In modern PET scanners , the block detector is used, in which small detectors are created by making partial cuts on the front surface of a block of detector crystal and each block detector is coupled on the back side to 2–4 PM tubes. A schematic block detector is shown in Fig. 13.1. Typically, each block is about 3 cm deep and grooved into 6 × 8, 7 × 8, or 8 × 8 elements by partial cuts through the crystal with a saw. Each element is considered a small detector. The cuts are made at varying depths, with the deepest cut at the edge of the block. The cuts are filled with opaque reflective materials to prevent spillover of light between elements. The size of each detector varies from 3 to 6.5 mm and is one of the important parameters that determine the spatial resolution.

The block detectors are arranged in an array of full or partial rings with a diameter of 80–90 cm. The full ring array may be in the form of a circular or hexagonal shape. Two configurations of block detectors adopted by several manufacturers are shown in Fig. 13.2. Siemens mCT has 32,448 crystals arranged in 192 block detectors with four PM tubes per block, whereas in Philips Healthcare’s Gemini TF Big Bore scanner, 28,336 crystals coupled to 420 PM tubes are arrayed in 28 pixelar modules.

In ideal coincidence counting in PET , the two 511-keV annihilation photons should be detected by the two detectors exactly at the same time. In reality, however, one photon may arrive at one detector earlier than the other in the opposite detector. This uncertainty in detection time is called the timing resolution or coincidence timing window. The timing resolution results from the difference in pulse formation in the detector primarily due to statistical variations in gain and scintillation decay time of the detector. Furthermore, there is a time delay in the arrival of one photon relative to the other, because of the difference in distances traveled by the two photons, particularly if the annihilation occurs at the edge of the FOV. This also adds to the timing resolution. For a whole-body scanner with a diameter of 1 m, the maximum distance traveled by one photon can be as large as 1 m, and the other photon travels almost no distance, if the annihilation occurs at the edge of the FOV. Because the velocity of light is 3 × 10⁸ m/s, the difference in the arrival times of the two photons is about 3–4 ns (time to travel 1 m). This is the limit of timing resolution of a PET scanner with 1-m diameter.

After annihilation, two timing signals A and B are formed with timing width, say τ, depending on the scanner system. Signal B may arrive at one detector just τ ahead of (Fig. 13.3a) or τ behind (Fig. 13.3b) the arrival of signal A, and both signals will be counted in coincidence. This is the extreme limit, and all other annihilation events overlapping in their time widths (Fig. 13.3c) will be counted as coincident events. Thus the timing resolution or coincidence timing window has to be a minimum of 2τ. The typical coincidence timing window of conventional PET scanners is set at 6–20 ns .

In a PET scanner, each detector element is connected by a coincidence circuit with a time window to a set of opposite detector elements (both in plane and axial) . The number of opposite detectors can vary from one to a maximum of half the total number of detectors present in a ring. Each detector element can be connected in coincidence to a maximum of half the total number N of opposite detector elements (N/2). Note that less than N/2 detectors can also be connected. As shown in Fig. 13.4, depending on the number of opposite detectors connected, each detector element has a number of projections that define an angle of acceptance . These angles of acceptance for all detector elements in the ring form the transaxial FOV. The angle of acceptance increases with the number of opposite detector elements connected in coincidence and, hence, the FOV.

It is beyond the scope of this book to describe in detail the principles of magnetic resonance (MR) imaging and the readers are referred to specific textbooks on MR imaging. The following is a brief summary of the subject.

