Ebook Physics for diagnostic radiology (3/E): Part 1

PHYSICS FOR
DIAGNOSTIC
RADIOLOGY
THIRD EDITION

P P Dendy, B Heaton
With contributions by
O W E Morrish, S J Yates, F I McKiddie, P H Jarritt, K E Goldstone,
A C Fairhead, T A Whittingham, E A Moore, and G Cusick

A TAY L O R & F R A N C I S B O O K



Physics for Diagnostic Radiology
Third Edition


Series in Medical Physics and Biomedical Engineering
Series Editors: John G Webster, Slavik Tabakov, Kwan-Hoong Ng
Other recent books in the series:
Nuclear Medicine Physics
J J Pedroso de Lima (Ed)
Handbook of Photonics for Boimedical Science
Valery V Tuchin (Ed)
Handbook of Anatomical Models for Radiation Dosimetry
Xie George Xu and Keith F Eckerman (Eds)
Fundamentals of MRI: An Interactive Learning Approach
Elizabeth Berry and Andrew J Bulpitt
Handbook of Optical Sensing of Glucose in Biological Fluids and Tissues
Valery V Tuchin (Ed)

Intelligent and Adaptive Systems in Medicine
Oliver C L Haas and Keith J Burnham
A Introduction to Radiation Protection in Medicine
Jamie V Trapp and Tomas Kron (Eds)
A Practical Approach to Medical Image Processing
Elizabeth Berry
Biomolecular Action of Ionizing Radiation
Shirley Lehnert
An Introduction to Rehabilitation Engineering
R A Cooper, H Ohnabe, and D A Hobson
The Physics of Modern Brachytherapy for Oncology
D Baltas, N Zamboglou, and L Sakelliou
Electrical Impedance Tomography
D Holder (Ed)
Contemporary IMRT
S Webb


Series in Medical Physics and Biomedical Engineering

Physics for Diagnostic Radiology
Third Edition

P P Dendy, B Heaton
With contributions by
O W E Morrish, S J Yates, F I McKiddie, P H Jarritt, K E Goldstone,
A C Fairhead, T A Whittingham, E A Moore, and G Cusick

Boca Raton London New York

CRC Press is an imprint of the
Taylor & Francis Group, an informa business

A TA Y L O R & F R A N C I S B O O K


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Contents
About the Series............................................................................................................................ vii
Acknowledgements........................................................................................................................ix
Introduction to the Third Edition.................................................................................................xi
Contributors....................................................................................................................................xv
1. Fundamentals of Radiation Physics and Radioactivity................................................... 1
P P Dendy and B Heaton
2. Production of X-Rays............................................................................................................ 23
P P Dendy and B Heaton
3. Interaction of X-Rays and Gamma Rays with Matter.................................................... 75
B Heaton and P P Dendy
4. Radiation Measurement..................................................................................................... 105
B Heaton and P P Dendy
5. The Image Receptor............................................................................................................ 133
O W E Morrish and P P Dendy
6. The Radiological Image..................................................................................................... 181
O W E Morrish and P P Dendy
7. Assessment of Image Quality and Optimisation......................................................... 219
P P Dendy and O W E Morrish
8. Tomographic Imaging with X-Rays................................................................................. 257
S J Yates and P P Dendy
9. Special Radiographic Techniques.................................................................................... 293
P P Dendy and B Heaton
10. Diagnostic Imaging with Radioactive Materials.......................................................... 337
F I McKiddie
11. Positron Emission Tomographic Imaging (PET)........................................................... 375
P H Jarritt
12. Radiobiology and Generic Radiation Risks.................................................................. 397

P P Dendy and B Heaton
13. Radiation Doses and Risks to Patients........................................................................... 427
K E Goldstone and P P Dendy
v


vi

Contents

14. Practical Radiation Protection and Legislation............................................................. 455
B Heaton and P P Dendy
15. Diagnostic Ultrasound....................................................................................................... 489
A C Fairhead and T A Whittingham
16. Magnetic Resonance Imaging........................................................................................... 563
Elizabeth A Moore
17. Digital Image Storage and Handling.............................................................................. 601
G Cusick
18. Multiple Choice Questions................................................................................................ 633


