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which decays slowly with a half‐life of 5700 years and is used to date fossils. The nuclides we use in nuclear medicine, however, are not naturally occurring but rather are made either by bombarding stable atoms or by splitting massive atoms. There are three basic types of equipment that are used to make medical nuclides: generators, cyclotrons, and nuclear reactors.

Generators

Generators are units that contain a radioactive “parent” nuclide with a relatively long half‐life that decays to a short‐lived “daughter” nuclide. The most commonly used generator is the technetium‐99m (^99mTc) generator (Figure 3.1), which consists of a heavily shielded column with molybdenum‐99 (⁹⁹Mo; parent) bound to the alumina of the column. The ^99mTc (daughter) is “milked” (eluted) by drawing sterile saline through the column into the vacuum vial. The parent ⁹Mo (small gray circles) remains on the column, but the daughter ^99mTc (white circles) is washed away in the saline.

      A generator like the one just described is frequently called a cow, the elution of the daughter nuclide is referred to as milking, and the surrounding lead is called a pig, a term used for any crude cast‐metal container. Another generator that is used extensively for cardiac imaging is the ⁸²Sr–⁸²Rb generator. Its design and construction is very similar to the ⁹⁹Mo–^99mTc generator but due to the 75 second half‐life of ⁸²Rb, the generator must be located on site—usually right next to the PET scanner where the generator is eluted and the solution is infused into the patient in one automated step.

Table 3.1 describes the features of three common generators.

      Activity curves for generators

      The formal mathematical description of time‐activity behavior for parent and daughter radionuclides is complicated because it involves the competition between the accumulation (caused by decay of the parent) and decay of the daughter. The plot of the curve describing the amount of daughter nuclide in a generator following elution has two segments. The first segment traces the period of rapid accumulation of the daughter nuclide and lasts for approximately four half‐lives of the daughter nuclide (which for ^99mTc is approximately 24 hours). The second segment of the curve traces what is called the period of equilibrium, during which time the amount of daughter nuclide decreases as the parent nuclide decays.

      Medical radionuclide generator systems, for practical reasons, have parent half‐lives longer than their daughters—in most cases much longer. We classify generators into two groups: those in which the parent half‐life is 10 to 100 times that of the daughter and those in which the parent half‐life is more than 100 times that of the daughter. In the first group, the activity of the daughter during equilibrium decreases perceptibly over time (when time is measured in units of daughter half‐lives). This is called transient equilibrium. On the other hand, the equilibrium segment of the curve for the second group is relatively flat. This is called secular equilibrium.

Figure 3.1 ⁹⁹mTechnetium generator.

Table 3.1 Characteristics of three commonly used generators

Generator (Parent–Daughter)	Clinical uses of daughter nuclide	Half‐life of parent (T1/2p)	Half‐life of daughter (T1/2d)	T1/2p/T1/2d
99Mo–99mTc (molybdenum‐99–technetium‐99m)	Used in most radiopharmaceuticals for nuclear studies	66 h	6 h	11
82Sr–82Rb (strontium‐82–rubidium‐82)	Cardiac perfusion imaging (PET)	25.5 days	75 s	29,000
68Ge–68Ga (germanium‐82–gallium‐82)	Neuroendocrine imaging (PET)	271 days	68 min	5,800

       Transient equilibrium

Transient equilibrium is illustrated in Figure 3.2. In this example, the half‐life of the parent nuclide is approximately 10 times that of the daughter. Following an elution that removes all of the available daughter, the amount of the daughter nuclide rapidly increases until the daughter activity slightly exceeds that of the parent at about four to five half‐lives. Thereafter the daughter activity declines at the same rate as the parent.

The preceding example of transient equilibrium is based on a decay scheme in which 100% of the parent nuclide decays to the daughter nuclide. However, in the commonly used ⁹⁹Mo–^99mTc generator, only 86% of the parent molybendum‐99 decays to the daughter technetium‐99m; the remainder decays directly to Technetium‐99 (Figure 3.3). As a result, the activity of ^99mTc is always less than the activity of ⁹⁹Mo (see Figure 3.3).

       Secular equilibrium

      For generators where the half‐life of the parent is greater than 100 times that of the daughter nuclide, since we are interested in time‐scales on the order of the daughter half‐life, we just consider the parent nuclide to be stable.

Secular equilibrium, like transient equilibrium, is achieved rapidly following an elution that removes all of the available daughter nuclide. Thereafter the activity of the daughter nuclide is approximately equal to that of the parent. However, the decay curve of the parent appears to be flat since its half‐life is so much longer than that of the daughter nuclide. An example of secular equilibrium can be seen with the ⁸²Sr–⁸²Rb generator (see Figure 3.4).

Cyclotrons

Cyclotrons are circular devices (Figure 3.5) in which charged particles such as protons and alpha particles are accelerated in a spiral path within a vacuum. The power supply provides a rapidly alternating voltage across the dees (the two halves of the circle). This produces a rapidly alternating electric field between the dees that accelerates the particles, which quickly acquire high kinetic energies. They spiral outward under the influence of the magnetic field until they have sufficient velocity and are deflected into a target.

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