MODELING INTERNAL RADIATION THERAPY
Egon L. van den Broek
Human-Centered Computing Consultancy, Vienna, Austria
Human-Media Interaction (HMI), Faculty of EEMCS, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands
Karakter University Center, Radboud University Medical Center Nijmegen
P.O. Box 9101, 6500 HB Nijmegen, The Netherlands
http://www.human-centeredcomputing.com/
Theo E. Schouten
Institute for Computing and Information Sciences, Radboud University Nijmegen
P.O. Box 9104, 6500 HE Nijmegen, The Netherlands
Keywords:
Radiation therapy, Modeling, Distance transform, FEED, Exact.
Abstract:
A new technique is described to model (internal) radiation therapy. It is founded on morphological processing,
in particular distance transforms. Its formal basis is presented as well as its implementation via the Fast Exact
Euclidean Distance (FEED) transform. Its use for all variations of internal radiation therapy is described. In a
benchmark trial, FEED proved to be truly exact as well as faster than a comparable technique. These features
can be of crucial importance in radiation therapy as the balance between maximization of treatment effect and
doses that cause unwanted damage to healthy tissue is fragile. This balance can be secured using the modeling
technique presented here.
1 INTRODUCTION
We propose a new technique to model the treatment
of malignant tumors through radiation therapy. This
technique is founded on principles from morpholog-
ical processing and computational geometry. It ex-
ploits the rather recent advances in imaging tech-
niques that enable accurate modeling of malignant tu-
mors (S¸. Iˇgdem et al., 2010; Zaidi et al., 2009). This
technique facilitates both fast and exact modeling of
radiation therapy by providing an accurate model of
the malignant tumor.
As cancer is life threatening and clinicians are
usually pressed for time, both speed and accuracy are
of the utmost importance. Moreover, the effectiveness
of the treatment heavily relies on the accuracy with
which the radiation therapy can be employed. The
fact that radiation therapy is usually given through
fractions of radiation, instead of one dose, makes this
even more challenging.
As this work is highly interdisciplinary, we will
first provide a brief introduction on radiation ther-
apy in Section 2 followed by a brief introduction
on morphological processing in Section 3. This in-
cludes a small benchmark trial in which the proposed
technique is compared with other related techniques.
Next, in Section 4, the previous two sections will be
linked and the proposed technique will be introduced.
Lastly, in Section 5 we will present the conclusions
and closing remarks.
2 RADIATION THERAPY
Radiation therapy (a.k.a. radiotherapy, x-ray therapy,
and irradiation) is the application of ionizing radiation
to eliminate cancer cells and shrink tumor tissue. The
ionizing radiation damages and often destroys cells in
the area being treated, as it damages the cells’ genetic
material. Approximately half of all cancer patients
receive radiation therapy in the absence or presence
of other treatments (e.g., chemotherapy or surgery).
Radiation therapy varies both in i) the types of
radiation and ii) the method of its delivery. Conse-
quently, radiation therapies can be executed with var-
ious characteristics. For example, a trade off can be
made between the depth of penetration of and the con-
trol over the radiation. Not only the method of radia-
tion therapy varies but also its goal. With the aim to
228
L. van den Broek E. and E. Schouten T..
MODELING INTERNAL RADIATION THERAPY.
DOI: 10.5220/0003172202280233
In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms (BIOINFORMATICS-2011), pages 228-233
ISBN: 978-989-8425-36-2
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
cure the patient, the destruction of an entire tumor is
the goal. With palliative radiation therapy, the aim is
to provide relief for the patient; in this case the goal is
usually to let the tumor shrink and spare healthy tissue
as much as possible.
Radiation therapy is used to treat solid tumors,
of almost every type (including leukemia and lym-
phoma). The radiation dose chosen depends on a
number of factors including the type of cancer and
the location of the tumor (i.e., whether or not it is near
vulnerable tissue).
2.1 Standards
Three types of radiation therapy can be distinguished:
external radiation therapy: from outside the body,
internal radiation therapy (i.e., brachytherapy):
placed inside the body, and
systemic radiation therapy: throughout the body.
