What would be the procedure if a neurologist quit a patient's care after ordering a pet scan but before the protocol was arranged and the scan scheduled; would neurologist be responsible for seeing the pet scan through and interpreting results?

If the neurologist is the only one available within your service area it would be considered abandonment. A reportable problem. If not, you are free to find a new neurologist and start the process over. Docs are not required to keep patients they decide they do not want to treat just like patients can decide to change docs. When they quit care properly, their responsibility stops.

There are ethical protocols for a physician to discontinue ongoing care, and, in most cases, a certified letter will suffice. Since the definition of abandonment care varies from state to state, it is difficult to provide guidance. Your State Board of Medical Examiners can provide full information.