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Part II
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Detailed Methodology Part
Physics of Radioguided Surgery:
https://t.me/med1917
Basic Principles and Methods of
Radiation Detection
Thomas Wendler, Uta Eberlein,
and
Michael Lassmann
2
Contents
2.1 Radioactivity 16
2.2
Half-Life 16
Decay Modes 18
2.3
+
2.3.1 β
2.3.2 β
2.3.3 Electron Capture 19
2.3.4 γ Decay 19
2.4
2.5
2.5.1 γ or X-Ray Interactions 20
2.6
2.6.1 Interactions with Electrons 23
2.6.2 Interactions with the Nucleus 23
2.6.3 β
2.6.4 Penetration of β Particles in Tissue 24
2.7
2.7.1
2.7.2 Photomultiplier Tubes 25
T. Wendler (*)
Lehrstuhl für Informatikanwendungen
in der Medizin & Augmented Reality,
Technische Universität München, Munich, Germany
Nuklearmedizinische Klinik und Poliklinik,
Klinikum rechts der Isar der Technischen
Universität München, Munich, Germany
e-mail: wendler@tum.de
U. Eberlein • M. Lassmann
Klinik und Poliklinik für Nuklearmedizin,
Universitätsklinikum Würzburg, Würzburg, Germany
Decay 18
−
Decay 18
Nuclides Used in Radioguided
Surgery
Interaction of Radiation and Matter 20
Interaction of β Particles 23
Detection of Radiation 24
Scintillator Crystals and Light Detection 25
20
+
Annihilation 24
2.7.3 Silicon Photomultipliers 26
2.7.4 Scintillating Crystals 26
2.8
Direct Radiation Detection 26
Collimation and Radiation Shielding 27
2.9
2.10
Measuring Radiation in the Human
Body 28
2.10.1 Interactions of Radiation with Tissue 29
2.10.2 γ or X-Ray Detection 29
2.10.3 β Detection 30
Pitfalls During Radioguided Surgery 30
2.11
2.11.1 Fast Measurements, Fast Movements 30
2.11.2 Shine-Through 31
2.11.3 Shadowing 32
Conclusions 32
References 32
Abstract
Radioguided surgery requires a significant
amount of technology for its implementation.
As a result, surgeons working in this field
must have a basic know-how that extends
beyond the standard surgical training and covers the relevant physics. Within this chapter
we have tried to synthesize the background
knowledge needed for a complete understanding of the most important aspects and processes. The terminology and the explanations
target people just starting in the field, and the
contents should prove readily intelligible as
long as the complete chapter is read.
© Springer International Publishing Switzerland 2016
K. Herrmann et al. (eds.), Radioguided Surgery: Current Applications and Innovative
Directions in Clinical Practice, DOI 10.1007/978-3-319-26051-8_2
15
16
22
()
=´
()
pT
//
2
()
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T. Wendler et al.
2.1 Radioactivity
Radioactivity is a manifestation of the weak force
or the weak nuclear force, one of the four fundamental physical interactions.1 Radioactivity,2 also
known as radioactive decay or nuclear decay, is a
process in which a nucleus of an unstable atom
(the “parent”) transforms into a more stable one
(the “daughter”) by releasing energy in the form
of particles and/or γ rays. The way in which this
energy is released depends on the internal structure of the parent nucleus. This structure is understood as the amount of protons and neutrons of
the nucleus as well as its level of excitation. In
order to distinguish atoms of the same chemical
element with a different nuclear structure and
energy content, reference is commonly made to
nuclides.
The officially accepted nomenclature for
nuclides is denoted by the mass number A, i.e.,
the sum of protons and neutrons, using one of the
following forms:
• Z-A, e.g., In-111, F-18
•AZ, e.g., 68Ga,
Commonly only one level of energy excitation
of a nucleus exists; however, some atoms may
have different so-called metastable levels of excitation (levels that are sufficiently stable to be
detected). In order to refine the nomenclature just
presented, such nuclides are designated by the
letter “m” following their mass number A, e.g.,
Tc-99m is a different nuclide from Tc-99 since
the former has a higher level energy. If there are
several metastable levels of energy, then an integer is added to the “m,” i.e., m
1
Today’s physics distinguishes four major independent
interactions: gravitation, electromagnetism, and the two
nuclear forces (the weak and the strong).
2
The term “radioactivity” derives from Marie Curie [1],
who discovered this process in radium, which was among
the first elements to be discovered by her and her husband,
Pierre, at the turn of the nineteenth century.
123
I
2
, m3, etc.