The radiation dose absorbed by the tissue is de-
noted in the unit cGy or Gy (i.e., respectively 1 and
100 rads, which was the previously used unit).
To maximize the destruction of cancer tissue and
minimize the damage to healthy tissue, the total dose
of radiation is usually given in a sequence of smaller
doses (a.k.a. fractions), given within a certain time
window.
In 1993, to facilitate the generation of a common
language and models for the procedures at all radio-
therapy centers the International Commission on Ra-
diation Units and Measurements (ICRU) defined the
goals for radiation therapy (Brianzoni et al., 2008). In
a nutshell, these directives state that the type of radi-
ation that needs to be given depends, amongst other
things, on a) the type of cancer, b) the location, in-
cluding the depth of the tumor in the body, c) the pa-
tient’s general health and medical history, and d) other
types of treatments possible. In practice, the ICRU
emphasized that this implies that two main factors are
central in making the choice of therapy (Brianzoni
et al., 2008): the volume definition and the quantity of
the radiation dose. To enable the best possible treat-
ment, the oncologist employs PET imaging to obtain
the best possible image (S¸. Iˇgdem et al., 2010).
2.2 The Definition of Volume
The definition of volume has multiple layers (Brian-
zoni et al., 2008), each having their own criteria; see
also Figure 1:
Gross Tumor Volume (GTV): the evident tumor.
Irradiated Volume
Treated Volume
PTV
CTV
GTV
Figure 1: The volumes distinguished in planning radiation
therapy, as defined by the International Commission on Ra-
diation Units and Measurements (Brianzoni et al., 2008).
GTV, CTV, and PTV denote respectively: gross tumor vol-
ume, clinical target volume, and planning target volume.
Clinical Target Volume (CTV): the area surround-
ing the tumor that could have subclinical suspect
disease. As such, the CTV is a clinical concept.
Planning Target Volume (PTV): GTV, CTV, and
a margin that takes into account a possible vari-
ation in shape, size, and position relative to the
treatment beams and organ motion. The PTV, as
a geometrical concept, which determines the pre-
scribed dose in the CTV.
Ideally, the PTV is the same as the Treated Volume
(TV) (see also Figure 1); however, in practice this is
often not the case. In any case, the Irradiated Volume
(IV) has to be taken into account. The IV receives ra-
diation and its impact on normal tissue should be con-
sidered as well in radiation therapy treatments. Self
evidently, the match between PTV and TV is of the
utmost importance.
In general, it is assumed that the dose of radiation
is near to homogeneous inside the PTV. Nevertheless,
it is important that radiation therapy is always eval-
uated. In particular, the level of homogeneity reg-
istered near the reference point doses and both the
minimum and maximum value inside the PTV have
to be evaluated. Several imaging techniques are em-
ployed for evaluation purpose: computed tomogra-
phy (CT), ultrasound, or magnetic resonance imaging
(MRI). For optimal results, these are often combined
with positron emission tomography (PET) (S¸. Iˇgdem
et al., 2010). The latter imaging technique is comple-
mentary to the former three.
In the next section, we will switch from the clin-
ical part of this study to its technical part. We start
by defining the basics on morphological processing.
Subsequently, we describe distance transformations,
the one applied in particular, and a benchmark trial.
MODELING INTERNAL RADIATION THERAPY
229
(a) (b) (c) (d) (e)
Figure 2: Five representations of the same test image, which illustrates the width of distance transforms (DT) that can be
applied: (a) the original, (b) after dilation, (c) DT that provides the extremes, (d) a discrete DT, and (e) a gradual DT.
3 MORPHOLOGICAL
PROCESSING
The image elements needed to represent malignant tu-
mor tissue can be extracted using morphological im-
age processing. Morphological operators can be con-
veniently described using set theoretic notation. Their
implementation is less straightforward as is illustrated
by the plethora of algorithms introduced (Borgefors
et al., 2003; Fabbri et al., 2008; Razmjooei and
Dudek, 2010).
Dilation (a.k.a. dilatation) and erosion are funda-
mental morphological image processing operations.
Many of the morphological algorithms applied are
founded on these two primitive operations.
