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

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148 Nuclear Medicine Physics

Scintillators are the most commonly used detectors in NM. They are gener-

ally inorganic substances in the form of solid crystals or organic substances

dissolved either in a liquid solution or in a solvent and later polymerized, that

is, formed into a solid solution. However, inorganic crystals are more widely

used in modern NM equipment for the detection of both x-rays and γ rays.

When γ rays with energy levels of up to 511 keV hit the crystal NaI (Tl),

several situations can occur:

1. No interaction

2. Interaction via the Compton effect

3. Interaction via the photoelectric effect

After the interaction of radiation through any of these mechanisms, new

events caused by the release of secondary electrons may occur in the crys-

tal, leading to generation of scintillation and the subsequent conversion into

electrical impulses in the PMT.

The many possible combinations that could lead to production of scintilla-

tion are outlined in Figure 5.9a.

The requirements of an ideal scintillator are highly efﬁcient detection, good

energy resolution, good intrinsic spatial resolution, low dead time, and lim-

ited cost. These parameters depend on attenuation length, luminosity, the

photoelectric fraction, and the decay constant of the detector [7].

Detection efﬁciency is critical in NM, as the dose administered to patients

must be as small as possible, which naturally entails low count rates. This

means that the scintillator thickness (measured in the axial direction) should

be at least equal to two attenuation lengths and, in fact, is usually equal

to three. However, intrinsic spatial resolution deteriorates with increased

thickness, because the probability of multiple interactions occurring in the

Gamma photon

(a)

(b)

Photoelectric effect

Compton effect

Electron

Photon

Photoelectron

Light P PLightPP

X-rays

Photomultiplier

tube

Optical interface

Nal(TI) crystal

Collimator

Gamma photons

FIGURE 5.9

(a) Possible combinations of processes that may lead to the generation of scintillation after the

interaction of the incident photon. (b) Portion of a slice showing a scintillation gamma camera

with total absorption of energy(1 and 3), or partial absorption of energy (2) by loss of the Compton

photon.

Radiation Detectors and Image Formation 149

crystal increases, involving the total absorption of photon energy. Thus, a

compromise must be reached between efﬁciency and spatial resolution.

The spatial resolution associated with the Anger logic is proportional to the

PMT diameter and inversely proportional to the square root of the number

of photoelectrons [7]. Therefore, the greater the yield of the scintillator (see

Equation 5.10), the better the intrinsic resolution. In the case of the gamma

camera, spatial resolution is mainly affected by the collimator, and intrinsic

resolution has a marginal impact. Thus, by using a scintillator with higher

luminosity the PMT diameter can be increased, which, in turn, can reduce the

cost of the detectors.

As we saw earlier (see Section 5.1.1), increasing the yield has a direct con-

sequence in terms of energy resolution, which can be used to discard the

photons subjected to Compton interaction.

When there is total absorption of photon energy, the accuracy of the

interaction position within the detector beneﬁts more if this is achieved by

photoelectric effect rather than by the Compton effect (see Section 5.1.1.1).

Until it is absorbed, a photon subjected to Compton interaction deposits its

energy in at least two separate locations, which degrade spatial resolution.

Hence, a high photoelectric fraction is desirable, and the atomic number of

the scintillator material is a major factor in this context.

Table 5.1 shows the principal properties of the main scintillators used either

in NM or in research and development. The table was compiled on the basis

of content [4,8–10], and from the Crystal Clear Web site [11] and the refer-

ences it provides. The density of the scintillator ρ is multiplied by the fourth

power of its effective atomic number Z

eff

, as the absorption by photoelectric

effect per unit of length is proportional to ρZ

3–4

eff

[8]. For 511 keV photons, the

probability of interaction by photoelectric effect at Z

eff

= 80 is less than 50%,

whereas the remaining 50% is due to the Compton effect. Depending on the

type and size of the scintillator crystal, the detection of the Compton elec-

tron in addition to the scattered photon may signiﬁcantly contribute to the

intensity of the full-energy peak, as demonstrated, for example, in positron

emission mammography (PEM) dedicated systems using LuAP scintillators

coupled to avalanche photodiode arrays [12]. In PET applications, a scintil-

lator with a small attenuation length is necessary in order to minimize the

crystal radial length, typically in the order of thrice the attenuation length.