MRI is based on the magnetic property of atomic nuclei . Protons and neutrons have magnetic moments due to inherent angular momentum and spin haphazardly (Fig. 13.7a). Nuclei containing even numbers of protons and neutrons possess no net magnetic moment, because of the cancellation of the individual magnetic moments by the even number of nucleons . Nuclei containing odd number of protons or neutrons, however, possess a net magnetic moment that has both a magnitude and a direction and behave like magnets. When these nuclei (or spins, as they are commonly called) are placed in a large external magnetic field (B₀), they align themselves (at a slight angle) in either parallel or antiparallel direction to the magnetic field and also precess (rotate) at a frequency proportional to the strength of the field (Fig. 13.7b). The parallel spins remain in the lower energy state and the antiparallel ones in the high energy state, the energy difference being ΔE. Normally a slightly greater number of spins exist in parallel direction and they increase with the increase in magnetic field strength. These excess spins result in a net magnetization (M_z) with a measurable magnetic moment parallel to the field of B₀ and they are said to be at equilibrium in the Z direction. If a radiofrequency pulse (RF), which is an oscillating electromagnetic field normally termed B₁, is applied perpendicular to B₀ at the precessional (resonant) frequency of the nuclei, the latter absorb energy from the RF field and make a transition to the high energy state. As a result, the longitudinal magnetization (M_z) flips towards the transverse plane (X–Y plane) at different angles depending on the strength of the RF pulse, thus causing transverse magnetization (M_xy). RF pulses that cause 90° flipping are called 90° pulses and produce maximum possible transverse magnetization (Fig. 13.8) and are commonly used in MR imaging. If a 180° pulse is applied, it will invert M_z to − M_z i.e. the longitudinal magnetization will be inverted in the opposite direction (Fig. 13.8).

Hydrogen atoms have one proton in the nucleus and are abundant in the living body mostly in the form of water (70 %), with the remainder in tissues and fat. When a patient is placed in a magnetic field (B₀) as in a MR machine, the tissues become magnetized due to excess parallel protons or spins that align with B₀ and remain at equilibrium. When an RF pulse (commonly 90° pulse) is applied perpendicular to B₀, the equilibrium of longitudinal magnetization is perturbed as a result of energy absorption from the RF field by the excess parallel spins of the nuclei, and the magnetization vector orients to the transverse or X–Y plane (at 90°for the 90° pulse). All nuclei remain in phase coherence, meaning magnetization vectors of all neighboring nuclei point to the same direction with maximum magnetization. If a receiver coil is placed perpendicular to the external field B₀, the transverse magnetization (maximum M_xy) induces a current or a sinusoidal MR signal in the receiver coil according to Faraday’s law of induction. This signal is called free induction decay (FID) signal and its size increases with the strength of the magnetic field B₀ and the magnitude of the RF pulse (B₁). As the RF field is switched off, the FID signal decays resulting in the return of all nuclei to the original state they had before. This return is called relaxation of the nuclei. Two types of basic relaxation occur in tissues simultaneously, T1 and T2, and both contribute to the decay of the MR signal.

In T1 relaxation , nuclei give off their excess energy by spin-lattice interaction to the surrounding molecular structures (lattice) and start to regrow magnetization along B_0, finally reaching the original value of maximum longitudinal magnetization at equilibrium. The rate of this regrowth is characterized by a tissue relaxation parameter called T1, which is defined by the time to recover 63 % of the maximum longitudinal magnetization following a 90° pulse (Fig. 13.9). T1 values depend on the vibrational frequencies and hence the physical characteristics of the molecules such as solid or liquid states, or stationary or moving structures.

In T2 relaxation following the shut-off of the RF pulse, all nuclei lose their phase coherence over time due to the random collision among neighboring nuclei (spin-spin interaction) thus losing energy to return to the original state of random phase. Random collision is caused by varying precessions of the nuclei at different velocities because of the small inhomogeneities of the magnetic field intrinsic to the structure of the tissues and also of the external field B₀. The dephasing results in a fast exponential decay of the MR signal characterized by the time T2, which is given by the time interval between peak transverse signal and 37 % of the peak (1/e) (Fig. 13.10).

T1 values increase with higher magnetic field and are normally much longer than T2 values for most tissues. Both T1 and T2 values depend on the composition of tissues. For example, fat has a short T1 and fluid (cerebrospinal fluid, cyst, etc.) has longer T1, so fat is seen as bright, whereas fluid appears as dark. Other tissues fall within the range between the two. On the other hand, mobile molecules such as blood exhibit a long T2, whereas nonmoving structures like bone have a short T2.