In general, nuclides that eventually undergo
nuclear decay are termed radioactive or, in
nuclear technology jargon, radionuclides. On the
other hand, nuclides that do not decay for a significant amount of time are termed stable.
A common representation of stable and unstable nuclides is the mass/atomic number plot
(Fig. 2.1), where all existing nuclides are plotted
and marked according to the main decay modes.
Normally the nuclides with a lower mass number
than the stable nuclides are β+ emitters, while
those with a higher mass number than the stable
nuclides are β− emitters.
2.2 Half-Life
Radioactive decay is a random process, which, as
such, cannot be predicted or triggered by any
external condition.3 According to quantum theory, the probability that a single radioactive atom
will decay follows an exponential law. This
means that independently of how long a radioactive atom has existed, the likelihood p that it will
decay within a certain period doubles at constant
time intervals. One of these intervals is called a
half-life, denoted T
In practice this means that for a given radionuclide, the number of radioactive atoms N will
diminish on average by half within one
half-life:
3
As mentioned above, radioactivity is an independent fun-
damental interaction.
:
1/2
´
pT
12 12
NT
()
12
/
0
N
=
Atomic number
2 Physics of Radioguided Surgery: Basic Principles and Methods of Radiation Detection
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17
Mass number
Na-35 Al-35 Si-35
Na-34 Mg-34 Al-34 Si-34
Na-33 Mg-33 Si-33
Na-32 Mg-32 Al-32 Si-32
Na-31 Mg-31 Al-31 Si-31
Na-30 Mg-30 Al-30 Si-30
Ne-29 Na-29 Mg-29 Al-29 Si-29
Ne-28 Na-28 Mg-28 Al-28 Si-28
Ne-27 Na-27 Mg-27 Al-27 Si-27
Ne-26 Na-26 Mg-26 Al-26 Si-26
F-25 Ne-25 Na-25 Mg-25 Al-25 Si-25
O-24 F-24 Ne-24 Na-24 Mg-24 Al-24 Si-24
O-23 F-23 Ne-23 Na-23 Mg-23 Al-23
N-22 O-22 F-22 Ne-22 Na-22 Mg-22 Al-22 Si-22
N-21 O-21 F-21 Ne-21 Na-21 Mg-21
C-20 N-20 O-20 F-20 Ne-20 Na-20 Mg-20
C-19 N-19 O-19 F-19 Ne-19
C-18 N-18 O-18 F-18 Ne-18
B-17 C-17 N-17 O-17 F-17 Ne-17
C-16 N-16 O-16
B-15 C-15 N-15 O-15
Be-14 B-14 C-14 N-14 O-14
B-13 C-13 N-13 O-13
Be-12 B-12 C-12 N-12
Li-11 Be-11 B-11 C-11
Be-10 B-10 C-10
Li-9 Be-9 C-9
He-8 Li-8 Be-8 B-8
Li-7 Be-7
He-6 Li-6
stable
He-4 α decay
H-3 He-3 β− decay
H-2 β+ decay / electron capture
H-1
Si-36
Fig. 2.1 Mass/atomic number plot for the first 15 elements
of the periodic table. The x-axis shows the atomic number,
which is the number of protons in the nucleus; the y-axis
shows the mass number, the sum of protons and neutrons.
The color indicates the main decay modes of the corresponding nuclide (Table generated using data extracted from [2])
18
te
→+ ++n
-+
F-18
+
O-18
0.2
%100%
Probability density
Percentage of maximum energy
https://t.me/med1917
T. Wendler et al.
In general the number of radioactive atoms N(t) at
a time t, with an amount N (t0) at a time point t0, is
given by
2
t
−
Nt Nt eN
=
()
×=
()
0
T
12ln/
()
t
−
l
×
0
The rate of decays per second (λ) of a radioactive
material is its radioactivity and is characteristic
for each nuclide. The SI unit used to describe one
decay per second is a Becquerel,4 Bq. Some
countries still use the unit Curie,5 Ci and
1 Ci = 3.7 × 1010 Bq. Common radioactivity values in radioguided surgery are kBq to MBq or
μCi to mCi.
2.3 Decay Modes
Depending on the nuclear structure and internal
energy of a nuclide, different types of radioactive
decay are likely. The most common or best
known are α, β, and γ decay; however, these are
not the only types. The types of decay most relevant to radioguided surgery are explained below.
e
ν
Fig. 2.2 Example of β+ decay: F-18 decays to 97 % in
O-18 with a half-life of 109.77
energy of 633.5
0.15
0.1
0.05
Fig. 2.3 Schematic shape of positron emission spectrum
as a function of the energy of the emitted positron. The
average energy of a positron is roughly two-thirds of the
maximum energy
keV (Data from [2])
0
0% 25% 50% 75
min and a β
+
maximum
2.3.1 β+ Decay
β+ decay (Fig. 2.2) is fundamental to the develop-
ment of positron emission tomography (PET) and
the use of PET nuclides in radioguided surgery.
