Bush__The_Essential_Physics_for_Medical_Imaging - Biomedical ...

TABLE 18-1. UNITS AND PREFIXES ASSOCIATED WITH VARIOUS QUANTITIESOF RADIOACTIVITYQuantity Symbol dps (Bq) dpmCurie Ci 3.7 x 10 10 2.22 X 10'2Millicurie mCi (10- 3 Ci) 3.7 x 10 7 2.22 X 10 9Microcurie J.!Ci(10- 6 Ci) 3.7 x 10 4 2.22 X 10 6Nanocurie nCi (10- 9 Ci) 3.7 X 10 1 2.22 X 10 3Picocurie pCi (10- 12 Ci) 3.7 x 10- 2 2.22The minus sign indicates that the number of radioactive atoms decaying per unittime (the decay rate or activity of the sample) decreases with time. The decay constantis equal to the fraction of the number of radioactive atoms remaining in a samplethat decay per unit time. The relationship between activity and 'Acan be seen byconsidering Equation 18-1 and substituting A for -dN/dt in Equation 18-3:The decay constant is characteristic of each radionuclide. For example the decayconstants for technetium-99m (T c-99m) and molybdenum 99 (Mo-99) are 0.1151hr- 1 and 0.252 day-I, respectively.Physical Half-LifeA useful parameter related to the decay constant is the physical half-life (T1/2or T p 1/2).The half-life is defined as the time required for the number of radioactive atoms in asample to decrease by one halE The number of radioactive atoms remaining in a sampleand the number of elapsed half-lives are related by the following equation:where N is number of radioactive atoms remaining, No is the initial number ofradioactive atoms, and n is the number of half-lives that have elapsed. The relationshipbetween time and the number of radioactive atoms remaining in a sampleis demonstrated with Tc-99m (T p 1/2 "" 6 hours) in Table 18-2.Mter 10 half-lives, the number of radioactive atoms in a sample is reduced byapproximately a thousand. Mter 20 half-lives, the number of radioactive atoms isreduced by approximately a million.Time(days)No. of physicalhalf-liveso0.250.50.7512.55‎2°‎‏/סN‏'‏‎2‎‏/סN‎2‎‏/סN 2‎2‎‏/סN 3‎2‎‏/סN 4NoI2'0NoI2 2o 10 65 X lO s2.5 X lO s1.25xlO s6.25 x 10 4=10 3=110502512.56.25=0.1 (10- 3 ) or (1/1000)No=0.000001 (10- 6 ) or (1/1,OOO,OOO)No"The influence of radioactive decay on the number of radioactive atoms in a sample is illustrated withtechnetium-99m, which has a physical half-life of 6 hours (0.25 days). The sample initially contains onemillion (10 6 ) radioactive atoms.