Lima J.J.Pedroso, de (ed.). Nuclear Medicine Physics

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138 Nuclear Medicine Physics

SPECT PET

Tomographic images

Multiple

images

Image

reconstruction

Multiple

images

Camera

rotation

Planar images

Yes

(electronic

collimation)

Two 511 keV

photons

emitted

simultaneously

in opoosite

collections

1 γ photon

99m

Tc: 140 keV

other energies

depending on

radioisotope

1 γ photon

1 position

γ emitter

emitter

Scintigraphy

Colimator

Detection

Labelling

Decay

Image

reconstruction

Tomographic images

FIGURE 5.1

Comparison between in vivo imaging methods in nuclear medicine, with regard to the detection

and production of images. The presence of the collimator for planar scintigraphy and SPECT

imaging, which is required in order to locate the radioactive source in relation to the detec-

tor, causes a very signiﬁcant loss of sensitivity in comparison with PET and degrades spatial

resolution, which deteriorates in proportion to the distance from the radioactive source to the

detector.

Detector

Q/C

FIGURE 5.2

Diagram of the equivalent circuitry connected to the detector and the typical voltage (V) response

of the circuitry.

Radiation Detectors and Image Formation 139

load circuit. The amplitude of the signal is proportional to the deposit charge

in the detector (V

max

= Q/C). For each efﬁcient interaction taking place in the

detector, there is a corresponding electrical pulse in the measuring circuit and

the pulse rate is, therefore, equivalent to the interaction rate in the detector.

Efﬁciency, energy resolution, and dead time are important factors in radi-

ation detectors. The efﬁciency of a detector links the number of photons

entering the active volume with the number of electrical impulses gener-

ated. For convenience, efﬁciency is studied in two separate ways: as absolute

efﬁciency and as intrinsic efﬁciency. Absolute efﬁciency is deﬁned as the ratio

between the number of pulses and the measured number of photons emitted

by the source [4]:

abs

number of measured pulses

number of emitted photons

. (5.1)

Conversely, intrinsic efﬁciency is deﬁned by taking into account only the

characteristics of the detector and, hence, is independent of the geometri-

cal characteristics of the measuring arrangement. Thus, intrinsic efﬁciency is

deﬁned by

int

number of measured pulses

number of incident photons in detector

. (5.2)

Considering a point source emitting isotropically, the relationship between

the two efﬁciencies is based only on geometrical arguments and is given by

int

4π

abs

, (5.3)

where Ω is the solid angle of the detector seen from the position of the point

source. Intrinsic efﬁciency depends on the material of the detector, the thick-

ness (measured in terms of the direction of the incident radiation), and the

energy of the incident radiation.

The energy resolution of a detector is deﬁned as the ability to discriminate

between two close radiation energies. The response of a detector to a real

monoenergetic source is not a narrow peak (mathematically, a delta function)

but a Gaussian distribution whose amplitude corresponds to the radiation

energy.

Formally, the energy resolution is given by the ratio between the full width

at half maximum (FWHM = ΔE) of the energy response of the detector to

monoenergetic radiation and the peak energy (E

) [4]. Two monoenergetic

sourcesare distinguished by a detector if the differencebetween their energies

is greater than the FWHM of the response curve (Figure 5.3).

Several factors contribute toward the deterioration of energy resolution in

a detector, such as statistical noise due to the discrete nature of the signal,

the noise caused by the detector and by the measuring circuit, and any devi-

140 Nuclear Medicine Physics

FWHM

H/2

(a) (b)

dN/dE

FWHM

FIGURE 5.3

(a) Response curve for a source point obtained by a real radiation detector. The xx axis represents

the energy of the signal, whereas the yy axis is the number of counts per interval of energy. (b)

Diagram of the minimum difference in energy that must exist in order to discriminate between

two monoenergetic sources.

ations from operating conditions during measurement. Although the latter

two sources of error are likely to be minimized by optimizing the detector, the

primary cause of noise is always present regardless of the detector. Statistical

noise is related to the fact that the charge deposited in the detector is discrete,

as it depends on the number of charge carriers. The number of charge carriers

is random and follows a certain distribution of probabilities. Assuming that

the process follows a Poisson distribution, for a given number N, of created

charges, the expected standard deviation is

√

N. Assuming further that the

response of the detector is linear to the number of charges generated, the

expected deposited energy (E

) should be equal to KN, where K is a constant

of proportionality. For a high number N of charges, the response of the detec-

tor follows a Gaussian distribution. For this distribution, the FWHM is equal

to 2.35σ, hence;

R =

FWHM

2.35K

√

= 2.35

√

. (5.4)

This relationship implies that statistical noise limits the energy resolution,

which can be improved if the number of charges per event increases.

