Answer to Question #12504 Submitted to "Ask the Experts"

Category: Instrumentation and Measurements — Instrument Calibration (IC)

The following question was answered by an expert in the appropriate field:

Q

I have an in-vivo monitoring system having NaI detectors of various sizes, and so the resolution is also different. I want to know the procedure to calculate the overall efficiency of the system. Should I calculate the efficiency and minimum detectable activity (MDA) of the individual systems and then add the MDAs to get the overall MDA or sum the net counts in all the detectors and find the square root of it and use the overall efficiency of the system to calculate the MDA.

A

As you know, in-vivo counting systems come in a variety of configurations. Some such as a simple chair system might use a single detector viewing the major portion of the body and intended to allow an estimation of the body content of radionuclides of interest. Others might use multiple detectors intended to provide additional information about the distribution of radioactivity in the body.

You do not provide details about your system, but you do note that it uses multiple detectors of different sizes. I assume that the detectors are located so as to view different parts of the body. At any rate, the individual detectors would exhibit different detection efficiencies for a given radionuclide in the body. Consequently, for a given radionuclide, the calculated MDAs for the different detectors would be different from each other since the MDA is calculated by dividing the appropriate net count rate by the counting efficiency. It is not appropriate in such an instance to add MDAs to obtain an effective MDA or to use the multiple MDAs to calculate an average MDA. The former approach would yield a larger MDA that would not be realistic, and the latter approach may not be properly weighted to yield a suitable MDA.

I do not know how the detectors are located in your system. If they are arranged to view different parts of the body they may serve the function of looking at the distribution of radioactivity in the body and, possibly, to quantify radioactivity content in specific tissues—e.g., radioiodine in the thyroid or radioactivity in the lungs. If this is the case, then efficiencies for one or more detector may be based on the determination of radioactivity content of a specific tissue and would not be directly suited to determining the quantity in the whole body.

If you use one detector's response to determine activity in a specific tissue, such as the thyroid, then the MDA for that detector would be for activity in the thyroid. If you want to assess activity in the whole body, then one detector should view the major portion of the body, and the efficiency determined for that detector would be for the activity distributed throughout the body. It would be possible to evaluate the efficiency of each detector based on radioactivity of a given radionuclide throughout the body. Then, the most appropriate MDA to use for whole body activity would likely be the MDA for the detector that yielded the smallest MDA. In summary, the appropriate MDA depends on how the detectors are being used as they monitor activity in all or in selected parts of the body.

Regarding summing of the net counts from all the detectors, and taking the square root of the sum, I am not sure what you mean when you say you might then apply the overall efficiency of the system to generate an MDA. I don’t know what the overall efficiency of the system represents, and it's not clear to me how you would use the square root of the count in conjunction with this "overall efficiency" to get the MDA.

Perhaps I am misunderstanding some of your intent. If so, I apologize. I hope the discussion is of some help to you.

George Chabot, PhD, CHP

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