About the Series
The Series in Medical Physics and Biomedical Engineering describes the applications of physical sciences, engineering, and mathematics in medicine and clinical research.
The series seeks (but is not restricted to) publications in the following topics:
• Artificial organs
• Assistive technology
• Bioinformatics
• Bioinstrumentation
• Biomaterials
• Biomechanics

• Biomedical engineering
• Clinical engineering
• Imaging
• Implants
• Medical computing and mathematics
• Medical/surgical devices

• Patient monitoring
• Physiological measurement
• Prosthetics
• Radiation protection, health physics, and dosimetry
• Regulatory issues
• Rehabilitation engineering
• Sports medicine
• Systems physiology
• Telemedicine
• Tissue engineering
• Treatment

The Series in Medical Physics and Biomedical Engineering is an international series that
meets the need for up-to-date texts in this rapidly developing field. Books in the series
range in level from introductory graduate textbooks and practical handbooks to more
advanced expositions of current research.
The Series in Medical Physics and Biomedical Engineering is the official book series of the
International Organization for Medical Physics.
The International Organization for Medical Physics
The International Organization for Medical Physics (IOMP), founded in 1963, is a scientific, educational, and professional organization of 76 national adhering organizations,
more than 16,500 individual members, several corporate members, and four international
regional organizations.
IOMP is administered by a council, which includes delegates from each of the adhering

national organizations. Regular meetings of the council are held electronically as well as
every three years at the World Congress on Medical Physics and Biomedical Engineering.
The president and other officers form the executive committee, and there are also committees covering the main areas of activity, including education and training, scientific,
professional relations, and publications.
Objectives
• To contribute to the advancement of medical physics in all its aspects
• To organize international cooperation in medical physics, especially in developing
countries
• To encourage and advise on the formation of national organizations of medical
physics in those countries which lack such organizations
vii


viii

About the Series

Activities
Official journals of the IOMP are Physics in Medicine and Biology and Medical Physics and
Physiological Measurement. The IOMP publishes a bulletin, Medical Physics World, twice a
year, which is distributed to all members.
A World Congress on Medical Physics and Biomedical Engineering is held every
three years in cooperation with IFMBE through the International Union for Physics and
Engineering Sciences in Medicine (IUPESM). A regionally based international conference
on medical physics is held between world congresses. IOMP also sponsors international
conferences, workshops, and courses. IOMP representatives contribute to various international committees and working groups.
The IOMP has several programs to assist medical physicists in developing countries.
The joint IOMP Library Programme supports 69 active libraries in 42 developing countries, and the Used Equipment Programme coordinates equipment donations. The Travel
Assistance Programme provides a limited number of grants to enable physicists to attend
the world congresses. The IOMP website is being developed to include a scientific database

of international standards in medical physics and a virtual education and resource center.
Information on the activities of the IOMP can be found on its website at www.iomp.org.


