BABE Ș-BOLYAI UNIVERSITY CLUJ -NAPOCA FACULTY OF ENVIRONMENTAL SCIENCE AND ENGINEERING Dosimetric and quality assurance procedure evaluation of the… [623154]

BABE Ș-BOLYAI UNIVERSITY CLUJ -NAPOCA
FACULTY OF ENVIRONMENTAL SCIENCE AND ENGINEERING

Dosimetric and quality assurance procedure
evaluation of the strut -adjusted SAVI hybrid
device used in accelerated partial breast
irradiation

DOCTORAL THESIS

SCIENTIFIC SUPERVISOR :
Prof. Univ.Dr. Constantin COSMA
Prof. Univ. Dr. Dumitru RISTOIU
DOCTORAL CANDIDATE:
Șerban MORCOVESCU

2017

ACKNOWLEDGMENTS

I enrolled into this doctoral degree program in 2006 strongly encouraged and
supported by the one who eventually had the bravery of taking on the responsibility of
being my supervisor and dissertation chair, Professor Dr. Constantin C OSMA, of blessed
memory. Unfortunately he is no longer with us and unable to partake of this special
moment, of seeing me cross ing the finish line. Time is never too generous. Prof. Dr.
Constantin COSMA has worked with me patiently during those years and helped me
eventually find and fine tune my area of research. He was a great mentor and invaluable
resource of wisdom and promoter of scientific debate and dialogue throughout the
program. Words are unable to express the loss of him, and the significance of his life in
my life. May the Lord grant him the peace and the rest he deserves and so much was
entitled to, after a life of hard work, done with dedication and unfailing passion.
I am therefore that much more grateful to Professor Dr. Dumi tru RISTOIU, for
being generous enough to adopt me, and to accept taking me under his wing as my
supervisior for the final stage of my doctoral program. His advice and leadership was in
fact vital and invaluable, and helped me correct, adjust, improve and finalize a thesis in
much need of trimming and format adjustments.
I owe a lot of gratitude to the special people and excellent professionals I started
working with and for in US A, Dr. Marius and Rodica Alecu from AROS LLC Texas , who
greatly helped me duri ng my first years of practice as a Therapeutical Medical Physicist in
Texas, always encouraging me to learn, study, settle, perfect and achieve my goals .
I am also grateful to Dr. Jeffery M orton , MD, from Texas Oncology Denton, my
practice Radiation Oncologist, and to all my colleagues and research partners , for the
constructive feedback , encouragement and opportunity to work on this c l i n i c a l
r e s e a r c h project , so well blended into my regular clinical schedu le.
L a s t , b u t n o t t h e l e a s t , h u g e t h a n k s t o m e w i f e A n c a a n d m y
e x t e n d e d f a m i l y for their unrelenting support , understanding and love they embraced
me with throughout the program.

Table of Contents
CHAPTER 1 INTRODUCTION ………………………….. ………………………….. ………………….. 5
CHAPTER 2 THEORETICAL ASPECTS ………………………….. ………………………….. …. 11
2.1. Ionizing Radiation. Fundamentals ………………………….. ………………………….. ……….. 11
2.2. Sources and types of ionizing radiation ………………………….. ………………………….. … 12
2.3 Energy transfer, absorption and attenuation ………………………….. ……………………….. 13
2.4. Interactions of photons with matter ………………………….. ………………………….. ………. 16
2.4.1. Photoelectric effect ………………………….. ………………………….. ………………………….. …….. 16
2.4.2. Compton effect ………………………….. ………………………….. ………………………….. ………….. 17
2.4.3 The Pair Production ………………………….. ………………………….. ………………………….. …….. 20
2.4.4 Interactions of charged particles with matter ………………………….. ………………………….. .. 21
2.5. Quantities describing the interaction of ionizing radiation with matter ………………. 22
2.5.1 Kerma ………………………….. ………………………….. ………………………….. ……………………….. 22
2.5.2 Exposure ………………………….. ………………………….. ………………………….. ……………………. 24
2.5.3. Absorbed Dose ………………………….. ………………………….. ………………………….. ………….. 25
2.6. Mea surement of ionizing radiation ………………………….. ………………………….. ………. 26
CHAPTER 3 BRACHYTHERAPY ………………………….. …. Error! Bookmark not defined.
3.1. High Dose Rate Brachytherapy – General Aspects . Error! Bookmark not defined.
3.1.1. Dose calculations in brachytherapy – TG43 formalism . Error! Bookmark not defined.
3.1.2. Novel computational algorithms – ACUR OS BV ……… Error! Bookmark not defined.
3.1.4 High Dose Rate unit description and source calibration . Error! Bookmark not defined.
CHAPTER 4 OVERVIEW OF BREAST CANCER TREATMENT MODALITIES
………………………….. ………………………….. ………………………….. . Error! Bookmark not defined.
4.1. Breast Cancer and anatomy ………………………….. …… Error! Bookmark not defined.
4.2. Treatment modalities ………………………….. ……………. Error! Bookmark not defined.
4.3. Brachytherapy in the treatment of breast cancer. Developments. . Erro r! Bookmark
not defined.
4.3.1 Partial breast irradiation. Brachytherapy devices and techniques. Error! Bookmark not
defined.
CHAPTER 5 DOSIMETRICAL EVALUATION OF A STRUT -ADJUSTED –
VOLUME -IMPLANT SAVI DEVICE USED FOR ACCELERATED PARTIAL
BREAST IRRADIATION ………………………….. ……………….. Error! Bookmark not defined.
5.1 Device description ………………………….. ………………… Error! Bookmark not defined.
5.2 Patient selection criteria ………………………….. ………… Error! Bookmark not defined.
5.3 Equipment ………………………….. ………………………….. . Error! Bookmark not defined.
5.4 Structure Definitions and Nomenclature ………………. Error! Bookmark not defined.
5.5 Treatment planning technique ………………………….. … Error! Bookmark not defined.
5.6 Dose prescription and optimization …………………….. Error! Bookmark not defined.
5.7 Evaluation of dosimetric advantages of the SAVI device compared to balloon -type
APBI devices ………………………….. ………………………….. … Error! B ookmark not defined.

