1. Equilibrium and Generators
Stephen M. Karesh, Ph.D.
Nuclear Medicine Department
Loyola University Medical Center
Maywood, IL 60153

2. Parent-Daughter Equilibria
Equilibrium is established in a parent/daughter mixture when the daughter’s half-life is shorter than that of the parent.

3. Transient Equilibrium Secular Equilibrium
TYPES OF EQUILIBRIA
Transient Equilibrium
Secular Equilibrium

4. Secular Equilibrium
a condition reached when the tphys of the parent is many times greater than the tphys of the daughter, e.g., times greater. To keep things in perspective, during 10 half-lives of the daughter, decay of the parent is negligible. Decay of the parent is represented by the flat line in the diagram below.

5. Secular Equilibrium
parent
activity
daughter
time tphys

6. Relationship Between Half-lives
In secular equilibrium
apparent physical
t = t
daughter parent

7. Transient Equilibrium
a condition reached when the tphys of the parent is approximately 10 times greater than the tphys of the daughter. A classical example is the 99Mo/99mTc Generator. During the 67 hr period representing 11 half-lives of 99mTc , 50% of the 99Mo has disappeared, as noted in diagram.
diagram here

8. Transient Equilibrium
Adaughter/Aparent = ~1.05
daughter
activity
daughter
parent
time tphys

9. Relationship Between Half-lives
In transient equilibrium
apparent physical
t = t
daughter parent

10. Time to Reach Equilibrium: Rule of Thumb
For transient equilibrium: reached in ~4 t½ of daughter. For Tc-99m, 23 hr
For secular equilibrium: reached in ~6 t½ of daughter

11. RADIOISOTOPE GENERATORS
A generator is a self-contained system housing a parent/daughter mixture in equilibrium. Designed to produce the daughter for some purpose usually separate from the parent.

12. RADIOISOTOPE GENERATORS
Generators produce certain short-lived radioisotopes on-site which cannot be shipped by commercial sources. To be useful, the parent's half-life must be long compared to the travel time required to transport the generator to recipient.

13. Ideal Generator Systems
1. If intended for clinical use, output of the generator must be sterile and pyrogen-free.
2. The chemical properties of the daughter must be different than those of the parent to permit separation of daughter from parent. Separations are usually performed by affinity or ion exchange chromatography.

14. Ideal Generator Systems
3. Generator should be eluted with 0.9% saline solution and should involve no violent chemical reactions. Human intervention should be minimal to minimize radiation dose.
4. Daughter isotope should be short-lived gamma-emitting nuclide (tphys = hrs-days)

15. Ideal Generator Systems
5. Physical half-life of parent should be short enough so daughter regrowth after elution is rapid, but long enough for practicality.
6. Daughter chemistry should be suitable for preparation of a wide variety of compounds, especially those in kit form.

16. Ideal Generator Systems
7. Very long-lived or stable granddaughter so no radiation dose is conferred to patient by decay of subsequent generations.
8. Inexpensive, effective shielding of generator, minimizing radiation dose to those using it.

17. Ideal Generator Systems
9. Generator is easily recharged (we do NOT recharge Mo/Tc generators, but store them in decay areas after their useful life is over).

18. DESIGN OF Ra/Rn GENERATOR COLUMN
222Rn gas
stopcock
226RaCl2 solution
stopcock
N2 gas

19. DESIGN OF Mo/Tc GENERATOR COLUMN
0.9% NaCl (eluant)
glass frit
Alumina
(Al2O3, aluminum oxide)
glass frit
99mTc04 (eluate)

20. A Dry Column Mo-99/Tc-99m Generator: Internal Construction
0.9%
NaCl
lead shielding
TcO4 in
evac vial
filter needle
99MoO4
0.2 mm filter
alumina column

21. Mo/Tc Generator: Principles of Operation
1. Prior to shipping the generator to the Nuclear Medicine Department, 99Mo sodium molybdate is immobilized on a column of alumina (Al2O3; aluminum oxide) due to its very high affinity for alumina.
2. 0.9% saline solution (the eluant) is passed through the column and Na pertechnetate, the daughter of 99Mo decay, is eluted from the column due to its almost total lack of affinity for alumina.

22. Mo/Tc Generator: Principles of Operation
3. The pertechnetate is collected in a shielded, evacuated sterile vial and calibrated prior to use. It is referred to as the eluate.
4. Quantitative removal of pertechnetate is attributed to the lack of affinity of pertechnetate for alumina, whereas molybdate is essentially completely and irreversibly bound to the alumina.

23. Mo/Tc Generator: Principles of Operation
5. When eluting the generator, the elution volume should be carefully controlled so a relatively constant radioconcentration is obtained every day.

24. CLINICALLY USEFUL RADIONUCLIDE GENERATORS
Enter Type of equilibrium e
b+, e, g
68Ge
> 68Ga
> 68Zn
275 d
1.14 hr
b+, e g
81Rb
> 81mKr
> 81Kr
4.7 hr
13 sec
b+, e, g e
82Sr
> 82Rb
> 82Kr
25d
75 sec
b-, g g
99Mo
> 99mTc
> 99Tc
67 hr
6 hr e g
113Sn
> 113mIn
> 113In
118 d
1.7 hr

25. CLINICALLY USEFUL RADIONUCLIDE GENERATORS
b+, e, g
secular
68Ge
> 68Ga
> 68Zn
275 d
1.14 hr
b+, e g
secular
81Rb
> 81mKr
> 81Kr
4.7 hr
13 sec
b+, e, g e
secular
82Sr
> 82Rb
> 82Kr
25d
75 sec
b-, g g
transient
99Mo
> 99mTc
> 99Tc
67 hr
6 hr e g
secular
113Sn
> 113mIn
> 113In
118 d
1.7 hr

26. Decay Scheme for 99Mo 99Mo 99mTc 99Tc 99Ru (Stable) b-, 67 hr g, 6 hr
b-, 2.2 X 105 yr
99Ru
(Stable)

27. POP TEST
99mTc-sulfur colloid never clears the liver. All of it will ultimately decay into 99Tc, which has a tphys of 2.2 X 105 yr. Why are you not concerned for your patient’s safety if 10 mCi of 99mTc sulfur colloid is injected into a patient?

28. Answer
For an isotope with a 220,000 yr half life:
= decay constant = 0.693/t1/2
= /220,000 yr = yr-1
Since only 3 millionths decays per year, the number of decays in a person’s lifetime would be negligible

29. What does this pattern represent?
Does the slope of the line represent
parent or daughter?

30. This pattern is an elution profile and represents daily elution for 1 week; elutions are spaced evenly since generator is eluted at the same time each morning. The slope of the line represents the parent’s decay.
Mon Tue Wed Thu Fri

31. Contact Information
Stephen Karesh, Ph.D.
Loyola University Medical Center
708/