Acknowledgements
We are grateful to many persons for constructive comments on and assistance with the
production of this book. In particular, we wish to thank Dr J Freudenberger, G Walker,
Dr G Buchheim, Dr K Bradshaw, Mr M Bartley, Professor G Barnes, Dr A Noel, D Goodman,
Dr A Parkin, Dr I S Hamilton, D A Johnson, I Wright, S Yates, E Hutcheon, M Streedharen
and K Anderson.
Figures 2.9, 2.15 and 2.28 are reproduced by permission of Siemens AG. Dura and
STRATON are registered trademarks of Siemens.
Figures 2.24 and 2.25 are reproduced by permission of Philips Electronics UK Ltd.
Figures 5.18 and 5.20 are reproduced by permission of Medical Physics Publishing.
Figure 5.26 is reproduced by permission of the British Institute of Radiology.
Figure 7.2a is reproduced by permission of Artinis Medical Systems.
Figures 7.3, 7.19, 7.20, 7.23, 7.24, 7.25 and 7.26 are reproduced by permission of the
British Institute of Radiology.
Figure 7.4 is reproduced by permission of The Royal Society, London UK (Campbell
F W, Phil Trans Soc B, 290, 5–9, 1980).
Figure 7.11 is reproduced by permission of Elsevier Publishing and Professor
P N T Wells (Scientific Basis of Medical Imaging edited by P N T Wells, 1982, figure
1.19, p. 18).
Figure 7.21 is reproduced by permission of the International Commission on
Radiation Units and Measurements.
Figure 7.22 is reproduced by permission of the Radiological Society of North
America Inc (Macmohon H, Vyborny C J, Metz C E et al. Radiology, 158, 21–26,
­figure 5, 1986).
Figure 9.13 is reproduced by permission of Dr J N P Higgins and H Szutowicz.
Figure 9.16 is reproduced by permission of Professor G T Barnes.

Figure 9.19 is reproduced by permission of Oxford University Press.
Figure 11.2 is reproduced by permission of Elsevier Publishing (Cherry S R,
Sorenson J A & Phelps M E. Physics in Nuclear Medicine, 3rd edition, 2003).
Figure 12.12 is reproduced by permission of the Radiological Society of North
America (Boyce J D, Land C E, & Shore R E. Risk of breast cancer following lowdose radiation exposure, Radiology, 131, 589–597, 1979).
Figures 12.14 and 12.17 and Table 12.2 are reproduced by permission of the British
Institute of Radiology.
Tables 13.1, 13.3, 13.4, 13.5 and 13.16 are reproduced by permission of the Health
Protection Agency, UK.
Tables 13.2, 13.8, 13.9, 13.10, 13.11, 13.12, 13.14 and 13.15 are reproduced by permission
of the British Institute of Radiology.

ix



Introduction to the Third Edition
Learn from yesterday, live for today, hope for tomorrow. The important thing
is not to stop questioning.
Albert Einstein
The first edition of this book, published in 1987, was written in response to a rapid development in the range of imaging techniques available to the diagnostic radiologist over
the previous 20 years and a marked increase in the sophistication of imaging equipment.
There was a clear need for a textbook that would explain the underlying physical principles of all the relevant imaging techniques at the appropriate level.
Since that time, there have been major developments in imaging techniques and the
physical principles behind them. Some of these were addressed in the second edition, published in 1999, notably the much greater importance attached to patient doses, the increasingly widespread use of digital radiography, the importance of both patient dose and
image quality in mammography, the increasing awareness of the need to protect staff and
related legislation. The chapters on ultrasound and magnetic resonance imaging (MRI)
were completely rewritten.
The past decade has seen yet more advances, and parts of the second edition are no longer ‘state of the art’. In this third edition all the chapters have been revised and brought
up-to-date, with major additions in the following areas:

• The image receptor—new material on digital receptors
• The radiological image—emphasising the differences between analogue and digital images
• Computed tomography—multi-slice CT and three-dimensional resolution, dual
energy applications, cone beam CT
• Special radiographic techniques—especially subtraction techniques and interventional radiology
• Positron emission tomography—a new chapter including aspects of multi-­modality
imaging (PET/CT)
• Radiation doses and risks to patients
• Data handling in radiology—a new chapter covering picture archiving and
communication systems (PACS), teleradiology, networks, archiving and related
factors
The second evolutionary change since 1987 has been in the scope of the anticipated readership. Radiologists in training are still a primary target, and there are many reasons to
emphasise the importance of physics education as a critical component of radiology training. As an imaging technique becomes more sophisticated it is essential for radiologists
to know ‘how it works’, thus providing them with a unique combination of anatomical,
physiological and physical information. This helps to differentiate the expertise of radiologists from that of other physicians who read images and helps to position radiology as a
xi


