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88 Nuclear Medicine Physics

and the Doppler broadening, relative to the energy m

, is given by

ΔE

∼

. (3.28)

The momentum of the thermalized positron is very small (almost zero)

when compared with the momentum of the electrons of the material; and so,

the momentum of the pair and also



and



are, in reality, very nearly the

transversal and longitudinal components of the electron linear momentum

relative to the emission direction of the annihilation radiation. In this way,

the experimental systems based on the measurement of the one-dimensional

angular shift (as referred before by 1D-ACAR) or of Doppler broadening of

the energy, ΔE, give information on momentum distribution of the electrons

involved in the annihilations.

A typical value for the momentum of the electrons in metals based on the

free electron model is 1.5 ×10

−24

kgms

−1

, which corresponds to an energy

spread of 1.4 keV. This value is, in general, larger than the resolution that

can be achieved with high-purity germanium detectors (HPGe), and so it is

possible to obtain information on the electron momentum distribution for

one material through Doppler broadening measurement of the annihilation

radiation. The corresponding maximum angular shift θ is 5.6 mrad, which

is naturally much larger than the angular resolution of the systems where

angular correlation is currently observed.

In Figure 3.7, a classic angular correlation system (Figure 3.7a) and a typ-

ical Doppler spectrometer (Figure 3.7b) are schematically represented. The

angular correlation system records the count rate N(θ), as expressed by

Equation 3.18, which contains the linear momentum density of the 511 keV

photons as a function of the angle θ. The need to obtain good resolutions (0.1–

0.5 mrad) with these experimental systems implies the use of thin collimators

and large sample-to-detector distances. Consequently, the coincidence count

rates are very low and the acquisition time becomes too much long. More

recent angular correlation systems (2D-ACAR) [30] use position-sensitive

gamma radiation detectors with good angular resolution. In this case, a two-

dimensional projection of the electron momentum distribution, as expressed

in Equation 3.17, is obtained. The very low count rate of these detection

systems is compensated by multiple coincidence techniques using multiple

detectorsystems or largedimension (area)position-sensitive detectors (Anger

chambers and multiwire proportional counters).

As described before, the information extracted from the energy spectrum of

the annihilation radiation obtained in Doppler broadening measurements is

equivalent to that obtained by the 1D-ACAR system. Effectively, using Equa-

tions 3.27 and 3.28 and considering that the expected values of the transversal

and longitudinal components of the momentum must be the same, we can

write:

∼

ΔE. (3.29)

Positron Physics 89

Sample

HPGe

detector

MCA

0.511 Me v

–

0.511 Me v

γγ

Coincidence

Memory

Det.2

Collimator

–

Det.1

(a)

(b)

FIGURE 3.7

Experimental conﬁguration for (a) 1D-ACAR. (b) Doppler broadening measurements.

The Doppler broadening systems have an equivalent angular resolution

that is poorer than the angular correlation systems, but they are quite often

an interesting alternative solution due to their considerable simplicity and

high efﬁciency.

Experimentally, the Doppler broadening system uses a high-purity ger-

manium gamma ray detector (HPGe) to obtain the energy spectrum of the

annihilation gamma radiation.

The Doppler broadening spectra contain, as previously indicated, infor-

mation on the contributions of each individual electron moment involved

in annihilations. This information can, in principle, be obtained from the

spectrum as so on as the resolution function of the detection system for the

measured energy is well known. Although there are different deconvolution

techniques specially adapted to the analysis of Doppler spectra, for example

in references [31–34], there exist some reluctance on their applications, which

are fundamentally due to two reasons: (1) the system resolution is intrinsi-

cally low and the identiﬁcation of the different components is only possible in

very simple cases (when higher precision on the determination of the electron

momentum distribution is needed, another technique, ACAR, with one order

of magnitude better resolution is normally used); and (2) in the majority of

the experiments in materials, the research is only concerned with the presence

and evolution of defects and these can be achieved using simpler techniques

and methods of analysis.