Given two sets A and B in Z
2
, the dilation of
A by B, is defined as
A B = {x|(B)
x
A 6=
/
0}, (1)
where (B)
x
denotes the translation of B by x =
(x
1
, x
2
), which is defined as:
(B)
x
= {c | c = b + x, b B} (2)
Hence, A B expands A if the origin is contained in
B, as is often the case.
The erosion of A by B, denoted A B, is the set
of all x such that B translated by x is completely con-
tained in A, which is defined as
A B = {x|(B)
x
A} (3)
Hence, A B decreases A.
Founded on these two morphological operations,
the 4-n and the 8-n dilation algorithms were devel-
oped (Rosenfeld and Pfaltz, 1966) for region grow-
ing purposes. These region growing algorithms are
founded on the city-block distance and the chessboard
distance measure. For 4-n and 8-n growth for an iso-
lated pixel at the origin, the set of pixels contained in
the dilated shape are respectively defined as:
C
4
(n) = {(x, y) Z
2
: |x| + |y| n}, (4)
C
8
(n) = {(x, y) Z
2
: |x| n, |y| n}, (5)
where n is the number of iterations.
To obtain a better approximationfor the Euclidean
distance (ED), Rosenfeld and Pfaltz recommended
the alternate use of the city-block and chessboard mo-
tions as early as 1966. This defines the octagonal dis-
tance, which provides a better approximation of the
ED than either of the distances separately.
3.1 Distance Transformation (DT)
Region growing algorithms can be applied to obtain
a distance transformation (DT). A DT (Rosenfeld and
Pfaltz, 1966) creates an image in which the value of
each pixel is its distance to the set of object pixels O
in the original image:
D(p) = min{dist(p, q), q O} (6)
The Euclidean DT (EDT) has been extensively
used in image processing and pattern recognition, ei-
ther by itself or as an important intermediate or an-
cillary method in applications. Examples of medi-
cal imaging methods that often involve EDT are: the
analysis of functional MRI data (Lu et al., 2003), im-
age registration (Salvi et al., 2007), and image seg-
mentation (Mazonakis et al., 2001).
Several methods for the calculation of EDT have
been introduced over the years, both for sequential
and parallel machines (Fabbri et al., 2008; Razmjooei
and Dudek, 2010; Schouten and van den Broek,
2010). However, in most cases this did not in-
volve exact EDT, but only approximations; for ex-
ample, (Cuisenaire and Macq, 1999; Razmjooei and
Dudek, 2010).
Unlike existing approaches such as (Cuisenaire
and Macq, 1999), we implemented EDT starting di-
rectly from Equation 6, or rather its inverse: each ob-
ject pixel o, in the set of object pixels (O) feeds its ED
to all background pixels b:
D(b) = if (b O) then 0 else . (7)
Subsequently, the adapted naive algorithm is:
BIOINFORMATICS 2011 - International Conference on Bioinformatics Models, Methods and Algorithms
230
Table 1: Timing results and the errors for three image sets on the city-block (or Chamfer 1,1) transform (Rosenfeld and Pfaltz,
1966), 2-scan method (EDT-2) (Shih and Wu, 2004), and the Fast Exact Euclidean Distance (FEED) (Schouten and van den
Broek, 2004; Schouten and van den Broek, 2010), which is the only one that truly provides an exact EDT.
Images Algorithms
Timing (in sec.) Errors (in %)
City-block EDT-2 FEED City-block EDT-2 FEED
standard objects 8.75 38.91 17.14 2.39 0.16
rotated objects 8.77 38.86 18.02 4.66 0.21
larger objects 8.64 37.94 19.94 4.14 0.51
average 8.72 38.57 18.37 3.73 0.29
foreach o O
determine: A
o
update: foreach a A
o
do
D(a) = min{D(a), ED
2
(o, a)},
(8)
where A
o
is the area where o should feeds distances
to. This results in an exact but computationally in-
expensive algorithm for EDT, which was baptized:
Fast Exact Euclidean Distance (FEED) transforma-
tion (Schouten and van den Broek, 2004).
3.2 Benchmark
A small benchmark trial was executed in which FEED
was compared with two other algorithms:
2-scan method (EDT-2) (Shih and Wu, 2004),
which should be preferred over (Cuisenaire and
Macq, 1999) fast EDT. This is the fastest EDT al-
gorithm and, as such, the ultimate test for FEED.
