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# Calculation of the volume of eluate required

In order to have sufficient activity to prepare the necessary patient doses of 99mTc-MDP, the volume of 99mTc to be withdrawn from the eluate vial must be calculated.

This is done in three stages:

a. Calculate the radioactivity concentration of the eluate in the eluate vial

Although the radioactivity concentration of the eluate should have been measured and recorded at the time of elution (see Eluting the generator, the concentration must be re-calculated at the time of preparation, since radioactive substances decay over time.

The radioactivity concentration can be calculated using the following formula: At = activity in 1 ml eluate at the present time of preparation
A0 = activity in 1 ml eluate at the time of elution
λ = decay constant of technetium-99m, in seconds-1
= ln 2/T1/2
= ln 2/(6.01 h x 3600 s/h)
= 3.20368 x 10-5 s-1
t   = time interval between elution and preparation, in seconds

b. Calculate the required activity of the patient doses at the time of preparation

Although the patient doses of 99mTc-MDP are pre-specified, there is usually a delay between the time at which the dose is prepared and the time at which it is injected into the patient.

During this time interval, the radioactivity concentration of the radiopharmaceutical will decrease as the radionuclide decays, which must be considered at the time of preparation.

Different patients will be injected at different times, so the dose for each patient must be calculated using the following formula: A0 = activity of dose at the time of preparation
At = activity of the dose at the time of injection
λ  = decay constant of technetium-99m, in seconds-1
= 3.20368 x 10-5 s-1
t = time interval between preparation and injection, in seconds

The total activity required for the multidose preparation can be found by summing each of these calculated patient doses. Usually a 10 % excess is then added to this total, to ensure that enough activity will be available.

c. Calculate the volume of eluate required for the preparation

This is found by dividing the required activity for the patient doses (calculated above, in b, measured in MBq) by the present radioactivity concentration of the eluate (calculated in a, measured in MBq per ml), to give the volume to be withdrawn from the eluate vial in millilitres.

See an example calculation.

Radioactive decay law and formulae, radionuclide decay modes and technetium-99m decay scheme are explained in detail in Chapter 1, Textbook of Radiopharmacy, Third Edition. Ed. C. Sampson. Gordon and Breach Science Publishers, Amsterdam.

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