Kluwer - Handbook of Biomedical Image Analysis Vol

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[2]Jonathan, M. and Paul, G., Intravascular Ultrasound imaging. Edited by, Jonathan M. Tobis and Paul G. Yock, Churchil Livinstone Inc., 1992, New York, USA.

[3]Yock, P. et al., Intravascular two dimensional catheter ultrasound, Initial clinical studies, abstracted, Circulations, No. 78 (Suppl II): II-21, 1988.

[4]Graham, S. et al., Assessment of arterial wall morphology using intravascular ultrasound in vitro and in patient, Circulations (Suppl II): II-56, 1989.

[5]Metz Jonas, A., Paul, G., and Fitzgerald Peter, J., Intravascular ultrasound basic interpretation, In: Beyond Angiography, Intravascular Ultrasound, State of the Art, Vol. XX, Congress of the ESC Vienna-Austria, Stanford University School of Medicine, California, 1998.

[6]Jumbo, G. and Raimund, E., Novel techniques of coronary artery imaging, In: Beyond Angiography, Intravascular Ultrasound, State of the Art, Vol. XX, Congress of the ESC Vienna-Austria, University of Essen, Germany, 1998.

[7]Korte, Chris L., Intravascular Ultrasound Elastography, Article compilation of its doctoral thesis, Interuniversity Cardiology Institute of the Netherlands (ICIN), 1999.

[8]Kearney, P. and Erbel, R., Imaging in the characterization laboratory, In: Beyond Angiography, Intravascular Ultrasound, State of the Art, Vol. XX, Congress of the ESC Viena-Austria, Johannes Gutenberg University, Mainz and University Clinic, Essen, Germany, 1998.

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[9]Berry, E. et al., Intravascular ultrasound-guided interventions in coronary artery disease, Tech. Rep., Healt Technology Assessment, NHS R D HTA Programme. A systematic literature review, with decisionsanalytic modelling of outcomes and cost-effectiveness, 2000.

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[14]Cheeke, D., Fundamentals and Applications of Ultrasonic Waves, CRC Press, Boca Raton, Florida, 2002.

[15]Thijssen, J. and Oosterveld, B., Performance of echographic equipment and potentials for tissue characterization, NATO ASI Series, Mathematics and Computer Science in Medical Imaging, Vol. F39, pp. 455–468, 1988.

[16]Zagzebski, J., Essential of Ultrasound Physics, Mosby, A. ed., Harcourt Health Sciences Company, 1996. St. Louis, Missouri.

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Chapter 2

Quantitative Functional Imaging with Positron Emission Tomography: Principles and Instrumentation

Koon-Pong Wong1

2.1 Introduction

The last few decades of the twentieth century have witnessed significant advances in medical imaging, which had been exclusively concerned with conventional film/screen X-ray imaging for more than 75 years after the discovery of X-ray by Wilhelm Rontgen¨ in 1895. In particular, when Allen Cormack and Godfrey Hounsfield introduced X-ray computed tomography (CT) independently in the early 1970s [1–3] based on the mathematical foundation laid by Radon [4] for reconstructing images of an object from its projections, the field of medical imaging was revolutionized. Imaging with X-ray CT has enabled us to view noninvasively, for the first time, the anatomic structure of internal organs with unprecedented precision and to recognize any gross pathology of organs and diseases. This also marked a new era of medical diagnostics with many invasive and potentially morbid procedures being substituted by noninvasive cross-sectional imaging.

The breakthrough development of X-ray CT was made possible by continuing advances in instrumentation and computer technologies, which also accelerated the development of other multi-dimensional imaging modalities that possess a great potential for providing, in addition to morphologic (structural)

1 Department of Electronic and Information Engineering, Hong Kong Polytechnic

University Hung Hom, Kowloon, Hong Kong

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information, dynamic and functional information on biochemical and pathophysiologic processes or organs of the human body. The importance of studying organ functions was recognized in the middle of the nineteenth century, but the actual relationship between physiological disturbances and anatomical lesions was not yet elucidated. This was partly due to the concept of disease classification, which was primarily based on anatomical lesions and causes of disease, during that period of time.

Recent advances in basic molecular and cell biology have led to a revolutionary change in our understanding of diseases. Instead of defining disease as structural changes or histopathological abnormality, it can be defined as alternations in cellular behavior that reflect functional changes. It is important to realize that in living systems, what we call function is a process that evolves over time as energy is produced during the life cycle or information is transferred and processed within cells, whereas structure is simply a snapshot of function at a particular time instant. Indeed, it is very common that in many diseases structural changes are completely absent, or physiological changes precede structural changes. A typical example is cancer, which consists of cells in which malfunctioning transformation has taken place owing to exposure to some environmental factors (e.g. viruses, bacteria, irradiation, saccharin, and a variety of chemical substances) that can cause altered membrane characteristics and cell metabolism, deformed cell morphology, etc. as a result of alternation in cell functions and damage in genes that control cell proliferation and migration. It was first hypothesized by Otto Warburg in 1930 that the rate of glucose metabolism (aerobic glycolysis) in tumors increases with higher degree of malignancy when compared to normal tissue [5], and this is regarded as one of the important indicators of tumor proliferation. If these biological characteristics could be evaluated in vivo, useful information may be obtained to study the nature of disease early in and throughout its evolution, as well as to identify and develop effective therapies for treatment. Functional imaging makes it possible to visualize and measure, with the use of appropriate imaging probes and agents, these complex pathophysiologic and biochemical processes in a living system in vivo in multi-dimensional domains (three-dimensional spatial domains plus a temporal domain).