The city-block (or Chamfer 1,1) distance (Rosen-
feld and Pfaltz, 1966), which served as a baseline.
Table 1 presents both the timing results and the er-
rors for the three algorithms as obtained through the
benchmark. With a rough estimation of the ED, the
city block distance outperformed the other two algo-
rithms by far with respect to execution times. Surpris-
ingly FEED was > 2× as fast as EDT-2. However,
more important than the algorithms’ execution times
are the errors they made compared to the exact EDT.
The city-block transform resulted for all three im-
age types in an error-level of less than 5%; see Ta-
ble 1. (Shih and Wu, 2004) claimed that their two
scan algorithm (EDT-2) provides exact EDs. How-
ever, although their algorithm was precise with 99%
precision, EDT-2 was not exact; see also Table 1. So,
FEED appeared to be the only algorithm that provided
truly exact ED for all instances. As such, FEED is of
interest to modeling radiation therapy, where speed is
important but exactness is even more important as it
determines the success of the therapy.
4 MODELING
In the previous two sections, the two ingredients of
this paper were introduced. In this section we will
bring both together and show how DTs, in particular
FEED, are of interest to radiation therapy. With this,
we may be introducing a new class of algorithms for
modeling radiation therapy.
Radiation therapy is among the main treatments
for cancer. As stated in Section 2 there are three types
of radiation therapy. We will show that morphological
processing can be of use for internal radiation therapy
as well as for external radiation therapy. However,
we will discuss the former type but will not discuss
details concerning the latter one. Morphological pro-
cessing is of no use for systemic radiation therapy.
So far, the DTs and their resulting distance maps
have been introduced as a basic, generic technique.
This is indeed the case; however, as stated in Sec-
tion 3.1, DTs know many applications (Borgefors
et al., 2003; Fabbri et al., 2008). We pose that radia-
tion therapy could and should become one of them.
Instead of test images (see Figure 2) or abstract
objects (see Table 1), we will take an image of a
malignant tumor as object. Nowadays imaging tech-
niques provide excellent means to localize tumor tis-
sue, as was mentioned in Section 2. So, let us assume
that a malignant tumor T has been successfully iden-
tified on an image. Then, all other space on the image
is denoted as background b; cf. Eqs. 7 and 8.
Let us now denote both the tumor T and the al-
ready defined background b as two types of back-
ground: b
T
b
s
. Subsequently, the radiation doses o
( O, with O denoting the complete radiation ther-
apy) can be placed within b
T
. Elements o transmit
their radiation that can be described via functions that
serve as distance measures. In this way, all elements
of the DT are described in terms of radiation therapy.
Having all elements defined, FEED can be applied
and a distance map can be generated; see also Sec-
tion 3.1. This distance map provides a map of the
MODELING INTERNAL RADIATION THERAPY
231
(a)
(b)
Figure 3: A model of radiation treatment of the central part
of the planning target volume (PTV; see also Section 2.2
and Figure 1): (a) Six radiation doses, indicated by arbi-
trary shapes. (b) A distance map as generated by FEED,
which models the amount of radiation delivered over the
area. Intensity indicates the amount of radiation. The white
line indicates the border of the malignant tumor.
radiation in both b
T
(i.e., the malignant tumor) and b
s
(i.e., the tissue surrounding the malignant tumor); see
also Section 3. The radiation dose each cell receives is
calculated in this way, which can be conveniently pre-
sented graphically. Figure 3a presents an artificially
created volume and six radiation doses placed within
it. The distribution of the radiation is visualized in
Figure 3b, where the intensity denotes the amount of
radiation, in this case as determined according to an
arbitrary function.
Radiation therapy involves more than the binary
distinction malignant tumor and healthy tissue, it em-
ploys volumes, as described in Section 2.2. After the
radiation oncologist has defined the GTV, CTV, PTV,
TV, and IR, the radiation in these distinct volumes can
be easily determined as well. So, for each volume the
quantity of the radiation dose can be easily modeled
in advance, which is one of the two main issues in
radiation therapy; see also Section 2.1.
