Dr. Koullias has pursued a diverse career in cardiovascular surgery that includes his residency in general surgery at New York Medical College, and Penn State University followed by his residency in cardiothoracic surgery at Yale University. He completed a 4-month fellowship in advanced thoracic aortic endovascular surgery at the German Heart Institute in Berlin, where he gained experience also in the management of aortic complications in patients with Marfan's disease. Subsequently, he joined a group practice in cardiac surgery in Peoria, IL, where he was an attending from 2007 to 2010, and had a faculty appointment at the University of Illinois. During this period, he gained further training in vascular and endovascular surgery at the Arizona Heart Institute.

An active scholar as well as clinician, he has numerous publications to his credit, including book co-authorships (The Role of the Endothelium in Coronary Artery Disease), numerous peer-reviewed articles, and several book chapters. His primary interest is advanced Limb Preservation vascular techniques and advanced wound care techniques He was the Director of Stony Brook Limb Preservation Center, and Co-Director of Stony Brook Southampton Center of Advanced wound healing and Hyperbaric Medicine. In 2024, he became Division Chief, Vascular and Endovascular surgery, at the Hospital of Saint Catherine’s of Siena. He also became the system Chief for limb Preservation, at the Catholic Health System in NY