Matter is composed of atoms and the characteristics of a specific form of matter are determined by the number and type of atoms that make it up. How atoms combine is a function of their electron structure. The electron structure is determined by the nuclear architecture. As we have yet to image the atom, its structure is based on a "most-probable" model that fits physical behaviors we observe. The probabilistic approach is based on the model of the atom proposed by Niels Bohr in 1913. The Bohr atom proposed a positively charged nucleus, surrounded by negatively charged electrons. A neutral atom is one in which the positive and negative charges are matched. A mismatch in these charges determines the ionic character of the atom, which is the basis for its chemistry. The electron configuration is also a source for emissions used in radionuclide imaging.
These emissions, or radiations, may be in either of the two forms: particulate or electromagnetic. The origins of either type of radiation may be from the nucleus or the electron structure.
Electrons are arranged around the nucleus in shells. The number of shells is determined by the number of electrons, which is, in turn, determined by the number of protons in the nucleus. The force exerted on these shells, called binding energy, is determined by the proximity of the shell to the nucleus. Higher binding energies are exerted on shells closest to the nucleus and conversely, lower binding energy for those more distant from the nucleus. The innermost shell is named the "K" shell and electrons in this shell are subject to the highest binding energy. The magnitude of that energy is dependent on the positive forces, which is determined by the number of protons in the nucleus. The shells more distant from the nucleus are named L, M, N, and so on. Each of these shells has lower binding energies as a result of their distance from the nucleus (Fig. 1-1).
Atomic structure. The nucleus is surrounded by electron shells. The binding energy decreases as the distance from the nucleus increases (K > L > M).
The radii of each of these shells increase as a function of their distance from the nucleus. An expression of this is given by assigning an integer value (1, 2, 3, …) to each shell. The lower values represent smaller radii. These integer values are called quantum numbers. Therefore, the K shell has a quantum number of 1, L = 2, M = 3, etc. This pattern continues until all available electrons are bound to a shell. The innermost shells are filled with electrons preferentially. The maximum number of electrons is specific to each shell and is calculated by 2n2, where n is the quantum number. Therefore, the maximum number of electrons for each shell is:
These shells are further subdivided into substates. The number of substates for each shell can be calculated by 2n – 1; therefore:
Each substate for a given shell will have a unique binding energy. For instance, the L shell has 3 substates, LI, LII, and LIII.1 Each of these has slightly different distances from the nucleus, and therefore slightly different binding energies (Fig. 1-2).2
Electron configuration. Electrons are arranged in subshells, as illustrated for the L shell. Each subshell has a unique binding energy.
Electrons in inner shells being under high binding energy and thus tightly bound to the nucleus are in an inherently low-energy state. Outer shell and free electrons are in an inherently higher-energy state. Therefore, to move an inner shell electron to an outer shell requires energy. The amount of energy required is simply the difference between binding energies.
Example: Binding energy for a hypothetical "K" shell = 100 keV and "L" = 50 keV. K100 – L50 = 50 keV of energy input to move the electron.
Conversely, the movement of an electron from an outer shell to an inner shell, L → K, yields energy. This energy yield results in the emission of radiation. The energy of the radiation is equal to the differences in binding energies of the shells. The radiation may take on two different forms: characteristic x-ray or Auger (oh-zhay) effect.
Example: Binding energy for a hypothetical "K" shell = 100 keV and "L" = 50 keV. K100 – L50 = 50 keV of energy given to the electron.
Characteristic x-rays are electromagnetic radiations (photons) that are created when an outer shell electron moves to fill an inner shell vacancy. This vacancy may occur for several reasons—to be discussed later. The energy of this photon is equal to the difference between binding energies. Since binding energies are determined by, or characteristic of, the number of protons in the nucleus, and it is the number of protons that determines an element's identity, the characteristic x-ray energies are specific to each element and the electron shells from which they originate. X-radiation is defined as an electromagnetic radiation originating outside the nucleus, therefore the term characteristic x-ray.
The Auger effect occurs under the same conditions as characteristic x-ray, that is, an inner shell vacancy being filled by an outer shell electron. The difference is that the excess energy from the cascading electron is radiated to another electron. This ejects that electron from its shell. This free electron will have kinetic energy equal to the difference in the binding energies less the binding energy of the shell of the free electron. The Auger effect is more common in elements with lower numbers of protons (Z number).1–3
The nucleus is composed mainly of neutrons and protons. Any particle contributing to the structure of the nucleus is called a nucleon. The conventional nomenclature to describe the nucleons is: .
The total mass of an atom is essentially the combined masses of the nucleons. Electrons contribute less than 1% to the total mass.1
Nuclides having the same number of protons (Z number) are called isotopes. Isotopes may exhibit different atomic masses (A number) and therefore have different numbers of neutrons (N number). Nuclides with the same N are called isotones and will be different elements, since the Z numbers are different. Nuclides with the same A number are called isobars and different elements as well.
