Introduction to PET Instrumentation

Sandra Kalman

TO THE EDITOR:

There is an error in your article “Introduction to PET Instrumentation” (1). I am not sure if it is a typographical error on your part—or if Dr. Turkington presented you with some erroneous text. On page 5 under the Heading “Projections,” the article says, “For a ring with n detectors, there are n-squared/2 ways to pair up the detectors . . .” This is incorrect. I believe it should say, “there are (n-squared minus n)/2 detectors.” If the article is correct, I would appreciate a description of how this can be. Thanks.

REFERENCES

↵
Turkington, TG. Introduction to PET instrumentation. JNMT 2001;29:4.−11.
OpenUrl Abstract/FREE Full Text

REPLY:

Thanks for your message. You are correct in that n²/2 is not the exact formula. The exact formula is (n² − n)/2, as you proposed.

For the large numbers of detectors typical in current PET detector rings, n²/2 (what I gave) is essentially the same as n(n − 1)/2 (the exact formula). For example, 600*600/2 = 180000 and 600*599/2 = 179700. I used the simpler formula because it is a very good approximation and because I think it makes the point more clearly that the number of pairs goes very closely with the square of the number of detectors. I probably should have said “approximately nⁿ/2.”