5.7.1. Study Motivation ………………………….. ……………………… Error! Bookmark not defined.
5.7.2. Materials and Methods ………………………….. ……………… Error! Bookmark not defined.
5.7.3. Results and Discussions ………………………….. …………….. Error! Bookmark not defined.
CHAPTER 6 COMPREHENSIVE DOSIMETRIC ANALYSIS OF THE SAVI
DEVICE ………………………….. ………………………….. …………….. Error! Bookmark not defined.
6.1. Study Motivation ………………………….. …………………. Error! Bookmark not defined.
6.2. M aterials and Methods ………………………….. …………. Error! Bookmark not defined.
6.3. Results and Discussions. Original contributions. ….. Error! Bookmark not defined.
6.3.1 Multi -institutional study on all SAVI type devices …….. Error! Bookmark not defined.
6.3.2 Single institution study results, on SAVI6 -1mini device – TG43 . Error! Bookmark not
defined.
6.3.3 Single institution study results, on SAVImini device – ACUROS Error! Bookmark not
defined.
CHAPTER 7 COMPREHE NSIVE EVALUATION OF A STRUT -ADJUSTED –
VOLUME -IMPLANT SAVI DEVICE QUALITY ASSURANCE PROGRAM .. Error!
Bookmark not defined.
7.1 Study motivation ………………………….. ………………….. Error! Bookmark not defined.
7.2 Pre -treatment Quality Assurance ………………………… Error! Bookmark not defined.
7.2.1. Imaging and documentation for treatment planning …… Error! Bookmark not defined.
7.2.2 Treatment Time Nomogram for Strut -Based Accelerated Partial Breast Applicators.
Original Contributions. ………………………….. ………………………. Error! Bookmark not defined.
7.3 During and post treatment Quality Assuranc e – Interfractional Variance. Original
Contributions. ………………………….. ………………………….. .. Error! Bookmark not defined.
7.3.1 Materials and Methods ………………………….. ………………. Error! Bookmark not defined.
7.3.2 Results and Discussion ………………………….. ………………. Error! Book mark not defined.
7.4 Overall Results and Discussion ………………………….. . Error! Bookmark not defined.
CHAPTER 8 CLINICAL RESULTS ………………………….. .. Error! Bookmark not defined.
CONCLUSIONS ………………………….. ………………………….. … Error! Bookmark not defined.
BIBLIOGRAPHY ………………………….. ………………………….. . Error! Bookmark not defined.
List of scientific papers presented at National and International Congresses and
Scientific Meetings ………………………….. ………………………….. Error! Bookmark not defined.

List of Figures………………………………………………………………………..
List of Tables…………………………………………………………………………
ACKNOWLEDGEMENTS………………………………………………………….
REFERENCES……………………………………………………………………….
LIST OF PUBLICATIONS………………………………………………………………

LIST OF PRESENTATIONS………………………………………………………..

6
CHAPTER 1 INTRODUCTION

Ever since the discovery of X -rays and of radioactivity, slightly more than a
century ago, the study of the nature and of the mechanisms of interaction of charged
particles became one of the most fertile research fields in the modern history of applied
science. This is mainly due to the fact that, like in Roentgen’s personal case, there was a
very strong connection an d an immediate application of these newly discovered physical
phenomena to the field of medicine. The fact that x -ray diagnostic radiography was
adopted widely in both Western Europe and America within just one year after Roentgen’s
discovery speaks very c learly about how prominently the new technology impacted the
field of medicine and how quickly it was adopted and adapted to new practical
applications.
Radiological physics and radiological medicine are the two closely related
scientific fields that were born shortly after, the former dealing with the science of
ionizing radiation and the way it interacts with matter, and the second dealing with how
the findings of the first are integrated and ap plied in the field of medicine.
Cancer is considered nowada ys as being one of the most aggressive large group s of
diseases that can affect the normal functionality of any part or organ the human body, due
to its ability to grow and spread uncontrolled. When cancer cells develop and are able to
involve nearby organ s, metastasis occur, with cancer cells able to migrate in other parts of
the body, away from the original tumor site. External (exposure to alcohol , tobacco,
chemicals) or internal (genetic background, metabolical) factors can influence the
evolution of ca ncer, but there are various different main methods currently available for
the treatment of cancer: systemic chemotherapy, surgery, radiotherapy, hormone therapy,
and targeted therapy. For the purpose of our research project, this thesis focuses on the
aplication of radiation therapy in the treatment of cancer, more specifically, of breast
cancer.
Breast cancer is among the most common cancer in women in the world , and the
most common in women in USA. Breast tumors are usually diagnosed and found during
routine examinations, either through mammography, ultrasound examination or regular
physical examination. Advanced mammographic techniques are able to identify tumor s as

7
small as a few millimeters, but small tumor formations are easily identified through
regular checks performed by the educated patient.
Treatment of breast cancer can be a combination of local management and
systemic treatment. Most breast cancer pati ents are treated with both using local and
systemic treatment regimens. The selection of local management is made based on
diagnosis, patient and disease related characteristics, and it consists of surgery and, of
much interest for us, radiation therapy. C hemotherapy and hormonal therapy are the
systemic treatment options available.
The main purpose of the use of local therapies is the eradication of the primary
local disease. Mastectomy is many times involved, with or without reconstruction, but in
most ca ses, breast -conserving surgery combined with radiation therapy is used with much
success. When radiation therapy is the sole and primary treatment option, the excision of
the tumor is usually followed by a course of radiation therapy , which can be 1) exter nal or
2) internal ( brachytherapy), meant to remove residual microscopic disease. This is a
conservative treatment modality, since it conserves the breast, decreases the chance of
recurrence and eradicates the residual tumor. Various irradiation techniques , traditional or
novel, are available and can be employed (Devlin et al., 2016; Baglan et al., 2001; Benitez
et al., 2004; Mooij et al., 2014). The normal treatment regimen for external beam therapy
consists of daily treatments delivered for 4 to 5 weeks w ith the use of a linear accelerator
and a combination of photon and electron beams. The electron beams are usually used as a
boost field that only targets to original tumor bed. Another radiation treatment option
currently available is the use of brachythe rapy. Interstitial needles or balloon type devices
are implanted at the site of the primary tumor bed and radiation is delivered remotely,
using afterloader techniques, or using permanent implants, a more recent treatment option
developed in Canada in the last years.
The research objective of this thesis is to quantify the dosimetric performance and
to evaluate quality assurance procedures for a device specifically designed for the
treatment of early stage breast cancer patients by means of High Dose Rate brachytherapy.
There are many studies done on these particular areas of research , many focused on the
dosimetry aspect ( Edmunson et al ., 2002; Dou et al ., 2011; Gurdalli et al ., 2011;
Scanderbeg et al., 2009 ), others on the quality assurance program implementation (Dou et