Isotopes having different N numbers are of particular interest to imagers because they have the same chemistry, since their Z numbers and, therefore, electron numbers are the same.1–5 Some isotopes exhibit the emission of radiations, which is due to the differences in the number of neutrons. These isotopes are called unstable. If all the stable isotopes of all elements are plotted, comparing proton number to neutron number, a pattern emerges as illustrated in Figure 1-3.
Line of stability. All naturally occurring stable nuclides fall along a distribution known as the line of stability (LOS). As illustrated, for light elements (Z < 20) N ~ Z and for heavier elements N ~ 1.5Z. Unstable elements, lying to the left of the LOS, are neutron rich; those lying to the right of the LOS are proton rich.
Elements with low Z numbers have proton to neutron ratios that are 1:1. As Z numbers increase, this ratio increases to as high as 1.5. This distribution of stable elements is called the line of stability. By definition, an element with a proton to neutron ratio that falls to either the left or right of the line of line of stability is unstable. The unstable isotopes, radioisotopes, are unstable because their nuclear configurations are either proton rich or neutron rich relative to stable configurations. These radioactive elements seek stability by undergoing transformations in their nuclear configurations to a more stable P ↔ N ratio. The type of transformation will be a result of P ↔ N ratio, that is, proton rich versus neutron rich. This type of transition is called the mode of decay.1–4
The goal of nuclear decay is to equate the balance of forces in the nucleus. The repelling forces originating from the positive charge (coulombic forces) of the protons, when matched by the attractive forces from within the nucleus (exchange forces), define stability. When these forces are mismatched, nuclear transformations (radioactive decay) result. The mode of decay will produce unique emissions and lead to a more stable nuclear configuration. In radionuclide imaging, the ideal mode of decay would result in a high yield of photons, at an energy that is efficiently detected by our imaging instrumentation. Photon emission is also desirable from the radiation safety and dosimetry perspectives, due to their lower probability of creating potentially damaging interactions as compared to particles. With these considerations, it is important to understand the modes of decay of 99mTechnetium, 201Thallium, and 82Rubidium—the most commonly used radionuclides used in nuclear cardiology.1,2,6
In an unstable nuclear configuration where the nucleus is neutron rich, β− decay occurs. To decrease the neutron–proton ratio, a neutron is converted to a proton and an energized electron is emitted. The expression of this nuclear transition is:
where n is the neutron, p the proton, e the electron, and ν the neutrino.
The neutrino (ν) behaves like a particle with no mass and is not critical to imaging considerations. The primary emission is the energized electron (e−). The nuclear configuration that results from β− decay is a daughter with a stable or more stable energy state and an additional proton in its nucleus.
Since the number of protons is changed, the elemental identity changes. This is called a transmutation. The daughter atomic mass (X) remains the same as the parent nucleus, and the energy carried off by the ejected electron called transition energy. This leads to a more balanced relationship of coulombic force (repelling forces due to the protons) and exchange force (attractive nuclear forces). The resulting emission of the energized electron, a β− particle, is of no use in imaging and contributes to an increase in radiation dose in a biologic system. This decay process may lead to a daughter that is not fully stable, but more stable than the parent.1,2
In nuclear configurations where the parent is proton rich, β+ decay may occur. In this mode of decay, a proton is converted to a neutron and the emission of an energized, positively charged electron (β+) results. The nuclear equation is:
The energy of the β+ particle contributes to resolving the transition energy between the unstable parent and more stable daughter, as in β− decay.
An important secondary emission will result from the formation of the β+ particle. Since there is an abundance of negatively charged electrons in nature, the resulting positively charged electron (β+) will be attracted to, and collide with, a free negatively charged electron. This collision results in the annihilation of both particles. The annihilation leads to the conversion of the mass of these particles to their equivalent energy state. This is expressed by Einstein's equation E = mc2, where E is energy, m the mass, and c the speed of light. This essentially states that energy and mass are simply two physical forms of the same thing. Therefore, two photons (E) are emitted, each with the energy equivalent to the mass (m) of an electron, which is 511 keV. Unique to this annihilation is that these photons are emitted in a 180-degree trajectory from each other. It is these photons that are detected and registered into an image in positron imaging. The change in nuclear configuration is a decrease in Z and increase in N.
