The main innervation to the diaphragm of the lung (primarily responsible for breathing) is the phrenic nerve. This nerve is formed from nerves in the 3rd through 5th cervical levels. The respiratory drive centers are in the brianstem. There are two reasons why someone may not breath properly during sleep. The first is that the airway may collapse and not allow air to be moved, this is what happens in obstructive sleep apnea. The second reason would involve dysfunction of the central repiratory drive centers in the brainstem. A sleep study would be a good test to differentiate these possibilities. To my knowledge the autonomic nerves do not play a major role in breathing. Many cardiologists have experience with autonomic dysfunction. You could also see a neurologist who specializes in autonomic dysfunction. Dr. Robert Shields is our expert at the Cleveland Clinic. I cannot comment on your prognosis without seeing you clinically. I encourage you to obtain a second opinion if you like. Good luck.
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Sorry for all of the questions, but I have not found anyone going through this.