8
al., 2010 ; Thomadsen, 2000; Ji et al ., 2016) , and several approaching both aspects
altogether (Gurdalli et al., 2007 ; Dou et al., 2012).
The numerous scientific papers published in the last two decade s is an undeniable
indicator that breast brachytherapy is one of the fastest growing medical procedures today .
Over the last two decades, breast conservation therapy (BCT) has been accepted as one of
the standard treatment regimens in patients with early -stage breast cancer. Especially since
the early 2000s, Accelerated Partial Breast Irradiation (APBI) has been embr aced with
great interest by both cancer care providers and breast cancer patients as a great and
efficient treatment alternative to conventional whole -breast irradiation. There is data that
indicates that APBI is an acceptable option of treatment for pr operly selected patients
(Arthur et al., 2003) .
Historically, partial breast irradiation was first performed with interstitial
implantation using multi -catheter brachytherapy that typically triggered the tumor bed plus
a generous margin of 2.0 -2.5 cm. Beca use of its procedural complexity, interstitial
brachytherapy was not widely adopted in the United States and eventually led to the
development of a number of other methods of delivering APBI, including intraoperative
radiotherapy with photons and electrons and conformal three -dimensional external -beam
approaches (Vaidya et. al , 2004) The MammoSite approach was eventually developed,
allowing for the delivery of hypofractionated high -dose rate brachytherapy to the tumor
bed in a relatively straightforward man ner, which eliminated many of the technical
difficulties inherent to traditional double -plane interstitial implants.
Many techniques, all image -guided, have been de signed and improved since the
beginning. The MammoSite® – Hologic, Bedford, MA – was envisio ned as an alternative
to the interstitial implants, replacing the insertion and treatment of many catheters with a
single catheter centered in a balloon that fills the lumpectomy cavity. This new technology
was widely adopted because of its decreased surgi cal procedural complexity, even though
it equated with less flexibility in dosimetrical control . A single source position is normally
used for balloon applicators, which, because of the anisotropic dose distribution of the
source, results both in low doses near the source axis and the escalation of the dose near
the surface of the balloon tends to about 2 times the prescription dose. That led to the
general recommendation of limiting the use of the balloon applicators to cases where the
minimal se paration between the balloon and the skin is larger than 6 mm. The trapping of

9
air pockets on the surface of the balloon during insertion, can pose real problems, since
those are pushing the target tissue away, making it even more difficult to achieve
acceptable dosimetric coverage.
After the launch and initial use of the single -lumen MammoSite, many other
treatment multicatheter d evices such as the multilumen Ma mmoSite (Hologic, Bedford,
MA), Contura Multi -Lumen Balloon (Contura MLB, SenoRx Inc.,Irvine, CA ), ClearPath
or Strut Adjusted Volume Implant (SAVI) were developed, in order to allow better
targeting of the primary tumor site and better sparing of the adjacent normal tissues and
organs. Among those, the SAVI device proves to be a unique solution for cases where
other APBI devices are not a fit (Morcovescu et al ., 2009). Because of its design, the
miniSAVI version of the SAVI applicator allowed excellent dosimetric conformance and
skin sparing for cases where the size of the breast and the location of the lumpectomy site
hindered the use of balloon -type devices, like MammoSite or Contura.
Strut -based applicat ors have been widely adopted in United States as an alternative to
balloon -type applicators in APBI, and were increasingly used at our practice sin ce early
2008. The Strut Adjusted Volume Implant (SAVI) applicator studied (Cianna Medical,
Aliso Viejo, CA), also focuses on the smallest of its kind (6 -1mini), which has been
especially used on patients with reduced breast or/and lumpectomy cavity size.
Our research is a comprehensive dosimetric evaluation of various coverage
parameters, and doses to adjacent critical structures have been estimated in all patients
included in a retrospective study encompassing more t han five years of cumulated clinical
data. Proposed improved guidelines for daily treatment clinical QA and workflow are also
presented and discussed.
The main body of our work consists on a comprehensive dosimetric analysis of
extensive clinical data, collected for all four differ ent size SAVI devices (SAVI6 -1mini,
SAVI6 -1, SAVI8 -1 and SAVI10 -1). Our study is structured and focused on two subsets of
data: 1) a major pool of data collected at a multi -institutional level, that presents the
dosimetric analysis of the entire range of S AVI applicators, and a 2) minor pool, a subset
of the entire data, considering patients implanted with the smallest of the SAVI devices,
the SAVI6 -1mini device, in our clinic only . The total number of patients included in our
multi -institutional pool study is 817. There were 14 different participating institutions
involved in the multi -institutional study, each providing data for all four SAVI device

10
models. The subset study presented on the SAVImini device is a single -institution study of
plans created for 121 patients , treated over the span of 5 years, from 2009 to 2014. We
have also performed intercomparison studies among different APBI devices, which
allowed us to highlight the various dosimetrical advantages of the SAVI device over the
balloon type dev ices.
The dosimetric parameters reported in this study include: cavity volume, volume of
the defined treatment region (PTV_EVAL), V90(%), V95(%), V100(%), V150(cc),
V200(cc), skin distance (minimum distance from the lumpectomy cavity wall to the skin),
chest wall and ipsilateral lung distances (mm), and the maximum doses to critical
structures (skin and chest -wall). Conformity Indexes (CI), related to reported air/seroma
and invagination volumes, were also evaluated. Our dosimetric coverage criteria for thi s
study was V90>90%, V150<50 cm3, V200<20 cm3. Additional constraints are placed to
try limiting the chest wall and skin doses to 100%. All dosimetric data , both the major
pool and minor subset, was stratified using 5 mm skin -bridge intervals, therefore
differentiating among cases with major or no PTV volume reduction.
The current thesis is structured in eight chapters, a short description of each being
presented in the following paragraphs.
Chapter 2 is meant to review the fundamental theoretical concept s and quantities
used to describe the interactions of ionizing radiation, both gamma and x -ray, with matter,
and the methods used to measure those quantities. We briefly surveyed the main types of
interactions of photons with matter, with an emphasis on the kinematics and probability of
the Compton interactions, as the Compton effect is the predominant mechanism of
interaction in the range of energies commonly u sed in radiotherapy.
Chapter 3 overviews general aspects of High Dose Rate Brachytherapy, with
special attention given to describing the standard TG43 dose calculation formalism
historically and widely used in USA for brachytherapy calculations, as well as to
addressing the novel computational algorithm commissioned and implemented in our
department, ACUROS BV, which allowed us to account for inhomogeneity corrections
and more realistically evaluated the extent to which these can become clinically relevant in
the setting of brachytherapy HDR planning and delivery.

