Abstract
This chapter presents the macroscopic theory of radioactivity in which ensembles of radioactive nuclei are considered rather than single nuclei. It begins with a review of the fundamentals of radioactivity and radioactive decay chains. The determination of the activity biodistribution requires measurements of the activity through either in vivo imaging or through in vitro assays of activity content in blood, plasma, and excreta. The theory behind such measurements is presented along two paths. The first is the derivation of corrections factors required in practical cases: background correction, decay compensation, and reference standard normalization. The second is through decision theory in which, on the basis of measurements, one decides whether or not activity is present and then quantifies the result if the decision is positive. Electronic radiation detectors (well counters, gamma cameras, and PET scanners) are all subject to dead time and this concept and the compensatory factors for it are derived. Paralyzable and nonparalyzable detectors are both considered.
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Notes
- 1.
For example, a typical clinically administered activity of 740 MBq of 99mTc consists of 2 × 1013 99mTc nuclei.
- 2.
The curie (Ci) is still in common use as a unit of activity. It was originally defined as the number of disintegrations per second of a 1 gram sample of radium measured at 3.7 × 1010 disintegrations per second, although later measurements demonstrated that this was 3.61 × 1010 disintegrations per second. Jennings (2007) noted that, in 1930, the unit of the Rutherford (rd) was defined as the amount of any radioactive isotope that disintegrated at the rate of 106 disintegrations per second. Currently, this would give 1 rd = 1 MBq.
- 3.
Accounting for the inefficiencies of the detector. In the case of a well-detector commonly used for nuclear medicine assays, inefficiencies arise due to absorption within the sample, “dead time” (discussed later), differences in sample volume from that of the calibration sample, etc.
- 4.
In the context of this discussion, an “event” is the decay of a radioactive nucleus.
- 5.
A “count” is a detected event.
- 6.
Consider, for example, a typical activity of 370 MBq of 18F administered intravenously. The concentration of 18F activity in whole blood will be less than about 70 kBq/mL, further reduced by clearance, any specific binding and physical decay.
- 7.
- 8.
It is assumed that the background counts are due to background radiation only and that any random, non-Poisson contributions due to, for example, electrical interference are not present.
- 9.
The normal curve is the Gaussian distribution for zero mean and unity standard deviation; it is also sometimes referred to as the standardized normal distribution.
- 10.
dpm = disintegrations per minute.
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McParland, B.J. (2010). Radioactive Decay: Macroscopic Theory. In: Nuclear Medicine Radiation Dosimetry. Springer, London. https://doi.org/10.1007/978-1-84882-126-2_5
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