90 Nuclear Medicine Physics

As an alternative to the deconvolution methods, parameters related to the

shape of the 511 keV peak of the annihilation radiation can be deﬁned. These

form parameters that present good sensitivity to shape variations of the

Doppler spectra, are integrals of counts obtained in deﬁned regions of the

spectrum, are normalized to the total area of the 511 keV peak, and can be

calculated after background subtraction.

The results of Doppler broadening measurements are, in general, discussed

in terms of these parameters. The form parameters more usually accepted are

the parameter S (abbreviation of “sharp”), introduced by MacKenzie [35], and

the parameter W (abbreviation of “wing”). The parameter S is deﬁned by the

ratio between the area of the peak central part, A

, and the total area of the

511 keV peak, A

, after background subtraction,

S =

, A



−E

N(E) dE. (3.30)

The parameter W corresponds to the sum of the count integrals in two

regions away from the central part but symmetrically placed in relation to

the peak centrum, which are also normalized to the total area of the 511 keV

peak:

S =

, A





N(E) dE +





N(E) dE (3.31)

In Figure 3.8, the integration regions for deﬁnition of each parameter are

schematically represented. The energy limits for each region are symmetri-

cally chosen around the central energy E

= 511 keV, taking E

±E

for the

parameter S calculation. The energy limits E

, E



, E

, and E



for the calculation

of W should be deﬁned to avoid effects related to the S parameter, consider-

ing that E

= (E



)



2 = (E



)



2. The choice of these limits should be

madeto obtain greatersensitivityof theparameter tovariations of themoment

distribution of the electrons involved in the annihilations associated with the

defects. However, it should be remembered here that positron annihilations

with low moment electrons, that is, the valence electrons, contribute most

strongly to the value of the parameter S. In contrast, positron annihilations

with high moment electrons, that is, the core electrons, contribute predomi-

nantly to the value of the parameter W. Due to this, these parameters are also

called valence parameter, I

, and core parameter, I

, respectively. Considering the

main type of annihilations contributing to the values of the form parameters,

it is possible to conclude that both parameters are sensitive to concentration

andtype of defects in the material, butthe W parameteris moresensitive to the

chemical ambient around the annihilation site. This sensitivity to the chem-

ical environment at the annihilation site is, indeed, taken as an advantage

Positron Physics 91

S = ——————

A+B+C

W = ——————

D+F

D+E+F

ΔE

= 2E

–

E′

dNγ/dEγdNγ/dEγ

505 510

Eγ (keV)

515

FIGURE 3.8

Deﬁnitions of the integration regions in the form parameters S and W. The energy windows are

placed symmetrically in relation to the value E

= 511 keV.

of the techniques measuring the electron momentum (Doppler and ACAR)

when the chemical environment of defects is under study. It should be men-

tioned here that the positron lifetime technique is a powerful technique that

is very sensitive to the electronic density on the defect environment and is

able to identify univocally the defects; however, it is not sensitive to electron

momentum densities.

The absolute values of the form parameters do not have, per se, a clear

physical meaning, as they depend on the position of the integration limits

±E

, E



, E

, and E



, which are not normalized) and are also strongly

dependent on the resolution function of the experimental system. In material

studies, only the changes in the parameter values (e.g., during a sample treat-

ment process) are relevant and considered as indicators of modiﬁcations of

the electron linear momentum distributions at the annihilation sites.

The positron annihilation techniques have been used with great success

in the identiﬁcation and characterization of defects in metals and semicon-

ductors as well as in chemistry, in particular in the characterization of new

materials with industrial applications, for example, polymers. This fact is nat-

urally associated with the high sensitivity and selectivity of the positron to

open-volume-type defects from the atomic scale (Angstrom) up to microcavi-

ties (some nanometers), as previously discussed in this chapter.An important

92 Nuclear Medicine Physics

aspect of the selectivity of the technique is the possibility of distinguishing

different chemical environments at the positron annihilation sites. At this

point, it becomes pertinent to raise the question as to how these remarkable

possibilities can be used in clinical diagnosis.

