Geometry of volumes in radiotherapy planning. A new method for a quantitative assessment.
ABSTRACT The purpose of the study was to develop a general method able to quantify the mutual disposition in the 3D space of critical organs with respect to the target when these structures are designed for a radiotherapy treatment plan. To that end, we introduce the "expansion intersection histogram", a function defined as the intersection between an organ at risk and the target volume, while the target is expanded in 3D.
A software was developed to calculate the expansion intersection histogram of anatomical structures exported in a DICOM format from a commercial treatment planning system. A virtual phantom with spherical and cylindrical objects arranged in different dispositions in the 3D space was created for testing the software under known conditions.
Expansion intersection histogram computation was tested against reference data derived analytically for spherical volumes, with a resulting maximum error of 0.5%. Specific geometric features derived from the expansion intersection histogram, such as the distance between a selected target and each different ideal volume included in the virtual phantom, well matched the corresponding theoretical expected values. The expansion intersection histogram was evaluated also for the anatomical structures of a real patient. Data show this method as a tool to effectively take into account the mutual disposition of each critical organ with respect to the target, summarized in characteristics of distance, shape and orientation. The expansion intersection histogram method integrates and extends other preexisting modalities for evaluating the geometrical relationships among radiotherapy volumes and could be used to improve planning optimization.
- SourceAvailable from: George Starkschall[show abstract] [hide abstract]
ABSTRACT: In recent years, the sophistication and complexity of clinical treatment planning and treatment planning systems has increased significantly, particularly including three-dimensional (3D) treatment planning systems, and the use of conformal treatment planning and delivery techniques. This has led to the need for a comprehensive set of quality assurance (QA) guidelines that can be applied to clinical treatment planning. This document is the report of Task Group 53 of the Radiation Therapy Committee of the American Association of Physicists in Medicine. The purpose of this report is to guide and assist the clinical medical physicist in developing and implementing a comprehensive but viable program of quality assurance for modern radiotherapy treatment planning. The scope of the QA needs for treatment planning is quite broad, encompassing image-based definition of patient anatomy, 3D beam descriptions for complex beams including multileaf collimator apertures, 3D dose calculation algorithms, and complex plan evaluation tools including dose volume histograms. The Task Group recommends an organizational framework for the task of creating a QA program which is individualized to the needs of each institution and addresses the issues of acceptance testing, commissioning the planning system and planning process, routine quality assurance, and ongoing QA of the planning process. This report, while not prescribing specific QA tests, provides the framework and guidance to allow radiation oncology physicists to design comprehensive and practical treatment planning QA programs for their clinics.Medical Physics 11/1998; 25(10):1773-829. · 2.91 Impact Factor
- Clinical Oncology 05/2007; 19(3 Suppl):S43. · 2.86 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: Computerized radiation therapy planning systems (RTPSs) are pivotal for treatment planning. The acceptance, commissioning, and quality control of RTPSs are uniquely complex and are described in the American Association of Physicists in Medicine Task Group Report 53 (1998) and International Atomic Energy Agency Technical Report Series No. 430 (2004). The International Atomic Energy Agency also developed a document and data package for use by vendors and purchasers to aid with acceptance testing of RTPSs. This document is based on International Electrotechnical Commission standard 62083 (2000) and describes both "type" tests to be performed in the factory and "site" tests to be performed in the clinic. The American Association of Physicists Task Group Report 67 described benchmark tests for the validation of dose calculation algorithms. Test data are being produced with the backing of the U.S. National Cancer Institute. However, significant challenges remain. Technology keeps evolving rapidly, thus requiring new quality assurance (QA) procedures. Intensity-modulated radiation therapy with its use of inverse optimization has added a new dimension to QA, because the results are not intuitively obvious. New technologies such as real-time ultrasound guidance for brachytherapy, TomoTherapy, and Cyberknife, require their own specialized RTPSs with unique QA requirements. On-line imaging allows for the generation of dose reconstructions using image warping techniques to determine the daily dose delivered to the patient. With increasing computer speeds, real-time reoptimization of treatment plans will become a reality. Gating technologies will require four-dimensional dose calculations to determine the actual dose delivered to tissue voxels. With these rapidly changing technologies, it is essential that a strong QA culture is invoked in every institution implementing these procedures and that new protocols are developed as a part of the clinical implementation process.International Journal of Radiation OncologyBiologyPhysics 02/2008; 71(1 Suppl):S23-7. · 4.52 Impact Factor
Key words: geometrical features,
quantification, radiotherapy volumes,
treatment plan optimization.