Within a β+ decay, a proton p in the nucleus of the
decaying atom converts into a neutron, emitting a
positively charged electron e
positron or antielectron) and a neutrino ν:
An example of this decay is F-18, the workhorse
for PET imaging, which emits a positron in
96.7 % of cases and converts into a negatively
charged O-18:
4
The unit Becquerel honors the discoverer of radioactiv-
ity, Henri Becquerel [1].
5
In honor of Marie and Pierre Curie, pioneers in the
understanding of radioactivity
pne
18 18
FOe®++
+
(also known as a
n
Following the law of conservation of energy, the
energy released in this nuclear decay is divided
between the positron, the neutrino and the daughter nuclide. As a result the positron has a continuous spectrum of energy with a fixed maximum
[3] (Fig. 2.3). In the case of F-18, the maximum
energy is 633.5 keV.
If the resulting nucleus after the decay is a
short-lived metastable state, the β
+
decay can be
followed by a prompt (almost immediate) γ decay
(see below, isomeric transition).
2.3.2 β− Decay
β− decay (Fig. 2.4) is commonly used in nuclear
medicine for therapy as these particles deposit
their energy very close to the place where they
have been emitted. Nevertheless, secondary γ
rays or bremstrahlung X-rays emitted can be
used for radioguided surgery, as in the case of
I-131, a nuclide used for therapy and imaging.
ev
-
FO®+
®+
AA
ZZ
I-131
-
Xe-131
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In the case of F-18, 3 % [2] of all decays are elec-
e
tron captures, which are described by
18 18
The drop in energy of the nucleus in this process
is emitted in the form of γ rays or is passed to an
ν
electron. In the particular case of F-18, there is
Fig. 2.4 Example of β− decay: I-131 decays to 89.9 % in
Xe-131 with a half-life of 8.02
energy of 606
MeV (Data from [2])
days and a β
–
maximum
one γ ray emission at 1.34 MeV.
Electron captures commonly result in additional radiation, since X-rays or light are also
frequently emitted. The explanation for this is
that the missing (captured) electron in the inner
Similar to β+ decay, where a charged particle
is expelled from the nucleus, in β− decay an electron e− is emitted. During this process a neutron n
transforms into a proton p, an electron e−, and an
antineutrino n:
np
®+ +
In I-131 different energy states are possible,
resulting in a variety of β− decays, each with a
different maximum energy. The most frequent
(89.9 % of all decays) maximum energy is
606 keV [2]:
131 131
IXee v®++
+-
orbit will then cause higher orbit electrons to fall
into the lower orbit, emitting characteristic
X-rays or light (Fig. 2.5). Alternatively the
energy may be passed to another outer shell electron, which is then expelled from the atom
(Auger effect6) [5].
A relevant example of an electron capture in
radioguided surgery is Co-57, used for the calibration of detectors, as described below:
57 57
Co Fe
The decay of Co-57 produces at least three γ rays
of relevance and a wide spectrum of characteristic X-rays (Table 2.1).
As in the β+ decay, there is no rule for the distribution of energy between electron, antineutrino,
and daughter nuclide, resulting in a spectrum
2.3.4 γ Decay
with a similar bell shape to that in Fig. 2.3.
Also, it is possible for a β− decay to be followed by an almost immediate (prompt) γ decay,
as happens during the β
−
decay of I-131, when
several γ rays are emitted, the most relevant being
at 364 keV.
The γ decay provides the foundation for
single- photon emission computed tomography
(SPECT).
There are two relevant types of γ emission in
radioguided surgery. The simplest derives from
an isomeric transition. In this case, a nucleus in
an excited state releases energy in the form of γ
2.3.3 Electron Capture
rays but its nuclear structure remains unchanged.
The excited state is normally denoted by a “*” to
A more interesting and complex decay mode is
the so-called electron capture [4] or inverse β
decay (Fig. 2.5).
Nuclei like F-18 also may become more stable
by capturing an electron from the inner orbits and
the right of the element symbol:
*
®
In the particular case when the excited state does
not generate a prompt emission but rather a
making a neutron out of it and a proton. A neutrino is also emitted in this case:
-
pe n+®+
n
6
Effect named after Pierre Auger, who in 1923 discovered
it independently from Lise Meitner, who was the first to
report on it shortly beforehand in 1922 [5]
19
n
n
20
ZZ
O-
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T. Wendler et al.
