Lima J.J.Pedroso, de (ed.). Nuclear Medicine Physics
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208 Nuclear Medicine Physics
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6
Imaging Methodologies
Nuno C. Ferreira, Francisco J. Caramelo, J. J. Pedroso de Lima,
Carina Guerreiro, M. Filomena Botelho, Durval C. Costa,
Hélder Araújo, and Paulo Crespo
CONTENTS
6.1 Physical Aspects of Nuclear Medicine Functional
Imaging ............................................211
6.2 Sources of Degradation in NM Imaging Methods ..............215
6.2.1 Introduction ....................................215
6.2.2 Correction of Image Degradation
Effects .........................................216
6.2.2.1 SPECT ..................................216
6.2.2.2 PET ....................................224
6.3 Image Processing .....................................238
6.3.1 Image Reconstruction .............................242
6.3.1.1 2D vs. 3D Reconstruction ....................243
6.3.1.2 2D Reconstruction .........................244
6.3.1.3 3D Reconstruction .........................251
6.3.1.4 Rebinning Methods ........................254
6.3.2 Concepts of Digital Image Processing .................257
6.3.2.1 Image Preprocessing .......................257
6.3.2.2 Point-Based Preprocessing ...................257
6.3.2.3 Gamma Correction ........................259
6.3.2.4 Logarithmic Transformations .................260
6.3.2.5 Histogram Processing ......................260
6.3.2.6 Correction of the Geometric
Distortion ...............................261
6.3.2.7 Color Preprocessing ........................262
6.3.3 Image Registration ...............................265
6.3.3.1 Dimension ...............................267
6.3.3.2 Nature of the Basis of Registration .............268
6.3.3.3 Nature and Domain of the Transformation .......268
6.3.3.4 Interaction ...............................270
6.3.3.5 Optimization .............................270
209
210 Nuclear Medicine Physics
6.3.3.6 Modalities ...............................277
6.3.3.7 Subject ..................................278
6.3.3.8 Object of Registration .......................278
6.3.3.9 Nonrigid Methods .........................278
6.4 Advanced Methods in Nuclear Oncology ....................281
6.4.1 Introduction ....................................281
6.4.2 Tumor Proliferation ...............................283
6.4.3 Tumor Metabolism ...............................283
6.4.4 Glucose Metabolism ..............................283
6.4.5 Nucleoside Metabolism ............................284
6.4.5.1 Thymidine ...............................285
6.4.5.2 Thymidine Derivatives ......................285
6.4.5.3 Other Nucleosides and Analogs ...............286
6.4.6 Amino Acids Metabolism ..........................286
6.4.7 Enzymes .......................................287
6.4.7.1 Thymidine Phosphorylase ...................287
6.4.7.2 Tyrosine Kinase ...........................288
6.4.8 Tumor Hypoxia ..................................288
6.4.9 Tumor Angiogenesis ..............................290
6.4.10 Apoptosis ......................................292
6.4.11 Multiple Drug Resistance ..........................293
6.4.12 Tumor Receptors .................................295
6.4.12.1 Folic Acid Receptors ........................296
6.4.12.2 Sigma Receptors ...........................296
6.4.12.3 Breast Cancer Receptors .....................296
6.4.12.4 Cholecystokinin-B/Gastrin
Receptors ................................297
6.4.12.5 Other Receptors ...........................297
6.4.13 Molecular Image as Target ..........................298
6.5 CNS: Physiological Models and Clinical Applications ..........299
6.5.1 Introduction ....................................299
6.5.2 Anatomical Basis .................................299
6.5.2.1 Brain ...................................300
6.5.2.2 Cerebellum ..............................305
6.5.2.3 Midbrain (Mesencephalon) ...................306
6.5.3 Physiological and Pharmacological Basis ...............306
6.5.3.1 Barriers .................................308
6.5.3.2 Factors Influencing Cerebral Capillary
Permeability ..............................315
6.5.3.3 Neurotransmitters .........................317
References ..............................................320
Imaging Methodologies 211
6.1 Physical Aspects of Nuclear Medicine Functional
Imaging
A medical image is a planar representation of the local values of a parameter
in a region or organ under study that is accessible to the eye. It is obtained by
projection or emission techniques or by indirect evaluation.
