Professor Stoodley is Head of Neurosurgery at Macquarie University Hospitals and School of Medicine and Health Sciences. Professor Stoodle has a clinical subspecialty qualification in neurovascular surgery. In addition to dealing with aneurysms and vascular malformations, he has been a leader in brain bypass surgery in Australia, particularly in the treatment of moyamoya and other occlusive diseases. In addition to his neurovascular expertise, Professor Stoodley is internationally recognized for his clinical treatment of Chiari malformation, syringomyelia and spinal cord tumors.

In addition to clinical research, Professor Stoodley leads the Macquarie University Neurosurgery Research Team. This is one of the largest neurosurgery research groups in Australasia, with world-leading research results in syringomyelia and CSF physiology and the development of new treatments for arteriovenous malformations. The work has attracted more than AU$3 million in research funding, including support from NHMRC, Australia's leading medical research funding agency, and The Column of Hope, a US-based organisation dedicated to advancing polio research and treatment. He has now published more than 100 publications and supervised more than 15 graduate students. He has given over 70 invited talks at Australian and international scientific conferences. In 2012, Professor Stoodley was awarded the John Mitchell Crouch Research Award by the Royal Australian College of Surgeons, the RACS' premier surgical research award.