European Nuclear Medicine Guide
The atomic nucleus consists of two different nucleon types named as: protons and neutrons. The protons are positively charged, while the neutrons are uncharged particles. The nucleus is surrounded with negatively charged electrons. The total number of nucleons in an atom is known as mass number (usually denoted as A), and the number of protons is called as the atomic number (denoted as Z). Atoms with different A but same Z are called isotopes of the element corresponding to atomic number Z[23] When indicating isotopes, generally the following notation is used:
(Eq. 1.)
The nuclide of an atom can be unstable in the presence of a certain ratio of protons and neutrons, and this can lead to an emission process called radioactive decay. Radioactive decay has three major forms: alpha (α), beta (β) and gamma (γ). In the case of α-emission, a helium nucleus, two neutrons and two protons, is expelled from the atom. Alpha decay occurs primarily among heavy elements and has only therapeutic interest in nuclear medicine. Beta decay can occur in two forms: β- and β+. During β- decay, a neutron in the nucleus is converted into a proton and an electron, and this is followed by ejection of the electron together with a neutrino (ν). The electron in this case is referred to as a β- particle, while the neutrino is a “particle” that has no mass or electric charge. In the case of β+ decay, a proton in the nucleus is transformed into a neutron and a positron, the anti-particle of the electron. This process is followed by emission of the positron together with a neutrino. We sometimes refer to α- and β-particles as charged particles, because they carry an electric charge. Gamma emission can occur in several ways. The atom has three possible states: the ground state, which is the most stable arrangement of the nucleons; the excited state, which is a very unstable state with only a transient existence; the metastable state, a further unstable state that, however, has a life-time longer than 10-12 s[24]. The nuclear transitions between different nucleon arrangements involve discrete and exact amounts of energy and can therefore result (in the direction of the ground state) in emission of particles or γ-rays. The energy difference between the states determines the γ-ray energy. Even a β- emission with a metastable daughter nucleus can result in a final γ-ray emission (2). Another way for γ-photon emission is through a β+ decay, when the ejected positron loses kinetic energy by inelastic interactions with atomic electrons. Then, a temporary particle called the positronium is formed with a final electron. This is followed by the annihilation process, while the mass of the positron and the electron are converted into two 511-keV γ-photons which are emitted simultaneously at about 180° with respect to each other [25].
Radioactivity of an isotope can be measured as disintegrations per second, and 1 disintegration per second is a unit called 1 bequerel (Bq). The traditional unit of curie (Ci) is still frequently used (1 mCi = 37 MBq). Radioactive atoms decay in an exponential fashion, and the time required for half of the atoms in a sample to decay is called as the half-life (T1/2). The radioactivity of a sample at a certain time point (t) can be calculated as:
A(t) =A(0) × exp(-ln2 × t/T1/2) (Eq.2.)
where A(0) is the radioactivity at time point 0 and T1/2 is the half-life of the isotope.
When describing interactions of radiation (electromagnetic and acoustic) with matter, it is necessary to consider whether the wavelength will cause any interaction with the target object (e.g. human tissue) or even result in total absorption of the radiation. There are three radiation wavelength ranges where the absorption characteristics can be used for the purpose of medical imaging[26]: the X-ray window (used in CT, planar X-ray, PET, gamma cameras and SPECT), the radiofrequency window (used in MRI), and the ultrasound window (used in ultrasonography) (Fig. 1).
Let us consider a radiation interaction as a single system. The comparison of the system before and after the interaction reveals that some quantities remain the same following the interaction. These quantities are often referred to as being conserved in the interaction. Such conserved quantities include total energy, momentum, and electric charge. With respect to ionization, a distinction is drawn between directly ionizing particles (charged particles) and indirectly ionizing particles (uncharged particles). Directly ionizing particles comprise the alpha particles (helium nuclei), beta particles (electrons), protons, and any other nuclei. Indirectly ionizing particles are the photons (in the adequate energy range) and neutrons. While there is a definite difference between the classical and quantum electrodynamic explanations of interactions between particles, within this chapter the classical model is applicable, since the focus is on which particles will survive, where they go, and what happens to their energy. On the atomic scale, it is practical to use the electron volt (eV) energy unit defined as the amount of energy an electron gains when it travels through a potential difference of 1 volt (1 eV = 1.6×10-19 J).
