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

 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

, the dilation of

A by B, is deﬁned as

A⊕ B = {x|(B)

∩ A 6=

0}, (1)

where (B)

denotes the translation of B by x =

, x

), which is deﬁned as:

(B)

= {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)

⊆ 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:

(n) = {(x, y) ∈ Z

: |x| + |y| ≤ n}, (4)

(n) = {(x, y) ∈ Z

: |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:

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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

update: foreach a ∈ A

D(a) = min{D(a), ED

(o, a)},

(8)

where A

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

. Subsequently, the radiation doses o

(∈ O, with O denoting the complete radiation ther-

apy) can be placed within b

. 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

(i.e., the malignant tumor) and b

(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.

REFERENCES

Borgefors, G., Nystr¨om, I., and Sanniti di Baja, G. (2003).

Discrete geometry for computer imagery. Discrete Ap-

plied Mathematics, 125(1):[special issue].

Bortfeld, T. (2006). IMRT: A review and preview. Physics

in Medicine and Biology, 51(13):R363–R379.

Brianzoni, E., Rossi, G., and Proietti, A. (2008). Gross Tu-

mor Volume and Clinical Target Volume: Anatomical

Computed Tomography and Functional FDG-PET,

volume 2, chapter 13, pages 225–234. Burlington,

MA, USA: Elsevier Academic Press.

Censor, Y., Galvin, J. M., Xiao, Y., and Langer, M.

(2008). Linear and nonlinear models and algorithms

in intensity-modulated radiation therapy (IMRT). Lin-

ear Algebra and its Applications, 428(5–6):1203–

1206.

S¸. Iˇgdem, Alc¸o, G., Ercan, T.,

Unalan, B., Kara, B., Geceer,

G., Akman, C., Zengin, F. O., Atilla, S., and Okkan,

S. (2010). The application of Positron Emission To-

mography/Computed Tomography in radiation treat-

ment planning: Effect on gross target volume deﬁni-

tion and treatment management. Clinical Oncology,

22(3):173–178.

Cuisenaire, O. and Macq, B. (1999). Fast Euclidean trans-

formation by propagation using multiple neighbor-

hoods. Computer Vision and Image Understanding,

76(2):163–172.

Fabbri, R., da F. Costa, L., Torelli, J. C., and Bruno, O. M.

(2008). 2D Euclidean distance transform algorithms:

A comparative survey. ACM Computing Surveys,

40(1):Article 2.

Lu, Y., Jiang, T., and Zang, Y. (2003). Region growing

method for the analysis of functional MRI data. Neu-

roImage, 20(1):455–465.

Mazonakis, M., Damilakis, J., Varveris, H., Prassopoulos,

P., and Gourtsoyiannis, N. (2001). Image segmenta-

tion in treatment planning for prostate cancer using

the region growing technique. British Journal of Ra-

diology, 74(879):243–249.

Razmjooei, S. and Dudek, P. (2010). Approximating Eu-

clidean distance transform with simple operations in

cellular processor arrays. In IEEE Proceedings of the

12th International Workshop on Cellular Nanoscale

Networks and their Applications (CNNA), pages 181–

185, Berkely, CA, USA. IEEE.

Rosenfeld, A. and Pfaltz, J. L. (1966). Sequential oper-

ations in digital picture processing. Journal of the

ACM, 13(4):471–494.

Salvi, J., Matabosch, C., Foﬁ, D., and Forest, J. (2007).

A review of recent range image registration methods

with accuracy evaluation. Image and Vision Comput-

ing, 25(5):578–596.

Schouten, T. E., Kuppens, H. C., and van den Broek, E. L.

(2006). Three dimensional fast exact Euclidean dis-

tance (3D-FEED) maps. Proceedings of SPIE (Vision

Geometry XIV), 6066:60660F.

Schouten, T. E. and van den Broek, E. L. (2004). Fast Ex-

act Euclidean Distance (FEED) Transformation. In

Kittler, J., Petrou, M., and Nixon, M., editors, Pro-

ceedings of the 17th IEEE International Conference

on Pattern Recognition (ICPR 2004), volume 3, pages

594–597, Cambridge, United Kingdom.

Schouten, T. E. and van den Broek, E. L. (2010). Incre-

mental Distance Transform (IDT). In Erc¸il, A., C¸etin,

M., Boyer, K., and Lee, S.-W., editors, Proceedings

of the 20th IEEE International Conference on Pattern

Recognition (ICPR), pages 237–240, Istanbul, Turkey.

Shih, F. Y. and Wu, Y.-T. (2004). Fast Euclidean distance

transformation in two scans using a 3 × 3 neighbor-

hood. Computer Vision and Image Understanding,

93(2):195–205.

Zaidi, H., Vees, H., and Wissmeyer, M. (2009). Molecular

PET/CT imaging-guided radiation therapy treatment

planning. Academic Radiology, 16(9):1108–1133.

MODELING INTERNAL RADIATION THERAPY

233