11
Chapter 4 offers an overview of the treatment modalities currently available for
breast cancer, with an emphasis on the brachyth erapeutical options . We surveyed the
brachytherapy devices currently used clinically in the USA, and highlight the device we
focused our research on, the SAVI device.
Chapter 5 presents the framework of our study, in which we describe the physical
characteristics of the SAVI device, the patient selection criteria, and we cl arify the main
dosimetric parameters used in evaluating the performance of this device. We present our
initial results with the device, on the background of a preliminary comparison study we
performed on the dosimetric performance of balloon type devices, MammoSite versus
Contura. We are showing that the SAVI device is the device of choice when there is a
need to treat lumpectomy cavities of volumes of less than 35 cm3, which are usually
entirely filled by properly inflated balloon devices.
Chapter 6 is the main body of our work consisting of a comprehensive dosimetric
analysis of extensive clinical data, collected for all four different size SAVI devices
(SAVI6 -1mini, SAVI6 -1, SAVI8 -1 and SAVI10 -1). Our study is structured and focused
on two subsets of dat a: 1) a major pool of data collected at a multi -institutional level, that
presents the dosimetric analysis of the entire range of SAVI app licators, and a 2) minor
pool, a subset of the entire data, considering patients implanted with the smallest of the
SAVI devices, the SAVI6 -1mini device, in our clinic only . The total number of patients
included in our multi -institutional pool study is 817. There were 14 different participating
institutions involved in the mul ti-institutional study, each providing data for all four SAVI
device models. The subset study presented on the SAVImini device is a single -institution
study of plans created for 121 patients , treated over the span of 5 years, from 2009 to
2014.
In chapter 7 we present our own contribution to designing a comprehensive quality
assurance program that deals with all stages of an APBI treatment process in a busy
radiotherapy department . We bring to light all possible un -common clinical situations, we
highlight the common practices and the extra measures we included into our customized
QA program, in an attempt to incorporate those into a comprehensive QA program
capable dealing with even the least frequent clinical situations .
The final results and conclusions of this multi -layered study are in fact
corroborated with the results of a 5 year long clinical study we were part of, that confirms

12
the validity of our dosimetrical study . This report also cofirmed outstanding target
coverage with excellent skin and rib sparing over the entire cohort of clinical data. We
concluded that t he SAVI applicators were designed to simplify brachytherapy APBI
compared to interstitial brachytherapy, allowing the advantages of brachytherapy over
other forms of accelerated partial breast radiation therapy accessible to more women. The
strut op en architecture design and mul tiple catheter options allow dose sculpting to each
patient’s unique anatomy and cavity lo cation. This flexi bility helps to overcome prior
concerns with skin spacing and tumor beds positioned between the overlying skin and
chestwall that limited patient eligibilit y. The clinical report presented at the end of this
thesis confirms excellent tumor control comparab le to other published APBI rates and
survival with low toxicity. Compared to external beam techniques for APBI,
brachytherapy seems to be as effective, with less toxicity.

CHAPTER 2 THEORETICAL ASPECTS
2.1. Ionizing Radiation. Fundamentals

13
The radiations of primary concern for us are the ones originating in atomic and
nuclear processes. Ionizing radiations are those radiations that can excite or ionize the
atoms of the material they interact with. They are usually identified with radiations that
surpass the minimal kinetic energy value of ~ 10 eV, the typical energy required by a
valence electron to escape an atom. The International Commission on Radiation Units and
Measurements (ICRU, 1971) makes a clear distinction between interactions of c harged
and uncharged particles, emphasizing the fact that there are two different mechanisms by
which the process of ionization can take place: directly and indirectly ionizing radiation.

2.2. Sources and types of ionizing radiation

It is therefore pro per and right to enumerate the most important sources and types
of radiations that can initiate and take part in an ionization process. An important source
consists of non -particulate radiations, 1) X-rays and 2) gamma -rays (γ-rays), which are
electromagne tic radiations of atomic or nuclear origin. They are created either due to the
interactions between energetic charged particles and atomic targets or due to nuclear
energetic instability (Betel, 1996) . The practical energy ranges of X -rays are stretching
from generating voltages of 0.1 KV all the way up to the megavoltage values, and are
normally grouped in voltage intervals, i.e. low -energy (0.1 -20 kV, diagnostic (20 -120kV),
orthovoltage (120 -300kV), intermediate (300kV -1 MV) and megavoltage (above 1 MV).
A graphic depiction of the mechanisms of X -ray production is shown in Figure 1.
Particulate radiations, 3) electrons (β -rays or δ -rays), 4) neutrons and other 5)
heavy charged particles (protons, alpha particles, etc), are either the products of
radioact ivity or nuclear reactions or are obtained through the process of acceleration in
high energy generators. The range of energies of interest in clinical radiological physics is
from a few eV (for electrons) to hundreds of MeV (for protons or alpha -particles ).

Figure 1 . Mechanisms of X -ray production

14
The main difference between the particulate and the non -particulate radiations has
to do with the process of energy deposition in matter, since this is a two -step process for
X-rays and γ -rays, a detail of much importance when describing and defining the b asic
concepts of radiation dosimetry. We will further discuss the most important concepts
describing the mechanism of interaction of ionizing radiation with matter.