An atom becomes ionized when it ejects at least one electron. Below an energy level of 13.6 eV, radiation is not able to induce ionization. Therefore, radiation with an energy higher than 13.6 eV is called ionizing, while radiation with an energy lower than 13.6 eV is called non-ionizing. According to the EURATOM Directive, “ionising radiation means energy transferred in the form of particles or electromagnetic waves of a wavelength of 100 nanometres or less (a frequency of 3×1015 hertz or more) capable of producing ions directly or indirectly”[27]. When an electron is not ejected from the atom by the radiation but is raised to a higher energy level, the atom enters an “excited” state, a process referred to as excitation. There is then a probability that an incident electron will cause ejection of the K-shell electron, in the case of higher atomic number elements, and the vacancy is filled with an outer shell electron (Fig. 2). During this process, the energy difference of the two shells is emitted in the form of electromagnetic radiation referred to as characteristic X-ray, since the energy is characteristic for the element. X-ray photons of different energy are emitted according to the characteristics of the electron shells of the atom. The incident electrons may only be repelled by the nucleus, and while they are continuously accelerated in the electric field of the nucleus, electromagnetic radiation is emitted in the X-ray spectrum. This is the so-called bremsstrahlung process. The classical electromagnetic explanation derives from the fact that an electric charge moving with constant velocity would not emit electromagnetic radiation, whereas in the event of acceleration, it would. Two typical X-ray emission spectra with 80 kV and 120 kV applied on the X-ray tube are displayed in Fig. 3.
The integral of the functions displayed in Fig. 3 (and therefore the total X-ray photon number) is proportional to the electric current and to the square of the voltage applied on the X-ray tube. The number of X-ray photons correlates strongly with the image quality in the case of CT imaging.
As described in the preceding sections, the difference between X-rays and γ-rays derive from their origin and are not necessarily observable in their energy. Both are forms of electromagnetic radiation and have a certain probability of passing through different processes based on their energy. The energy of X-rays and γ-rays in nuclear medicine applications regularly causes three kinds of interactions: photoelectric absorption, Compton scatter, and pair production. The last-mentioned occurs when a photon interacts with the electric field of a charged particle, and the photon disappears while its energy is used to create a positive–negative electron pair (an electron and a positron). Because both the positron and the electron have a rest mass equivalent to 0.511 MeV, the minimum photon energy necessary for pair production is 1.022 MeV. In nuclear medicine applications, this photon energy is rarely used, and therefore we focus below on the other two interactions.
During the photoelectric effect or photoelectric absorption (PEA), the target atom absorbs the total energy of the incident photon. While the photon disappears, this energy is used to eject one of the orbital electrons, which is therefore called a photoelectron. The kinetic energy of the photoelectron is equal to the difference between the incident photon energy and the binding energy of the electron shell from which it was ejected[24]. The kinetic energy of the photoelectron is deposited in the near site of the interaction during excitation and ionization processes. Photoelectron ejection from the innermost electron shell is most probable if sufficient incident photon energy is available. A schematic representation of PEA is shown in Fig. 4.
During Compton scattering (CS), the incident photon interacts with a loosely bound outer shell orbital electron. In this case the energy of the incident photon greatly exceeds the binding energy; the photon will not disappear, but after it has been deflected with a scattering angle (θ) and some of its energy is transferred to a recoil electron. This interaction looks somewhat like a collision between a photon and a “free” electron. The scattering angle distribution depends largely on the incident photon energy[24]. The process of CS is depicted schematically in Fig. 5.
These interactions (PEA and CS) do not cause ionization directly as do the charged-particle interactions, but the ejection of orbital electrons and the creation of positive-negative electrons will cause ionization and, therefore, result in radiobiological effects.
Both PEA and CS lead to missing or misplaced information when using nuclear medicine imaging techniques. The true signal is therefore attenuated, and the final image data need to be corrected for this attenuation. In general, the absorption of any radiation can be described as follows:
Ix ~ I0 e-μx (Eq. 3.)
where I0 is the intensity of the photon bundle impinging on the tissue, x is the length of tissue through which the radiation has to penetrate, Ix is the intensity of after attenuation by the tissue, and µ is the attenuation coefficient. The formula in Eq. 3 applies for both X-ray and γ-ray photon energies. Therefore, the eµx factor gives the probability that an attenuating interaction will occur throughout the tissue length x. The thickness of an absorber (e.g. body tissue) that decreases the original intensity of radiation (I0) by one-half is called the half-value layer (HVL). In some radiation protection applications (such as shielding) it is useful to calculate the tenth-value layer (TVL), i.e., the thickness of the absorber that decreases the radiation intensity by the factor of 10[24]. The total attenuation of a certain tissue is the sum of the PEA and CS attenuation coefficients and varies based on the photon energy. This effect is displayed in Fig. 6 for bone and muscle density tissues. It can be observed that PEA becomes less dominant at around 50 keV, and that most of the interactions are CS for higher photon energies.