Advances in physics and technology since the end of the nineteenth century
have brought imaging methods such as conventional radiology, scintigraphy,
ultrasound, computed tomography (CT), and magnetic resonance imaging
(MRI) to medicine.
There has been a steady stream of remarkable improvements in these tech-
niques in recent years, providing powerful diagnostic tools and opening up
increasingly sophisticated and promising perspectives.
In very general terms, the techniques of medical imaging can be divided
into two categories: passive and active.
The passive techniques use only endogenous signals spontaneously gener-
ated in the human body, for example, thermography and the visualization of
electrical activity of the brain.
The active techniques make use of the properties of various forms of radi-
ant energy from exogenous sources that can propagate through the matter
and provide information, either anatomical or physiological. Examples are
radiology and ultrasound.
In addition, based on the properties or parameters that are acquired, the
medical images can be divided into morphological (anatomical) images and
functional (physiological) images. The morphological images provide infor-
mation about physical structures, form, and some properties of the mass
of patients. They tend to have good resolution (≤1 mm). Examples are
conventional radiography, MRI, CT, and ultrasound.
Functional images portray the movement of materials associated with the
physiological processes that occur in patients. They are images containing
information, in some cases quantitative, on metabolism and other aspects
of biological dynamics [1]. Examples of this category are images provided
by radioisotopic techniques: single-photon emission computed tomography
(SPECT), positron emission tomography (PET), and emerging techniques
such as functional magnetic resonance imaging (fMRI).
Thefunctional imagesof nuclearmedicine (NM)generally have poor spatial
resolution (3–5 mm or more).
The medical images directly obtained from the detectors are often repre-
sented by analog functions with two variables of position x and y in the
image plane or, in some techniques, with three variables of position x, y, and
z in the domain of 3D image space.
When it comes to image sequences, a new variable, time t, is added, giving
rise to functions of three or four variables, with dynamic information I(x, y, t)
and I(x, y, z, t), respectively.
212 Nuclear Medicine Physics
In NM, the range of existence of the image function I corresponds to
values of activity (or concentration of the tracer) below the limits imposed
by radioprotection criteria, in the image points (x, y) or (x, y, z), at a particular
time (t).
When it comes to handling the results for a list of parameters, it is often
convenient to use the images in vector or matrix notation.
A matrix is a rectangular table of values that can represent an image. For
a matrix I with n rows and m columns, Iij is the value of the matrix element
corresponding to the line i and column j, where i ranges from 1 to n and j
varies from 1 to m.
A vector can be represented as a list of values and is usually written as a
column. Some operators in image processing are represented by vectors. For
a vector w with n components, w
i
refers to component i, which would vary
from 1 to n. A vector of intensity w is equivalent to a column matrix of n by 1.
Scalar functions are used to describe monochrome images, but for colour
images it is necessary to use vector functions that represent the three compo-
nents of color:
I
R
(x, y, t), I
G
(x, y, t), I
B
(x, y, t), (6.1)
where R is for Red, G is for Green, and B is for Blue.
Other vector functions with multiparametric components can be found in
some medical images such as MRI.
The use of vector and matrix operators can simplify the resolution of com-
plexsystems ofequations andfacilitate theexecution ofmany tasksin imaging
sciences [2].
Analog image functions I(x, y, t) are not suitable for processing in digi-
tal computers, and this justifies the systematic transition from conventional
analog images (using film) to digital mapping, which has been occurring in
medical imaging since the 1960s.
Digitization converts analog functions into digital functions.
In planar digital images, x, y, and t are discrete finite quantities. In NM
images, the digitization of images involves either the values of activity or
these and the parameters of position.
