Unit I: Physics Associated with Nuclear Medicine Instrumentation Part A: Atomic Structure and Radiation’s Interaction with Matter Lecture 2 CLRS 321 Nuclear Medicine Physics and Instrumentation 1

Lecture 2 Objectives (From your Textbook) Name and describe the primary forms of radioactive decay. Diagram the schematics of the various radioactive decay processes. Define Decay Constant. Use the General form of the radioactive decay equation to calculate precalibration and post calibration quantities of radioactivity. List the radioactive units and define curie and becquerel. Write the equations for average half-life and effective half-life and calculate effective and biological half-lives.

Decay Schematics Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-11, p 49.

Recently has become relevant to nuclear medicine –Helium nucleus (2 protons, 2 neutrons) with no electrons. –+ 2 charge (it immediately wants two negative charges, i.e. electrons) –An electron stripper. Excites and steals electrons from surrounding atoms, thus creating ion pairs (a positive ion and a negative ion). –One Alpha can produce hundreds of thousands of ion pairs—very, very bad for biochemistry. Decay Processes: Alpha Decay

Radium 223 Radon 219 Polonium 215 α α T 1/2 = 11.4 hrs T 1/2 = 4 sec T 1/2 = 1.8 msec

Decay Processes: Beta Decay Used in nuclear medicine for therapies High Velocity, negatively charged electron emitted from a neutron-heavy nucleus Neutron  proton + beta + antineutrino + energy –Energy=kinetic energy to beta + instantaneous gamma emission 1 MeV beta specific ionization: 45 ion pairs/cm –(1 MeV Alpha specific ionization: 60,000 ion pairs/cm) But beta more penetrating than alpha n = p + β - + v + energy

Decay Processes: Beta Decay Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-12, 2-13, p 49.

Decay Processes: Gamma Decay Result of a nucleus in a higher energy state Energy needs to be released for the nucleus to return to a more stable lower energy state May result as part of alpha and beta decay, or from a metastable nucleus

Like the electron shells, an atomic nucleus can have different energy states of specific energies. A nucleus of a certain type of atom will have specific “quantum”-like levels of energized states. It dissipates the energy by emitting electromagnetic radiation (gamma rays) at energies equivalent to the energized state. Paul Early, D. Bruce Sodee, Principles and Practice of Nuclear Medicine, 2nd Ed., (St. Louis: Mosby 1995), pg. 15. Decay Processes: Gamma Decay Energy States of the Nucleus

Decay Processes Isomeric Tranisition –Energized state of a nucleus: metastable –Transitions by releasing energy in the form of a gamma photon –Parent & daughter have same atomic mass and number –Unlike I-131 and some beta emitters, the gamma emission is not instantaneous –Not really a disintegration but a change in energy state of the nucleus. –Prime example: Tc-99m  Tc-99

Decay Processes: Beta Decay to Isomeric Transition Decay Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-14, p 49.

Decay Processes: Positron Emission P + N +   2 X 511 keV 180  M. Crosthwaite “Nuclear Medicine not Unclear Medicine” Happens with proton-rich nuclei, or either decay will occur by electron capture (explanation to follow).

Decay Processes: Positron Emission

Decay Processes: Electron Capture Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-15, p 50.

Decay Processes: Internal Conversion Often accompanies isomeric transition

Complex Decay Schemes Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Fig. 2-16, p 50.

Multiple Gamma Emissions Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), Table 2-1, p 50.

Decay Constant (λ): –Average proportion of atoms present that will decay over a selected period of time. ex: 0.33/hour, means that 1/3 of atoms will decay in an hour Mathematics of Decay Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 50.

Using calculus, we can derive the following: We can figure out the number of atoms remaining after the passage of a given amount of time (t). What is e???? Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 50. Mathematics of Decay

Change of atoms is directly related to decay and therefore atomic disintegration Disintegration is directly related to radioactivity (or Activity), Therefore… Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 51. Mathematics of Decay

Easier to use half-life (T 1/2 ) than decay constant (λ). Mathematics of Decay We know that we’ll have half of the activity after one half life (T 1/2 ) The natural log (ln) of the natural log base (e) to a given power is equal to that exponent. The natural log (ln) of 2 = (try it in your calculator) Using substitution…

Decay Factor The “Decay Factor” (DF) can be multiplied against an original amount of activity to determine the amount of activity present after a period of time. Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 51. Mathematics of Decay

Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 51. Mathematics of Decay

Decay example (from book) Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 51. Mathematics of Decay

Radioactivity Units: Units, in General Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 3.

Radioactivity Units Anytime a nuclide changes form it “disintegrates” to take on the new form. Radioactivity is measured according to the number of these disintegrations per unit time. Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 52.

Radioactivity Units Becquerel (Bq) –SI unit –Based on a radioactive sample that decays at 1 disintegration per second (dps) –Because NM doses are much larger (mCi— 3.7 X 10 7 dps), we usually convert to mega Becquerels (Mbq—a million [10 6 ] Becquerels) 1 mCi = 37 MBq Example:

Radioactivity Units

Average decay time: Other Decay Calculations Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 52.

Effective Half-life Other Decay Calculations

Effective half-life –Besides decaying the radionuclide is also being metabolized by biological process, so effective half-life tells us about the activity remaining in the body after time. –The decay constants for biological process and decay are cumulative. Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 52. Other Decay Calculations

λ = 0.693/T 1/2 for both bio and radioactive (or physical) half-lives Dividing each side of the decay constant equation by 0.693, we get… Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 52. Other Decay Calculations

That equation can also be expressed as… Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 52. Other Decay Calculations

Effective Half-life Example (from book) –Tc-99m MAA in the lungs Physical half-life of Tc-99m is 6 hrs Biological half-life of MAA is 3 hrs OR (The answer is 2 hrs) Other Decay Calculations

Next time: Interactions of ionizing radiation with matter /08/30/the-amazing-colossal-man-1957 /