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

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168 Nuclear Medicine Physics

The energy of an incident photon in the scintillator is partially converted

into visible or near UV light (scintillation) and then transformed into an

ampliﬁed electrical signal by a PMT. The intrinsic energy resolution expresses

the ability of the detector (without collimator) to differentiate between two

photons of different energies. Of particular importance is the differentiation

between photopeak and scattered photons. The value is given by the energy

range that corresponds to the photopeak width at half height expressed as a

percentage of the energy of the photopeak.

Impulses of the total absorption peak correspond to the total energy absorp-

tion of the incident photon and can result from (a) interaction in the crystal by

photoelectric effect, with both the photoelectron energy and the X-radiation

energy due to electron transition or Auger electrons being dissipated in the

crystal and (b) interaction by Compton effect followed by absorption of the

Compton electron and the scattered photon by the crystal.

The PMT collects the light generated in the crystal by γ rays, by ionization

and excitation, giving rise to electrical signals that contain information about

the energy and position of the interactions taking place in the crystal. The

interactions that occur in the crystal are processed individually, which require

the use of fast electronics and low dead time in the detector to allow high

counting rates [36].

The proportionality between the energy transferred and the electrical

impulse produced allows the scintillation detector to be used for gamma

radiation spectrometry.

The gamma spectrum, that is, the distribution of the number of pulses for

each amplitude value, from zero to a maximum value (for each energy value

dissipated in the crystal), can be obtained with a pulse height analyzer.

These signals are sent to charge ampliﬁers wherethey areampliﬁed to be the

input of position circuits, which then computes the individual coordinates, x

and y, of the detections. These steps should be performed by digital circuits.

The performance of the scintillation camera is compromised by an intrinsic

spatial resolution close to 3 mm, aggravated by the response of the collimator

and by deterioration with the distance to the detector. These factors lead to

poor spatial resolution compared with the morphological techniques. Reso-

lution distances expected for the scintillation camera are of the order of 5 mm

for most exams of deep organs.

Poor spatial resolution leads to the partial volume effect that prevents the

collection of quantitative information about the intensity of objects whose

size is less than twice the system resolution distance.

Planar scintigraphy produces 2D images of 3D objects. The planar images

are impaired by the overlap of active and nonactive regions that limit the

contrast and the functional accuracy of the information.

Radial acquisition around the object followed by reconstruction allows the

acquisition of tomographic maps in NM [37].

Currently, most studies show only stationary distribution of activity, and

the analysis of the resulting images is mainly qualitative.

Radiation Detectors and Image Formation 169

The problem of quantiﬁcation in SPECT is complex, because it is necessary

to determine the distribution and concentration of an unknown tracer in an

unknown set of absorbent tissues.

Quantiﬁcation through the use of dynamic and quantitative functional

imaging can, however, improve the quality of diagnosis with SPECT; but

this objective is only approximately achieved in some studies.

Although conceptually the gamma camera has not undergone major

changes over time, the same does not hold for the design, the detectors, and

the materials used to make it. One of the most easily recognized changes is the

number of heads that the current gamma cameras have. The gamma camera

quickly evolved to increase the number of heads from one to two and then

to three. This development meant an improvement in sensitivity, which, in

turn, led to a reduction of the dose of radioactivity administered and/or the

time taken for the examination (Figure 5.19).

Moreover, in recent years, new devices have emerged:

1. Cameras with multiple small crystals. PMTsare used in a new design.

2. Cameras with photodiodes. Silicon diodes are used instead of

PMTs. CsI scintillators are used, as their emission spectrum ﬁts the

photodiodes better.

3. Compton effect cameras.

4. Cameras with CZT detectors; this is a semiconductor detector capable

of operating at room temperature.

5.3.1.1 Collimators

The collimator is a device that is placed between the crystal and the object

of study and consists of a gamma radiation absorbing material with thou-

sands of holes distributed in a network [38]. This makes it possible to select

certain directions of the incident photons and to ﬁlter scattered rays that are

not suitable for the formation of the image. Despite making the technique less

FIGURE 5.19

Gamma cameras.

170 Nuclear Medicine Physics

efﬁcient by reducing the counting rate, collimators are essential for the forma-

tion of the image, as the gamma photons cannot be refracted; and, therefore,

lenses cannot be used, as they can with photons in the visible range.