This, in turn, minimizes the parallax effect responsible for radial degradation

of the images at voxels further away from the isocenter of the tomograph

[13]. The photoeffect fraction together with the photopeak energy resolution

are indeed important for high full-energy peak intensity and, consequently,

for high-efﬁciency detection of events valid for reconstruction; a low level of

Compton-scattered photons in the patient, which would otherwise show up

as a continuous blur in the images; and a high true-to-random coincidence

ratio, because random events are more affected by Compton photons than by

true events [14]. The photon yield and the decay constant of the scintillator

play their role in minimizing the coincidence–time resolution τ achievable by

150 Nuclear Medicine Physics

TABLE 5.1

Properties of Scintillators with Application in Nuclear Medicine

Atten. Luminosity Decay Fluores-

ρ Length Photoelectric Hygros- (photons/ Const. Emission ΔE/E cence Refractive Clinical

Scintillator (g/cm

) (mm) Fraction (%) copicity keV) (ns) Peak (nm) (% FWHM) (%/ms) Index Application

NaI: Tl 3.67 29.1 17 Yes 41 230 410 5.6 0.3–5/6 1.85 SPECT

CSI: Na 4.51 22.9 21 Yes 40 630 420 7.4 0.5–5/6 XII

CSI: Tl 4.51 22.9 21 Little 66 >800 420 6.6 0.5–5/6 PET, SPECT, CT

CSF 4.64 20 23 High 2 3 390 1.48 TOF-PET

BaF

4.89 20.5 17 Little 2 0.7 220 10 1.54 TOF-PET

BGO (Bi

) 7.13 10.1 40 No 9 300 480 9 0.005–3 2.15 PET

LSO (Lu

SiO

:Ce) 7.4 11.4 32 No 26 40 420 7.9 <0.1/6 1.82 TOF-PET

1.8

0.2

SiO

:Ce 7.1 11.5 No 26 41 420 7–9 <0.1/6 1.81 TOF-PET

LuYSiO

: Ce 6 16.7 21 No 26 420 7–9 <0.1/6 TOF-PET

LuAP (LuAlO

:Ce) 8.3 10.5 30 No 12 18 365 ∼ 15 1.94 TOF-PET

LPS (Lu

:Ce) 6.2 14.1 29 No 30 30 380 ∼10 1.74 TOF-PET

GSO (Gd

SiO

:Ce) 6.7 14.1 25 No 8 60 440 7.8 1.85 PET

YAP (YalO

) 5.5 21.3 4.2 No 21 30 350 4.3 1.95 PET

LaCl

:Ce 3.86 27.8 14 Yes 46 25 (65%) 353 3.3 1.9 SPECT

LaBr

:Ce 5.3 21.3 13 Yes 61 35 (90%) 358 2.9 1.9 SPECT

CeBr

5.2 21.5 14 Yes 68 17 370 3.4 TOF-PET

LXe (liquid xenon) 3.06 30.4 21 — 11 27 (30%) 165 22/16 DOI-PET

Ideal (PET) >6 <12 >30 No >8 <300 300–500 <10

Radiation Detectors and Image Formation 151

the system. A small time resolution is essential to achieve the lowest random

coincidence rate C

possible, as C

= 2τC

, where C

and C

are the singles

count rates in detectors and i and j form the LOR ij. Further, a small scintilla-

tion decay time is also necessary for minimizing dead time, that is, the time

in which a coincidence cannot be registered, because the PET system is busy

handling a previous coincident event. Several parts of the system contribute

to the dead time, and the detector is one of them. In addition to its inﬂuence on

energy resolution, a high light yield is also important for achieving optimum

spatial resolution in the detector in systems using scintillation-light-sharing

methods to reduce the number of readout electronic channels [15–17].

