants (Fig. 4c). The red areas indicate

the potential for negative CTV-to-PTV margins for parts of

the prostate. This resulted because the PTV was planned

with 100% isodose coverage, whereas underdosed areas

were scored when the local dose at the CTV surface decreased

to less than the 95% level. However, larger margins were

needed at the apex (6 mm) and at the seminal vesicles (8 mm).

For the gold marker protocol, excluding observer variabil-

ity (Fig 4d), that is, performing the dose analysis in relation to

the delineated CTVs, the margin required for the seminal ves-

icles resulted from the morphologic changes of the seminal

vesicles and the rotations of the CTV that could not be cor-

rected by applying translational corrections. However, the

margin at the apex could be reduced to 1 mm if the ground

truth CTV was delineated by each observer. Therefore, the

relatively large margin at the apex using the gold marker pro-

tocol was merely the result of the high observer variability at

this location (Fig. 4e). In Fig. 4e, the observer variability for

each node was calculated by computing the standard devia-

tion of the Euclidean distances between the node of the aver-

age delineated CTV and the closest surface element of the

individual CTV. In addition, because of the coplanar beam

arrangement of the IMRT technique, the greatest dose

Fig. 3. Example of skin marker treatment simulation with zero clinical target volume-to-planning target volume margin.For each fraction, dose was recomputed using initial beam configurations but taking into account current patient setup andanatomy using corresponding computed tomography (CT) image. Surface model-based deformable image registration sys-tem was used to warp delivered dose distributions back to planning computed tomography scan. Purple indicates 100%dose level; red, 95% dose level.


Fig. 4. Margin maps for three different protocols for daily setup using (a) skin markers, (b) pelvic bony anatomy, and (c)implanted gold markers. (d) Image similar to that in Fig. c, without taking interobserver variability into account. (e) Ob-server variability and (f) average distance between planning target volume surface and planned 95% isodose surface of tightnonclinical plans.


gradients were observed near the apex, which also led to

a margin increase.

Table 1 summarizes the separate margins for the corpus of

the prostate and seminal vesicles from the margin maps

(Fig. 4a-c). A second simulation run was performed, this

time using ellipsoidal CTV-to-PTV margin kernels to validate

the correctness of the margins. Figure 5 shows the worst-case

distance between the CTV and the accumulated 95% isodose

surface when applying the new margin after elimination of the

nine most outlying simulation results. The negative values in-

dicated that the accumulated 95% isodose surface encom-

passed the CTV for all remaining simulations.

DISCUSSION

General reflectionsIn this study, adequate CTV-to-PTV margins for prostate

irradiation were derived by simulating 90 treatments in

changing geometry using repeat CT imaging. It was our im-

pression that our sample distribution of 30 patients and three

observers yielded statistically meaningful results for two rea-

sons. First, the margins in this study were rather similar to the

margins resulting from an intermediate analysis of the first

Table 1. Margins for six key directions for corpus of prostateand seminal vesicles derived from data shown in Fig. 4a–c

Skin markers Bony anatomy Gold markers

Margin(mm) Prostate

Seminalvesicles Prostate

Seminalvesicles Prostate

Seminalvesicles

Cranial 8 15 5 13 4 8Caudal 11 15 9 13 6 8Left 4 15 3 13 2 8Right 4 15 3 13 2 8Ventral 8 15 7 13 2 8Dorsal 11 15 8 13 2 8

20 patients (data not shown). Second, all margin maps

were highly left-right symmetric, whereas the margin of a ver-

tex at the left side was determined by another sample (i.e.,patient) than its right-side counterpart. Thus, the amount of

left–right symmetry can be considered as a measure of the

strength of the sample size.

We strived for a 99% coverage of the PTV with the 100%

isodose level. In contrast, in many clinics, this PTV coverage

is required for the 95% level, meaning that the 95% isodose

surface touches the PTV surface at some locations. As a re-

sult, the margin maps (Figs. 4a–c) will not be directly valid

for these other institutions and should be corrected by the av-

erage distance between the PTV surface and the 95% isodose

surface (Fig. 4f).

In general, small margins were sufficient for the corpus of

the prostate, although a larger margin was required at the

apex owing to the observer variability and the steep dose

fall-off resulting from the co-planar IMRT beam arrange-

ment. The largest margins were needed at the seminal vesi-

cles, mainly because of the morphologic changes of the

seminal vesicles.

Comparison with margin recipe of van Herk et al.