xii

Introduction to the Third Edition

s­ cience-based practice. There is a need for substantial additional educational resources
in physics and better integration of physics into clinical training (Hendee 2006; Bresolin
et al. 2008).
However, experience with the first and second editions of the book has shown that it is
a useful text for other groups, including radiographers/technicians engaged in academic
training and undergraduates in new courses in imaging sciences. It is a good introductory text for master’s degree courses in medical physics and for physicists following the
training programme in diagnostic radiology recommended by the European Federation
of Organisations in Medical Physics (EFOMP—in preparation). It will also be of value to

teachers of physics to radiologists and radiographers.
Many features of the first and second editions have been retained:
• The material is presented in a logical order. After an introductory chapter of basic
physics, Chapters 2 to 7 follow through the X-ray imaging process—production
of X-rays, interaction with the patient, radiation measurement, the image receptor, the radiological image and the assessment of image quality. Chapters 8 and 9
cover more advanced techniques with X-rays and Chapters 10 and 11 cover imaging with radioactive materials. Chapters 12 through 14 deal with radiobiology and
risk and radiation protection. Chapters 15 and 16 cover imaging with non-ionising
radiation (ultrasound and MRI) and finally Chapter 17 discusses data handling in
a modern, electronic radiology department.
• Extensive cross-referencing is used to acknowledge the fact that much of the subject matter is very interactive, without the need for undue repetition.
• Lateral thinking has been encouraged wherever possible, for example, pointing
out the similarities in the use of the exponential in radioactive decay, attenuation
of X-rays and MRI.
• There are exercises at the end of each chapter and, at the end of the book, there are
multiple choice questions (MCQs), at an appropriate level and sometimes drawing
on material from more than one chapter, to assist readers in assessing their understanding of the basic principles. The MCQs are not designed to provide comprehensive coverage of any particular syllabus because other books are available for
this purpose.
• Text references and recommendations for further reading are given at the end of
each chapter.
There are two major changes in the layout:



1.Each chapter begins with a summary of the main teaching points.
2.To accommodate some variation in the background knowledge of readers, some
insights have been included. These are not essential to a first reading but cover
more subtle points that may involve ideas presented later in the book or require a
somewhat greater knowledge of physics or mathematics.

And finally—why the quotation from Einstein? Digital imaging, molecular imaging and

functional imaging have great potential in medicine, but as they develop they will inevitably require a better knowledge of physics and become more quantitative. We have tried


Introduction to the Third Edition

xiii

to show the way forward to both radiologists and scientists who are prepared to ask the
question, Why?

References
Bresolin L, Bissett III GS, Hendee WR and Kwakwa FA, Methods and resources for physics education
in radiology residence programmes, Radiology, 249, 640–643, 2008.
EFOMP, Guidelines for education and training of medical physicists in radiology—in preparation,
European Federation of Organisations for Medical Physics.
Hendee WR, An opportunity for radiology, Radiology, 238, 389–394, 2006.



Contributors
G Cusick
Medical Physics and Bioengineering
UCL Hospitals NHS Foundation Trust
London, United Kingdom

F I McKiddie
Department of Nuclear Medicine
NHS Grampian
Aberdeen, United Kingdom

P P Dendy (Retired)
East Anglian Regional Radiation
Protection Service
Cambridge University Hospitals NHS
Foundation Trust
Cambridge, United Kingdom

Elizabeth A Moore
Philips Healthcare
Best, the Netherlands

A C Fairhead
Department of Biomedical Physics and
Bioengineering
NHS Grampian
Aberdeen, United Kingdom
K E Goldstone
East Anglian Regional Radiation
Protection Service
Cambridge University Hospitals NHS
Foundation Trust
Cambridge, United Kingdom
B Heaton
Aberdeen Radiation Protection Services
Aberdeen, United Kingdom