Gabriele Carabelli and Sarah Frasca
for the helpful technical assistance in
the transfer of patient DICOM data
between the different imaging radio-
therapy workstations. We also thank
Marta Calanchi and Donatella De
Tommaso for being the promoters of
a fruitful collaboration between the
National Cancer Institute and the De-
partment of Mathematics of the Uni-
versity of Milan.
Correspondence to: Stefano Tomatis,
Medical Physics Unit, Fondazione IR-
CCS Istituto Nazionale Tumori, Via
Venezian 1, 20133, Milan, Italy.
Received January 20, 2010;
accepted February 23, 2011.
Geometry of volumes in radiotherapy planning.
A new method for a quantitative assessment
Stefano Tomatis1, Mauro Carrara1, Elisa Massafra2, Giovanni Naldi2,
Mauro Palazzi3, Ester Orlandi4, and Renato Marchesini5
1Medical Physics Unit, Fondazione IRCCS Istituto Nazionale Tumori, Milan;2Department of
Mathematics, University of Milan, Milan;3Radiotherapy Unit, Azienda Ospedaliera Ospedale
Niguarda Ca’ Granda, Milan;4Radiotherapy Unit, Fondazione IRCCS Istituto Nazionale Tumori,
Milan;5Department of Physics, University of Milan, Milan, Italy
Aims and background. The purpose of the study was to develop a general method
able to quantify the mutual disposition in the 3D space of critical organs with respect
to the target when these structures are designed for a radiotherapy treatment plan.To
that end, we introduce the “expansion intersection histogram”, a function defined as
the intersection between an organ at risk and the target volume, while the target is ex-
panded in 3D.
Methods and study design. A software was developed to calculate the expansion in-
tersection histogram of anatomical structures exported in a DICOM format from a
commercial treatment planning system. A virtual phantom with spherical and cylin-
drical objects arranged in different dispositions in the 3D space was created for test-
ing the software under known conditions.
Results and conclusions. Expansion intersection histogram computation was tested
against reference data derived analytically for spherical volumes, with a resulting
maximum error of 0.5%. Specific geometric features derived from the expansion in-
tersection histogram, such as the distance between a selected target and each differ-
ent ideal volume included in the virtual phantom, well matched the corresponding
theoretical expected values. The expansion intersection histogram was evaluated al-
so for the anatomical structures of a real patient. Data show this method as a tool to
to the target, summarized in characteristics of distance, shape and orientation. The
expansion intersection histogram method integrates and extends other preexisting
modalities for evaluating the geometrical relationships among radiotherapy volumes
and could be used to improve planning optimization.
these requirements, the complexity of radiotherapy techniques has steadily increased
under a strong technological impulse, especially in recent decades. A full historical
overview can be found elsewhere1. Computer and medical imaging has provided new
approaches to improve the balance of coverage of target versus normal tissues, with
computer-aided optimization and control of planning, delivery and verification. Tradi-
tional three-dimensional (3D) conformal radiation therapy refined to intensity-modu-
is used to generate customized non-uniform fluence of photons using a medical Linac
nique, other nonstandard approaches are in use today, such as tomotherapy and robot-
ic Linacs (CyberKnife). Depending on the different tumor
sites and clinical goals, these advances in turn required
improved real-time verification imaging, initially based
on electronic portal imaging devices and now on volu-
metric imaging, leading to the rapidly increasing avail-
ability of image-guided radiotherapy techniques2-6.
As a fundamental part of the complex process of real-
izing a radiotherapy treatment, planning is often a de-
manding task that sometimes requires several hours for
optimization. The planner work load depends on the
employed technique and dose constraints but, at the
same time, on the spatial distribution of the designed
anatomical structures, with major care needed when
critical organs are closer to the target volume.
How can the particular disposition of the structures of
interest in a patient be rated? A complete answer to this
basic question has not yet been provided, but it would
allow a quantitative assessment of the influence of
structure geometries on treatment plan results. A desir-
able consequence of such an evaluation would be a bet-
ter control for plan optimization and a standardization
of the planning procedures and results.