2.3 Energy transfer, absorption and attenuation

Ionizing x -ray or gamma photons indirect ly deposit their energy by interacting
with the atoms of the material and producing high energy electrons. These electrons then
lose their energy by three major mechanisms: photoelectric effect, Compton effect and
pair-production, and by two other minor on es, of not much interest for radiological
physics: coherent scattering and photonuclear reactions.
The energy absorption process is a complex phenomenon, of mutual interchange
and interaction between particulate and non -particulate radiations (Cember, 198 3). Highly
energetic x -ray or gamma -ray beams have a wide array of applications in radiotherapy and
are the principal method of producing particulate radiation beams, mainly electron
fascicules, for the same purpose. In fact, highly energetic photon beams are extremely
useful in clinical applications exactly because they are capable of transferring their energy
to the target materials or tissues by ejecting orbital electrons from their otherwise
relatively stable energetic states. These high -speed electrons have then the capability of
producing ionization and excitation of other atoms along their own paths of interaction.
This energy deposition and absorption process can be of great use when occurring inside
living tissues, since it has the potential of dest roying or damaging the reproduction
capacity of tumor cells and tissues.
A photon beam consists of a very large number of photons, of various energies,
and in order to characterize the way this beam of radiation interacts with the material it
transverse, some basic quantities of statistical nature were introduced:
1. The fluence (Φ) is the ratio between the number of photons dN that enter a finite
sphere surrounding the point of measurement and the cross -sectional area da of the
imaginary sphere:

15

dadN
(2.1)
usually expressed in units of m-2 or cm-2.
2. The fluence rate or flux density (φ) is the fluence dΦ per unit time dt,

dtd
(1.2)
and is expressed in units of m-2 s-1.
3. Energy fluence (Ψ) is the quotient of the total energy dE carried by all dN rays
entering the imaginary sphere and the cross -section da of that sphere,

dadE
(2.3)
usually expressed in units of J m-2 or erg cm-2. For the special case of a monoenergetic
beam,
dE = dN· hν (3.4)
where hν is the individual kinetic energy of any photon in the beam.
4. Energy fluence rate or energy flux density (ψ) is the energy fluence per unit time:

dtd
(4.5)
The quantities listed above are of much importance and useful in many practical
applications but they are not descriptive in terms of the energy and type of the photon
beams. These factors become extremely important especially when talking about radiation
detection and measurement.
Especially when discussing about uncharged ionizing radiations we have to
introduce a very important concept, i.e., exponential attenuation . Charged ionizing
radiations interact with the matter in a much more sophisticated way, through small
interactions, and their gradual attenuation is not described by an exponential function
(Meredith, 1972) . An uncharged particle can pass through matter without losing a
significant a mount of energy, while a charged particle always loses some or all of its
energy.

16
A beam of uncharged particles has therefore no specific range and its energy
degradation mainly depends on its energetic profile. A monoenergetic beam is attenuated
exponentially, according to this equation:
dN = – μN dx or I(x) = I 0e-μx (5.6)

where dN is the reduction in the number of incident photons, N is the initial number of
incident photons in the beam, I(x) is the intensity transmitted by a thickness x , I0 is the
incident energy on the target material and μ is the attenuation coefficient . When the beam
consists of a spectrum of photon energies, the attenuation is not exactly exponential, since
photons of different energies are attenuated differently in the medium, with the lower
energy photons being preferentially removed from the beam.
The mass attenuation coefficient , μ/ρ (cm2/g), is a more relevant indicator of the
attenuation of a photon beam in a medium, since it factors out the density of the material
and it brings into discussion its atomic composition. An even more relevant quan tity is the
electronic attenuation coefficient μ e,

01
Ne cm2 / electron
(6.7)
since, ultimately, the attenuation of the photon beam and the inherent energy deposition in
the medium depends mainly on the electronic composition and characteristics of the target
material. Two other important processes take place when a photon interacts with the
electrons in a medium, described by two other coefficients:
i) energy transfer coefficient, μ tr:

 hEavg
tr
tr (7.8)
where
avg
trE is the average energy transferred into kinetic energy of charged particles per
interaction and μ is the attenuation coefficient of the material, and
ii) energy absorption coefficient, μ en:
μen = μtr (1 – g) (8.9)

17
where g is the fraction of the energy of secondary charged particles lost to bremsstrahlung
in the material. Energy transfer and energy absorption are the two processes by which the
energy of a photon beam is imparted to the surrounding electrons. A photon can have
multiple interactions in which its energy is converted into kinetic energy of the electrons it
interacts with, and then these high speed electrons impart their energy with other electrons
trough ionization or excitation. Part of their energy is lost in bremmstrahlung processes
and does not contribute to the energy absorbed in that specific volume. The energy
absorption coefficient is the q uantity of special interest for radiotherapy since it is used in
evaluations of the energy absorbed in tissues, therefore prone to producing biological
effects.
2.4. Interactions of photons with matter

As we mentioned earlier, there are five different me chanisms by which the photons
are interacting with matter. Each of these can be represented by its own attenuation
coefficient, characteristic for the energy of the incident photon and for the atomic number
of the absorbing material. The total attenuation coefficient can be expressed as the sum of
all these individual coefficients:






 ph c coh (9.10)
where μcoh, τ, σ c, π, and μph are the attenuation coefficients for coherent scattering,
photoelectric effect, Compton effect, pair production and photo disintegration,
respectively. The coherent scattering, or Rayleigh scattering, involves no energy
absorption but only scattering of t he low energy incident photons at small angles relative
to their initial path, especially in high atomic number materials. It has no major relevance
in radiation dosimetry. The process of photo disintegration is, at the other end of the
energy interval, on ly occurring for photon energies above 10 MeV, and is, for that reason,
not taken into account when dealing with the dosimetry of X -rays in the range of clinically
relevant energies.
2.4.1. Photoelectric effect

The photoelectric effect is a phenomenon in which a photon interacts with and
imparts part of its energy to the orbital electrons of a target atom, ejecting them from the

18
atom. The ejection of the photoelectron results in the creation of a shell vacancy th at can
be subsequently filled by an outer orbital electron, with the emission of characteristic x –
rays. Auger electrons can also be produced by the re -absorption of these characteristic x –
rays inside the mother atom (Figure 2).

