Decay correction for radiopharmaceuticals: Tc-99m and F-18 dosing time tables
A radiopharmaceutical dose is prescribed as an activity at the time of administration, but it is measured, labelled and shipped at some other time. Between the two the activity falls, and with half-lives of 6.0072 hours for Tc-99m and 109.77 minutes for F-18 the change is large enough to matter within a morning. This note gives the remaining fraction at 15-minute steps for both nuclides, works two examples of finding when a dose can be given, and lists the mistakes that most often put an administered activity outside its range. The dose calibrator reading before administration is always the measurement that counts; these tables tell you what that reading should be.
The correction
Activity decays as A = A₀·2−t/T½, where A₀ is the activity at the reference time, t the time since then and T½ the half-life. The factor 2−t/T½ is the remaining fraction, and it is all the tables below contain. Two rules cover every use of them:
- Forward in time, multiply. The activity at a later time is the reference activity multiplied by the fraction for the elapsed time.
- Back in time, divide. The activity that must be drawn now for a dose needed later is the prescribed activity divided by the fraction for the delay.
To find the time at which a given fraction is reached, invert the law: t = T½·log₂(A₀/A). The half-lives used here are the evaluated values in the IAEA Livechart decay data: 6.0072 hours for Tc-99m and 109.77 minutes for F-18. The decay calculator uses the same values and gives the factor for any interval to more figures than the tables.
Tc-99m remaining fraction, 0 to 12 hours
Read the row for the whole hours elapsed and the column for the extra minutes. The figure is the percentage of the reference activity that remains.
| Elapsed | :00 | :15 | :30 | :45 |
|---|---|---|---|---|
| 0 h | 100.0 | 97.2 | 94.4 | 91.7 |
| 1 h | 89.1 | 86.6 | 84.1 | 81.7 |
| 2 h | 79.4 | 77.1 | 74.9 | 72.8 |
| 3 h | 70.7 | 68.7 | 66.8 | 64.9 |
| 4 h | 63.0 | 61.2 | 59.5 | 57.8 |
| 5 h | 56.2 | 54.6 | 53.0 | 51.5 |
| 6 h | 50.0 | 48.6 | 47.2 | 45.9 |
| 7 h | 44.6 | 43.3 | 42.1 | 40.9 |
| 8 h | 39.7 | 38.6 | 37.5 | 36.4 |
| 9 h | 35.4 | 34.4 | 33.4 | 32.5 |
| 10 h | 31.5 | 30.6 | 29.8 | 28.9 |
| 11 h | 28.1 | 27.3 | 26.5 | 25.8 |
| 12 h | 25.0 |
Remaining activity in percent of the reference activity, Tc-99m, T½ = 6.0072 hours.
Tc-99m loses about 0.2% of its activity per minute, so a quarter of an hour either way changes a dose by a few percent, and after six hours half remains. A generator eluate or a kit prepared at the start of the day is down to 25.0% by the end of a twelve-hour shift, and falls to a tenth after 19 h 57 min.
F-18 remaining fraction, 0 to 6 hours
| Elapsed | :00 | :15 | :30 | :45 |
|---|---|---|---|---|
| 0 h | 100.0 | 91.0 | 82.7 | 75.3 |
| 1 h | 68.5 | 62.3 | 56.6 | 51.5 |
| 2 h | 46.9 | 42.6 | 38.8 | 35.3 |
| 3 h | 32.1 | 29.2 | 26.6 | 24.2 |
| 4 h | 22.0 | 20.0 | 18.2 | 16.5 |
| 5 h | 15.0 | 13.7 | 12.4 | 11.3 |
| 6 h | 10.3 |
Remaining activity in percent of the reference activity, F-18, T½ = 109.77 min.
F-18 loses about 0.6% per minute. Ten minutes leave 93.9%, and an hour 68.5%. Because the loss is so fast, F-18 doses are usually ordered from the supplier with a calibration time and an activity at that time, and the site works out the activity at injection from that pair, not from the time the dose arrives.