By far, the most commonly used scintillator for NM applications is the

thallium-activated sodium iodide crystal NaI(Tl), used in combination with a

PMT readout mostly not only in single-photon emission systems but also

in high-resolution PET scanners [18]. Other scintillators that are particu-

larly suitable for PET at present are BGO, LSO, LuAP, LPS, GSO, and YAP

(Table 5.1). The most widely used in commercial PET systems is BGO, which

has a high detection efﬁciency for 511 keV photons (a crystal with 3 cm depth

has nearly three attenuation lengths), a high photoeffect fraction, and a rela-

tively low production cost. The main disadvantages of BGO are its rather long

decay time of 300 ns and low light yield in comparison with other scintillators

such as LSO, leading to inferior time and energy resolutions,respectively. One

of the most suitable scintillator materials for PET is LSO. It has a high number

ρZ

eff

; and high light yield, a short decay time, and relatively good mechani-

cal properties necessary for high-throughput manufacturing. Due to its short

decay constant, a time resolution of 1.2 ns has been already achieved in com-

mercial PET scanners [19], whereas BGO-based tomographs typically present

12 ns. Therefore, renewed interest in proﬁting from the time-of-ﬂight (TOF)

information in LSO-based tomographs has emerged [20]. For completeness,

it must be stated that several groups have been actively developing new PET

methods and techniques using noble elements, such as liquid xenon (LXe) in

scintillation and ionization correlated modes in order to solve the problem of

parallax error in PET [21,22].

Current commercial PET scanners generally use detector module readouts

in Anger logic, that is, one scintillator detector block is implemented with

saw cuts deﬁning individual pixels and the scintillation light is read by several

PMTs [20]. The analog ratio among the PMT signals yields the coordinate of

the hit crystal [23]. This reduces the number of electronic readout channels by

a factor proportional to the ratio between the number of individual crystals

and the PMT but, on the other hand, increases the detector dead time per front

areaunit

∗

bythe sameamount and introducesa spatial resolutiondegradation

typically of 2 mm added in quadrature to the other factors inﬂuencing the

spatial resolution of the tomography [24].

∗

The detector dead time per unit area is a ﬁgure of merit commonly used to describe the

effective detector dead time due to the scintillator decay time together with the readout scheme

implemented.

152 Nuclear Medicine Physics

5.1.2.4 Photomultipliers

The reasons for using PMTs for scintillation light readouts are their much

higher gain and better noise characteristics in comparison with other more

compact light detectors such as silicon-based avalanche photodiode arrays.

A PMT consists of a photocathode and several dynodes. The photocathode

is located near the window of the PMT and is composed of a photosensi-

tive material. The photons coming from the scintillator crystal interact with

the photocathode, transferring its energy to the electrons of the photocath-

ode material. The electrons ejected by the photocathode are then accelerated

toward the ﬁrst dynode. The electrons interact with the ﬁrst dynode causing

the ejection of more electrons that are accelerated, by another voltage dif-

ference, toward the second dynode. This process is repeated with the charge

multiplying at each stage between the dynodes. The charge is ﬁnally collected

at the anode generating a signal, which, after it is ampliﬁed and shaped, is

the input of a pulse height analyzer circuit and position circuit.

The ﬁnal amplitude of the signal is proportional to the light energy of the

scintillation within the crystal, which, in turn, is proportional to the energy

lost by the incident radiation that produced the scintillation.

Figure 5.10 shows a diagram of a scintillation detector and the assembly

that is generally used to obtain the voltage between dynodes.

The steps described above can be analyzed and quantiﬁed independently

to deduce an equation that reﬂects the performance of a PMT.

300 V

Photocathode

Gamma

photon

Scintillation

Crystal

NaI(TI)

Accelarator

electrode

Dynodes

Anode

–

400 V 500 V

1200 V

1300 V

1400 V

0 V

Signal

200 V

FIGURE 5.10

Diagram of a photomultiplier tube. The photons incident on the window of the PMT cause

electrons to be emitted in the photocathode that are accelerated along a chain of electrodes under

high tension, leading to multiplication of the charge. The voltage of the dynodes is obtained by

dividing the output of the voltage source by a series of high-value resistors (MΩ).

Radiation Detectors and Image Formation 153

When a photon with energy Eγ interacts with the crystal and produces N

ﬂuorescence photons of individual energy E, the total light energy released is

= N

E. (5.9)

The light yield of a scintillator crystal is deﬁned by the relationship

λ =

(5.10)

For the NaI (Tl), the light yield can be up to 0.1.

From the N

photons of light emitted within the crystal in all directions,

only a number N

reaches the photocathode. This is called the optical yield, for

the optical quotient

ω =

, (5.11)

which, under optimum conditions, may equal 0.5.

Part of these N

photons will produce a photoelectric effect in the photo-

cathode.