Figure 2. The photoelectric effect.
The probability of the photoelectric effect depends on the energy of the incident
photon and on the atomic number of the absorbing material. This dependence is expressed
as

33
EZ (10.11)
and is at the foundation of many applications in diagnostic radiology. Low energy X -rays,
when used for therapeutical purposes, are highly absorbed in bone, due to its high Z. The
direction the photoelectrons are emitted is either close to 90o degree for low energy
photons or in a more forward direction for higher energy photons. The photoelectric effect
in water is predominant at energies around 30 keV but is almost nonexistent for photon
energies above 100 keV.
2.4.2. Compton effect

The Compton effect ref ers to the interaction between a photon and a stationary or
unbound electron, i.e. loosely bound electrons that can be considered “free” electrons
because of their weak and low energetic binding inside the atom, when compared with the
energy of the inciden t photon . The Compton effect is the dominant effect in the range of
energies regurarly dealt with in brachytherapy, therefore we will summarize important
theoretical aspects of this physical phenomenon.
2.4.2.1. The kinematics of the Compton effect

In terms of kinematics, the equations that describe the Compton effect are the
following:

19

) cos1)( /(1'2 
 
cmhhh
o
(11.12)

T = hν – hν’ (12.13)

)2tan() 1( cos2 
cmh
o (13.14)

where moc2 is the rest energy of the electron and T is its kinetic energy, ω and θ are the
scatter angle of the photon and o f the electron, respectively . Figure 3. represents the
collision between a photon of energy hν with an unbounded electron that has no kinetic
energy (being in a stationary state). The forward momemntum of the incident photon is
transferred to the electron in the form of kinetic energy T, which then is scattered at angle
θ, with both kinetic energy a nd momentum conserved during the process.

Figure 3. The Compton effect.

Compton scattering is nearly elastic for low energy photons, and is able to transfer
almost its entire energy to the recoiling electron. Special cases of the Compton effect are
a) the direct hit , when the energy transferred to the electron is maximum and the scattered
photon travels backward at minimum energy, b) 90-degree photon scatter , when the
photon is scattered at right angles ( ω=90o) and the photon and, c) grazing hit , when t he
photoelectron is deflected at 90o and the scattered photon continues on the forward
direction ( ω=0o). When the energy of the incident photon is high, if the radiation is
scattered at right angles it attains a maximum energy of 0.511 MeV, and if the radi ation is
scattered backwards it attains the energy of 0.255 MeV. These are special situations of
much importance in calculating shield barrier and wall thicknesses against scattered
radiation.

20
Because the Compton interaction practically involves electrons weakly bound in
the atom, it is independent of the atomic number Z of the material. Even more, since the
number of electrons per gram decreases slowly but steadily with Z, the Compton mass
attenuation coefficient is practically the same for all materials. Therefore, σ c/μ ∞ 1/E,
since the Compton effect decreases with increasing the photon energy. In the range of
photon energies commonly used in radiation therapy, the Compton effect is the most
relevant mode of interaction of incident photons with the absorbing medium.

2.4.2.2 Probability of Compton Interactions

J.J. Thompson was the one who first introduced the concept of the probability of
Compton interactions, theory which assu med that the free electron oscillates under the
influence of the electric vector of an electromagnetic incident wave. The electron is not
transferred any of the kinetic energy of the process, but it releases a photon of the same
energy as of the incident o ne in an elastic scattering.
The differential cross section per electron for a photon scattered at angle ω, per
unit solid angle, is expressed as:
𝑑 𝜎0𝑒
𝑑𝛺 𝜑= (𝑟02
2) (1+ 𝑐𝑜𝑠2𝜔) (14.15)
in units of cm2 sr-1 per electron. The quantity r o = e2/moc2 = 2.818 x 10-13 is the “classical
electron radius”.
The total Thomson scattering cross section per electron, 𝜎0𝑒, can be obtained by
integrating the last equation, over all directions of scatteri ng. This is simp lified by
assuming cylindrical symmetry and integrating over 0≤ ω ≤π, with the annular element of
solid angle given by dΩ φ = 2π sin ω dω, in terms of angle ω:
𝜎0𝑒= ∫ 𝑑 𝜎0𝑒𝜋
𝜑=0= 𝜋𝑟02∫ (1+ 𝑐𝑜𝑠2𝜔)𝜋
𝜑=0sin𝜔𝑑𝜔=
= 8𝜋𝑟02
3=6.65 𝑥 10−25 𝑐𝑚2/𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑛 (15.16)

21
Because this cross section value predicted in J.J. Thomson’s theoretical description
of the Compton process is too large for photon energies ℎ𝜈 > 0.01 MeV, further theoretical
work was done by Dirac and Nishina in 1928, by applying Dirac’s relativistic theory to
describe the Compton interaction process (Attix, 1986) . They were able to better predict
and more comprehensively express the differenti al cross section for photon scattering, as
𝑑 𝜎0𝑒
𝑑𝛺 𝜑= (𝑟02
2) (ℎ𝜈′
ℎ𝜈)2
(ℎ𝜈′
ℎ𝜈+ ℎ𝜈
ℎ𝜈′− sin2𝜔) (16.17)

with ℎ𝜈′ given by Eq. (2.12) . Since for low energies ℎ𝜈′ ≈ ℎ𝜈, Eq. (2.17) becomes
𝑑 𝜎0𝑒
𝑑𝛺 𝜑= (𝑟02
2) (2− 𝑠𝑖𝑛2𝜔)= (𝑟02
2) (1+ 𝑐𝑜𝑠2𝜔) (17.18)

form identical to Eq. (2.15) , proving that the Klein Nishina differential cross section is
simply the Thompson cross section for the special case of low photon energies.
If we integr ate Eq ( 2.17) over all photons scattering angles ω, the total Klein
Nishina cross section per electron becomes:
𝜎𝑒=2𝜋∫𝑑 𝜈𝑒
𝑑𝛺 𝜑𝜋
𝜑=0 sin𝜔·𝑑𝜔=
= 𝜋·𝑟02∫(ℎ𝜈′
ℎ𝜈)2
(ℎ𝜈′
ℎ𝜈+ ℎ𝜈
ℎ𝜈′− sin2𝜔)𝜋
0 sin𝜔·𝑑𝜔=

= 2𝜋·𝑟02{1+𝛼
𝛼2 [2(1+𝛼)
1+2𝛼− 𝑙𝑛(1+2𝛼)
𝛼]+ 𝑙𝑛(1+2𝛼)
2𝛼− 1+3𝛼
(1+2𝛼)2} (18.19)

where α = hν/m0c2, with m0c2 = 0.511 MeV and hν also expressed in MeV.