Worked example: the latest time a Tc-99m dose can be given
A syringe is dispensed at 07:45 holding 925 MBq of Tc-99m for a study prescribed at 740 MBq. The patient is late. What is the latest time the syringe still holds the prescribed activity?
The required fraction is 740/925 = 0.800, that is 80.0%. In the Tc-99m table, 1 h 45 leaves 81.7% and 2 h leaves 79.4%, so the answer lies between the two. The exact elapsed time is t = T½·log₂(925/740) = 1 h 56 min, and the latest time is 09:41. At 09:30 the syringe holds 756 MBq; at 10:00 it holds 713 MBq, below the prescription.
Note the direction of rounding. A latest time is rounded down to the whole minute, because at the next minute the activity is already below the target. An earliest time, as in the next example, is rounded up.
Worked example: the window for an F-18 dose
An F-18 dose is calibrated at 370 MBq at 09:00. Suppose the department accepts an administered activity within ±10% of the prescribed 370 MBq, that is between 333 and 407 MBq — the tolerance itself is set locally and varies. Between which clock times can the dose be given as it stands?
Before 09:00 the activity is higher than 370 MBq. It reaches 407 MBq, the upper limit, at t = −T½·log₂(407/370), about a quarter of an hour before the calibration time, so the earliest whole minute inside the window is 08:45. After 09:00 it reaches the lower limit of 333 MBq at t = T½·log₂(370/333), and the latest whole minute is 09:16. The window is 31 minutes wide. A delay of 45 minutes past the calibration time leaves 278 MBq, 75.3% of the prescription — the F-18 table gives the same 75.3% at 0 h :45. To give 370 MBq at 09:45 the dose would have had to be calibrated at 492 MBq for 09:00.
The same tolerance around a Tc-99m dose gives a window 3.3 times wider — the ratio of the two half-lives — which is why a late-running schedule is a much greater concern for PET than for conventional nuclear medicine.
Common mistakes
Using the wrong reference time
A dose label carries an activity and the time it applies to. That reference time is not necessarily the time of dispensing, of delivery or of measurement, and suppliers state the calibration time separately for exactly this reason. Correcting from the delivery time instead of the calibration time shifts every later figure by the delay between the two. Write the clock time next to every measured activity, on the label and in the record, and correct from that pair.
Mixing minutes and hours
The elapsed time and the half-life must be in the same unit. Entering 90 for an elapsed time of 90 minutes with the Tc-99m half-life in hours treats it as 90 hours. The correct fraction after 90 minutes is 84.1% for Tc-99m and 56.6% for F-18. A result that is almost zero, or a fraction above one, is the sign of this mistake.
Correcting in the wrong direction
Multiplying when you should divide gives a dose that is low by the square of the factor. For an F-18 dose drawn an hour ahead, the right activity is the prescription divided by 0.685; multiplying instead leaves the patient with 46.9% of the prescribed activity. A quick check is that the activity drawn ahead must always be larger than the prescription.
Mixing activity units
Many prescriptions and older records are in millicuries, and dose calibrators can display either unit. One millicurie is exactly 0 MBq; a 20 mCi dose is 1 MBq. Confirm the unit on the display before reading it. The unit converter gives the exact factor.
Clock and time-zone errors
A dose shipped from a supplier may be labelled with a clock that differs from the department's, and the change to and from summer time moves the clock by an hour without moving the decay. Use one clock for the whole calculation, and use the 24-hour clock so that 01:00 and 13:00 are not confused.
Forgetting what stays in the syringe
The activity administered is the activity in the syringe before injection minus what remains in it afterwards. The residual is measured in the dose calibrator after injection where the procedure requires it; decay correction cannot account for it.
Where to go next
- Decay — the activity after any interval, the time to reach a target, and a half-life from two measurements.
- Unit converter — becquerels and curies with the exact factor.
- Positron emitters and 511 keV — shielding F-18 and its decay through a working day.
- Half-value and tenth-value layers — how much lead a Tc-99m syringe needs.
- Tc-99m and F-18 — the full data pages.