It was only very recently that the positron annihilation techniques had

started being applied to biological systems. Although the information is still

limited, there are clear indications of the applicability of positron techniques

on these systems. Shape parameters, S and W, of the annihilation radiation

observed in tissue samples (rat skin in this example) that have been exposed

to successive ultraviolet light irradiations [36] show a clear dependence of the

irradiation dose. In addition, it is well known that certain types of cancerous

tumors present a signiﬁcant deﬁcit in the amount of oxygen. Such chemical

changes in the tissues lead to variations in the annihilation radiation charac-

teristics as well as in the Ps pick-off rate, which imply a change in the observed

3γ/2γ fraction. Factors such as these are likely, in future, to stimulate the use

of positron annihilation gamma radiation in medical diagnostics. However,

quite a few changes and optimizations have to be made to the current positron

systems to achieve the prompt response needed for medicine.

Let us now discuss the annihilation techniques that could be applied:

• Positron lifetime measurements: This technique will need a relatively

short-lived positron emitter radioactive isotope, which, at the same

time, would also emit a γ photon to indicate the birth of the positron.

In addition, fast-response detectors would be needed (typical time

resolution 250 ps) and acquisition times would be very long. With

the inclusion of such features, the PET system would become quite

exotic but, in practice, impossible to apply to living bodies.

• Annihilation radiation Doppler broadening measurements: This

technique needs a gamma detector with high energy resolution, typ-

ically with full width at half maximum (FWHM) lower than 2 keV

for the 511 keV peak. Actually, such energy resolutions are achieved

with HPGe semiconductor detectors (which need to be cooled to

liquid nitrogen temperature) and with CdTeZn (which operates at

room temperature). With this technique, simultaneous information

on the chemical environment at the annihilation site and on the 3γ/2γ

fraction can be achieved.

As discussed in Chapter 6 on the image reconstruction of tissues and

organs in PET, only the time coincidence of the two annihilation gammas

with approximate energy of 511 keV is required; and it is not necessary to

record any other information produced by the radiation. In general, in the

conventional PET systems, the gamma ray detectors arebased on the coupling

of BGO scintillators to photomultipliers. With this conﬁguration, excel-

lent radiation detection efﬁciency and good spatial resolution are achieved.

Unfortunately, these detectors have poor energy resolution; typically, the

Positron Physics 93

511 keV peak has 12% FWHM, which is not enough to provide the detailed

information that can be achieved through the annihilation radiation Doppler

broadening technique.

With the development of PET systems, and particularly with the inclusion

of better energy resolution detectors, it will be possible to achieve a more

complete characterization of the chemical environment at the annihilation

site and also of the 3γ/2γ fraction, with a signiﬁcant improvement in the

clinical diagnostics given by PET.

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2007.