There is no doubt that substantial progress has been achieved in delivering health care more efficiently and in improving disease management, and

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that diagnostic imaging techniques have played a decisive role in routine clinical practice in almost all disciplines of contemporary medicine. With further development of functional imaging techniques, in conjunction with continuing progress in molecular biology and functional genomics, it is anticipated that we will be able to visualize and determine the actual molecular errors in a specific disease within a decade or so, and be able to incorporate this biological information into clinical management of that particular group of patients. This is definitely not achievable with the use of structural imaging techniques.

In this chapter, we will take a quick tour of a functional imaging technique called positron emission tomography (PET), which, in conjunction with singlephoton emission computed tomography (SPECT), is commonly known as emission computed tomography. PET is a primer biologic imaging tool, being able to provide in vivo quantitative functional information in most organ systems of the body. In the following sections, an overview of this imaging technique is provided, including the basic principles and instrumentation, methods of image reconstruction from projections, some specific correction factors necessary to achieve quantitative images, as well as basic assumptions and special requirements for quantitation. Paradigms based on the framework of tracer kinetic modeling for absolute quantification of physiological parameters of interest are also introduced. However, as they deem inappropriate for inclusion in this book, topics on hardware technologies (e.g. display and archival units, data-acquisition computer system, electronics circuitry, array processors, etc.) of a PET system, operating principles of a cyclotron, as well as design and development of radiopharmaceuticals are not discussed in this chapter.

2.2 A Brief History of PET

The development of PET has involved efforts of investigators from diverse disciplines and spanned almost the whole twentieth century. At the turn of the twentieth century, Ernest Rutherford and Frederick Soddy (who coined the term isotope) reported their studies on the nature and cause of radioactivity in McGill University [6]. Their work on radioactive half-life and exponential decay is the foundation for medical applications of radioisotopes, including the breakthrough development of emission computed tomography.

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The existence of positively charged electrons (positrons) was postulated by Paul Dirac in 1928, based on Einstein’s theory of relativity and the equations of quantum mechanics [7]. It was first observed experimentally by Carl Anderson in 1932 [8], for which he was awarded the Nobel Prize for Physics in 1936. The phenomenon of positron annihilation that gives rise to gamma rays was observed by Joliot [9] and Thibaud [10] in 1933. It was shown later that, in general, two photons are simultaneously emitted in almost exactly opposite directions whenever a positron passes through matter [11]. The use of positron emitters for medical imaging purposes was first suggested by Wrenn et al. [12] and Sweet [13] in the early 1950s. The first successful positron imaging device was described by Brownell and Sweet [14]. The system was used for two-dimensional imaging of positron-emitting radionuclides (copper-64 and arsenic-75) distribution to locate brain tumors in human, using a pair of NaI(Tl) detectors. In 1963, Kuhl and Edwards introduced the concept of transverseand longitudinal-section scanning with single-photon emitting radionuclides [15] and a device (Mark IV scanner), which consisted of a square array of 32 NaI(T1) detectors, was built later for constructing images by superimposing multiple cross sections of transverse axial scans [16]. Although the reconstruction method was very primitive and the reconstructed images were severely blurred, the development of PET was accelerated by the introduction of transverse axial X-ray CT for radiography by Cormack and Hounsfield [1–3]. There have also been a number of techniques developed for performing emission tomography during the early 1970s [17–19], but all of these approaches were limited by inadequate mathematical reconstruction algorithms, insufficient angular sampling frequency, image distortions due to photon attenuation and some other statistical limitations.

The first positron computed tomograph was developed in 1975 by TerPogossian et al. [20]. This system was referred to as positron emission transaxial tomography (PETT II), which consisted of a hexagonal array of NaI(T1) detectors connected in coincidence between opposite pairs. The filteredbackprojection (FBP) reconstruction method was adopted in that system, and the quality of the reconstructed images was markedly improved. The first wholebody positron computed tomograph (PETT III) was developed shortly thereafter and it was used in human studies [21–24]. This system was subsequently redesigned and manufactured by EG&G/ORTEC as the commercial PET scanner, ECAT [25].