The margins found in the present study were also com-

pared with results from the margin recipe of van Herk et al.(9). Assuming perfect prostate positioning by aligning the

gold markers within the prostate, the systematic and random

positioning uncertainties of the CTV can be deduced from the

different registration vectors (Table 3). The overall mean sys-

tematic error D was calculated by averaging the systematic

errors for all patients. On average, when the prostate was

aligned at the skin markers or using the pelvic anatomy,

a small systematic dorsal shift was observed. Similar effects

were reported in a multi-CT study by Zelefsky et al. (13) and,

more recently, by Nijkamp et al. (14), in which the investiga-

tors discussed their clinical experience with an adaptive

Fig. 5. Maps of ‘‘worst-case’’ distances between clinical target volume and accumulated 95% isodose surface when ap-plying ellipsoidal margin kernels from Table 1 for 90% of patients using setup protocols based on (a) skin markers, (b)pelvic bony anatomy, and (c) implanted gold markers. For example, purple areas indicate regions in which 95% isodosesurface encompassed clinical target volume with margin of $3 mm for 90% of patient population.


Table 2. CTV positioning errors, observer variability, standard deviation describing penumbra, and average distance betweenPTV and 95% isodose

Skin markers (mm) Bony anatomy (mm) Gold markers (mm)

Variable D S s D S s D S s Sobs (mm) sp (mm) dPTV/95% (mm)

Cranial �0.2 2.4 3.0 �0.3 2.4 2.0 0.0 0.0 0.0 2.0 5.0 3.0Caudal 0.2 2.4 3.0 0.3 2.4 2.0 0.0 0.0 0.0 3.2 5.0 2.0Left 0.0 1.5 2.0 0.0 0.5 0.5 0.0 0.0 0.0 1.7 7.0 3.5Right 0.0 1.5 2.0 0.0 0.5 0.5 0.0 0.0 0.0 1.7 7.0 3.5Ventral 1.9 3.7 2.8 �1.1 2.7 1.9 0.0 0.0 0.0 2.0 7.0 3.5Dorsal 1.9 3.7 2.8 1.1 2.7 1.9 0.0 0.0 0.0 1.5 7.0 3.5

Abbreviations: D = overall mean systematic CTV positioning error; S = systematic error; s = random error; Sobs = observer variability; sp =standard deviation describing penumbra; dPTV/95% = average distance between PTV and 95% isodose; CTV = clinical target volume; PTV =planning target volume.

radiotherapy protocol using cone-beam CT. The translational

systematic and random setup errors of the CTV, expressed as

standard deviations, are symbolized by S and s, respectively,

and are consistent with previously published results (14–16).

The observer variability in the present study was denoted by

Sobs (Fig. 4e) and showed very good agreement with the data

reported by van Herk et al. (9), in which they cited Rasch

et al. (17).

The simplified linear version of the ‘‘van Herk’’ margin

recipe (M = 2.5S + 0.7s) assumes a standard deviation de-

scribing the penumbra width sp equal to 0.32 cm, corre-

sponding to the penumbra of a single beam. In our IMRT

plans, sp was larger (the approximate values are listed in

Table 2), which is why we chose to use the original recipe

for comparison. Furthermore, the validity of the margin rec-

ipe was based on the conservative assumption that the 95%

isodose surface coincides with the entire PTV surface. How-

ever, it has been our clinical experience that, when using

IMRT techniques, 99% of the PTV can be covered with

the 100% isodose, with acceptable dose levels to the critical

regions and without overdosing the PTV >105%. Thus, the

margin outcome of the recipe was therefore corrected for

dPTV/95%, the (average) distance between PTV and 95%

(Fig, 4f and Table 2). The original margin recipe would

then become

Table 3. Comparison of margins for corpus of prostate usingdose warping technique* and modified recipe of van Herket al. (9) using input data derived directly from registration

vectorsy

Skin markers Bony anatomy Gold markers

MarginPresentstudy

van Herket al. (9)

Presentstudy

van Herket al. (9)

Presentstudy

van Herket al. (9)

Cranial 8 7 5 5 4 3Caudal 11 9 9 9 6 6Left 4 3 3 1 2 1Right 4 3 3 1 2 1Ventral 8 6 7 4 2 2Dorsal 11 9 8 6 2 1

* See Table 1.y Listed in Table 2.

M ¼ 2:5ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 þ S2

obs

qþ 1:64

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2 þ s2

p

q� 1:64sp

� dPTV/95% þ D (3)

where D represents the systematic difference averaged for

all patients between the position and shape of the CTV as

defined in the treatment preparation phase and the posi-

tion and shape of the mean CTV in the treatment phase

(18).

The data in Table 3 compare the margins according to

Eq. 3 to the outcome of the present study for the corpus

of the prostate, illustrating good agreement between our

full four-dimensional dose warping technique and the statis-

tical approach using only the registration vectors. Nonethe-

less, the comparison is not valid for the margins of the

seminal vesicles, because the high values of these margins

were merely the result of the deformation of the seminal

vesicles and, to a lesser extent, the rotations of the complete

CTV, neither of which were incorporated into the margin

recipe.