O W E Morrish
East Anglian Regional Radiation
Protection Service
Cambridge University Hospitals NHS

Foundation Trust
Cambridge, United Kingdom
T A Whittingham
Regional Medical Physics Department
Newcastle General Hospital
Newcastle upon Tyne, United Kingdom
S J Yates
East Anglian Regional Radiation
Protection Service
Cambridge University Hospitals NHS
Foundation Trust
Cambridge, United Kingdom

P H Jarritt
Clinical Director of Medical Physics and
Clinical Engineering
Department of Medical Physics and
Clinical Engineering
Cambridge University Hospitals NHS
Foundation Trust
Cambridge, United Kingdom

xv



1
Fundamentals of Radiation
Physics and Radioactivity
P P Dendy and B Heaton

SUMMARY
• Why some atoms are unstable is explained.
• The processes involved in radioactive decay are presented.
• The concepts of physical and biological half-life and the mathematical explanation of secular equilibrium are addressed.
• The basic physical properties of X and gamma photons and the importance
of the K shell electrons in diagnostic radiology are explained.
• The basic concepts of the quantum nature of electromagnetic (EM) radiation and energy, the inverse square law and the interaction of radiation with
­matter are introduced.

CONTENTS
1.1 Structure of the Atom.............................................................................................................2
1.2 Nuclear Stability and Instability.......................................................................................... 4
1.3 Radioactive Concentration and Specific Activity............................................................... 6
1.3.1 Radioactive Concentration........................................................................................ 6
1.3.2 Specific Activity..........................................................................................................7
1.4 Radioactive Decay Processes................................................................................................7
1.4.1 β– Decay........................................................................................................................7
1.4.2 β+ Decay........................................................................................................................7
1.4.3 α Decay.........................................................................................................................8
1.5 Exponential Decay.................................................................................................................. 8
1.6 Half-life.....................................................................................................................................9
1.7 Secular and Transient Equilibrium.................................................................................... 11
1.8 Biological and Effective Half-Life....................................................................................... 13
1.9 Gamma Radiation................................................................................................................. 14
1.10 X-rays and Gamma Rays as Forms of Electromagnetic Radiation................................ 14
1.11 Quantum Properties of Radiation...................................................................................... 16
1.12 Inverse Square Law.............................................................................................................. 17
1.13 Interaction of Radiation with Matter................................................................................. 17
1.14 Linear Energy Transfer........................................................................................................ 19

1


2

Physics for Diagnostic Radiology

1.15 Energy Changes in Radiological Physics.......................................................................... 19
1.16 Conclusion............................................................................................................................. 21
Further Reading ............................................................................................................................ 21
Exercises.......................................................................................................................................... 21

1.1  Structure of the Atom
All matter is made up of atoms, each of which has an essentially similar structure. All
atoms are formed of small, dense, positively charged nuclei, typically some 10−14 m in
diameter, orbited at much larger distances (about 10 –10 m) by negatively charged, very
light particles. The atom as a whole is electrically neutral. Note that because matter
consists mainly of empty space, radiation may penetrate many atoms before a collision
results.
The positive charge in the nucleus consists of a number of protons each of which has a
charge of 1.6 × 10 –19 coulombs (C) and a mass of 1.7 × 10 –27 kilograms (kg). The negative
charges are electrons. An electron carries the same numerical charge as the proton, but
of  opposite sign. However, an electron has only about 1/2000th the mass of the proton
(9 × 10 –31 kg). Each element is characterised by a specific number of protons, and an equal
number of orbital electrons. This is called the atomic number and is normally denoted by
the symbol Z. For example, Z for aluminium is 13, whereas for lead Z = 82.
Electrons are most likely to be at fairly well-defined distances from the nucleus and are
described as being in ‘shells’ around the nucleus (Figure 1.1). More important than the
distance of the electron from the nucleus is the electrostatic force that binds the electron
to the nucleus, or the amount of energy the electron would have to be given to escape

from the field of the nucleus. This is equal to the amount of energy a free electron will lose
when it is captured by the electrostatic field of a nucleus. It is possible to think in terms

(a)

e–

(b)

e–

e–

+1

+8
e–

–

e

K shell

e–

e–
e–
K shell
e–

Hydrogen

L shell

Oxygen

FIGURE 1.1
Examples of atomic structure. (a) Hydrogen with one K shell electron. (b) Oxygen with two K shell electrons
and six L shell electrons.


