1. CLRS 321 Nuclear Medicine Physics and Instrumentation 1
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

2. 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.

3. 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.

4. Decay Processes: Alpha Decay
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.

5. Decay Processes: Alpha Decay
Radium 223
T1/2 = 11.4 hrs α
Radon 219
T1/2 = 4 sec α
Polonium 215
T1/2 = 1.8 msec

6. 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

7. 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.

8. 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

9. Decay Processes: Gamma Decay
Energy States of the 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.

10. 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

11. 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.

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

13. Decay Processes: Positron Emission

14. 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.

15. Decay Processes: Internal Conversion
Often accompanies isomeric transition

16. 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.

17. 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.

18. Mathematics of Decay 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
Paul Christian & Kristen M. Waterstram-Rich, Nuclear Medicine and Pet/CT: Technology and Techniques, 6th Ed. (St. Louis: Mosby 2004), p 50.

19. Mathematics of Decay 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.

20. 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.

21. Mathematics of Decay
Easier to use half-life (T1/2) than decay constant (λ).
We know that we’ll have half of the activity after one half life (T1/2)
The natural log (ln) of the natural log base (e) to a given power is equal to that exponent.
Using substitution…
The natural log (ln) of 2 = (try it in your calculator)

22. Mathematics of Decay 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.

23. 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.

24. 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.

25. 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.

26. 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.

27. 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 107 dps), we usually convert to mega Becquerels (Mbq—a million [106] Becquerels)
1 mCi = 37 MBq
Example:

28. Radioactivity Units

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

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

31. 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.

32. Other Decay Calculations
λ = 0.693/T1/2 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.

33. 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.

34. 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)

35. Interactions of ionizing radiation with matter
Next time:
Interactions of ionizing radiation with matter