MR signals depend on proton density, T1 and T2 relaxation time constants of different tissues in the body. One can obtain sufficient contrast between tissues by manipulating the timing, order, polarity and repetition frequency of RF pulses and B₀. Tailoring of these parameters is alluded to as pulse sequence, the application of which depends on the type of tissue being imaged. Three major types of pulse sequences are spin echo (SE), inversion recovery (IR) and gradient recalled echo (GRE), the details of which are available in standard physics books. In spin echo pulse sequence, a 90° pulse is applied to cause transverse magnetization in tissues, followed by a 180° pulse to reverse it to the longitudinal magnetization. When all spins are rephased, an RF “echo” (a measureable MR signal) is produced and the time between the 90° pulse and the peak of the echo is called the time of echo (TE). The time between two successive 90° pulses is called the repetition time (TR). A spin-echo sequence of a short TR (e.g., 250–1000 ms) and a short TE (less than 25 ms) highlights the T1 difference in tissues and is called T1-weighting, whereas a combination of a long TR (2500–6500 ms) and a long TE (more than 75 ms) emphasizes T2 differences in tissues and hence the T2-weighting. In an IR pulse sequence, an 180° pulse is applied causing net longitudinal magnetization along the − Z direction that moves towards equilibrium along the + Z direction due to spin-lattice interaction. But a 90° pulse is applied before reaching equilibrium whereby the longitudinal magnetization flips to the X–Y plane ultimately producing a FID signal. This technique is used to generate contrast between tissues with very different T1 values by adjusting the inversion recovery time (the time between the inversion 180° pulse and the 90° pulse). In GRE pulse sequence, small angle RF pulses (typically 20–60°) are applied in rapid succession to tissues. The technique is useful in eliminating the artifacts arising from respiratory motion by having a breath-hold acquisition. A given pulse sequence is chosen on the basis of tissue characteristics defined by the T1 and T2 relaxation times and proton density.

Paramagnetic contrast agents, commonly gadolinium chelates such as Gd-DTPA, when injected intravenously, accumulate in extra vascular space over time and shorten both T1 and T2 values. But at a commonly used concentration of these contrast agents, better contrast are obtained in T1- weighted images.

An MR scanner is made up of coils of special metal alloys shaped in a cylindrical bore and cooled by liquid helium. Electric current is applied through the coils, which induces a constant magnetic field along the bore of the magnet. The magnets used in most clinical machines are superconducting magnets. In open MR systems commonly used for claustrophobic patients, two disc-shaped magnets are positioned with a gap in between to accommodate patients. An RF coil is used to perturb the magnetization of the atomic nuclei. The same coil or separate coils are used to receive the echo signals from the tissue. Integrated in machines are a patient table, magnetic shielding, and various monitoring equipment and, of course, a dedicated computer. Currently, the maximum available field strength of the clinical MR machines is 3.0 T, whereas it is limited to 1.2 T in open MR systems.

Integration of PET with MR into a single unit faces several hurdles, which have been overcome over the years to some degree. First, the commonly used photomultiplier tubes are sensitive to the radiofrequency of the magnetic field causing artifacts in PET images, now they are replaced by magnetic field-insensitive avalanche photodiodes. Next, compact PET detectors must be designed and shielded to incorporate into the MR unit so that radiofrequency does not interfere with the PET data processing. Unlike PET/CT where simultaneous PET and CT data acquisitions are not feasible because of the crossover of pulses, an integrated PET/MR offers an advantage of simultaneous data acquisition since the radiofrequency pulse and the radiation pulse do not interfere with each other, thus reducing the time of scanning. Since unlike CT imaging, there is no x-ray attenuation in MR imaging for attenuation correction in PET, a new way of attenuation correction need to be devised. Also in the absence of radiation from MR unit, PET/MR offers a low radiation dose to the patient.