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2.3 Modes of Decay

The nucleus of an atom contains both protons and neutrons, which are collectively known as nucleons. In a stable nucleus, the number of protons and neutrons is such that the repulsive electrostatic force between the positively charged protons is balanced by the very strong attractive nuclear forces which act on all nucleons. It is possible to create unstable isotopes which have an excess number of protons using nuclear reactors or cyclotrons. These proton-rich

(or neutron-deficient) isotopes can have two means of decay that will reduce the excess positive charge on the nucleus: (1) electron capture and (2) positron emission.

If the nucleus does not have sufficient energy to decay by positron emission (to be described next), it will decay by electron capture, whereby the nucleus captures one of the orbital electrons from the inner shells and combines this with the proton to form a neutron, while the vacancy in the inner electron shell is immediately filled by an electron from a higher energy shell, resulting in emission of characteristics X-rays whose energies are carried off by the neutrino:

A X	+	e−	−→	A Y	+	ν	(2.1)
Z				Z−1

where Z represents the atomic number of the atom X, A is the mass number, e− is an electron, and ν is a neutrino, which has a very small mass and zero charge. Electron capture occurs in heavier proton-rich nuclides with higher likelihood due to the closer proximity of the inner (usually K or L) shell electrons to the nucleus and the greater magnitude of the Coulombic attractive force from the positive charges. The characteristics X-ray energy increases with the mass number of the nuclides. For example, the decay of 125I produces 27 keV characteristics X-ray which is used for in vitro counting, whereas the decay of

201Tl produces characteristics X-rays ranged from 68 to 80 keV which are used in gamma-camera imaging.

The major radioactive decay mechanism for positron emitters used in PET is positron emission, whereby a proton in the nucleus is transformed into a neutron and a positron. The positron (β+) has exactly the same mass and same magnitude of charge as the electron except that the charge being carried is positive. The nuclear equation for positron emission can be written as

A X	−→	A Y	+	β+	+	ν	(2.2)
Z		Z−1

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Table 2.1: Properties of some commonly used positron-emitting isotopes
		β+	E	max	Half-life	Range
Radionuclide	Production	fraction	(MeV)a		(min)	(mm)b
Carbon-11 (11C)	Cyclotron	0.99	0.96		20.4	0.28
Fluorine-18 (18F)	Cyclotron	0.97	0.64		109.7	0.22
Nitrogen-13 (13N)	Cyclotron	1.00	1.19		9.96	0.45
Oxygen-15 (15O)	Cyclotron	1.00	1.72		2.07	1.04
Gallium-68 (68Ga)	Cyclotron	0.89	1.90		68.3	1.35
Rubidium-82 (82Rb)	Generator	0.96	3.35		1.25	2.6

a Emax = maximal positron energy.

b Approximated distance that a positron traveled before annihilation, expressed in full width at half

maximum (FWHM).

For positron emission to be energetically feasible, the total energy difference between the parent and the daughter states should be at least 1.022 MeV, which is the energy equivalent of a positron and an electron, according to Einstein’s energy–mass equivalence: E = mc2. The energy difference between the parent and the daughter states is shared between the positron and the neutrino. In other words, the emitted positrons have a spectrum of energies, whose maximum is given by

Emax = E(ZA X) − E(Z−A1Y) − 1.022 MeV.

(2.3)

Typically, the likelihood of positron emission is higher for elements with lower atomic number, but for proton-rich nuclei with intermediate atomic number both decay modes are competing with each other. Table 2.1 lists some commonly used positron-emitting isotopes and their properties. Positron emitters are of special interest in medicine because the main elements (e.g. carbon, oxygen and nitrogen) that constitute living organisms have isotopes that emit positrons. The only exception is hydrogen for which fluorine-18 is an analogue.

2.4 Positron Annihilation

The positron will have some initial energy after emission from the parent nucleus. It travels a short distance from the nucleus, scatters and collides with loosely bound electrons nearby before fusing with one of them to form positronium (which has a very short half-life, ≈10−7 s) and then annihilates. Their

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511 keV

Annihilation

Nucleus

e+

e+	-
	e

Positron scattering

from multiple electrons 180o ± 0.25 in tissue

e+ Positron

e− Electron

511 keV

Figure 2.1: Positron emission and annihilation. A positron is emitted from a proton-rich nucleus, losing energy by scattering from atomic electrons in tissue before annihilating with an electron to produce two 511 keV photons (or gamma rays) which are moving 180◦ (±0.25◦ FWHM) apart.

mass converts into energy in the form of two 511 keV photons, which are indistinguishable from gamma rays. To simultaneously conserve both momentum and energy, the photons are emitted 180◦ to each other. Figure 2.1 shows the positron annihilation and the emission of two 511 keV photons. The detection of these two 511 keV photons forms the basis of PET imaging.

2.5 Coincidence Detection

Since the probability that both 511 keV photons will escape from the body without scattering is very high in general, the line along which the positron annihilation occurred (i.e. the line of response, LoR) can be defined if both photons can be detected with two detectors at opposite ends of the line, as illustrated in Fig. 2.2. As the distance that a positron traveled before annihilation is generally very small, this is a good approximation to the line along which the emitted photons must be located. The scheme for detection of photon emissions is called