The walls that conﬁne the holes are called the collimator septa. The thickness

of the collimator, the diameter of holes, and the septa thickness relate directly

to the properties of the image. The dimensions of the collimator are the same

as the crystal and it can be square or circular in shape. The material gener-

ally used for collimators is lead, because it combines a high density with a

high atomic number. Ahigh-density material is required, because it is directly

related to the attenuation coefﬁcient, which must be high to ensure gamma

photon absorption. Further, the atomic number should be high to ensure that

the fraction of interactions by photoelectric effect is greater than the fraction

of interactions by Compton and Rayleigh–Thomson scattering. We recall here

that in the NM energy range (80–511 keV), the fraction of the photoelectric

effect increases with atomic number. This condition is essential to image qual-

ity since the secondary photons, produced by the Compton effect or by elastic

scattering, will degrade the image.

Other materials such as tungsten, gold, or tantalum exhibit the required

characteristics for their use in collimators; however, the high unit and/or

manufacturing cost of the collimator make the use of these materials

impracticable.

Collimators differ mainly in their geometry. The usual distinctions are

between parallel-hole, convergent, divergent, and pinhole collimators. The

holes in the collimators may also differ in shape with the three basic ones

being square, triangular, or hexagonal (Figure 5.20).

Theparallel-hole collimator isthe most widelyused, in whichis the arrange-

ment of holes is perpendicular to the surface of the crystal. In this case, the

image has the same size as the object, regardless of distance from the collima-

tor to the subject. This characteristic is intrinsic to the orthogonal projection

that is provided (Figure 5.21).

When the organ under study is smaller than the crystal of the gamma cam-

era, a converging collimator can be used, which can use all the surface of

the crystal to build the image. In this case, the geometry is not orthogonal,

FIGURE 5.20

Various types of hole arrays in collimators.

Radiation Detectors and Image Formation 171

FIGURE 5.21

Schematic of a parallel-hole collimator. The size of the object is preserved.

causing a magniﬁcation that depends on the distance of the collimator to the

object (Figure 5.22).

The diverging collimator is the inverted version of the converging collima-

tor and is used when attempting to increase the camera ﬁeld of view. The

image obtained is smaller than the real object (Figure 5.23).

The pinhole collimator is based on the camera obscura in which light rays

pass through a small opening and are projected to form an inverted image.

Since the rays have to pass through a small hole, only a small percentage of

the emitted photons can reach the crystal; and, consequently, one of the major

disadvantages of the pinhole is its reduced sensitivity. Another drawback is

the distortion that occurs as a result of the ﬁnite size of the hole. However, the

possibility of magnifying and improving spatial resolution makes the pinhole

the preferred choice for studies of small organs (Figure 5.24).

The use of collimators has direct implications for both the resolution and

sensitivity of the system. These factors can be analyzed based on geometric

arguments. Resolution is deﬁned as the ability to discriminate two points close

together and is given by the FWHM of the response PSF (Figure 5.25).

FIGURE 5.22

Schematic of a converging collimator.

172 Nuclear Medicine Physics

FIGURE 5.23

Schematic of a diverging collimator.

Consider a point source at a distance, f , from a gamma camera with a

parallel-hole collimator with septa thickness s and hole diameter h. Let 

represent the height of the septa and c the distance of the collimator to the

scintillator crystal. The angle α is deﬁned as the angle between a ray perpen-

dicular to the crystal and the oblique ray of maximum inclination that still

reaches the crystal. Taking into account the geometrical aspects considered

and using the properties of similar triangles, it is deduced that

d =



(c + + f ). (5.37)

The expression shows that the characteristics of the collimator inﬂuence

the spatial resolution. Given that, generally, the distance from the source to

the collimator f is greater than the height of the septa, , and the distance

FIGURE 5.24

Schematic of a pinhole collimator.

Radiation Detectors and Image Formation 173

Crystal

FIGURE 5.25

Variation of spatial resolution with depth. Geometric relations associated with the resolution of a

collimator.

from the collimator to the crystal c the factors that determine resolution are

the distance from the source to the collimator and the relation between the

septa thickness and the hole diameter (d ≈ hf /). Thus, the smaller the holes

(h) relative to the height of the septa (), the lower the resolution distance d.

That is, the greater will be the power to discriminate two point sources that

are very close. Another conclusion to be drawn from Equation 5.36, which

is also shown in Figure 5.25, is that the spatial resolution varies with the

distance from the source to the collimator. The further the collimator is from

the sources, the worse the resolution will be.

Another aspect that must be taken into account is the geometric efﬁciency

of the collimator, which is deﬁned as the fraction of the number of photons

isotropically emitted and the number of photons effectively collimated [39].