X-ray
F-18
Fig. 2.5 Example of electron capture: F-18 decays to
3 % in O-18 [2], capturing an electron from the K shell. A
neutrino is also emitted in the first step (not shown). The
Table 2.1
X-rays of Co-57
γ rays Characteristic X-rays
E (keV) P (%) E (keV) P (%) X-ray
14.4 9.16 0.7 0.56 Fe L
122.1 85.60 0.72 0.42 Fe L
136.5 10.68 6.39 16.40 Fe K
692 0.16 6.4 32.60 Fe K
Data taken from [2]
The most frequent γ rays and characteristic
α1
β1
α2
α1
7.06 1.99 Fe K
7.06 3.88 Fe K
β3
β1
delayed emission, one speaks of a metastable state,
which is denoted by an “m,” as explained above:
Am A
®
Tc-99m is an example of a pure γ decay producing several γ rays, the 142-keV γ ray being the
most relevant.
2.4 Nuclides Used
in Radioguided Surgery
To close this section, Table 2.2 lists the most relevant nuclides in radioguided surgery.
2.5 Interaction of Radiation
and Matter
O-18
K shell electron hole is replaced by an L shell electron,
resulting in the emission of a characteristic X-ray or an
Auger electron
source is detected during the surgical procedure
and also how and whether the radiation reaches
the detector. Commonly a distinction is drawn
between interactions of charged particles (β
β− particles) and γ or X-rays.
2.5.1 γ or X-Ray Interactions
When a γ or an X-ray (a photon) hits an atom, its
energy can be transferred to the atom and in particular to its electrons. There are two major interactions that need to be considered at the levels of
energy used in radioguided surgery.
The first interaction takes place when the energy
of an incident photon is completely absorbed by an
electron. In this case one speaks of the photoelectric
7
effect
(Fig. 2.6). In the photoelectric effect, as the
energy of the photon is completely transferred, the
photon disappears (complete absorption). Further,
the electron that has received this energy is expelled
from the atom. This effect commonly occurs if the
incident photon hits a lower shell electron.
The expelled electron is commonly called a
photoelectron, and it carries the kinetic energy
resulting from the energy of the incident photon
minus the binding energy of the electron when it
was in the atom. As a result a photoelectric effect
can only happen if the incident photon has sufficient energy to free an electron in the given atom.
+
and
After a radioactive decay, the emitted particles
interact with matter. These interactions play a relevant role in the way in which the radioactive
7
The first explanation of the photoelectric effect in
terms of currently accepted physics comes from Albert
Einstein [6].
()
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Table 2.2 Most frequent nuclides used in radioguided surgery for both intraoperative detection and calibration
Nuclide Half-life
C-11 20.4
F-18 109.7
Na-22 2.60 a EC (γ) 1.27
Co-57 271.8
Ga-68 67.6
Zr-89 78.4
Tc-99m 6.01
In-111 2.80
I-123 13.3
I-124 4.18
I-125 59.4
I-131 8.02
Data taken from [
PET nuclides are used for direct β
tion. In particular I-125 is used for solid markers implanted in tissue interventionally to guide surgical resection
QC quality control, EC electron capture, IT isomeric transition
min β
min β
days EC (γ) 122 keV 86 Calibration/QC
min β
h EC (γ) 909 keV 100 None
h IT 142 keV 89 SPECT
days EC (γ) 171 keV 90 SPECT
h EC (γ) 158 keV 83 SPECT
days EC (γ) 602 keV 63 None
days EC (γ) 35 keV 7 Marker
days IT 364 keV 82 SPECT
2]
Main decay
modes
+
+
+
β
EC (γ) 136
+
+
β
+
β
EC (γ) 245
EC (X) 27
EC (X) 31
EC (γ) 722
EC (γ) 1.69
+
β
+
β
EC (γ) 27
EC (γ) 31
IT 637
-
β
−
β
+
detection or detection of annihilation photons. SPECT nuclides are used for γ detec-
γ, X, or max. β
energy
960 keV 100 PET
633 keV 97 PET
MeV 100 None
546 keV 90 Calibration/QC
keV 11 Calibration/QC
1.90 MeV 88 PET
2.92 MeV 9 PET
902 keV 23 PET
keV 94 SPECT
keV 72 None
keV 12 None
keV 10 None
MeV 11 None
1.53 MeV 12 PET
2.14 MeV 11 PET
keV 100 Marker
keV 20 Marker
keV 7 None
333 keV 7 Therapy
606 keV 90 Therapy
Probability of
emission (%) Use
21
Of major relevance is the fact that if an electron expelled is from a low shell, it is common for
a characteristic X-ray or light to be emitted, as
described in the section on γ decay.