This paper presents a new computational approach
based on what we call an expansion intersection his-
togram (EIH), a function defined as the intersection be-
tween an organ at risk (OAR) and the target volume,
while the target is expanded in 3D through a scanning
procedure. This function is able to represent quantita-
tively the geometrical features of OARs, summarized in
characteristics of distance, shape and orientation of
such organs with respect to the target. The EIH compu-
tational approach is presented, and the correctness of
our calculations are verified under known conditions.
Data from a real patient treated for head and neck can-
cer are also shown to discuss the relation between geo-
metric features and EIH behavior in a clinical context.
Materials and methods
Definition of EIH
the fraction of the OAR volume that intersects the target
expanded isotropically, plotted at all possible different ex-
pansion values. To illustrate this concept, let us consider
the ideal example of a 50-mm-diameter spherical target
facing a spherical organ of the same size (Figure 1). By
volume in common with the expanded target can be plot-
ted in function of the corresponding expansion value.The
full graph is obtained when the organ is completely in-
values covering the whole range between 0 and 1. A 25-
mm expansion of the targetis alsoshown in Figure 1,with
a resulting intersection of about 40% of the OAR volume.
In general, the definition of the EIH applies to organ
and tumor volumes of an arbitrary shape, potentially
disposed at different mutual distances. Dealing with
volumes designed for radiotherapy planning, the target
and organ may also overlap. In this case, it is convenient
to let the expansion procedure work also in a reverse
fashion by means of target contractions, corresponding
to negative expansion values. This solution makes it
possible to extend the EIH for overlapped objects with
continuity down to the null intersection value, i.e., the
point representing the tangency condition.
The ideal example in Figure 1 represents a basic setup
in which the structures are in contact. The correspon-
ding EIH is shown in Figure 2 as a solid line.The two ad-
ditional plots in the Figure show how this reference EIH
is modified by shifting the organ center 10 mm towards
the target center (negative shift) and 10 mm apart (pos-
itive shift).The effect of overlapped volumes on the EIH
is shown in Figure 2 for the organ shifted 10 mm to-
wards the target.
Separation,saturation and expansion range
Allowing also negative expansions of the target vol-
ume, the EIH is virtually defined on the entire x axis.
However, a useful restricted definition range for expan-
sions, defined as the “expansion range”, can be identi-
fied without loss of information. The lower boundary of
this range is the target expansion value needed to
“touch” the healthy structure, so that expansion and or-
gan are tangent. At lower expansion values, the EIH is
always zero.We define this quantity as the “separation”,
since it represents a useful way to measure the distance
of the organ from the target. By this definition it follows
that, in the case of superimposed organ and target, sep-
aration is a negative amount. The meaning of the dis-
504 S TOMATIS, M CARRARA, E MASSAFRA ET AL
-50 -40 -30 -20 -10
30 40 50
60 70 80
Figure 1 - Idealized spherical “target” and “organ”. The two 50 mm
diameter spheres are in contact. A 25-mm target expansion (trans-
parent sphere around target) intersects the organ for a fraction of
40% of its volume.
tance between two generic objects is usually represent-
ed by the shortest of the distances between any two of
their respective points7.Althoughnegative distances are
not usually defined, introduction of the separation is a
way to generalize the concept of distance also for over-
lapped objects because it includes the traditional defi-
nition in the other cases. In a similar manner, the upper
boundary corresponds to the smallest target expansion
totally including the organ. Since the EIH is always 1
above this limit, we refer to the upper boundary as the
“saturation” value. The “expansion range” included be-
tween the two above-described limits defines the organ
dimension from the target point of view. Figure 3 shows
the definitions and terms given above.
The volume fraction of an organ in common with its
target (overlap) is represented by the EIH at zero expan-
sion. In the example of Figure 2, the separation is equal
to the organ shift. Overlap for the organ shifted 10 mm
towards the target is 5.6%, and the expansion range is 50
mm in all cases.
