Our Pulmonary and Critical Care Medicine Fellowship program offers a three-year pulmonary/critical care training experience in New Orleans, a unique and very enjoyable city. During their training, our fellows manage a diverse patient population while rotating through the following facilities: ... Tulane University School of Medicine. 1430. About the Program. Our pulmonary & critical care medicine fellowship program is designed to provide fellows with a balanced exposure to a wide variety of pulmonary diseases and critical care conditions through experiences in the ICU, inpatient consult services, and outpatient continuity clinics.