1. Selected calculations involving radiopharmaceuticals Dr. Osama A. A. Ahmed

2. 2 Selected calculations involving radiopharmaceuticals Isotopes are chemically identical but physically may differ slightly in mass. Different types of atomes (nuclides) of the same chemical element, each having different number of neutrons. Isotopes can be classified as stable or unstable. Unstable isotopes characterized by radioactive transformations, so called radioactive. The radioactive isotopes are called radioisotopes or radionuclides. Radioisotopes are naturally occurring or artificially produced. In the process of radioactivity, an unstable isotope undergoes changes until a stable is reached, and in the transformation it emits energy in the form of radiation. Individual radioisotopes differ in the rate of radioactive decay, but in each case, a definite time is required for the half of the original atoms to decay. This time is called the half-life of the radioisotopes.

3. Dr. Osama A. A. Ahmed3 Selected calculations involving radiopharmaceuticals The rate of decay is always a constant raction of the total number of undecomposed atoms present. Where N is the number of undecomposed atoms at time t and is the decay constant or the fraction disintegrating per unit time. the exponential decay law

4. Dr. Osama A. A. Ahmed4 Selected calculations involving radiopharmaceuticals Units of radioactivity: absolute units, total number of atoms disintegrating per unit time. The basic unit is the curie (Ci), that quantity of a radioisotop in which 3.7 X 10 10 (37 billion) atoms disintegrate per second. Also, millicurie (mCi) 10 -3 Ci, microcurie (  Ci) 10 -6 Ci, and nanocurie or millimicrocurie (nCi) 10 -9 Ci The international system (SI) unit for radioactivity is the becquerel (Bq), defined as 1 disintegration per second. Also, Kilobecquerel (kBq) 10 3 Bq, megabecquerel (MBq) 10 6 Bq, and gigabecquerel (GBq) 10 9 Bq 1 Ci = 3.7 X 10 10 Bq = 3.7 X 10 4 MBq 1 Bq = 2.7 X 10 -11 Ci 1 MBq = 2.7 X 10 -5 Ci = 2.7 X 10 -2 mCi = 0.027 mCi = 27  Ci Example: A thallous chloride Tl 201 injection has a labeled activity of 550 microcurie (  Ci). Express this activity in terms of megabecquerels. 550  Ci = 0.55 mCi 1 mCi 37 MBq 0.55 mCi X MBq X = 20.35 MBq

5. Dr. Osama A. A. Ahmed5 Selected calculations involving radiopharmaceuticals Example: The disintegration constant of a radioisotope is 0.02496 day -1. Calculate the half-life of the radioisotope. = 0.693/0.02496 day-1= 27.76 or 27.8 days Example: the half-life of 198 Au is 2.7 days. Calculate the disintegration constant. 2.7 days = 0.693/ = 0.693/2.7 = 0.2567 day -1

6. Dr. Osama A. A. Ahmed6 Selected calculations involving radiopharmaceuticals Example: the original quantity of a radioisotope is given as 500 mCi (18.5 MBq)/ml. if the quantity remaining after 16 days is 125 mCi (4.625 MBq)/ml, calculate: A) the disintegration constant B) the half life of the radioisotope A) = (2.303/16) log 500/125 = 0.08666 day -1 B = 0.693/0.08666 day-1= 8.0 days