A Determining MDA for the Dual Label Counting method with the LSC

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The discussion focuses on determining the Minimum Detectable Activity (MDA) for Pb-210 using the dual label counting method with liquid scintillation counting (LSC). The user successfully measures Sr-90 using ROI gating to exclude Pb-210, but faces challenges with Pb-210 due to its overlap with Sr-90. They calculate the background for Pb-210 by combining measured counts and estimated Sr-90 contributions, using this data to apply the MDA formula. The user believes their approach is valid, as treating Sr-90 counts as background is acceptable, and they assert that the efficiency obtained from a pure Pb-210 standard remains applicable. Ultimately, they conclude that the MDA for Pb-210 varies based on the Sr-90 concentration in the sample.
sgstudent
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Hi, I am measuring Pb-210 and Sr-90 with the LSC and using the dual label counting method to determine the activity levels of Pb-210. Results are good, but now I am figuring out whether my method of determining the MDA of Pb-210 is correct.

For Sr-90 it is simple - I just do ROI gating to exclude Pb-210 and determine the efficiency and background in this region. Then I use the MDA formula to get it. Likewise, I calculate the Sr-90 activities by taking the Sr-90 CPS in this region and dividing it by my method's recovery*efficiency in this ROI region.

But for Pb-210, it is completely overlapped by Sr-90, so what I do is to have my background as a sum of the measured background in the Pb-210 region, and also the Sr-90 counts in that Pb-210 region. So I calculated the Sr-90 counts in the Pb-210 region by taking the Sr-90 activity and multiplying it by my method's recovery*Sr-90 efficiency in the Pb-210 region. This multiplication gives me the contribution of Sr-90 CPS in the Pb-210 region, which I add to the background counts. Since I have the efficiency of Pb-210 from a pure standard and the background CPS, I plug them into the MDA formula to get it.

I feel like this method is valid because treating the Sr-90 counts as background is perfectly fine to me since it feels the same having a very high background. Anyways this is the same as having a very accurate process blank to be where we can calculate more exactly the background count rate. And also I think that the efficiency I obtained from the pure standard of Pb-210 still holds for this MDA calculation, because empirically we do use that efficiency in the Dual-label counting method, and also scientifically, the efficiency should not change even if the background is higher since there is no quench effect happening (just a systematic increase in the count rates on the y-axis of the LSC spectrum).

And so the conclusion I have is that the MDA for Pb-210 is not going to be a fixed number, but depends on how much Sr-90 is in the sample.

Does anyone have any experience with such MDA calculations with the Dual-label counting method? I have not found many publications that explicitly shown their method of calculating the MDA.
 
Theoretical physicist C.N. Yang died at the age of 103 years on October 18, 2025. He is the Yang in Yang-Mills theory, which he and his collaborators devised in 1953, which is a generic quantum field theory that is used by scientists to study amplitudes (i.e. vector probabilities) that are foundational in all Standard Model processes and most quantum gravity theories. He also won a Nobel prize in 1957 for his work on CP violation. (I didn't see the post in General Discussions at PF on his...

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