An alternative to β+ decay in proton-rich nuclear configuration, is electron capture. This mode of decay is defined as the capture of a K-shell electron by the nucleus, the subsequent combination with a proton, and creation of a neutron. The nuclear expression is therefore:
The vacancy left by the captured electron would then be filled by an outer shell electron. A cascade of an electron, filling subsequent vacancies, creates secondary emissions called, characteristic x-rays and Auger electrons. The energies of these emissions will be characteristic of the binding energy of the daughter, since the nuclear transition occurred prior to the production of the x-rays and Auger electrons. It is the characteristic x-rays that are imaged in 201Tl myocardial perfusion imaging. The energy of the x-rays is determined by the binding energy of 201Hg, the daughter of the decay of 201Tl. Electron capture decreases proton–neutron ratio.1
Isometric Transitions and Internal Conversions
The daughter of the decay of a radioactive parent will ideally be in its most stable energy configuration or ground state. This does not always occur, leading to either of two unstable states; excited state or metastable state. Excited states are very unstable and exist for very short time periods, usually less than 10−12 seconds. Metastable states, however, may exist for several hours. These metastable states lead to the release of energy in the form of radiation, without changing the proton–neutron ratios. The parent nucleus has the same nuclear structure as the daughter, but in a more stable energy configuration. This form of decay is called an isometric transition and results in electromagnetic emissions called γ-rays. These radiations are the same as x-rays, differing only by their location of origin, that is, the nucleus. As noted with the production of characteristic x-rays, there is a competing process, resulting in a particulate radiation. This process is called internal conversion. For any given metastable state, there is a specific ratio of isometric transitions to internal conversions. In imaging, the higher percentage of isometric transitions compared to internal conversions is preferred due to the resulting higher yield of photons. The decay of 99mTc to 99Tc is an example of an isometric transition of the metastable state (99mTc). The percent occurrence of isometric transitions of a population of 99mTc nuclei is approximately 87%. For example, for every 100 decays of 99mTc nuclei, there is a yield of 87 γ photons and 13 internal conversion electrons.
For any given mode of decay, should the daughter be metastable, there will be the emission of γ-photons and internal conversion electrons as secondary emissions. This will be indicated as [B−, γ], [B+, γ], [EC, γ], and so forth. The internal conversion electron yield, in ratio to γ-photon yield, is specific to a given radionuclide.1,2,5
In unstable nuclei with very high atomic masses, the most probable mode of decay is α decay. An alpha particle consists of two protons and two neurons, which is essentially a helium nucleus. Alpha decay results in a daughter with a Z number of 2 less than the parent and an atomic mass less by 4 relative to the parent.
Due to its high charges and heavy mass, the alpha particle has a very short travel distance in matter and deposits its energy very quickly. It has no application in diagnostic imaging and induces significant potential for biologic damage.1,3
The modes of decay may be expressed graphically, called decay schemes. Decay schemes graphically illustrate all possible nuclear transitions that unstable nuclei undergo. They are often accompanied by tables with detailed information about the transitions such as the percentage occurrence, isomeric transitions, internal conversions, characteristic x-rays, Auger electrons, and biologic dose information.
In decay schemes, the nuclear energy levels are expressed as horizontal lines. The space between these lines represents the transition energy (Q).
The types of emissions are depicted by a unique direction of a line (Fig. 1-4).
Decay schemes. This figure illustrates the configurations of decay schemes for the different modes of decay. The schemes move to the left for proton-rich radionuclides and to the right for radionuclides that are neutron rich.
Note the arrows may be angled to either the right or left. In neutron-rich parents, the mode of decay "shifts" the daughter to the right, corresponding to the shift on to the line of stability graph. Conversely, a mode of decay for a proton-rich parent moves to the left, toward the line of stability.
The tables that accompany decay schemes provide additional detail including the secondary emissions, as mentioned earlier. Since many of the secondary emissions are particulate, that is, electrons, these data are of particular interest in radiation dosimetry. In the decay scheme for 201Tl, the data regarding the characteristic x-rays of 201Hg are in these tables.
Not all nuclear transitions lead to a stable daughter. The β− decay of 99Mo yields 99mTc, which then decays to 99mTc by isometric transitions and internal conversions. 99mTc decays to 99Tc with an 87% frequency through isometric transitions. Therefore, for every 100 decays of 99mTc, we observe 87 γ-rays and 13 internal conversion electrons, as stated earlier. This higher yield of photons makes 99mTc a very desirable radionuclide for imaging. A sample of 99Mo would always contain some proportion of 99mTc and 99Tc. Since both parent and daughter are decaying, the relative activities would reach equilibrium, based on their half-lives. These states of equilibrium are employed when using both technetium and rubidium generators. When the parent half-life is marginally longer than that of the daughter, the amount of the daughter in the mixture will reach a maximum over a period of time. That elapsed time will be a multiple of half-lives of the daughter. If the daughter radionuclide is removed from the mixture, the same multiple of half-lives will have to occur, before the maximum amount of the daughter is subsequently reached. This equilibrium state is called transient equilibrium.2,4 It is this transient state that is the basis of 99mTc production from 99Mo–99mTc generators (Fig. 1-5).
Transient equilibrium. When the parent half-life is marginally longer than that of the daughter, the amount of daughter activity will reach a maximum after relatively few daughter half-lives have passed. 99Mo and 99mTc typically reach transient equilibrium after approximately four 99mTc half-lives.
In parent–daughter mixtures where the half-life of the parent is markedly longer than that of the daughter, secular equilibrium is reached. In this state of equilibrium, the concentration of the parent is decreasing so slowly relative to the daughter that the mixture appears to have the half-life of the parent. It is this equilibrium that is the basis for the 82Sr–82Rb generators used in 82Rb PET imaging (Fig. 1-6).1
Secular equilibrium. When the parent half-life is considerably longer than that of the daughter, the amount of parent activity will decrease very little over time. Therefore, many more daughter half-lives must pass before equilibrium is reached. An example is 82Sr with a half-life of 25 days and 82Rb with a 1.2-minute half-life.