In the CT energy range (20–140 keV) both the CS and the PEA effect are present, but above 30–40 keV, CS is dominant. For most single-photon emission computed tomography (SPECT) examinations, too, the photon energy results mainly in CS. During SPECT, collimators are used to eliminate at least a portion of the events scattered in the body, however, the missing signals result in a need for attenuation correction (Fig. 7). In modern hybrid SPECT/CT systems, the CT images of the patient are used for the purpose of attenuation correction. This procedure includes co-registration, energy scaling (from CT energy to SPECT energy), and resolution scaling.
In a PET system, the coincidence events registered during data acquisition derive not just from true coincidences, rather, they are also biased by the so-called scattered and random events. The γ-photons (originating from the annihilation process) with 511-keV energy have a very low probability for PEA but a significant probability of undergoing CS (over 95%) (Fig. 8). This scatter can occur in the body and change the direction of the γ-photon while the coincidence is assigned to a misleading line of response (LOR). During 3D PET, a very large number of single γ-photons reach the detector ring, including from sections of the body outside of the field of view. Because the coincidence time window is not infinitely narrow (usually between 5 and 10 ns), there is a high likelihood that two single photons from two different annihilation events will arrive during the given coincidence time window and result in a random coincidence event. These random events then contribute to the noise level of the final images. The final detected count rate will consist of the count rates mentioned above as:
M ~ Atten×T+S+R (Eq. 4.)
where M is the measured count rate, Atten is the attenuation effect, T is the true count rate, S is the scatter count rate and R is the random count rate. Random events, attenuation, and CS will result in a distorted PET signal and, therefore, have a great impact on the image data. Because of the geometry of the patient, these interactions cause severe attenuation that is more prominent in the inner parts of the body and lower at the surface. As discussed above, the results of these interactions are the removal of primary photons from a given LOR and the potential detection of scattered photons in a different LOR. Thus, attenuation and scatter are side effects of the same physical process. Corrections are necessary and include removal of the estimated scatter fraction from the LORs. Moreover, it is necessary to subsequently correct each LOR for the fraction of events missing from that LOR.
The probability that a γ-photon will escape the body depends on the distance between the annihilation site and the surface (x) multiplied by the attenuation coefficient of the tissue (µ). The probability of detecting both photons is the product of the individual probabilities that one of the photons will escape the body (1). Therefore, only the diameter (D) of the patient along the LOR contributes to the equation for this probability (Eq. 5) regardless of the distance of the annihilation site from the surface:
p=p2× p1= e-μ(D-x)) × e-μx= e-μD (Eq. 5.)
Attenuation of the signal from a given LOR can be measured with different algorithms from CT or MR images of the same patient. This so-called µ-map is generated using a bilinear scaling method in the case of CT images. For MRI, segmentation algorithms are routinely employed using a Dixon sequence. Besides attenuation correction, scatter and random corrections are performed on the raw data of PET images. It must be emphasized that all corrections will contribute to the overall noise characteristics of the reconstructed images, while the average image pixel values will be unbiased and will refer more closely to the true signal.
Acknowledgements: The author would like to express his gratitude to Dr. Laszlo Balkay for his advice and thoughtful conversations during the writing process, and to Dr. Nicola Belcari for his help in the figure presentations.
Figure 1.
Attenuation of electromagnetic radiation by human tissue for a wide spectrum of wavelengths. The X-ray window is used in CT, planar X-ray, PET, gamma cameras and SPECT while the radiofrequency window is used in MRI. Acoustic radiation is strongly absorbed for wavelengths below 1 mm and therefore is only useful for medical imaging purposes in the ultrasound window (1). UV, Ultraviolet; IR, infrared; MW, microwave.
Figure 2.
When an outer shell electron moves to fill the inner shell vacancy, characteristic X-rays are emitted in accordance with the energy difference between the electron shells.
Figure 3.
X-ray spectra with different voltages applied on the X-ray tube (120 kV and 80 kV). Peaks in the spectrum represent X-ray photons originating from the characteristic X-ray process, while the wide spectrum is the result of the bremsstrahlung effect.
Figure 4.
Schematic representation of PEA
Figure 5.
Schematic representation of CS
Figure 6.
Dependence of total, photoelectric and Compton scatter attenuation coefficient on photon energy for bone and muscle tissues (courtesy of Dr. Nicola Belcari) (4).
Figure 7.
Schematic diagram of single-photon emissions and detection. The detected signal needs to be corrected for PEA and CS
Figure 8.
Attenuation probability of a given LOR: because of the coincidence detection, the probability of detection of both photons (p = p1 × p2) depends on the attenuation coefficient (µ) and the diameter (D) along the LOR and is independent of the distance of the annihilation site from the surface (x)