To maximize the destruction of the malignant tu-
mor and minimize the damage to healthy tissue, the
total dose radiation O is usually given in a sequence
of smaller doses o, given within a certain time win-
dow (Brianzoni et al., 2008). So, a sequence of DTs
has to be conducted over time to model this. In its
most simple form, this process can be modeled by
a linear combination of the distance maps to each
other (Censor et al., 2008).
As denoted in Section 2.1, other treatments may
accompany radiation therapy. One of the possibili-
ties is that multiple radiation therapies are conducted,
each having their owncharacteristics (Brianzoniet al.,
2008). Such a process can be modeled similarly as the
sequence of radiation doses.
When applying multiple radiation therapies, it can
be of interest to know which therapy has its biggest
impact on which parts of the patient. Each therapy
then has its distance map or output matrix. Then, the
radiation therapy that provides the maximum radia-
tion can be placed in a second output matrix. The
maximum radiation dose indicates the amount of cer-
tainty (or weight) that the pixel belongs to the class.
In this way, a matrix is generated with the therapy
labels as elements. This can also be visualized by dif-
ferent color ranges for each therapy. In addition, a
multi-therapy distance map can be generated.
5 DISCUSSION
This paper introduced the application of distance
transformations (DT) for modeling radiation therapy.
It started with brief introductions on radiation ther-
apy, which illustrated the importance of the accuracy
of treatment, and morphological processes (e.g., DT).
Subsequently, we described how DT can be applied
to model radiation therapy. We described how the dif-
ferent volumes as denoted in radiation therapy can be
taken into account, how sequences of radiation doses
can be modeled and even how multiple simultane-
ously conducted radiation therapies can be modeled.
This paper introduced a vivid approach for mod-
eling radiation therapy. However, the technique pro-
posed awaits thorough testing. Two types of tests
can be distinguished: a) the application of the tech-
nique on data gathered from radiation oncologists and
b) a benchmark of the technique proposed with es-
tablished techniques currently employed. Moreover,
this modeling technique did not yet take into account
a range of complicating factors such as the com-
plex functions that describe the transfer of radiation
through several types of tissue. So, it is evident that a
vast amount of work has to be done before the tech-
nique introduced here can establish itself.
This article assumed 2D images of the malignant
tissue. However, 3D radiation therapy has already
been introduced. This is particularly useful for ex-
ternal radiation therapy, where radiation beams go
through the patient’s body. Such 3D images can be
obtained using CT, MRI, PET, or single photon emis-
sion computed tomography (SPECT) (S¸. Iˇgdem et al.,
2010). Although not discussed in this article, FEED
can also be applied on 3D images (Schouten et al.,
BIOINFORMATICS 2011 - International Conference on Bioinformatics Models, Methods and Algorithms
232
2006) and video (Schouten and van den Broek, 2010).
A relatively new type of therapy is Intensity-
Modulated Radiation Therapy (IMRT) (Bortfeld,
2006). IMRT utilizes radiation beams of varying in-
tensities to transmit different doses of radiation to
small areas of tissue simultaneously. This provides
the means to transmit higher doses of radiation within
the malignant tumor and lower doses to healthy tissue
(cf. Figure 1). As discussed in the previous section,
sequences of radiation doses are no problem to model.
This is no different when these doses have different
intensities and is independent of whether or not they
are given in sequence or in parallel.
On the whole, this article introduced a new tech-
nique to model internal radiation therapy. On the one
hand, its use still has to be shown on medical data
sets and it has to be compared with other established
techniques. On the other hand, i) its formal basis and
implementation are sound; ii) its use for all variations
of internal radiation therapy is described as well; and
iii) it has been shown to be exact as well as fast. This
100% accuracy, in particular, can be of crucial impor-
tance for radiation therapy purposes as the balance
between maximization of treatment effect and doses
that cause unwanted damage to healthy tissue is frag-
ile (Censor et al., 2008). The future will learn whether
or not this technique can indeed secure this balance
and, consequently, will redeem its promises.
ACKNOWLEDGEMENTS
We thank the three anonymous reviewers for their
constructive suggestions. Further, we thank Lynn
Packwood for proof reading this article.
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