Physics and Instrumentation of Cardiac Single Photon Emission Computed Tomography

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CHAPTER 20 Physics and Instrumentation of Cardiac Single Photon Emission Computed Tomography

Successful performance and interpretation of cardiac single photon emission computed tomography (SPECT) studies relies on a basic understanding of the physics and instrumentation that allows for the generation of the images. The first practical system for the in vivo imaging of radionuclides was developed in the late 1950s by Anger and became commercially available in 1962.1 Despite more than 45 years of use and technical advances, the basic physics and design principles used today for cardiac SPECT imaging are remarkably similar to Anger’s initial concept.

This chapter provides the reader with a basic understanding of the physical principles underlying cardiac SPECT imaging, with a particular focus on how basic physics impacts image acquisition and the problems of imaging artifacts. We also focus on the basic aspects of SPECT imaging camera design and briefly highlight advances in new solid-state detector systems.

PHYSICS AND SPECT IMAGING

Basic Atomic Structure

The classically described structure of an atom is known as the Bohr atom. It depicts a set of electrons orbiting the nucleus in stable electron shells (K, L, M, N) (Fig. 20-1). Each of the shells represents an energy state, with the innermost shell (K) associated with the greatest potential energy. Each electron’s energy state is defined further by a discrete set of four quantum numbers per electron. The Pauli exclusion principle states that no two electrons in the same atom can have an identical set of quantum numbers. By definition, a stable atom exists in its lowest possible energy state. When the energy state of an electron is increased (i.e., moved to a higher energy orbital shell or via absorption of external energy), the electron emits energy spontaneously as it returns to its lower, more stable energy state. This emission of energy by unstable electrons provides one mechanism for radionuclide imaging and is described in detail in the next section.

Electrons orbit a nucleus composed of a dense conglomerate of protons and neutrons that are bound together by a network of so-called strong nuclear forces. A proton contains a charge of 1.6 × 10−19 coulombs, which is the exact opposite charge of an electron. Neutrons are particles of slightly greater mass than protons, but are uncharged. The number of protons present in its nucleus, or Z number, defines each element, whereas the mass number, or A, represents the number of protons plus the number of neutrons. Specific nomenclature defines the relationship between the number of protons and neutrons in a nucleus (Table 20-1). The ratio of protons to neutrons defines the stability of a particular nucleus (Fig. 20-2); the transformation of an unstable nucleus to a more stable state is responsible for many of the radioactive emissions used in nuclear imaging.

TABLE 20-1 Nuclear Nomenclature

Name Symbol Description
Z number ZX Number of protons
A number AX Mass number; number of neutrons + protons
N number N Number of neutrons
Nuclide   Common elementary characteristics
Isomer m Equal protons and neutrons, different energy state (e.g., Tc 99m)
Isotope   Same number of protons; Z1 = Z2
Isotone   Same number of neutrons; N1 = N2
Isobar   Same mass number; A1 = A2

Radioactivity: Electron Transition, Unstable Nuclei, and Radioactive Decay

Radiation refers to the transfer of energy across distance, and can be in the form of kinetic energy transfer through the interaction of charged particles or through electromagnetic energy transfer in the form of photons. Our discussion focuses primarily on the physics of electromagnetic/photon radiation because this is the most relevant to cardiac nuclear imaging. A photon is a massless, chargeless carrier of energy that behaves much like a wave, traveling at the speed of light. Photons generated from energy transitions occurring in the electron cloud are termed x-rays, and photons emitted from nuclear transitions are termed gamma rays.

The energy (E) transmitted by a photon is proportional to its wavelength (λ, in nm). Because photons travel at the speed of light (c), the energy carried by a photon (in keV) is governed by the equation:

image

Photons released from different radionuclides have different wavelengths and different energies. The characteristic energy (or energies) of photons released from different radionuclides plays a crucial role in image generation (photopeak generation) and in the creation of imaging artifacts (e.g., attenuation, scatter).