Radiopharmaceuticals: Development

and Main Applications

Antero Abrunhosa and M. Isabel Prata

CONTENTS

4.1 Overview ........................................... 96

4.2 Molecular Target Selection ............................... 97

4.3 Tracer Molecule ....................................... 98

4.4 Radionuclide Selection .................................100

4.5 Labeling Position .....................................102

4.6 Radiosynthesis .......................................103

4.7 PET Nuclides: Reactions and Radiopharmaceuticals ...........104

4.7.1 Carbon-11 ......................................104

4.7.2 Fluorine-18 .....................................105

4.7.2.1 Deoxyglucose Method ......................106

4.8 SPECT Radionuclides ..................................108

4.8.1 Technetium-99m: Production, Coordination Chemistry, and

Radiopharmaceuticals .............................109

4.8.2 Gallium and Indium: Radioisotopes and Their

Coordination Chemistry ...........................115

4.8.2.1 Gallium and Indium Ligands .................116

4.8.2.2 Gallium and Indium Radiopharmaceuticals ......118

4.8.3 Copper Radioisotopes and Copper Coordination

Chemistry ......................................120

4.9 Monoclonal Antibodies and Peptides in

Molecular Imaging ....................................121

4.9.1 Monoclonal Antibodies ............................121

4.9.2 Peptides .......................................122

4.10 Radiopharmaceutical Quality Control: Radiochemical Purity,

Speciﬁc Activity, and Radiolysis ...........................125

4.11 Advances in Radiopharmaceutical Development and New Trends

in Radiochemistry .....................................125

References ..............................................126

Further Reading ..........................................132

96 Nuclear Medicine Physics

4.1 Overview

One of the bases of NM is the ability to produce molecules that are capable

of acting as selective markers for the biophysical, biochemical, or pharma-

cological processes that are of interest. Over recent decades, thousands of

molecules have been labeled with emitting nuclides for studying more than

a hundred different processes in the human body. The unparalleled ability of

these molecules to depict in vivo metabolic pathways and interactions has led

to the development of a new scientiﬁc area: molecular imaging. In this chapter,

we will describe the main questions related to the use of radiopharmaceuticals

in molecular imaging studies and indicate some of their principal applications

in clinical and research studies.

Amolecular imaging study with radiopharmaceuticals usually begins with

a clinical or research question that needs to be answered (Figure 4.1), fre-

quently placed in the form of a model (paradigm) that is then confronted

with the experimental results (“proof of action” approach). To answer this

question, we have to select a molecular target, that is, a physiological process

Clinical or research question

Molecular target selection

Choice of tracer molecule

Selection of the radionuclide

Radiolabeling

Result

In vivo study

FIGURE 4.1

Main steps of a molecular imaging study with radiopharmaceuticals.

Radiopharmaceuticals 97

that is altered by the pathology that we want to study. For this molecular

target, we select a tracer molecule that has the right physicochemical charac-

teristics to map that process. The molecule is then labeled with an appropriate

emitting nuclide which will enable us to perform the in vivo study that will

allow us to obtain, if completely successful, a ﬁnal image, which is frequently

quantitative, and that will enable us to answer the initial question.

4.2 Molecular Target Selection

The quantiﬁcation of a parameter of interest related to a certain physiologi-

cal process imposes certain conditions on the chosen molecular target. First,

we need a sufﬁciently high concentration of target molecules (e.g., recep-

tors, enzymes, and transporters) in the region of interest, with minimal target

occupation to avoid interfering with the process, to allow a sufﬁciently potent

in vivo signal for the study to be made.

This potency of the signal is normally represented by the kinetic parameter

binding potential (BP), deﬁned as

BP =

max

(4.1)

in which β

max

is the density of molecular targets in the region of interest, and

is the kinetic dissociation constant between the chosen tracer molecule and

the target [1].

Second, we need the structure we intend to visualize to be anatomically

separable, bearing in mind the spatial resolution of the scanner used. This can

be a problem for certain applications, for example, in neurology or with small

metastases in oncology. Nevertheless, it is important to note that sometimes,

if the signal-to-noise ratio is high, it is possible to observe structures with

dimensions below the spatial resolution of the camera used, although, in this

case, quantiﬁcation would be impossible due to the so-called partial volume

effect (see Chapter 6).

In the majority of studies, steady-state conditions would also be required

with regard to the occupation of the active sites by endogenous molecules, in

order to avoid interference concerning the afﬁnity of the radiopharmaceutical

for its active site. However, in some cases, this capacity of an endogenous

molecule to displace the radiopharmaceutical from its active site can be

exploited in order to measure, indirectly, a physiological effect that promotes

its variation after an internal or external stimulus [2].

Table 4.1 lists some of the radiopharmaceuticals developed for the three

main clinical areas of application: oncology, cardiology, and neuroscience,

with the indication of the physiological process or molecular target they use.