Assuming an inﬁnite plane of activity in the air,the detector response is invari-

ant with regard to the distance to the plane; so the geometric efﬁciency, Ω

,is

generally deﬁned, assuming that the plane is adjacent to the collimator. Given

the deﬁnition of geometric efﬁciency, we have

Number of collimated photons

Number of emitted photons

Total hole area

Total area

4π

, (5.38)

where Ω is the solid angle in which a hole is seen from the center of the section

in a plane in contact with the collimator. Thus, the geometric efﬁciency, Ω

is best described by

(d +s)

4π

= k





(h +s)



, (5.39)

where k is a factor that reﬂects the properties associated with the type of

hole (hexagonal, triangular, or quadrangular), h is the size of the hole, s is the

septum thickness, and 

is the effective thickness of the collimator.

174 Nuclear Medicine Physics

5.3.1.2 Data Acquisition

In gamma scintigraphy, a simple 2D projection is formed perpendicular to

a given direction, keeping both the gamma camera and the patient at rest

during data acquisition (Figure 5.26a). The result is an image similar to a

radiographic projection.

In SPECT, one or more gamma cameras are rotated around the patient to

acquire a large number of projections along different directions (Figure 5.26b).

These projections are combined using standard tomographic reconstruction

algorithms to build a 3D volume representing the radiotracer’s activity. This

volume may then be digitally manipulated to produce 2D images of the

activity distribution along any chosen direction. Current SPECT scanner tech-

nology uses two or three gamma cameras, known as detector heads, which

rotate around the patient in circular or elliptical trajectories, known as orbits

[40]. Decay events are accumulated at ﬁxed points of the orbit, usually 3

◦

or 6

◦

apart.As a rule, the heads complete a full 360

◦

rotation to minimize geometric

distortions in the reconstructed images; such distortions may arise from the

dependence of the spatial resolution of each head on the distance from the

radioactive source to the head’s collimator (Figure 5.26c).

5.3.1.3 Data Storage

5.3.1.3.1 Data Formats: List-Mode and Histograms

The mapping of each gamma photon detected in the active volume of the

scanner allows the raw data in these nuclear techniques to be compiled in

a sequential list of detection events, where each entry stores a certain set of

Number of

photon counts

(a) (b) (c)

FIGURE 5.26

(a) Production of a 2D projection in gamma scintigraphy along a given direction. The gamma

camera and the patient remain still during data acquisition. (b) Production of multiple 2D pro-

jections in a SPECT scan with a dual-head scanner. The projections are taken at ﬁxed positions

along the orbit of the heads as these rotate around the patient. (c) Typical geometric distor-

tions generated in the reconstructed images of two point-like sources placed symmetrically

relative to the detector axis, for a 180

◦

orbit (left) and a 360

◦

orbit (right) in a single-head SPECT

scanner.

Radiation Detectors and Image Formation 175

relevant information about the event. This information includes the position

at which the photon interacted with the scintillation detector or the energy

deposited by the photon. This data format, known as list mode [41], is, how-

ever, generally inappropriate for image reconstruction; and the histogram

data format is usually preferred.The histogram, a 2D array of integers, groups

the recorded events according to the location where the photon was detected

[42]. The active volume of the scanner is therefore, discretized into channels

or bins, and the total number of photons detected in each bin is counted dur-

ing the exam. For gamma scintigraphy scans, the correspondence between

array entries and scanner bins is chosen so that a unique histogram coincides

with the 2D projection of the activity distribution along the direction of the

collimator channels [40].

In SPECT imaging, the detection events are stored in several histograms,

known as sinograms. Contrary to what one would assume, sinograms are not

the 2D projections of the activity distribution along the acquisition positions

of the orbit. Instead, they are assembled in a way that turns out to be more

suitable for the image reconstruction algorithms [43].

Most SPECT scanners record the raw event data in list-mode format, con-

verting it later to histogram format. This conversion is easily performed once

the discretization of the scanner’s active volume is known relative to the

location of the heads. Although the histogram is better suited to image recon-

struction, list-mode data have a larger information content which is often

important for the correction of physical effects that decrease image quality,

suchas scatteredradiation [44]. Further,itis themost ﬂexibleformat, as,unlike

histogram data, list-mode data do not depend on the particular discretization

resulting from dividing up the scanner’s active area into channels.

