How do doctors diagnose a dislocated elbow?
First, the doctor will make sure your nerves and arteries are unhurt by checking your pulse, making sure you can feel normally, move your fingers and wrist, and make sure that blood is flowing normally to your hand. Next, you'll get X-rays. Sometimes, breaks in the bone can look like dislocations, and some breaks happen when dislocations occur. If the doctor thinks you may have an injured artery, you may get more tests, such as an arteriogram (an X-ray of your artery).
From: Elbow Dislocation WebMD Medical Reference
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