A minimal cardiac model that accurately captures the essential cardio- vascular system dynamics has been developed. Standard parameter identification methods for this model are highly non-linear and non-convex, hindering clinical application, given the limited measurements available in an intensive care unit. This paper presents an integral based identification method that transforms the problem into a linear, convex problem. Five common disease states including four fundamental types of shock, are identified to within 10% without false identification. Clinically, it enables medical staff to rapidly obtain a patient specific model to assist in diagnosis and therapy selection.