3

Fundamentals of Radiation Physics and Radioactivity

(a)
Electrons
3M
8L

2K

Energy (keV)
0
–0.005
–0.08

–1.5

(b)
Electrons
2P
12 O

Energy (keV)
0
–0.02
–0.07

32 N

–0.6

18 M

–2.8

8L

–11.0

2K

–69.5

FIGURE 1.2
Typical electron energy levels. (a) Aluminium (Z = 13). (b) Tungsten (Z = 74).

of an energy ‘well’ that gets deeper as the electron is trapped in shells closer and closer

to the nucleus.
The unit in which electron energies are measured is the electron volt (eV)—this is the energy
one electron would gain if it were accelerated through 1 volt of potential difference. One
thousand electron volts is a kilo electron volt (keV) and one million electron volts is a mega
electron volt (MeV). Some typical electron shell energies are shown in Figure 1.2. Note that




1.If a free electron is assumed to have zero energy, all electrons within atoms have
negative energy—that is, they are bound to the nucleus and must be given energy
to escape.
2.The energy levels are not equally spaced and the difference between the K shell
and the L shell is much bigger than any of the other differences between shells
further away from the nucleus. Shells are distinguished by being given a letter.
The innermost shell is the K shell and subsequent shells follow in alphabetical
order. When a shell is full (e.g. the M shell can only hold 18 electrons) the next
outer shell starts to fill up.

The K shell energies of many elements are important in several aspects of the physics of
radiology and a table of their various values and where they are used for different aspects
of radiology is given in Table 1.1. This table will be useful for reference when reading the
subsequent chapters.
The X-ray energies of interest in diagnostic radiology are between 10 and 120 keV. Below
10 keV too many X-rays are absorbed in the body, above 120 keV too few X-rays are stopped
by the image receptor. However, higher energy gamma photons are used when imaging
with radioactive materials where the imaging process is quite different.
Insight
K Shell Energies
The most important energy level in imaging is the K shell energy. The L shell energies are small

(lead 15.2 keV, tungsten 12.1 keV, caesium 5.7 keV, for example) and are mostly outside the energy
range of interest in radiology (we have set the lower limit at 10 keV, some L shell energies are


4

Physics for Diagnostic Radiology

TABLE 1.1
K Shell Energies for Various Elements and the Aspect of Radiology Where They
Are Important
Element
Carbon
Oxygen
Aluminium
Silicon
Phosphorus
Sulphur
Calcium
Copper
Germanium
Selenium
Molybdenum
Rhodium
Palladium
Caesium
Barium
Iodine
Gadolinium
Erbium

Ytterbium
Tungsten
Lead

Area of Application
(a)
(a)
(b)
(c)
(a)
(a)
(a)
(f)
(c)
(c)
(b and e)
(e)
(e)
(c)
(d and f)
(c and d)
(c)
(b)
(c)
(e)
(f)

Z Number
 6
 8

13
14
15
16
20
29
32
34
42
45
46
55
56
53
54
68
70
74
82

K Shell Energy (keV)
0.28
0.53
1.6
1.8
2.1
2.5
4.0
9.0
11.1

12.7
20.0
23.2
24.4
36.0
37.4
33.2
50.2
57.5
61.3
69.5
88.0

(a) Body tissue components—but the X-rays associated with these K shells have too low an
energy to have any external effect and are absorbed in the body.
(b)  Used to filter the beam emerging from the X-ray tube.
(c)  Used as a detector (in a monitor) or an image receptor of X-ray photons.
(d)  Used as a contrast agent to highlight a part of the body.
(e)  Used to influence the spectral output of an X-ray tube.
(f)  Used as shielding from X-ray photons.

