Dr. Brannon completed his undergraduate training at Louisiana State University in Shreveport where he studied biological sciences. He completed his medical degree and psychiatric residency at Louisiana State University Medical while also serving as chief resident. He was voted Teacher of the Year 2001-2002 at Louisiana State University Health Science Center in Shreveport.

Dr. Brannon has helped facilitate more than 80 clinical drug trials involving such illnesses as anxiety, bipolar disorder, depression, dementia, insomnia, and schizophrenia. He has authored numerous articles, which have appeared in Psychosomatics, The Journal of Depression and Anxiety, The Journal of Pain and Symptom Management and on eMedicine.com.