Radiation can involve energy contained either in electrons or in the nucleus. An electron of a particular element exists in a characteristic energy state defined by its unique quantum number. This energy is a combination of the kinetic energy of motion of the electron and potential energy between the electron and the charges contained within the nucleus. The strength of this potential energy is proportional to the number of protons in the nucleus, and is inversely proportional to the distance of the electron from the nucleus. A heavy element (i.e., large Z number) with many protons exerts more force on an orbital electron and has more potential energy, and an inner shell electron has greater potential energy than an outer shell electron. This potential energy is commonly referred to as the binding energy for that electron and represents the energy required to separate that electron from the atom. With the introduction of energy equal to its binding energy, an electron can be removed from an atom with a resulting orbital electron vacancy. This process is called ionization. In contrast to ionization, if the energy transmitted to the orbital electron is insufficient to remove it from its shell, the transferred energy is dissipated as heat in a process known as excitation.

Two types of ionization electron transition can occur. In heavy elements (elements with a high number of protons, or Z number), a characteristic x-ray is produced when an electron from an outer shell fills an inner shell vacancy (Fig. 20-3). The energy difference between two electron shells is characteristic of the element, given the different Z number and nuclear charge that define that element. The energy released as the characteristic x-ray represents the difference in potential energy between the outer shell electron and its new quantum state in the inner shell. The movement of an electron from an outer shell to an inner shell produces an x-ray with a characteristic energy, which can be described as a K, L, M, or N x-ray, and the energy of a characteristic x-ray from a particular element can be predicted based on the subatomic structure of the element. An example of a characteristic x-ray emission is the 68- to 70-keV mercury characteristic x-ray that is emitted from thallium 201.

Another mechanism of electron transition that leads to energy emission occurs when an outer shell electron fills an inner shell vacancy, but transfers the energy difference to an outer shell orbital electron (rather than emitting a characteristic x-ray), leading to the emission of an Auger electron (see Fig. 20-3). Because the release of an Auger electron leads to an orbital vacancy, a cascade of subsequent characteristic x-rays or further Auger electrons can occur after the initial emission. Auger electrons are usually produced when orbital electron vacancies are filled in elements of low Z number.

Besides energy transfer involving electrons, energy can also be released from the nucleus. Unstable nuclei can release energy in an attempt to reach a more stable energy state through the process of radioactive decay. This process is also called nuclear transformation. Radioactive decay of a particular unstable nucleus can occur in a series of decay steps, involving one or more of the types of radioactive decay described subsequently. Molybdenum-99 decays by β emission (discussed in detail later) to Tc 99m. Tc 99m undergoes subsequent gamma emission by isomeric transition producing the stable daughter Tc 99m. The “m” notation refers to a metastable excited nucleus with a measurable life span before its decay (approximately 10−12 seconds), which is an intermediate between the “excited” and “stable” states.

Radioactive decay can involve particulate and nonparticulate emissions. Different types of radioactive decay are described in Table 20-2 and include alpha particle emission, beta particle emission, positron emission, electron capture, gamma ray emission, and internal conversion.

Alpha particles are equivalent to a He nucleus (two protons, two neutrons). Alpha particles are massive in size compared with other particulate emissions, and because of their large size cannot travel far in matter before an interaction occurs, and their energy is released. Because alpha particles cannot travel significant distances, their use in imaging is limited. The much higher linear energy transfer of alpha particles compared with beta particles or gamma photons results in significantly greater effective doses of absorbed radiation.

Beta particle emission occurs when a nucleus is unstable because of an elevated neutron/proton ratio (Fig. 20-4). When this occurs, a neutron is converted to a proton with the emission of an electron (β) and an antineutrino (υ). Because of the ejection of the electron and antineutrino from the nucleus, the daughter has an atomic number that is one greater than the parent. This decreases the instability generated by the elevated number of neutrons.

In contrast to beta particle (β) emission, when a nucleus is unstable because of an increased number of protons, radioactive decay can occur through positron emission (β+) or electron capture (see Fig. 20-4). A positron, which is effectively an electron with a positive charge, is emitted during times of proton excess with the simultaneous generation of a neutron. When a positron is emitted from the nucleus, it quickly encounters an electron in the environment, leading to the annihilation of both particles. This annihilation event converts all of the mass of the two particles into energy, with the subsequent generation of two photons of equal energy that travel at 180 degrees to each other. Because the total energy generated by the annihilation reaction is 1.02 MeV, each of the photons emitted from the reaction carries an energy of 511 keV. The high energy of these photons and their simultaneous generation allowing for coincidence detection underlie the mechanisms for positron emission tomography (PET).