Let N

be the number of ejected photoelectrons. The ratio

ξ =

, (5.12)

is the quantum yield of the photocathode. For the antimony-cesium this yield

is around 0.1.

Only a portion, N

of the N

photoelectrons, reaches the ﬁrst dynode. The

term collection yield is usually employed to describe the relationship

χ =

, (5.13)

which may be close to a unit.

Each dynode will multiply the number of electrons up to a certain, very

high, factor that depends on the voltage difference between the dynodes and

the coating substance. The gain (A) of a dynode is the ratio between the

number of electrons emitted and the number of incident electrons.

If n is the number of dynodes, the total gain of the PMT is

G = A

. (5.14)

The total charge received by the anode after a photon of energy Eγ has

released N

visible photons in the crystal is

Q = N

ωξχGe, (5.15)

where e represents the electron charge.

154 Nuclear Medicine Physics

Equation 5.15 can be rewritten as

Q =

ωξχGe. (5.16)

Q = λ

ωξχGe. (5.17)

In this expression, the values E, λ, ω, ξ, χ, and e are constant and speciﬁc

for a certain crystal-photomultiplier set.

For a given voltage difference between dynodes, the gain G is constant.

Thus, we can write

Q = E

T, (5.18)

where

T = λ

ωξχGe. (5.19)

The light yield is deﬁned by assuming that all the energy Eγ of the photon

is absorbed, creating N

visible photons. Therefore, we can conclude that the

charge collected by the anode of a PMT coupled to the crystal is proportional

to the energy of the incident photon when it is fully absorbed by photoelectric

effect or when multiple interactions occur in the crystal, leading to the loss of

the total energy of the incident γ photon.

When the energy of a photon is not totally absorbed, the charge collected

at the anode is only proportional to the energy absorbed.

This is the case, for example, when one or more Compton interactions occur

and the photon is scattered on leaving the crystal.

5.1.2.5 Variants and Alternatives

The photomultiplier is the photodetector used in the overwhelming major-

ity of current systems used in conventional NM, namely PET and SPECT.

Continuous improvements have been made to its technology, but there are

some intrinsic limitations that preclude its use in new applications. They are,

for example, inappropriateness for use in the new multimodal PET or MRI

(magnetic resonance imaging) systems, as their sensitivity to magnetic ﬁelds

and their relatively large dimensions prohibit use in systems with very high

resolution, such as those dedicated to small animals. Fortunately, variants

of the traditional PMTs and other alternative devices exist with a perfor-

mance suitable for the requirements predicted for the near future, which are

expected to include systems with the ability to measure TOF (requiring a

short response time) and depth of interaction (for which small size and high

efﬁciency are advantageous), possibly with better energy and time resolu-

tion. Other photodetectors providing a sufﬁciently high-gain bandwidth for

Radiation Detectors and Image Formation 155

use in PET applications are multianode PMT [25], metal channel dynode PMT

[26], hybrid PMT [27], micro-channelplate PMT (MCP-PMT) [28], visible light

photon counters (VLPC) [29], and Geiger-mode avalanche photodiodes [30].

The latter has been gaining in importance due to its low-cost, compactness,

ability to operate at room temperature, insensitivity to magnetic ﬁeld and

hadrons, and good timing characteristics in low-light environments, with

pixel recovery times of about 20 ns. The avalanche photodiodes (APDs) and

variants (HAPDs—Hybrid Avalanche Photodiodes and PSAPDs—Position

Sensitive APDs, among others) are compact, have high quantum efﬁciency

and high gain, and are insensitive to magnetic ﬁelds. Although presenting

high noise levels, the APDs have a performance suited to the development of

high-resolution PET systems that are compatible with MRI. The silicon PIN

diodes are small, with high quantum efﬁciency and insensitivity to magnetic

ﬁelds, but they have a low gain and need preampliﬁers with low noise. Other

technologies involving silicon-based PMTs are also available and are being

rapidly developed, in addition to devices based on CCDs (charge-coupled

devices).

5.1.3 Signal Acquisition Electronics

The basic structure of the signal acquisition module is represented in

Figure 5.11.

Detectors generate a signal that is a pulse of current lasting a few microsec-

onds. The electric charge contained in these pulses is related to the energy

deposited within the detector volume by the ionizing radiation. It is neces-

sary to transform the current pulse to a voltage pulse in such a way that

the amplitude is proportional to the deposited energy. The preampliﬁer, with

huge input impedance and low output impedance, is the device responsible

for this transformation, while also allowing for the adjustment of impedance.