Software implementation and testing
Software was developed to analyze anatomical struc-
ture data from a commercial treatment planning system
(TPS) (Xio, CMS Inc, St Louis, MO, USA) and to obtain
For this purpose, a data file containing all information
about the contoured anatomical structures of the TPS
was exported from Xio into DICOM format8. This DI-
COM structure set file was elaborated with a separate
computer using routines and functions written by us in
the MATLAB©software developing environment (The
Mathworks, Natick, MA, USA).
To show examples and to test the EIH behavior in
different known geometrical situations, structures of
various shapes, such as spheres and cylinders, were
created in a virtual phantom using Xio geometrical
design tools. To test the accuracy of our software com-
putations, contours of the two spherical organ and
target shown in the example of Figure 1 were included
in the virtual phantom to allow a comparison between
the measured organ EIH and reference data derived
from an analytical formula. The analytical expression
for the volume intersection between two spheres is
presented in its general form in Appendix I. Other ob-
jects included in the software phantom are shown in
Figure 4. Taking object number 1 in the Figure as the
target, theoretical separation and saturation values
can easily be determined by means of geometrical
considerations on the distances occurring between
each virtual organ and the selected ideal target. The
ideal values are reported in Figure 4B and 4D for each
involved object. The data were used as a reference to
test the results obtained from the EIH software com-
putations. The slice thickness for the software phan-
tom was set at 1 mm.
An example of EIH evaluation was made also on
anatomical structure data from a real patient, which were
outlined and sent to the XioTPS from a Focal contouring
workstation (CMS Inc). The DICOM structure files of the
virtual phantom and the real patient were exported from
Xio for data processing on a separate computer.
Results of the comparison between the reference ana-
lytical calculation and the test measurement performed
GEOMETRIC FEATURES OF RADIOTHERAPYVOLUMES505
Figure 2 - EIH for the two example spheres illustrated in Figure 1 (sol-
id line) and for a ±10 mm shift of the organ center with respect to
the target center. Dotted line, positive shift (away from target);
dashed line, negative shift (towards target). Insert, cross section of
the geometrical setup with organ shift. Diameter of each involved
volume is 50 mm.
10 mm shift away from target
10 mm shift towards target
-10 -505 10 152025 30 354045 505560
Figure 3 - Separation, saturation and expansion range. Inner ring,
target; middle ring, target expansion corresponding to the separa-
tion point; outer ring, target expansion corresponding to the satu-
(EIH lower bound)
(EIH upper bound)
with our software for the two-sphere geometry reported
between test and reference data was 0.5%. Considering
in Figure 4, with object #1 selected as target, the EIH was
generated by the software for each of the other volumes
(organ). EIH measured for the different virtual organs are
shown in Figure 6.Results for the numerical computation
of separation and saturation are also reported in Figure 6.
To show and discuss an example based on real con-
tour data in a typical clinical situation, a case with a
cancer in the head and neck anatomical region was
selected. Although potentially all the contoured vol-
umes could be taken into account, we focused on the
high-dose target for which the planned dose was 70
Gy and on the spinal cord, brainstem and right
parotid gland, which were selected as OAR. Geometry
representation of the volumes and the corresponding
506 S TOMATIS, M CARRARA, E MASSAFRA ET AL
Figure 4 - Design of structures of known geometries at different locations in the 3D space. A) 3D view. B) Side view. C) Top view (objects out-
line). Considering object #1 as the target, arrows in B) indicate separation or saturation for each other object. These theoretical values are
evaluated geometrically and are summarized in D). The size of the squares in the grid is 5 mm.
obj# separation saturation
225.00 mm 75.00 mm
3 10.00 mm 89.13 mm
45.00 mm45.00 mm
Figure 5 - Comparison between theoretical evaluation and EIH cal-
culation based on geometries on a virtual phantom. The setup is the
same as in Figure 1. Analytical reference data are derived from for-
mulas in Appendix I applied for this geometry.
0 10203040 50
Figure 6 - Software generated EIH for the geometrical objects #2, #3
and #4 depicted in Figure 4. The graphs of the selected volumes dif-
fer from one another depending on dimension and position relative
to the target (object #1 in Figure 4). Insert, numerical computations
of separation and saturation for the selected organs.
obj# separation saturation
010 203040 50607080 90
measured EIH are reported in Figure 7. The obtained
values for separation, saturation and overlap are also
shown in Figure 7.
