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There is no good way to diagnose CRPS. The tests they give can often be painful and don't tell the whole story. The best physician to see is an Anesthesiologist or Neurologist. I had two nerve conduction studies performed that where very, very painful that showed I was having slowing and abnormal nerve speeds. I would not wish this test upon anyone who has CRPS. Bone Scan is another test that can be done. Other times X-rays can show CRPS related bone loss.
Honestly, the best test is temperature tests from one limb to the other. Anything over 1/2 °C change along with a history of other symptoms is a good indicator. For example my affected foot was 5 °C colder than my other foot. that's almost 10° F difference. Very painful.