The dead time of a detector is usually deﬁned as the time that should exist

between two separate events so that they can be measured as two different

electrical signals. Depending on the type of detector, the limiting factor is

either the detection process or the associated electronic circuit.

5.1.1.1 Interaction of Radiation with Matter

When gamma (or x) rays focus directly on an object and cross it, some photons

interact with the particles of the object and their energy can be absorbed or

Radiation Detectors and Image Formation 141

scattered. The process of absorption and dispersion of radiation is generally

known as attenuation (Figure 5.4).

The intensity (energy per unit areaand per unit time) of the radiation emerg-

ing from the object is less than the incident intensity, and the fraction of

transmission depends on the density, atomic number, and thickness of the

material and the radiation energy.

The attenuation resulting from the interaction of gamma radiation with the

particles of the medium is not a unique process—a single interaction rarely

results in the incident photon changing to another form of energy. Usually,

several interactions are needed until all the photon energy is transformed.

Therefore, attenuation results from all processes involved, that is, the pho-

toelectric effect, the Compton effect, the Rayleigh–Thomson effect and, for

energies above 1.022 MeV, the production of pairs.

Figure 5.5 shows the total attenuation coefﬁcient for water and for lead

in terms of incident gamma radiation energy. The usual range of energies

for gamma radiation in NM is 80–511 keV, corresponding approximately to

the shaded area in the chart. For water (the main constituent of biological

tissues), the predominant effect in the energy range in question is the Comp-

ton effect, and the occurrence of the photoelectric effect is much smaller. On

the other hand, for lead the photoelectric effect is predominant in the same

energy range. The total attenuation of water is low, which is fundamental to

the success of PET and SPECT imaging, whereas the attenuation character-

istics of lead are essential for collimators and the shielding devices used in

radioprotection.

The photoelectric effect occurs when the incident photon transfers its total

energy to an electron of an atom, which is ejected with a kinetic energy equal

to the difference between the energy of the incident photon and the binding

energy (E

= hν −E



). The ejection of the electron causes the atom to become

an ion for a short period of time. This excited state remains until a more

energetic electron occupies the hole created, emitting a photon with energy

that is equal to the difference between the energies of the initial and ﬁnal

I = I

–μ x

FIGURE 5.4

Illustration of how the attenuation experienced by a monoenergetic beam when crossed by an

object of thickness x. I

is the intensity of the incident radiation beam, reduced to I after crossing

the object. The reduction fraction is given by e

−μx

, where μ is the linear attenuation coefﬁcient

of the medium crossed by the radiation.

142 Nuclear Medicine Physics

1.0E+03

μ (cm

/g)

μ (cm

/g)

Lead attenuation coefficient for different energies

Water attenuation coefficient for different energies

Rayleigh effect

Compton effect

Photoelectric effect

Pairs production (nuclear)

Pairs production (atomic)

Total attenuation

Rayleigh effect

Compton effect

Photoelectric effect

Pairs production (nuclear)

Pairs production (atomic)

Total attenuation

1.0E+02

1.0E+01

1.0E+00

1.0E–01

1.0E–02

1.0E–03

1.0E–04

1.0E–05

1.0E–06

1.0E–07

1.0E–08

1.0E–09

1.0E+03

(a)

(b)

1.0E+02

1.0E+01

1.0E+00

1.0E–01

1.0E–02

1.0E–03

1.0E–04

1.0E–05

1.0E–06

1.0E–07

1.0E–08

1.0E–09

1.0E–02 1.0E–01 1.0E+00

Energy (MeV)

1.0E+01 1.0E+02

1.0E–02 1.0E–01 1.0E+00

Energy (MeV)

1.0E+01 1.0E+02

FIGURE 5.5

(a) Variation of the water attenuation coefﬁcient with energy. The total attenuation is the com-

bined effect of the four mechanisms. (Data from: http://physics.nist.gov/PhysRefData/Xcom/

html/xcom1.html.) (b) Variation of the lead attenuation coefﬁcient with energy. The total atten-

uation is the combined effect of the four mechanisms. (Data from: http://physics.nist.gov/

PhysRefData/Xcom/html/xcom1.html.)

states of the electron. The radiation emitted, which is generally termed char-

acteristic x-ray, is usually absorbed later by the detector. The probability of

the occurrence of the photoelectric effect depends on the fourth power of the

atomic number (Z), which is easily observable in Figure 5.5.

The Compton effect or Compton scattering, occurs when a photon interacts

with an electron, causing deﬂection of the photon, which sends part of the

energy to the electron that recoils (Figure 5.6).