The preampliﬁer gain is usually small (≈1) (Figure 5.12).

Preamplifier

Main

amplifier

SCACounterTimer

MCA

FIGURE 5.11

Basic diagram of the electronic module used in detector signal acquisition. (Adapted from N. T.

Ranger, Radiographics, 19(2):481–502, 1999.)

156 Nuclear Medicine Physics

(a) (b)

out

load

ideal

FIGURE 5.12

(a) Signal input stage; the triangle represents an operational ampliﬁer and the input impedance

(ideally inﬁnite) is represented by Z

. (b) output stage that can be seen as a voltage generator in

series with a resistor; Z

out

represents the output impedance, which is as small as possible.

The output signal of the preampliﬁer enters the ampliﬁer where it is ampli-

ﬁed and shaped. The typical gain for this stage is 1000, and the appropriate

shaping is required for the height pulse analysis. Impulse shaping depends

on the electronic circuitry for peak analysis, which is performed by a single or

a multichannel analyzer. Since both single and multichannel analyzers mea-

sure the pulse amplitude in relation to a voltage reference, it is essential that,

between pulses, the output from the ampliﬁer quickly returns to the stable

voltage reference [32]. It is, therefore, also essential to implement a restoration

baseline circuit.

The output of the ampliﬁer is a symmetrical voltage pulse (usually unipo-

lar) whose amplitude is proportional to the energy deposited in the PMT.

Thus, analysis of the signal amplitude provides information on the energy

of the radiation detected, which can then be used to accept or reject events.

For this purpose, as already noted, single or multichannel analyzers can be

used. In the case of the former, only pulses that present amplitudes within

a certain range are accepted for counting. In this case, only radiation with a

particular energy is measured and the channel presents a certain width that

determines energy resolution. With the multichannel analyzer, a histogram of

amplitudes is created, corresponding to an energy spectrum. This histogram

can be obtained through the use of an analog-to-digital converter (ADC).

The PET and SPECT cameras that perform coincidence require the detec-

tors to operate in coincidence mode. This mode requiresa number of detectors

operating simultaneously. When a photon is detected, the corresponding out-

put signal of the PMTs is used to generate a time signal that accurately

indicates the instant t of photon detection. The time signal is then sent to

an electronic unit that processes the measurement of coincidences within a

time window Δt with all the other detectors in the system. The unit detects

a coincidence if there is a time signal from another crystal in the time range

(t, t +2Δt). The time window has to be carefully chosen and should take into

account the temporal resolution of the system, which measures the existing

uncertainty in determining the instant of the photon detection. If Δt is too

Radiation Detectors and Image Formation 157

small in comparison with the temporal resolution of the system, fewer true

coincidences than those that actually exist may be identiﬁed; and if, on the

other hand, Δt is too large, it increases the probability of detecting random

coincidences. When Δt is very small, that is, less than 3 ns, the difference in

the time intervals required by the two photons resulting from annihilation

to reach the detectors becomes important. There are systems based on scin-

tillators that are very fast and can use TOF information to improve spatial

resolution and reduce the noise in the image.

Another important aspect of signal processing that must be taken into

account is how to determine the position of radiation interaction inside the

crystal. The interaction of a gamma photon with the crystal produces numer-

ous scintillation photons that are detected by several PMTs. The sum of the

charge measured by all PMTs is proportional to the energy of the gamma pho-

ton energy, and it is reasonable to assume the charge distribution is such that

it is more intense near the interaction position and less intense further away

from it. Anger logic is based on this assumption and enables the position of

the gamma photon in the scintillator to be determined by a weighted average.

Let X and Y be the axes of a coordinate system whose origin is at the centre

of each crystal. A position (x

, y

) is associated with each PMT, f , which is

the position at the center of the PMT window in the coordinate system in

question (Figure 5.13). In a given event, each PMT gives a measurement a

The position of a particular event will be given as if it were a center of mass

calculation [33], that is,

X =



f =1



f =1

and Y =



f =1



f =1

. (5.20)

FIGURE 5.13

Diagram showing the arrangement of PMTs in a gamma camera and their relationship in

determining position using Anger logic.