We propose a novel method for quantification of the
arrangement of anatomical structures designed by the
radiotherapist for radiotherapy planning. Software algo-
rithms to obtain automatically EIH involve intersection
and expansion of volumes. 3D-margining algorithms9,10
and Boolean functions to manage radiotherapy volumes
are a standard in current TPS with different software im-
plementations11. These features should be submitted to
quality control12-14. Although the aim of the paper is not
perform logical operations on volumes, results in Figure
5 show good agreement between test and reference val-
ues, indicating the acceptable quality of our computa-
tions. The computed separations and saturations shown
also in good agreement with the corresponding theoreti-
cal expected values reported in Figure 4D, and within the
1-mm resolution limit of our 3D calculation grid.
Depending on the mutual target-organ arrangement in
trends expressed within the expansion range. Looking at
Figure 6, it is interesting to observe the peculiar trend of
get expansion is effective only along the direction of the z
axis. As regards object #3, the target expansion acts later-
til a final constant value, the slope change occurring near
the 30 mm expansion required by the target to reach the
opposite side of the object. In approaching a symmetrical
EIH itself tends to be more regular and its behavior more
similar to a sort of sigmoid, as is the case of object #2. In
and organ, the EIH will depend on volume dimensions
(radii) and on center-to-center distance according to the
theory (see Appendix I). In general, the slope of the curve
for an organ small with respect to the target will be steep-
er than that of a large organ.
In Figure 7, target, brainstem, spinal cord and right
parotid gland are represented by data of a real patient
treated for a head and neck cancer. The brainstem and
#3 in Figure 6 because the organ disposition is similar.
Nevertheless, according to the definition of separation,
EIH analysis allows to determine that volume for organ
#3 is 5.2 mm closer to its target than to the spinal cord,
whose separation has been evaluated to be 15.1 mm.
Data from the present study indicate that variations
among different EIH diagrams are related to the different
entation, features that, to a different extent, affect the
GEOMETRIC FEATURES OF RADIOTHERAPYVOLUMES 507
right parotid -9.4 mm31.9 mm 9.2%
spinal cord 15.1 mm160.0 mm–
brainstem24.2 mm77.8 mm–
Figure 7 - Representation of a real case of cancer in the head and neck region. A) 3D view for the target, spinal cord, brainstem and right parotid
gland. B) Corresponding EIH for the selected OAR. Insert in B), evaluation of separation, saturation and overlap for the selected structures.
dosimetric output. Although the method is purely geo-
metrical, it is also true that an unfavorable geometry set-
up can cause difficulty in attaining the dose objectives in
a radiotherapy plan. Of course, the proximity of some
sensitive organ to the therapy target could prevent a sat-
isfactory target coverage or even sparing of the organ it-
self. A typical example of this situation may be the treat-
ment of a head and neck cancer, for the presence of a va-
riety of important critical organs in this body region.
Among these, spinal cord and brainstem, optical path-
ways, and/or parotid glands may be very close to a pri-
ther typical example, prostate cancer treatment with ex-
ing damage mainly to the rectum and bladder while cov-
ering the primary target with doses generally up to 78 Gy.
See for example the RTOG list of protocols15including
dose prescriptions and constraints for different radiation
therapy techniques and tumor sites.
An example of the assessment of a correlation be-
tween the position of the parotid gland and the dose
achievable in an IMRT treatment plan can be found in
the literature16. In this case, the organ position is quan-
tified as the salivary gland overlap with the primary
high-dose planning target volume (PTV). It is notewor-
thy in our example that the found (negative) separation
value (-9.4 mm) could have been different for a different
gland shape or orientation even for the same overlap. In
fact, the EIH adds to the simple information of the or-
gan overlapping with the target information about the
way in which such superimposition takes place.
Recently, other investigators were able to demon-
strate a significant relationship between geometry of
volumes and dosimetric aspects. Dose distribution
goals in different IMRT treatment contexts were related
to geometrical features of the involved anatomical
ical organs were the main determinants for supporting
the authors conclusions, the geometry quantification
was based only on the overlap between target and OAR,
which was evaluated manually using TPS functions.
Due to the lack of a geometry descriptor holding for all
volume arrangements and able to take the distance
among structures into account, it was not possible by
these methods to draw any conclusion when OAR were
not superimposed to the target.