slightly above this). Since the (negative) K shell energy is a measure of how tightly bound these two
electrons are held by the positive charge on the nucleus, the binding energy of the K shell increases
as the atomic number increases as can be seen in Table 1.1. As noted in Table 1.1 K shell energies
have important applications in the shape of the X-ray spectra (Section 2.2), filters (Section 3.8),
intensifying screens, scintillation detectors and digital receptors (Chapter 5) and contrast agents
(Section 6.3.4).

1.2  Nuclear Stability and Instability
If a large number of protons were forced together in a nucleus they would immediately

explode owing to electrostatic repulsion. Very short-range attractive forces are therefore
required within the nucleus for stability, and these are provided by neutrons, uncharged
particles with a mass almost identical to that of the proton.


5

Fundamentals of Radiation Physics and Radioactivity

The total number of protons and neutrons, collectively referred to as nucleons, within the
nucleus is called the mass number, usually given the symbol A. Each particular combination of Z and A defines a nuclide. One notation used to describe a nuclide is AZN.
The number of protons Z defines the element N, so for hydrogen Z = 1, for oxygen Z = 8
and so on, but the number of neutrons is variable. Therefore an alternative and generally
simpler notation that carries all necessary information is N-A. The notation AZN will only
be used for equations where it is important to check that the number of protons and the
number of nucleons balance.
Nuclides that have the same number of protons but different numbers of neutrons are
known as isotopes. Thus O-16, the most abundant isotope of oxygen, has 8 protons (by definition) and 8 neutrons. O-17 is the isotope of oxygen which has 8 protons and 9 neutrons.
Since isotopes have the same number of protons and hence when neutral the same number
of orbital electrons, they have the same chemical properties.
The number of neutrons required to stabilise a given number of protons lies within fairly
narrow limits and Figure 1.3a shows a plot of these numbers. Note that for many elements
of biological importance the number of neutrons is equal to the number of protons, but the
most abundant form of hydrogen, which has one proton but no neutrons, is an important
exception. At higher atomic numbers the number of neutrons begins to increase faster
than the number of protons—lead, for example, has 126 neutrons but only 82 protons.
An alternative way to display the data is to plot the sum of neutrons and protons against
the number of protons (Figure 1.3b). This is essentially a plot of nuclear mass against
(a)
208

82 Pb

120

(b)
127
53

60
40
30

β– decay

α decay

20
10

1H
1

Mass (P + N)

Number of neutrons

80

40
20Ca

α decay
β– decay
β+ decay

β+ decay
16O
8
12C
6

10

20

30

50

80

Charge (P)

Number of protons

FIGURE 1.3
Graphs showing the relationship between number of neutrons and number of protons for the most abundant stable
elements. (a) Number of neutrons plotted against number of protons. The dashed line is at 45°. The cross-hatched area
shows the range of values for which the nucleus is likely to be stable. (b) Total number of nucleons (neutrons and protons) plotted against number of protons. On each graph the changes associated with β+, β– and α decay are shown.

6

Physics for Diagnostic Radiology

nuclear charge (or the total charge on the orbiting electrons). This concept will be useful
when considering the interaction of ionising radiation with matter, and in Section 3.4.3 the
near constancy of mass/charge (A/Z is close to 2) for most of the biological range of elements will be considered in more detail.
If the ratio of neutrons to protons is outside narrow limits, the nuclide is radioactive or
a radionuclide. For example, H-1 (normal hydrogen) is stable, H-2 (deuterium) is also stable,
but H-3 (tritium) is radioactive. A nuclide may be radioactive because it has too many or
too few neutrons.
A simple way to make radioactive nuclei is to bombard a stable element with a flux of
neutrons in a reactor. For example, radioactive phosphorus may be made by the reaction
shown below:
31
15