A separate process by which a proton-rich nucleus can obtain nuclear stability is through electron capture (see Fig. 20-4). In electron capture, an inner shell electron combines with a nuclear proton to form a neutron, creating a more stable nucleus. An outer shell electron fills the vacant inner shell with the subsequent generation of characteristic x-rays or Auger electrons. Positron emission and electron capture are competitive processes, with β+ emission occurring more frequently in “lighter” elements, and electron capture occurring in “heavier” elements. The characteristic x-rays that are produced during thallium 201 decay (described previously) are produced through electron capture.

Gamma ray emission occurs during nuclear transformation when the process of radioactive decay does not completely dissipate the energy required for the atom to reach its most stable state. Gamma rays are a form of electromagnetic radiation with variable energy without mass or charge (i.e., a photon). Gamma rays carry off the excess nuclear energy through the process of isomeric transition. Isomeric transition occurs when a metastable nucleus is present from a prior radioactive decay. This can commonly occur after β decay, but can also occur as a consequence of internal conversion (see Fig. 20-4), where an unstable nucleus transfers its energy to an inner shell (K or L) electron, leading to its expulsion as a conversion electron. An outer shell electron, releasing energy via a characteristic x-ray or Auger electron, fills the subsequent electron vacancy. The ability of gamma rays to penetrate tissue (and be used as an imaging tool) depends on their energy. An example of isomeric transition is the gamma photon emitted from the decay of the metastable Tc 99m nucleus.

Radioactive Decay

Radioactive decay is a spontaneous process that can be described by mathematical modeling of the probability of decay. Although it is impossible to predict the exact moment of decay for a particular unstable nucleus, it is possible to predict how many unstable nuclei of an element will decay over time. This time is commonly referred to as the half-life (image) of the element, or the time it takes for a spontaneously decaying radionuclide to decrease its activity by 50%. The image of a radionuclide is a function of its exponential rate of decay (dN/dt) or activity (A), and this rate of decay is specific for an element and related to the decay constant (λ) by:

image

or

image

To describe the number of radioactive nuclei present (Nt) at a given time (t) compared with the number present initially (N0), one can solve the previous differential equation, yielding:

image

If we solve this equation for the time at which one half of the original quantity of nuclei are present (image), or:

image

then

image

This exponential decay relationship and the concept of the decay constant are clinically useful. Because the decay constants for clinically relevant radionuclides are known, if the activity at a particular time (i.e., arrival of a radiopharmaceutical shipment) is known, one can calculate the activity present at a point of time in the future when it is to be used. The Système International unit of activity of radioactivity is the becquerel (Bq; 1 Bq = 1 decay/second), although the curie (Ci; 1  Ci = 3.7 × 1010 decay/second) is commonly used in clinical settings: 1 Bq = 27 × 10−12 Ci. When a radionuclide is mixed with a nonradioactive carrier, the specific activity of the nuclide is expressed as activity per gram (Bq/g).

Manufacture of Radionuclides

Medical radionuclides can be produced in a nuclear reactor, cyclotron, or a generator on site. This section describes the production of three commonly employed radionuclides in nuclear cardiology: thallium 201, Tc 99m, and rubidium 82.

Thallium 201 is usually produced in a cyclotron from the proton-bombardment of nonradioactive thallium 203, lead, or bismuth. Additionally, thallium 201 can be produced from lead 201 (image 9.3 hours) by a generator-based method. Most cyclotron-produced radionuclides have an elevated proton/neutron ratio, and decay by electron capture or positron emission. Because of its long image (74 hours), thallium 201 can be transported from the cyclotron to the end-user.

In contrast to thallium 201, Tc 99m can be produced on-site using a commercially available generator (Fig. 20-5) from nuclear reactor–produced molybdenum 99. Molybdenum 99 is a fission reaction product of 235U. As molybdenum 99 slowly undergoes β decay with a image of 66 hours, 87.5% of the decay product is Tc 99m, with the remaining 12.5% being the stable isomer Tc 99. When the generator is prepared at the radiopharmaceutical manufacturer, molybdenum 99 is tightly bound to a supporting alumina (Al2O3) column. Molybdenum 99 is more negatively charged than Tc 99m, and Tc 99m can be eluted (“milked”) from the column with normal saline into a collection vial as Tc 99m-pertechnetate.