5.3.1.3.2 SPECT Sinograms

The histogram data structure used in SPECT is the sinogram, which consists

of a 2D array with the photon counts along all possible directions in a plane

perpendicular to the rotation axis of the scanner [43]. The two indexes of

each sinogram entry identify the spatial orientation of the detected photons

stored in that entry, according to the radial coordinate x

and the azimuthal

angle, φ, shown in Figure 5.27. These two coordinates are deﬁned using a

reference frame OX

linked to one of the scanner’s heads, obtained from

the negative rotation of the stationary frame OXY ﬁxed to the scanner by

an angle φ ∈[0; 2π]. In the stationary reference frame OXY, the origin O is

located in the scanner’s axis, and OX and OY are, respectively, the horizontal

and vertical directions (Figure 5.27a and b). An additional axis OZ allows

an axial coordinate, z, to be deﬁned for each sinogram, locating it along the

scanner’s axis (Figure 5.27b). The set of sinograms acquired for a given object

in all the planes is compiled in a 3D array s(x

, φ, z). It should be noted that

the number of elements in each dimension of the sinogram depends on the

discretization of the scanner’s heads (dimension corresponding to x

) as well

as on the number of acquisition angles used (dimension corresponding to φ).

176 Nuclear Medicine Physics

Sinogram

Number of photon

counts

(a) (b)

FIGURE 5.27

(a) Deﬁnition of the x

and φ coordinates for a photon emission direction (dashed line) in the

reference frame linked to one of the heads, and corresponding location in the sinogram.

(b) Orientation of the stationary reference frame XYZ. The XY, YZ, and XZ planes are usually

referred to as the transaxial, sagittal, and coronal planes.

If the scanner has more than one head, the number of counts along a direction

labeled by a set of x

, φ, and z values is the sum of all counts detected in each

head for that direction.

According to its deﬁnition, each row of the sinogram groups photon emis-

sion directions that are all parallel and deﬁnes an angle φ with the horizontal;

whereas each column groups different directions, but all with the same radial

coordinate x

, that is, which are tangent to a circle of radius x

centered in

O (Figure 5.28). Mathematically, a sinogram is the 2D radon transform of an

object [45] and is so called, because a point-like source of photons always

gives rise to a sinusoidal pattern in its sinogram [43] (Figure 5.28).

The way photon counts are organized in a sinogram is particularly appro-

priate for image reconstruction algorithms, as each entry stores the number of

photons emitted in a well-deﬁned direction, which, in the absence of effects

such as Compton scattering or self-absorption, is proportional to the total

activity of the radiotracer along that direction. Each row of the sinogram is,

thus, the set of parallel projections of the activity (or, more simply, the projec-

tion of the activity) of the imaged object along the direction φ in the plane z,

p(x

, φ, z) [43]:

p(x

, φ, z) = s(x

, φ, z). (5.40)

The set of activity projections along all possible orientations in a given z

plane is the information used to reconstruct the image in that plane. The

ﬁnal result of typical image reconstruction algorithms is an image volume

consisting of all reconstructed planes stacked together.

Radiation Detectors and Image Formation 177

Sinogram Sinogram Sinogram

FIGURE 5.28

(a) Representation of all photon emission directions involved in the deﬁnition of a sinogram row

(left) and column (right). (b) Sinogram originated froma point-like source located in the scanner’s

axis (A) and away from that axis (B). As a function of φ, the sinogram describes a complete sine

wave for a rotation of 360

◦

, with an amplitude equal to the source-axis distance.

5.3.1.4 Preprocessing of Data

The reconstruction of a SPECT image assumes that the number of photon

counts in each emission direction is proportional to the integrated activity

of the object over that direction. There are, however, several factors that dis-

turb the counting and change that proportionality. These are mainly physical

effects, such as the occurrence of Compton scattering in the patient, which

leads to disperse radiation or photon ﬂux attenuation due to interaction

between the emitted photons and the patient’s body. Thereare differentstrate-

gies for the correction of those effects, most of which pre-process the acquired

data before image reconstruction. This preprocessing, known as data correc-

tion, is a key factor in ensuring that the reconstructed image is a reliable

estimate of the activity distribution of the object being studied. The main

effects corrected and methods used are addressed in Chapter 6.

5.3.1.5 Image Reconstruction

The SPECT imaging is a tomographic technique that generates slices of the

object, showing the radiotracer distribution in the patient’s volume. Recon-

structing the image from the number of photon counts along different spatial

directions starts presuming that, in the absence of attenuation and Compton

scattering, the number of photons detected in a given direction is, as pre-

viously mentioned, proportional to the integral of the activity distribution