0
P + 01 n = 32
15 P + 0 γ

(the emission of a gamma ray as part of this reaction will be discussed later). However, this
method of production results in a radionuclide that is mixed with the stable isotope since
the number of protons in the nucleus has not changed and not all the P-31 is converted to
P-32. Radionuclides that are ‘carrier free’ can be produced by bombarding with charged
particles such as protons or deuterons, in a cyclotron; for example, if sulphur is bombarded
with protons,

34
16



34
S + 11 p = 17
Cl + 01 n

The radioactive product is now a different element and thus may be separated by chemical
methods.
The activity of a source is a measure of its rate of decay or the number of disintegrations per
second. In the International System of Units it is measured in becquerels (Bq) where 1 Bq is
equal to one disintegration per second. The becquerel has replaced the older unit of the curie
(Ci), but since the latter is still encountered in textbooks and older published papers and is
still actively used in some countries, it is important to know the conversion factor.


1 Ci = 3.7 × 1010 Bq

Hence,
1 mCi (millicurie) = 3.7 × 107 Bq (37 megabecqerels or MBq)
1 µCi (microcurie) = 3.7 × 104 Bq (37 kilobecquerels or kBq)

1.3  Radioactive Concentration and Specific Activity
These two concepts are frequently confused.
1.3.1  Radioactive Concentration
This relates to the amount of radioactivity per unit volume. Hence it will be expressed
in Bq ml–1. It is important to consider the radioactive concentration when giving a bolus

Fundamentals of Radiation Physics and Radioactivity

7

injection. If one wishes to inject a large activity of technetium-99m (Tc-99m) in a small volume, perhaps for a dynamic nuclear medicine investigation, it is preferable to elute a ‘new’
molybdenum-technetium generator when the yield might be 8 GBq (200 mCi) in a 10 ml
eluate [0.8 GBq ml–1 (20 mCi ml–1)] rather than an old generator when the yield might be
only about 2 GBq (50 mCi) [0.2 GBq ml–1 (5 mCi ml–1)]. For a fuller discussion of the production of Tc-99m and its use in nuclear medicine see Section 1.7 and Chapter 10.
1.3.2  Specific Activity
This relates to the proportion of nuclei of the element of interest that are actually labelled.
Non-radioactive material, for example iodine-127 (I-127) in a sample of I-125 may be present as a result of the preparation procedure or may have been added as carrier. The unit for
the total number of atoms or nuclei present is the mole so the proportion that are radioactive or the specific activity can be expressed in Bq mol–1 or Bq kg –1. The specific activity of a
preparation should always be checked since it determines the total amount of the element
being administered. Modern radiopharmaceuticals generally have a very high specific
activity so the total amount of the element administered is very small, and problems such
as iodine sensitivity do not normally arise in diagnostic nuclear medicine.
Insight
Pure Radionuclides
The number of molecules in one gram-molecular weight is 6.02 × 1023 (Avogadro’s number). Very
few radionuclide solutions or solids are pure radionuclide. Most consist of radioactivity mixed
with some form of non-radioactive carrier.

1.4  Radioactive Decay Processes
Three types of radioactive decay that result in the emission of charged particles will be
considered at this stage.
1.4.1  𝛃– Decay
A negative β particle is an electron. Its emission is actually a very complex process but it
will suffice here to think of a change in the nucleus in which a neutron is converted into a
proton. The particles are emitted with a range of energies. Note that although the process

results in emission of electrons, it is a nuclear process and has nothing to do with the orbiting
electrons.
The mass of the nucleus remains unchanged but its charge increases by one, thus this
change is favoured by nuclides which have too many neutrons.
1.4.2  𝛃+ Decay
A positive β particle, or positron, is the anti-particle to an electron, having the same mass
and an equal but opposite charge. Again, its precise mode of production is complex but