The relationship between the energy of the photon, E

, before interacting

with the electron and the energy of the deﬂected photon, E



, for a given angle

Radiation Detectors and Image Formation 143

Recoil electron

Incident photon

Scattered photon

E′ = hv ′

= hv

FIGURE 5.6

Diagram showing the Compton effect—the interaction of a photon with an electron results in

the deﬂection of the photon, which transfers energy to the electron. This interaction results in

a scattered photon with lower energy (longer wavelength) and the recoil of the electron. (Data

from http://physics.nist.gov/PhysRefData/Xcom/html/xcom1.html.)

θ can be obtained from the law of conservation of linear momentum and the

law of conservation of energy. The application of these laws results in the

expression:



1 +(E

)(1 −cos θ)

, (5.5)

where m

is the energy of the electron at rest.

Compton scattering is anisotropic, that is, the probability of a photon being

deﬂective is not equal in all directions. The Klein–Nishina formula describes

scatter probability in terms of direction:

dσ

dΩ



,θ

−P

,θ

sen(θ) +P

,θ



, (5.6)

where r

is the classical electron radius and P

,θ

is the ratio of the energies

before and after Compton deﬂection:

,θ



1 +(E

)(1 −cos θ)

. (5.7)

The value dσ/dΩ is usually known as the differential cross section and

represents the probability of a photon being scattered in the solid angle dΩ.

Rayleigh–Thomson scattering is also known as elastic scattering, as the

kinetic energy is conserved. The probability of this effect occurring is greater

for low-energy photons (<10 keV) that are deﬂected with no loss of energy

when interacting with an atom.

Since pair production is an interaction mechanism that occurs when the

energy is greater than 1.022 MeV, it is therefore, not observed in the energy

144 Nuclear Medicine Physics

ranges associated with NM. The pair production mechanism can be sum-

marized as the interaction of a high-energy photon with the nucleus ﬁeld

or the electron ﬁeld in which the photon is annihilated, producing an

electron–positron pair.

Photoabsorption is a mechanism that occurs only with high-energy pho-

tons, in which a photon is captured by the nucleus, which then de-excites

emitting one or more particles.

5.1.2 Gamma Radiation Detectors

The success of detection depends on the efﬁcacy of the radiation interaction

with the detector, because what is actually measured are the products of inter-

action. Measurement is mainly based on the fast electrons that result from the

interaction of radiation with matter.The maximum energyof these electrons is

equal to the energy of the incident photon; the electrons gradually lose their

energy through interaction with the atoms of the medium that are ionized

or excited. The charge produced is collected either directly via proportional

counters or semiconductor detectors or indirectly via crystal scintillators.

5.1.2.1 Gas-Filled Detectors

Gas-ﬁlled detectors are composed of two electrodes separated by a gaseous

atmosphere. Generally, the container that encloses the gas is one of the elec-

trodes (cathode), and the other electrode (anode) is a thin wire running

through the center of the system [4] (Figure 5.7).

Gamma radiation interacts with the gas contained in the detector causing,

in certain circumstances, ionization and the consequent ejection of electrons.

These are accelerated toward the anode and, if fully collected by the anode,

produce a measurable electric current. Hence, the detector operates as an

ionization chamber.

When the external voltage transfers enough kinetic energy to electrons,they

produce new ionized atoms emitting more electrons—the avalanche effect.

The negative charge created during this process is then collected by the anode,

causing an electrical impulse which is the signal that is actually measured

(see Section 5.1.1). For a certain range of the electric ﬁeld, the signal obtained

is proportional to the number of electron–ion pairs generated by incident

radiation. In this case, the detector is designated as a proportional counter

and operates in the proportionality region, which represents the conventional

mode of operation for these detectors.

In sufﬁciently high electric ﬁelds, the avalanche effect extends to the entire

anode, which leads to a loss of proportionality in the relationship between

the charge produced and the energy released by the incident radiation. The

signal from the detector always has the same amplitude, therefore meaning

that the detector operates in the Geiger–Müller region.

Radiation Detectors and Image Formation 145

Signal

FIGURE 5.7

Equivalent circuit diagram of a gas detector. The electric ﬁeld created within the detector acceler-

ates the electrons produced by the interaction of radiation with the gas, which are then collected

at the anode (internal wire).

5.1.2.2 Semiconductor Detectors

The semiconductor detector most commonly used in the detection of gamma

radiation is the germanium–lithium detector. This type of detector has been

used in gamma radiation spectroscopy since the 1960s. In comparison with

gas detectors, these detectors offer the advantage of a smaller size and larger

density. An additional interesting feature is the excellent energy resolution.

However, until recently, these detectors required a cooling device in order

to operate efﬁciently, which limited their use in medical imaging. With the

emergence of detectors such as the CdZnTe (CZT), which can operate at room

temperature, this limitation has disappeared and gamma cameras using these

semiconductor detectors are now available. Nevertheless, the energy resolu-

tion of CZT detectors is lower than that of germanium detectors, although

still higher than scintillator detectors. There are also solid-state detectors (sil-

icon) that require no cooling devices but can only be used with low-energy

radiation (tens of keV).