In the first case, the data are sampled for discrete values of spatial coor-
dinates, and small image elements with dimensions that depend on the
detectors used are defined. We can, thus, represent a sampled image as a
function
f (m, n) = f (mΔx, nΔy) (6.2)
with 0 ≤ m ≤ M,0≤ n ≤ N, and where Δx and Δy are the sampling intervals
alongtwo normaldirectionsx and y, respectively. Theelementary area(ΔyΔx)
is called a pixel (image element).
The values of activity in the interval between the minimum and maximum
that can be attributed to pixels of a particular image arequantified in a discrete
form as binary numbers in a set of intervals that depends on the number of
Imaging Methodologies 213
bits (depth) available. Current options for the medical image data are 8 bits
(256 intervals), 12 bits (4096 intervals), or 16 bits (65,536 intervals).
In NM, the selective uptake in tissues or organs or spatiotemporalvariations
of distributions of biomolecules labeled with gamma or positron emitters
yield images which contain functional data that are often quantitative, in
addition to morphology.
In NM, the values of the pixels that make up a digital image represent
values of the activity in volume elements of the object, called voxels, which,
in the example of planar scintigraphy, are projected on the image plane as
pixels.
Thus, a digital 2D image of NM is a mapping of binary integer numbers
representing, on a plane, the quantified activity of discrete volume samples
of the object. The dimensions of the voxel and pixel depend on the technique
used. In tomography studies, the volume of the voxel is the product of the
pixel area and the slice thickness.
The accuracy associated with each pixel value depends on the number of
bits assigned to it. The error associated with each pixel value depends on the
number of events accumulated.
In a 3D image, voxels with dimensions (Δx, Δy, Δz) have average values of
activity I(x, y, z) expressed as binary numbers and with the identification of
the spatial position of the element (x, y, z).
NM has several special features that strongly influence the type of informa-
tion which is made available in NM imaging studies.
The emission of radiation by the organs or tissues under study is the basis
of imaging methods in NM.
The detection in NM refers to only the radiation emitted by radioactive
atoms that exist in the object, which is typically gamma radiation, that is,
electromagnetic radiation with a very short wavelength (<1.24 × 10
−10
m).
Substances with marked radioisotopes (tracers) are administered to
patients, and these are chemically the same (or functionally identical) as the
native molecules to be studied; but they are physically different, as they are
identifiable by the emission of radiation. NM shows spatiotemporal changes
of the distribution of biological molecules in the human body by identifying
and tracking the labeled replicas. It is now understood that the static images
of a biological system, in a particular moment, may be entirely inappropriate,
because dynamics is the essence of physiology and life.
The information that is transmitted by NM is essentially functional and
inherently different from that provided by other imaging methods such as
CT (computed tomography with x-rays) or ultrasound, which are essentially
structural.
Physiological or functional information is a general term that encompasses
metabolism, secretion and excretion (kidney, liver), and movements of organs
(heart, lungs, and blood) [1].
This information is important, especially in early detection and diagno-
sis, because metabolic disturbances precede the structural changes in the
214 Nuclear Medicine Physics
evolution of pathological processes and also as the dimensions of functional
lesions are often different from the sizes of corresponding anatomical lesions.
It is also remarkable that all these processes may be viewed using NM
techniques without any interference to the biological system, because the
amounts of tracer used are extremely small. For example, the mass of
99m
TcO
−
4
injected in a study with 20 mCi (740 MBq) of this ion is about 3.9 ×10
−9
g.
The NM images represent mere distributions of appropriate radioactive
agents within the body. Nonradioactive matter, which may or not be related
to the amount of radioactivity present, is ignored during detection or con-
sidered only for the purposes of correction of attenuation. This may also
suggest that good signal or noise ratios are to be expected in NM images.
This is true in many cases but not a rule, because often you want to see the
contrast between slightly different concentrations of radioactive material and
not between radioactive and nonradioactive tissue.
In NM images, the geometric limits of the matter that did not uptake
radioactive material are undetectable and are often assumed or ignored. Only
the limits of the distribution of radioactive atoms are known, and even these
not very clear, due to limitations in the spatial resolution of NM images.