Rubidium 82 is the most commonly used PET tracer for evaluating myocardial perfusion. Rubidium 82 is produced from the electron capture decay of cyclotron-produced strontium 82 (image 25.3 days). Similar to a Tc 99m generator, strontium 82 is adsorbed on a shielded column (stannic oxide), and rubidium 82 is eluted from the generator with normal saline. Because the image of rubidium 82 is short (75 seconds), the generator elution occurs directly into the patient’s intravenous line. In addition to rubidium 82, other PET tracers may be used for assessment of cardiac perfusion, metabolism, and viability, including [2-18F]-2-fluoro-2-deoxyglucose (18FDG), [13N]-ammonia, [1-11C]-glucose, and [1-11C]-palmitate. These tracers are generated by a cyclotron, however, and because of their short half-lives, generally must be produced by an on-site cyclotron. The exception is 18FDG, which has a image of 110 minutes and can be produced by a cyclotron in a radiopharmaceutical network for regional distribution.

Interactions with Matter

The interactions of radiation with matter depend on the type of radiation and the composition of the interacting matter. Generally, the interactions of charged particles with matter (alpha particles, beta particles, and electrons) can lead to ionization and excitation as described earlier. In addition, another charged particle interaction is called bremsstrahlung, which involves the interaction of charged particles (electrons) with the strong forces in the nucleus, leading to photon emission. Because most medical imaging involves photon (gamma and x-ray) detection, our discussion focuses on the three primary ways photons interact with matter: photoelectric effect, Compton scatter, and pair production (Fig. 20-6).

The photoelectric effect is the photon-matter interaction responsible for the production of a photoelectron in scintillation crystals (used in gamma camera detectors—see later). In the photoelectric effect, a photon interacts with an orbital electron; if the photon’s energy is greater than the binding energy of the electron, the electron is ejected from its orbital shell with an energy equal to the energy of the incident photon minus the binding energy of the electron. The net effect is a 100% conversion of the photon’s electromechanical energy. Three main ancillary radiations can occur as a consequence of the photoelectric effect. The first two involve the production of secondary electrons, the high-energy photoelectron from the initial photon interaction and an Auger electron as the orbital electron’s position is filled. The other radiation occurs with the production of a characteristic x-ray during the initial photon-orbital electron interaction.

Compton scatter occurs when a photon interacts with a loosely bound electron. The photon releases part of its energy to the interacting electron, proportional to the incident angle of interaction (0 to 90 degrees) between the photon and electron. In contrast to the photoelectric effect, the photon in Compton scatter is not destroyed. The two types of radiation products during a Compton scatter interaction include the scattered photon and the interacting electron, termed the recoil electron. The subsequent path of travel of the scattered photon and recoil electron are altered during this interaction, producing “scatter” of the photon from its original path. The angle of the photon after Compton scatter depends on the energy of the incident photon, with lower energy incident photons more likely to have a greater angle of deflection after this interaction. This scatter of photons from their original angle of travel provides a significant difficulty for defining from where these photons originated during an imaging procedure.

The final type of interaction between a photon and matter is called pair production. When a high-energy photon (>1.02 MeV) interacts with a nucleus, the photon’s energy can be converted to mass with the production of a positive (β+) and a negative (β) electron. The amount of energy required to create the mass of an electron is 0.51 MeV; pair production does not occur with photons less than 1.02 MeV and does not occur during normal cardiac imaging procedures.

The probability of a particular type of interaction between a photon and matter depends on the energy of the photon and the Z number of the material (Fig. 20-7). In elements with a high Z number, an interaction with a low-energy (<1 MeV) photon has a high likelihood of interacting via the photoelectric effect, whereas high-energy photons predominantly interact via pair production. Compton scatter occurs when photons carrying an energy in the range associated with radionuclides that are used in medical imaging (60 to 500 keV) interact with matter with a high density of loosely bound electrons (i.e., high physical density tissues such as bone) and is for the most part independent of the Z number of the absorbing material. The most likely effect of an imaging photon interaction within the human body before its arrival at the detection camera is one of Compton scatter.

