Dr Brennan is an Australian Neurosurgeon operating at Royal Prince Alfred Hospital and North Shore Private Hospital. He has subspecialty training in disorders of the spine, brain tumours, and cerebrovascular disease.

He graduated from the University of NSW with first class honours in 1991, and was awarded the University Medal in Medicine.

Dr Brennan trained at Sydney’s St Vincent's, Royal North Shore, Royal Prince Alfred, and The New Children's Hospitals, obtaining Fellowship of the Royal Australasian College of Surgeons (FRACS) in 1999. He furthered his training with 18 months overseas fellowship in neurotrauma, spine surgery, and cerebrovascular neurosurgery at the University of Toronto in Canada out of Sunnybrook and The Toronto Western Hospitals.

He is involved in the teaching of junior neurosurgeons and holds the position of Supervisor of Advanced Training for the RACS Surgical Education and Training Program in neurosurgery at RPA hospital. He has contributed to Australasian wide curriculum sub-committees to help frame the structure of neurosurgical training through the RACS. He is also the trauma committee representative for neurosurgery at RPA.

His national and international professional associations include the Australian Medical Association, the Neurosurgical Society of Australasia, the Congress of Neurological Surgeons, and the Royal Australasian College of Surgeons.