Thinking in terms of waves alone, this poor spatial resolution appears to
be in disagreement with the small wavelength of the γ rays. The nature of
physical interactions for the energies of gamma radiation justifies this appar-
ent anomaly, impeding the occurrence of phenomena such as refraction and
reflection. Strong technical limitations and the often unfavourable statistics
of photons in NM techniques also contribute to the poor definition of images
in NM.
One of the biggest problems that conventional single-photon NM has had
to face since its inception is related to the fact that the vast majority of biolog-
ical molecules consist of elements with low atomic numbers. This simple fact
is a real disaster for conventional NM. In fact, there are no emitters of gamma
radiation, with usable lifetimes and that enable external detection, among the
artificial radioisotopes of biological elements of low atomic number (C, O, H,
N, S). The artificial radioisotopes of these elements, with useful periods, are
pure beta emitters (β
−
or positrons).
This led to the development of molecules labeled with nonbiological
gamma emitting radioisotopes of elements of high Z that are supposed to
behave similar to the native molecules, at least in the initial metabolic steps.
With the exception of some radioisotopes of elements such as iodine, iron, and
sodium, which have important roles in human metabolism, and some biolog-
ical molecules containing heavy elements in their constitution (vitamin B12,
hemoglobin, etc.), the techniques of conventional NM use radiopharmaceu-
ticals that are intrinsically different from the molecules that are to be studied.
The history of conventional NM is also the history of the steps that were taken
to overcome this and other difficulties and ultimately to use this technology
with the original concept of using isotopic tracers.
Imaging Methodologies 215
Biological systems are defined by multiple variables and are poorly rep-
resented, in general, by a single parameter, as happens in medical images.
In fact, the information provided by most imaging techniques refers to
only one or a few parameters, probably having minimal biological involve-
ment with the pathological condition under study and, even so, suffering
constraints of various types (intrinsic, technical, protection of patients, etc.).
Despite such constraints, the use of a particular technique of choice in specific
situations can provide important information.
CT reports on the local average density of electrons (or the average atomic
number Z) in voxels, elements that are basically imaginary slices of the patient
and whose average properties are transcribed in pixels. This information is
quantitative. The differences in the parameters for conventional radiogra-
phy and CT make it possible to distinguish bone from soft tissue, fat tissue,
etc. MRI reports on the proton density and chemical bonds or interactions.
The differences can distinguish between gray matter and white, soft tissue of
nerves, etc. Ultrasound signals detect the changes in acoustic impedance in
the media they pass through. These variations identify contours, the presence
of masses, changes in structure, etc [3,4].
We have stated that the information provided by most medical imaging
modalities was limited to a single parameter; but we have not drawn atten-
tion to the great exception, that is, NM, whose images are not confined to
reporting on a single parameter, as dozens of different molecules are used
in this speciality, with specific information. The NM images provide func-
tional information associated with the labeled molecules that we use. This
sets NM imaging apart from other techniques that can only report on one
or a few properties. Thus, PET and SPECT are as many techniques as the
number of molecules that we are able to label. These new medical imag-
ing techniques have become windows for the noninvasive observation of the
anatomy, physiology, and human pathophysiology and are essential to the
practice of modern medicine.
Overall, with medical imaging, one tries to detect changes in complex
and multiparametric systems, measuring essentially a limited number of
parameters, and in the case of projection techniques, previously changing
the geometry.
NM imaging is an exception in terms of the number of parameters
evaluated, because each labeled molecule administered provides specific
functional information.
6.2 Sources of Degradation in NM Imaging Methods
6.2.1 Introduction
An NM image is only a rough representation of what we wish to see in
living organisms. This simple observation is equally valid for planar images
216 Nuclear Medicine Physics
obtained by scintigraphy in a gamma camera; a set of raw data, such as pro-
jection data acquired in a SPECT or PET study; a series of axial, sagittal,
or transaxial slices obtained by tomographic reconstruction; or calculated
parametric images of a physiological parameter of interest, such as the local
cerebral blood flow. Not only do these images have an error associated with
each pixel or voxel value, resulting from various physical and technical fac-
tors affecting the measurement, but also if not properly taken into account this
error can spread to any calculation or inference we make from these images,
whether to obtain a simple curve of activity over time, a clinical diagnosis
report, or the choice of a particular treatment.