The final concept in the interactions with photons with matter is called attenuation and refers to the percentage of photons that interact with a given thickness of matter. Photons that interact with matter by one of the aforementioned processes do not pass through the matter directly, or are “attenuated.” The amount of attenuation occurring in a given material depends on the energy of the photon beam and the thickness of the material (x) and the Z number. The Z number defines the linear attenuation coefficient (µ) for the particular material, with higher Z number elements increasing the probability of photon attenuation. The mathematical equation that describes the number of photons for a given energy that pass through a material (Ix) compared with the number of incident photons (I0) is:

image

Because photon beams occur with variable energy, it is useful to express the amount of thickness of a particular material that leads to the attenuation of one half of a particular photon energy beam. This is termed the half value thickness (HVT) of a material, and is defined by the linear attenuation coefficient (µ) for that material by the equation:

image

INSTRUMENTATION AND SPECT IMAGING

SPECT imaging uses the photons arising from radioactive decay to generate an image of the coronary perfusion of the heart. This technique requires a method of detecting photons, defining the spatial origination of these photons, determining their energy characteristics and number, and displaying an interpretable image of these data. This section details the basic instrumentation that makes up gamma (Anger) cameras and highlights some more recent innovations in this technology.

The prototypic gamma detector is composed of the following elements (Fig. 20-8): collimator, scintillation crystal, light pipe, photomultiplier tubes, preamplifiers/amplifiers, pulse-height analyzer, positioning circuitry, analog-to-digital converter, and display device. A photon emitted from a patient must travel along a path that allows it to pass through the collimator holes where it encounters the scintillation crystal. In the scintillation crystal, the photon’s energy is converted to light. The photomultiplier tubes detect this light and generate an electrical signal relative to the intensity of the detected light. These electrical signals are individually detected and allow for determination of the originating location of the photon by the use of computerized electronics and algorithms, and are amplified and converted to a digital image. The details of each component of the gamma detector are discussed in sequence.

Collimators

A collimator is a device that restricts the passage of photons into the scintillation crystal to select for photons traveling along particular paths. Because radionuclides emit photons in all directions, a collimator ensures that only photons traveling along the desired path from the patient are available for detection. Collimators are typically made of lead and are composed of multiple holes of defined diameter and depth, separated by intervening septa. To reach the scintillation crystal, photons must pass through one of these holes, traveling parallel to the long axis of the hole. Otherwise, the photons are absorbed by the septa. The most commonly used collimator type in SPECT imaging is a parallel-hole collimator (Fig. 20-9). Other types of collimators include slant-hole, converging, diverging, and pin-hole.

The choice of a particular collimator depends on the object being imaged, the energy of the imaging photon, and the desired relationship between image sensitivity and resolution, with sensitivity defined as the percentage of emitted photons from a given source that are able to pass through the collimator and interact with the crystal. As part of the ability to restrict or permit photon transmission, collimators also affect the spatial resolution of the camera. The spatial resolution is usually measured by imaging a point source of radioactivity, and is measured as the width of a plot of image intensity (peak photon counts) versus distance and is expressed at one half of the maximum intensity (Fig. 20-10). This measurement of resolution is termed the full width half maximum (FWHM), with small FWHM values indicating that a camera can resolve two distinct points that are more closely spaced. For two different collimators with identical hole lengths, those with smaller diameter holes have lower sensitivity, but are able to resolve photon sources that are closely opposed. Similarly, thicker septa can also decrease sensitivity, but increase resolution. Most gamma camera systems used clinically today have a FWHM of approximately 9 mm for 140 keV Tc 99m gamma photons emitted 10 cm from the detector head. The most common collimator used in SPECT imaging is a parallel hole design, termed the low-energy all purpose collimator.

Photomultiplier Tubes

The flashes of light produced by the scintillation crystal are detected and converted to an electrical signal by a type of photodetector called a photomultiplier tube. This device is a cathode-tipped vacuum tube, which produces an electron every time it is struck by a light photon. This electron signal is “multiplied” within the tube every time an electron strikes one of the tube’s dynodes to produce a measurable signal for each light emission from the scintillation crystal. The number of photons produced by the scintillation crystal is proportional to the number of photons that interact with the crystal. For each approximately 10 photons that enter a photomultiplier tube, only 1 to 3 electrons would be produced without amplification. The photomultiplier tube increases the electron output to approximately 105 to 108 electrons, however, allowing a measurable electrical signal to be available for image generation. This electronic signal that exits the photomultiplier tube is increased further using preamplifiers and amplifiers.