The working principle of semiconductor detectors is based on the formation

of electron–hole pairs whose displacement leads to a measurable electrical

signal.

A semiconductor can be deﬁned as a solid whose valence band is complete

whenT = 0 K but whose forbidden band isso small (few eV) that electronscan

be easily thermally excited (at room temperature) and pass to the conduction

band [5]. If the forbidden band is larger, the number of electrons capable

of moving to the conduction band is much smaller and the material is then

classiﬁed as an insulator.

146 Nuclear Medicine Physics

For each electron excited to the conduction band in a semiconductor, a hole

is created in the valence band whose mobility is only a fraction of the mobility

of the electrons. In this situation, conduction of an electric current may exist

if an electric ﬁeld is applied. However, the electric conductivity is lower than

that of metal materials and depends on temperature.

A semiconductor that is free of impurities has an equal number of electrons

in the conduction band and holes in the valence band, as the electrons are

thermically excited; and there is a one-to-one relationship between electrons

and holes. A semiconductor with these characteristics is known as intrinsic

or undoped. Considering the concentration of electrons (n) in the conduction

band and the concentration of holes (p) in the valence band, it can be easily

inferred that, for an intrinsic semiconductor:

n = p. (5.8)

The doping of pure semiconductors with appropriate impurities leads to

situations in which the previous relationship is not maintained and, con-

sequently, there may be an excess of electrons or an excess of holes. The

materials obtained by this process are known as n-type semiconductors or

p-type semiconductors, respectively.

A semiconductor with two adjacent regions, a p-region and a n-region,

demonstrates properties suitable for use as radiation detector. In the pn junc-

tion, there is diffusion of electrons from the n to the p region and a diffusion of

holes in the opposite direction. This process creates a voltage difference in the

pn junction. Near the pn junction, a region is created—the depletion region—

in which thereis balance of chargecarriers. The depletion region has favorable

features as a means of detecting radiation, as any electron that is created in

this region is accelerated into the n side and any created hole is accelerated

into the p side. However, in a nonpolarized pn junction, the depletion region

is small and the junction capacitance is high; hence, the spontaneous electric

ﬁeld generated is of low intensity and does not allow the charge carriers to

move quickly. For these reasons, the pn junction is generally polarized when

used as a radiation detector in real applications.

Figure 5.8 shows a diagram of a typical semiconductor detector. The radia-

tion interacts with the detector, perhapscausing ionization and, therefore, free

charges, which are accelerated by the imposed electric ﬁeld. The charge cre-

ated is then collected by the polarization electrodes, generating an electrical

signal.

The incident photons are absorbed at the pn junction of the semiconductor

crystal, which is affected by a high-voltage difference, creating a large number

of electron–hole pairs. For each electron–hole pair produced, approximately

3–5 eV are expended on average, and the total number of pairs is proportional

to the gamma photon energy. With NaI (Tl) crystal, about 30 eV are needed to

create one ionization and to produce one scintillation within the crystal. The

number of electron–hole pairs produced is about 6–10 times greater than the

amount of scintillation.

Radiation Detectors and Image Formation 147

Signal

Depletion region

FIGURE 5.8

Equivalent circuit diagram of a semiconductor detector. The detector is an inversely polarized pn

junction. When the gamma radiation produces an electron–hole, the charge is conducted through

the sensitive region (depletion region) generating a measurable signal.

The energy resolution of the CZT gamma camera is approximately 5%,

compared with about 14% for the NaI (Tl) gamma camera. The fact that the

CZT gamma camera does not use photomultiplier tubes (PMT) is also an

advantage.

The most recent CZT crystals are slightly more efﬁcient than NaI (Tl). The

intrinsic spatial resolution of CZT gamma cameras is also greater, being

approximately 2–3 mm compared with 3–4 mm for the NaI (Tl) gamma

cameras, at 140 keV.

In addition, the collection time for the electron–hole pairs is at least 100

times shorter than the decay time of the scintillation crystal NaI (Tl), which

allows for an increase in the counting speed (250,000 count/s).

The CZT camera weighs about 100 times less, is considerably smaller than

the scintillation camera, and can, therefore, be easily moved between different

hospital departments.

These differences result in several advantages for image quality, such

as improved contrast due to greater efﬁciency, higher energy resolution,

and accuracy of position determination (intrinsic resolution), which is also

enhanced as an effect of the modular structure [6].

5.1.2.3 Scintillation Detectors

Scintillators convert high-energy gamma photons into photons with wave-

length in the visible range, which, in turn, are detected using PMT. The PMT

collect the light created in the crystal by the γ rays, generating electrical sig-

nals that contain information about the energy of the interactions taking place

in the crystal.