When we analyze an NM image, we must be aware that each pixel value
has a statistical error and that typically this error is, in relative terms, far
greaterthan the errors occurring on a photograph or radiograph. If we had the
tools to indicate the exact extent of this error, we could eventually correct the
measured value and thus obtain a perfect image. However, the error affecting
each pixel is only known as an uncertainty range. We must be aware of this
uncertainty, because it ultimately tells us to what extent we can trust NM
images.
There are several factors affecting the quality of NM images: they are not
very clear, with pixels of several millimeters that do not correspond to the
actual detail of the body; they are discrete versions of a continuous reality.
The counts in pixels or voxels are affected by statistical noise, which itself
gives rise to fluctuations that add to the effects of blurring caused by the
response of the camera, the distortion due to the attenuation of radiation,
the loss of contrast caused by Compton effect, the patterns of spatial vari-
ations of the efficiency of detectors, the effects of filters, and the simplistic
assumptions made during image reconstruction. When some of these effects
are compensated for, using appropriate methods, the corrections themselves
often introduce new random and systematic errors, which are expected to be
smaller than the systematic errors they are supposed to correct.
The presence of such errors or artifacts is unavoidable. Awareness of their
origin, amplitude, shape, and how they are distributed in the image gives us
an opportunity both to better understand the virtues and vices of the image
formation processes, leading to the development of better systems, and to
improve the perception and interpretation of information in order to draw
the appropriate conclusions based on the actual content of the images.
6.2.2 Correction of Image Degradation Effects
6.2.2.1 SPECT
6.2.2.1.1 Attenuation Correction
After having been emitted in the decay process of molecular markers, the
gammaphotons inSPECT travel agiven distanceinside thebody ofthe patient
beforehittingthe detector.Alongthat path all photonshave a finiteprobability
Imaging Methodologies 217
of interacting with the tissues of the patient, which leads to the attenuation
of the photon flux emitted by the activity distribution of the marker. Since
the attenuation of the photons emitted in a particular point of the activity
distribution depends on the length traveled by the photons inside the patient,
the reconstruction of the activity distribution directly from the raw measured
projections usually ascribes less activity to the regions of the patient that are
thicker and less to those that are thinner, as shown in Figure 6.1.
The correction of attenuation implies knowing the relation between the
number of photons emitted by the activity distribution along each direction
in space and the number of photons which actually hit the detector heads of
the camera in that direction. This relationdepends on the probability that each
photon emitted in each point of that direction has to interact along its path,
which, in turn, depends on both the nature of the different structures that the
photons pass through and the distance traveled in each of those structures.
The situation is quite complex, as it involves knowing the attenuation map of
the patient, that is, the value of the linear attenuation coefficient in all points
imaged by the scanner [5].
Determining the attenuation map is therefore crucial to correcting attenua-
tion in SPECT. When there is no independent way of obtaining it other than
from the projections acquired with the SPECT scanner, the attenuation map
has to be simultaneously determined with the activity distribution. This nec-
essarilyimplies using aniterative methodto perform theimage reconstruction
and the computation of a map precise enough [6–8]. When it is possible to
obtain the attenuation map by other methods, that information can be used
No attenuation
(a)
(b)
x
r
x
r
With attenuation
FIGURE 6.1
Attenuation effect in SPECT. (a) Diagram of a uniform activity distribution and its nonattenuated
and attenuated theoretical projections along a chosen direction (supposing the inexistence of
statistical noise and scattered radiation). (b) Reconstructed image of the activity distribution
using the attenuated projections. The central region of the reconstruction exhibits lower activity
than the original distribution.