Intrafraction motionNo intrafraction uncertainties were taken into account in

our study, assuming little dosimetric effect of the intrafrac-

tion movement of the CTV. Litzenberg et al. (15) reported

on prostate motion in 11 patients monitored with electro-

magnetic tracking of implanted transponders. Kotte et al.(19) recently presented the intrafraction motion for

11,426 fractions. Both studies found small intrafraction mo-

tion in the left–right direction (sif # 0.4 mm) and moderate

intrafraction motion in the ventral-dorsal and craniocaudal

direction (sif #1.1 mm). For a single fraction, the intrafrac-

tion motion might cause a systematic effect, but with an in-

creasing number of fractions, the systematic component

will average out. The only remaining component was ran-

dom error that results in dose blurring. Because the dose

blurring described by the penumbra sp is at least approxi-

mately 5 mm, the net effect of the intrafraction blurring

also becomes very small. The margin increase can be esti-

mated by


DM ¼ 2:5

� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 þ S2

obs þ n�1s2if

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiS2 þ S2

obs

q �

þ 1:64� ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

s2 þ s2p þ s2

if

q�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffis2 þ s2

p

q �(4)

where n is the number fractions. Only in a very extreme case

(sif = 3 mm, n = 15, S = s = 0, Sobs = 0.15 mm, sp = 5 mm),

will the margin increase be 2 mm. More regularly, the margin

increase as an effect of the intrafraction movements will be

#0.1 mm.

CONCLUSIONS

Novel voxel tracking techniques enable us to calculate the

accumulated dose distributions using quantitative image-

based measurements. Anisotropic CTV-to-PTV margins

for prostate irradiation were designed to ensure a minimal

dose to the CTV of 95% for 90% of the patients, with the pre-

requisite that 99% of the PTV be covered by the 100% dose

level in the planning phase. Without setup correction, mar-

gins of approximately 11 mm for the corpus of the prostate

and 15 mm for the seminal vesicles were required. These

margins were slightly reduced to 8 and 13 mm, respectively,

when aligning the patient using the bony anatomy, and to 3

and 8 mm, respectively, when aligning the patient using im-

planted gold markers. A larger margin at the apex was re-

quired to account for the significant observer variability,

with steep dose gradients at this location (11 mm using

skin marker registration, 9 mm using bony anatomy registra-

tion, and 6 mm using gold marker registration).

REFERENCES

1. Bel A, Van Herk M, Bartelink H, et al. A verification procedureto improve patient set-up accuracy using portal images. Radio-ther Oncol 1993;29:253–260.

2. de Boer HC, Heijmen BJ. A protocol for the reduction of sys-tematic patient setup errors with minimal portal imaging work-load. Int J Radiat Oncol Biol Phys 2001;50:1350–1365.

3. Balter JM, Lam KL, Sandler HM, et al. Automated localizationof the prostate at the time of treatment using implanted radi-opaque markers: technical feasibility. Int J Radiat Oncol BiolPhys 1995;33:1281–1286.

4. Vigneault E, Pouliot J, Laverdiere J, et al. Electronic portal im-aging device detection of radiopaque markers for the evaluationof prostate position during megavoltage irradiation: A clinicalstudy. Int J Radiat Oncol Biol Phys 1997;37:205–212.

5. Schallenkamp JM, Herman MG, Kruse JJ, et al. Prostate posi-tion relative to pelvic bony anatomy based on intraprostaticgold markers and electronic portal imaging. Int J Radiat OncolBiol Phys 2005;63:800–811.

6. De Neve W, van den Heuvel F, De Beukeleer M, et al. Routineclinical on-line portal imaging followed by immediate field ad-justment using a tele-controlled patient couch. Radiother Oncol1992;24:45–54.

7. van der Heide UA, Kotte AN, Dehnad H, et al. Analysis of fidu-cial marker-based position verification in the external beam ra-diotherapy of patients with prostate cancer. Radiother Oncol2007;82:38–45.

8. Stroom JC, de Boer HC, Huizenga H, et al. Inclusion of geomet-rical uncertainties in radiotherapy treatment planning by meansof coverage probability. Int J Radiat Oncol Biol Phys 1999;43:905–919.

9. van Herk M, Remeijer P, Rasch C, et al. The probability of cor-rect target dosage: Dose–-population histograms for derivingtreatment margins in radiotherapy. Int J Radiat Oncol BiolPhys 2000;47:1121–1135.