In the present work, we propose a general data set to
objectively describe the geometrical features of virtual-
ly all OAR designed for a treatment plan with respect to
each target for any tumor site. Some features evaluated
from the EIH, such as separation or the EIH value at ze-
ro expansion (overlap), can readily be correlated to
EIH data has still to be investigated. For serial organs,
the most significant part of the EIH is likely the one
close to the organ separation, because complete dam-
age of such structures may arise even when small organ
portions are involved with doses above the threshold
value (for example, 45 Gy for the spinal cord or 54-55 Gy
for the brainstem and optical pathways). In contrast, for
parallel organs, a more detailed description of the organ
geometry may be required and the EIH calculation in a
wider range could be of use, especially for organs close
to the target. Finally, at least for those radiotherapy
techniques able to conform the dose all around the tu-
mor, such as 3D conformal radiation therapy or espe-
cially IMRT, for several critical organs complete EIH in-
formation is not required, and the involved intersection
calculations should be stopped at a fixed shorter upper
boundary even if the organ has not reached its satura-
tion.This upper limit can be set at 3 cm for most practi-
In order to add a useful support to our theory, we ana-
lyzed preliminary correlation results obtained with a se-
ries of 81 patients treated for head and neck cancer at
our institution. For this purpose, besides the separation
and overlap parameters, another feature was derived
from the EIH diagram, namely: “trend”. This quantity is
defined as the first derivative of the EIH 5 mm beyond
tersection between the target expanded 5 mm inside the
organ and the organ itself and is an evaluation of the or-
gan area facing the target. All 81 patients were treated
with an IMRT technique up to a dose of 70 Gy in the pri-
mary tumor site (HD-PTV). A correlation analysis was
performed between the extracted parameters and the
percentage of the HD-PTV volume covered by at least
the organ. Due to the generally non-normal distribution
of our parameters, correlation coefficients were evaluat-
ed according to a nonparametric method (Spearman
rank correlation coefficient). All separation parameters
for the spinal cord, brainstem and optical pathways
showed highly significant correlations (P<<0.01) with
V95%. The correlation coefficient, r, ranged from 0.38 to
0.46. Overlap mostly occurred for parotid glands only,
but it did not show any significant association with tar-
get coverage. Salivary glands separation was significant-
ly correlated with V95% for the contralateral parotid
alone (r = 0.28, P = 0.01), whereas separation (r = -0.31),
overlap (r = 0.34) and trend (r = 0.31) for the homolateral
gland were significantly associated to its mean dose (P
<0.01). Finally, trend for the brainstem was significantly
correlated (r = -0.25, P = 0.03) withV95%. Although high-
ly significant, our data showed a “medium” correlation,
with r values not very close to 1. This is not surprising,
since the geometric arrangement of organs is a very im-
portant component determining the dosimetric output,
though not the only one. Other factors, such as planning
time, patient conditions, clinical judgement and degree
of standardization of treatment/planning procedures,
may play an important role.
Although these data are encouraging, a representative
population of patients should be analyzed to answer all
508 S TOMATIS, M CARRARA, E MASSAFRA ET AL
the questions concerning full use of the EIH, and the re-
lationship between dose and EIH data should be deter-
mined taking the dose output from the TPS as the de-
pendent variable in a multivariate statistical test.
We demonstrated the EIH method to be a valid tool to
quantify the reciprocal positioning of critical organs
of distance, shape and orientation. Two important
points of the EIH, i.e., the value at zero expansion (over-
lap) and the separation of an organ from the target, are
to be correlated to the patient dose and can be easily ex-
tracted from EIH data.
With the EIH a function is created that includes and ex-
tends all other pre-existing procedures for the evaluation
This new method based on a scanning of target expan-
lowing the automated extraction of the “separation” fea-
ture, which has been shown to be a natural extension to
negative values of the usual concept of distance.
Work is in progress to set a statistical model to relate
try as provided by a TPS.
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General analytical formula derived to evaluate the
volume intersection for two spheres:
let R and r be the two spheres radii and d the center-to-
center distance. The volume intersection is a function
V(R, r, d) analytically expressed as follows:
GEOMETRIC FEATURES OF RADIOTHERAPYVOLUMES509