If a photon is not completely absorbed by an
atom, one speaks of the Compton8 effect
(Fig. 2.7). Therein only part of the energy of a
photon is transferred to an electron. As a result, a
lower energy photon is scattered in a direction
which can be calculated from its final energy. As
in the photoelectric effect, the electron absorbing
8
In honor of Arthur H. Compton, who first observed and
reported this in 1923 [7]
the energy is expelled from the atom. Commonly
this electron is called a Compton recoil electron.
This effect takes place with higher shell electrons
that are loosely bound.
Given an energy E0 of the incident photon, a
final energy E (θ), and a scattering angle θ, one
has
2
Emc
e
E
q
=
()
mc E
0
2
+-
e
0
1cos
q
In the above formula, the constant me is the mass
of an electron and c the speed of light. The constant mec2 is commonly given as 511 keV.
22
ll
xx
()
ts
mts
=+
)
x
https://t.me/med1917
Fig. 2.6 Photoelectric
effect, where a photon
is completely absorbed
by an atom. Its energy
is transferred to an
electron, which is then
expelled from the atom
T. Wendler et al.
Photon
photon of
energy E
Fig. 2.7 The Compton effect, wherein a photon is scattered by a loosely bound electron of an outer shell, losing energy
and freeing the electron with which it collided
0
θ
photon of
energy
E(q
Following this formula the scattering can
be in any direction. Photons that are scattered
I
0
I(x)
by 180° or “backscattered” lose the most
energy.
The likelihood that a photon will undergo a
photoelectric or a Compton effect depends on
its energy and the material through which it
passes. A way to model this takes into account
the fact that, given a certain path through a
material, the likelihood that a photon will be
absorbed follows an exponential law. An
amount I
distance x of a material is absorbed, resulting
of gamma rays or X-rays passing a
0
Fig. 2.8 Attenuation of intensity of γ rays crossing a dis-
tance x of a material
in a diminished amount I(x), as shown in
Fig. 2.8:
Ix Ie
--
=
0
The coefficient τl is the linear attenuation coefficient due to the photoelectric effect, and σl is the
linear attenuation coefficient due to the Compton
effect.
Commonly one uses the linear attenuation
coefficient μl due to both interactions:
ll l
The distribution between the photoelectric effect
and the Compton effect depends on the material
and the energy of the incident photons (see
Fig. 2.9 as example for water).
0.01 0.1 1
Energy in MeV
σ
Incident
particl
β
2 Physics of Radioguided Surgery: Basic Principles and Methods of Radiation Detection
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Fig. 2.9 Relative
value of mass
attenuation coefficient
for the photoelectric
and the Compton
effect for water as a
function of the energy
of the incident photon
(Data taken from [
8])
/g
2
Mass attenuation coefficient in cm
10
1
0.1
0.01
0.001
23
τ
Fig. 2.10 Collision
between a β particle
and an electron,
generating a secondary
electron and slowing
down the β particle
β
e
The quantity used in Fig. 2.9 is the mass attenuation coefficient μm, which can be derived from
the linear attenuation coefficient μl and the density of the material ρ.
2.6 Interaction of β Particles
β+ and β− are charged particles. As a result, their
interactions with matter are mainly dominated by
their charge and the interaction of it with electrons or the nucleus. In these interactions the
charged particles lose energy. Among these interactions, the particular case of β+ annihilation
plays an important role in radioguided surgery.
Secondary
electron
Slower
particle
In the collision with an electron, the charged
particle passes energy to the orbital electron,
expelling it from its orbit. This expelled electron is
frequently referred to as a secondary electron
(Fig.
2.10). As explained in the section on γ decay,
the fact that an electron is expelled can cause emission of a characteristic X-ray.
Even if the β particle does not collide with an
orbital electron, it may still pass energy to it,
bringing it to a higher excitation level. In this
case, of course, the β particle still loses energy
and slows down, but no secondary electron is
generated.
2.6.2 Interactions with the Nucleus
2.6.1 Interactions with Electrons
There are two main interactions of β particles
with electrons: collision with an orbital electron
and orbital electron excitation.
A β particle can interact not only with electrons
but also with the nuclei of the atoms in its path.
This interaction normally results in a major
change in the trajectory of the β particle and the
emission of photons. These photons are known as
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