Multiple photomultiplier tubes are arranged in an array on top of the scintillation crystal, coupled to the scintillation crystal by an optical glass–transparent gel interface that has the same refractive index as the scintillation crystal. This glass-gel coupling is termed the light pipe raising the photomultiplier tubes above the surface of the scintillation crystal. This height allows for multiple tubes to visualize a scintillation event, allowing the camera array to localize the scintillation event within the X, Y plane. Event localization is one of the hallmarks of the gamma camera and allows for generation of a SPECT image (Fig. 20-11).

Event Localization

A gamma camera uses the concept of proportional energy generation from scintillation events to ascribe arithmetically each event to a particular location within the crystal. This process was initially described by Anger,1 and is summarized as follows: Each scintillation event is simultaneously detected at multiple photomultiplier tubes, and the photomultiplier tube overlying the event receives the largest proportion of light generated from that event. Other photomultiplier tubes near to, but not directly overlying, the scintillation event receive proportionally less light from the event. The thickness of the light pipe enables simultaneous visualization of scintillation events by multiple photomultiplier tubes by elevating them a critical distance above the crystal. By integrating all of the signals from all of the photomultiplier tubes from each scintillation event using positioning circuitry, the X, Y coordinates of each scintillation event can be obtained. The “intrinsic resolution” of a particular gamma camera refers to the accuracy of the positioning circuitry and computer algorithms to determine the location of a scintillation event. “Extrinsic resolution” refers to the combination of the resolution of the collimator along with intrinsic resolution.

Energy Discrimination

In addition to being able to determine the physical location of a scintillation event, a photomultiplier array can discriminate the energy of the exciting photon. This permits the use of acquisition protocols that specifically detect scintillation events from photons from a particular radionuclide, and can allow for simultaneous acquisition of images using two radionuclides of different energies. In simplistic terms, a photomultiplier array visualizes all of the light produced by a given scintillation event, although each individual photomultiplier tube visualizes only a portion of the light. By summing all of the signals from all of the photomultiplier tubes in an array, it is possible to know the total amount of light for a given scintillation event. Because the light produced by a given scintillation event is proportional to the energy of the exciting photon, the summed signal from the photomultiplier tubes is proportional to the exciting photon’s energy and is known as the “photopeak,” which approximates a gaussian distribution for a given radionuclide photon emission.

In actuality, not all photons interact in a linear fashion with respect to energy and light generation because of the combined effects of Compton scatter and instrumental uncertainty. The gamma camera can be set up to acquire only events that meet certain energy criteria, or fall within an “energy window” around the photopeak. This energy window is generated by a pulse-height analyzer, which rejects the photon signals that do not fall within a predetermined range surrounding the photopeak.

Image Generation

When a scintillation event has been localized and falls within the required energy window for detection, the generation of an image can occur. First, the analog signal obtained from the energy peak needs to be converted to a digital signal using an analog-to-digital converter. This digital signal can be transformed from a spatial domain to a frequency domain by way of the Fourier transformation.

When the event localized digital information is in the frequency domain, it can be used for the construction of an image. Classically, SPECT images have been constructed by “back projecting” sequentially acquired planar images obtained by rotating the camera around the patient onto an imaginary center point to create the three-dimensional SPECT image. This method requires the raw projection data to be passed through a so-called ramp filter to omit certain frequencies (filter “cutoff”) and enhance other frequencies (“power”) to optimize image quality. This method of SPECT reconstruction is termed filtered back projection. Filters function to remove inherent reconstruction artifacts (particularly the “star” artifact inherent in back projection), optimize the signal-to-noise ratio in image reconstruction, and provide image enhancement. This method allows for rapid image reconstruction, but loss of image information occurs because of filtering.

Newer reconstruction algorithms have sought to reconstruct SPECT images using a mathematical computational method called iterative reconstruction. Iterative methods use mathematical equations to model the particular imaging physics and geometry of the acquisition and to reconstruct the image after discriminating the image into pixels. Each of these pixels represents an unknown value at the beginning of the reconstruction, which after passing the projection data through multiple “iterations” of the mathematical equations, approaches a recognizable image. This method allows for image generation in the setting of low counts, scatter, and noise. This method of image reconstruction also permits the image to be reconstructed using information acquired from an attenuation map, correcting for nonuniform attenuation. After reconstruction by filtered back projection or iterative reconstruction, a tomographic image can be displayed and statistically quantified and interpreted.