2.4.3 The Pair Production

This mechanism of interaction takes place when the energy of the incident photon
is greater than the threshold energy of 1.02 MeV. In this process there is a strong

22
interaction between the electromagnetic field of the atomic nucleus and the incident
photon in which the photon releases and imparts its entire energy to a newly created pair
of particles, a negative electron (e-) and a positron (e+) (see Figure 4).

Figure 4 . Pair production
Because the pair production is a process of interaction with the ener getic field of
the nucleus, it greatly depends on the atomic number, its probability increasing with higher
Z. The pair production mass attenuation coefficient π/ρ is proportional to Z2. This
mechanism predominates for energies above 25 MeV.
In conclusion , the total mass attenuation coefficient is large at low energies (<
100keV) due to the predominance of the photoelectric effect, then slightly decreases with
energy up to 25 MeV, in the Compton effect predominance region (and remains relatively
independen t of Z), and increases slightly above 25 MeV due to the predominance of pair
production.
2.4.4 Interactions of charged particles with matter

Charged particles interaction and exchange of energy with matter is very different
then the one specific to photon beams. This is due to the Coulombian nature of interaction
between a moving charged particle and the bound electrons or with the nucleus. Any
charged particle is losing its energy through a process of successive interactions and
energy losses with the surrounding medium. The heavier the particle is, the smaller the
number of interactions will be. In the case of electrons , a Bragg peak is not observed
because they exchange energy in multiple successive scattering interactions. Neutrons
have a very complex nature of interaction, and their dosimetry very intricate exactly
because they create a multitude of other types of radiations (heavy particles, neutrons,
gamma rays) when they interact with matter. Heavy particles lose their ener gy at a very
high rate, proportional with the square of the particle charge and inversely proportional
with its velocity. The Bragg peak indicates a high energy loss related to the slowing down
process that takes place.

23

Figure 5 . Spread Out Bragg peak fo r a proton beam

It is possible to manipulate and use weighted superposition methods in order to
obtain a much flatter and broader Bragg peak, as shown in Figure 5 above, for a proton
beam. The red the dose curve represents the Bragg peak of a monoenerget ic, thin pencil
beam of protons. By grouping multiple Bragg peaks of different proton ranges and
energies together, it is possible to deposit a homogenous dose in the target region (Perez,
1992) . The resulting (range -modulated) proton beam distribution is called Spread Out
Bragg Peak (SOBP, indicated in blue). The dose degradation with depth curve of an X -ray
beam is shown in green. The picture shows that protons deposit a much smaller dose than
X-rays outside plateau region, which can be of great applicabi lity when a uniform
deposition of energy in a medium is desired.

2.5. Quantities describing the interaction of ionizing radiation with matter

The quantities describing the interaction of radiation with matter are 1) Kerma, K ,
a quantity that describes the energy transfer from indirectly ionizing radiations (photons)
to charged particles, 2) the Exposure, X , a quantity that describes gamma or X -ray beams
in terms of their ability to ionize a volume of air, and 3) the Absorbed Dose, D , a quantity
that describes the energy transfer from directly ionizing radiations to matter.
2.5.1 Kerma

The Kerma K (kinetic energy released in a medium) can be defined by introducing
another quantity, the energy transfer, E tr, in a volume V, and the radiant energy, R :
Etr = R i – Ro + Q (19.20)
where
Ri is the radiant energy of uncharged particles entering volume V,

24
Ro is the radiant energy of uncharged particles exiting volume V, except that
created through radiative losses of kinetic energy by charged particles inside
volume V, and
Q is the net energy derived from rest mass in V.
All processes, in which the kinetic en ergy of a charged particle is converted into
kinetic energy of a photon, either by bremsstrahlung or by in -flight annihilation of
positrons, are considered radiative losses.
The radiant energy R is defined as the energy of particles (excluding the rest
energy), emitted, received or transferred to a medium. Etr does not reflect how the energy
imparted to charged particles is spent inside the specified volume V, and does not count
for the energies by charged particles in volume V.
Kerma K is defined simply as

dmdEKtr (20.21)

the total energy transferred to charged particles by uncharged particles, per unit mass,
including the radiative loss energy but excluding the energy axchenged among charged
particles in volume V. The unit of kerma is gray (Gy), which equals 1 J/kg. The special
unit for kerma is rad. There is a strong relation between kerma and enegy fluence for
photons, and for monoenergetic x -ray beams of energy E, that transv erse a material of
atomic number Z, this can be expressed as

gK
ZEen
ZEtr






11
, ,
 (21.22)

where μ tr/ρ is the mass energy transfer coefficient, μ en/ρ is the mass energy absorption
coefficient, Ψ the energy fluence at the point A of measurement and K is the kerma at
point A in that volume. The energy gained by an electron after an interaction with an x -ray
photon can be partially lost as ionization energy in collision interactions with the atomic
electrons of the ab sorbent, or by radiative interactions, whit the emission of secondary x –
ray photons. We can therefore make a distinction between two components of kerma,

25
K = K col + K rad =
gg
ZEen
ZEen






1, ,
 (22.23)

where K col is the collision kerma and K rad is the radiation kerma. The collision component
of kerma, K col, is a very important quantity used when discussing the concept of charged –
particle equilibrium (CPE) in a given volume V, and can be viewed as the net energy
transferred to the charged particles, since it does not incorporate the radiant energy losses
Rrad of the charged particles originated in V,
Enet = R i – Ro – Rrad + Q = E tr – Rrad (23.24)

2.5.2 Exposure

Exposure is another important quantity for radiological physics, one that has
historical precedence over the concepts of kerma and absorbed dose. It is a measure of
ionization produced in air by photons and is defined as the quotient of the absolute value
of the total charge, dQ, of the ions of one sign produced in air when all the electrons
liberated by photons in air mass dm are completely stopped in air,

dmdQX (24.25)
its SI unit is coulomb per kilogram (C/kg), and its special unit is roentgen (1R). Exposure
can be expressed in relationship with the collision component of kerma by knowing that
the mean energy required to produce an ion pair in air is almost constant for al l electron
energies, and has a value of W = 33.97 eV/ion pair. Therefore X equates to K col as follows:



WeKXair
col =
air airen
airWe




 (25.26)
where e/W is the average energy required per unit charged of ionization produced.
Exposure is a quantity that applies only to uncharged radiations below 3MeV, and is a
measure of ionization in air only.

