Answer to Question #9599 Submitted to "Ask the Experts"

Category: Instrumentation and Measurements — Surveys and Measurements (SM)

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

Why does a chi-square test not produce reliable results when performed on a gamma camera?

The kinds of QC/QA (quality control/quality assurance) tests normally performed routinely on a gamma camera, such as uniformity and resolution, tend to be image performance oriented, and quality imaging is not as dependent on some statistical considerations as are count results associated with some other detection systems, such as NaI(Tl) detector systems used for thyroid measurements and NaI(Tl) well counters used for a variety of sample measurements. However, based on theoretical considerations, if a properly selected source is held in a fixed position relative to the camera detector, a series of counts is taken, and the chi-square statistic is evaluated, I would expect the result to be valid and provide a true indication of whether the count distribution is what one would expect for a normal distribution. There are some reasons why such a test may not be valid, leading to a failure of the chi-square test.

An important consideration is the count rate resulting from the source exposure. When gamma cameras are used for their intended purpose the count rates may be quite high and, in some cases, the high count rate may result in losses of counts due to dead time effects. The manufacturer may specify a maximum count rate for a particular camera but operation, even at count rates considerably below this maximum, may still produce notable dead time losses. The maximum count rate that a manufacturer specifies is often dictated by restrictions on the pulse pileup phenomenon (when two or more pulses add together and appear as one pulse of higher energy) rather than on dead time losses. Dead time losses represent unrecorded counts, and these losses produce erroneous counting statistics. Such dead time losses are a common reason for failure of the chi-square test, often by yielding chi-square values smaller than acceptable.

Another requirement for a successful chi-square test is that the source position and camera position be held constant during the test. Any changes in position may result in measurable changes in count rate that can affect the outcome, usually resulting in greater than expected chi-square values. The presence of the gamma camera collimator may exaggerate consequences of small changes in position compared to the case when no collimator is present.

A test may also fail whenever there are circumstances that lead to instabilities in camera operating parameters. Such failure would not necessarily mean that the chi-square statistic was not valid but that unexpected variability was present in the system; this should alert one to investigate the cause of such variability.

In conclusion, if you want to perform a chi-square test, I would suggest you select and position your gamma-emitting source so that the count rate from the camera is perhaps less than one percent of the manufacturer’s specified maximum count rate, preferably less than about 1,000 counts per second. This should be low enough to reduce dead time losses to an acceptable level. Make sure the source remains fixed at the same location for all the counts, and make no changes in the camera operating parameters or position.

Good luck.

George Chabot, PhD, CHP

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