10. Kaus MR, Brock KK, Pekar V, et al. Assessment of a model-based deformable image registration approach for radiation

therapy planning. Int J Radiat Oncol Biol Phys 2007;68:572–580.

11. Kestin L, Goldstein N, Vicini F, et al. Treatment of prostate can-cer with radiotherapy: Should the entire seminal vesicles be in-cluded in the clinical target volume? Int J Radiat Oncol BiolPhys 2002;54:686–697.

12. Korman HJ, Watson RB, Civantos F, et al. Radical prostatec-tomy: Is complete resection of the seminal vesicles really neces-sary? J Urol 1996;156:1081–1083.

13. Zelefsky MJ, Crean D, Mageras GS, et al. Quantification andpredictors of prostate position variability in 50 patients evalu-ated with multiple CT scans during conformal radiotherapy.Radiother Oncol 1999;50:225–234.

14. Nijkamp J, Pos FJ, Nuver TT, et al. Adaptive radiotherapy forprostate cancer using kilovoltage cone-beam computed tomog-raphy: First clinical results. Int J Radiat Oncol Biol Phys 2008;70:75–82.

15. Litzenberg DW, Balter JM, Hadley SW, et al. Influence of intra-fraction motion on margins for prostate radiotherapy. Int JRadiat Oncol Biol Phys 2006;65:548–553.

16. Nederveen AJ, Dehnad H, van der Heide UA, et al. Comparisonof megavoltage position verification for prostate irradiationbased on bony anatomy and implanted fiducials. RadiotherOncol 2003;68:81–88.

17. Rasch C, Barillot I, Remeijer P, et al. Definition of the prostatein CT and MRI: A multi-observer study. Int J Radiat Oncol BiolPhys 1999;43:57–66.

18. Meijer GJ, Rasch C, Remeijer P, et al. Three-dimensional anal-ysis of delineation errors, setup errors, and organ motion duringradiotherapy of bladder cancer. Int J Radiat Oncol Biol Phys2003;55:1277–1287.

19. Kotte AN, Hofman P, Lagendijk JJ, et al. Intrafraction motionof the prostate during external-beam radiation therapy: Analysisof 427 patients with implanted fiducial markers. Int J RadiatOncol Biol Phys 2007;69:419–425.


APPENDIX

We first defined the following variables in a one-dimensional

error model to each sampling direction: xi, a surface element

of the CTV as delineated by observer i, xd/95%i , the distance

between xi and the 95% isodose level in the planned (or accu-

mulated) dose distribution and

m0i ¼ ðn� dÞ�1,

ð1� dÞxi þ

Xn

jsi

xj

!

a weighted average of xi with 0 # d # 1.

If d = 0, mi0 expresses the arithmetic mean delineation for

all observers; if d = 1, mi0 expresses the arithmetic mean de-

lineation for all observers other than observer i. Given a set

of uncorrelated random variables xi with variances s2 (xi)

and real constants ci, then

s2�X

cixi

�¼X

c2i s2ðxiÞ (A1)

Consequently, the variation of the difference between the

95% isodose ðxi þ xd/95%i Þ and the weighted average mi

0

can be expressed as

s2�xi þ xd/95%

i � m0i�

¼ s2�xd/95%

i

�þ s2

xi � ðn� dÞ�1,

ð1� dÞxi þ

Xn

jsi

xj

!!

¼ s2�xd/95%

i

�þ s2

ðn� dÞ�1,

ðn� dÞxi � ð1� dÞxi �

Xn

jsi

xj

!!

¼ s2�xd/95%

i

�þ ðn� dÞ�2,

�ðn� 1Þ2þðn� 1Þ

�s2ðxiÞ;

¼ s2�xd/95%

i

�þ ðn� dÞ�2,nðn� 1Þs2ðxiÞ ðA2Þ

If we now require that the variance of this difference is

equal to the variance of the difference between the 95% iso-

dose and the true population mean m, or

s2�xi þ xd/95%

i � m0i�¼ s2

�xi þ xd/95%

i � m�

¼ s2ðxiÞ þ s2�xd/95%

i

�then

d ¼ n�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffinðn� 1Þ

pFor n = 3, d ¼

ffiffiffi6p� 2 or, if we have three observers inde-

pendently delineating the CTV, the variance of the distance

between the isodose surface of a plan based on the CTV

of Observer 1 and the weighted average ðffiffiffi6p� 2Þx1þ

x2 þ x3Þ=ffiffiffi6p

is equal to the variance of the distance between

the isodose surface and the true population mean.

Documents

What CTV-to-PTV Margins Should Be Applied for Prostate Irradiation? Four-Dimensional Quantitative Assessment Using Model-Based Deformable Image Registration Techniques