26
2.5.3. Absorbed Dose

The absorbed dose is a quantity that is relevant to all types of ionizing radiation
fields, whether indirectly or directly ionizing. The absorbed dose is the ratio between the
mean energy dE imparted by ionizing radiation to a material of mass dm,

dmdED (26.27)
its SI unit is gray (Gy) and its special unit is rad ( radiation absorbed dose), like for kerma.
There is a strong relationship between absorbed dose and collision kerma and it brings into
discussion the concept of electronic equilibrium in a given absorbing volume. Kerma is
maximum at surface and decreases with depth and the dose builds up to a maximum and
then decreases with depth, proportionally with kerma. If we intro duce a new quantity, β,
defined as

colKD
(27.28)
we can differentiate between two different electronic equilibrium regions: for β < 1, we
are in the electronic build -up region , when β = 1, electronic equilibrium is achieved, and
when β >1, we are referring to the region of transient electronic region. This is graphically
lustrated in Figure 6 below.

Figure 6. Absorbed dose and collision kerma relationship, for a megavoltage photon beam
In the transient electronic equilibrium region, the absorbed dose is greater than
kerma because of the combined effect of photon attenuation and the predominantly
forward motion of electrons in the field. β is k nown for various photon energies in
different medium like air and water and it varies with energy.
The relationship between absorbed dose and photon energy fluence Ψ at a point
where transient electronic equilibrium exists is

27
D = β • (μ/ρ) • Ψ (28.29)

At the foundation of radiation dosimetry stays the relationship that can be
established between absorbed dose, kerma and exposure, in conditions of electron
equilibrium. Because for energetic photon beams, in the order of a few MeV, the photon
fluence at a certain point in the medium is related to and depends on the photon fluence
some distance upstream of the point of interest, the process of photon attenuation is taken
into account and energy -dependant corrections need to be co nsidered. A rigorous
determination of absorbed dose form exposure is limited to energies up to ~ 1 MeV, when
charged particle equilibrium ca be achieved. In these conditions,
Dair = (K col)air = X • W/e = 0.876 (rad/R) • X(R) (29.30)
where 0.876 is the roentgen -to-rad conversion factor for air, under electronic equilibrium
conditions.
2.6. Measurement of ionizing radiation

The measurement of ionizing radiation effects was performed in a somehow non –
quantitative way at the beginning of the 20 -th century, when the science of radiology was
born. Biological and chemical effects, like the amount of reddening of human skin, where
considered. But in late 1920’s, the ICRU introduced the unit of exposure, the roentgen, as
a unit of measuring x -ray radiation exposure.
For the first time, the concept of electronic equilibrium was introduced and applied
to the ionization produced by x -rays in free-air ion chamber , which consisted of a
coupling of ion -collection plates connected to a voltage.
The free -air ionization chamber is design for the measurement of roentgen, and it
becam e the primary standard used for the calibration of other exposure and dose
measuring devices. A fee -air chamber is a parallel plate camber; a voltage of ~ 100 V/cm
is applied across the plates and because of this voltage, the electrons created when any x –
ray beam crosses and ionizes the chamber’s air volume are accelerated between and
collected on the plates. The ionization is then measured for a length defined by the

28
limiting electrical field lines between the plates, defined by the adjacent guard electrod es
(see Figure 7 below). The collected charge is then converted in units of exposure.

Figure 7. Free-air ionization chamber
It was for practical reasons that other devices where designed for the purpose of measuring
dose and exposure. Thimble chambers ( Figure 8) are ionization

Figure 8. Thimble ionization chamber

chambers of small volumes that function on the same principle as free -air ionization
devices. Special theories were developed in order to describe the process of charge
collection and measurem ent for small cavities of air enclosed in a very thin solid material,
the walls of the chamber, since conditions of electronic equilibrium must be achieved. The
effective Z of the chamber walls and central electrode need to carefully selected as most of
the electrons producing ionization inside such a cavity originate in the immediate
surroundings of the small air cavity. The exposure measured with a thimble chamber is
obtained from

AQX1 (30.31)
where Q is the ionization charge in the cavity volume of denity ρ and volume υ; A is a the
fraction of the energy fluence transmitted through the wall.
Other types of chambers are used for measuring x -rays if higher energies. In 1955,
Farmer designed a chamber that became the standard measurement device for all energies
in the therapeutical range. Its collecting volume is 0.6 cm3, its walls are made of graphite,
its central electrode of aluminum and the insulator of polytrichlorofluorethylene. The
charged collec ted is measured by another device, the electrometer, which holds a constant
bias voltage of ~ 300 V on the collector. The electrometer charge reading is converted in
units of exposure by applying various correction factors like pressure and temperature
correction, ion chamber calibration factor for a given energy, stem correction, etc.

29
The dosimetry of ionizing radiation is a very complex topic in the field of medical
physics, because of its high degree of applicability in radiotherapy (Knoll, 2000) . Major
concepts, quantities and units are to be thoroughly understood, since they are the
foundation of all the computational systems and models that were and are still used in the
evaluation and measurement of dose deposited in tissues by ionizing radiation, the
fundamental process that contributed to the emergence of novel fields of medicine, like
radiology, radiation oncology, nuclear medicine.
The calculation of dose in both external beam therapy and brachytherapy is a very
complex process because of the complexity of factors that are to be taken into account.
Only the fundamental factors were presented in this paper but many other are included in
current dose calculation formalisms, especially because the evolveme nt of new
technologies that were adopted into the clinical environment nowadays. Special treatment
procedures like intensity modulated radiation therapy IMRT, stereotactic radiosurgery
SRS, tomotherapy are in use today, and specific factors are to included and accounted for
into dose computations for these new technologies.