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

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

Transient Equilibrium Secular Equilibrium TYPES OF EQUILIBRIA Transient Equilibrium Secular Equilibrium

Secular Equilibrium a condition reached when the tphys of the parent is many times greater than the tphys of the daughter, e.g., 100-1000 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.

Secular Equilibrium parent activity daughter time 10 tphys

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

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

Transient Equilibrium Adaughter/Aparent = ~1.05 daughter activity daughter parent time 10 tphys

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

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

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.

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.

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.

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)

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.

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.

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).

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

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

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

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.

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.

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.

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

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

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

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?

Answer For an isotope with a 220,000 yr half life: = decay constant = 0.693/t1/2 = 0.693/220,000 yr = 0.00000315 yr-1 Since only 3 millionths decays per year, the number of decays in a person’s lifetime would be negligible

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

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

Contact Information Stephen Karesh, Ph.D. Loyola University Medical Center nucmedconsultants@comcast.net www.nucmedconsultants.com www.nucmedtutorials.com 708/216-5257