A noninvasive patient-specific method is provided to aid in the analysis, diagnosis, prediction or treatment of hemodynamics of the cardiovascular system of a patient. Coronary blood flow and pressure can be predicted using a 3-D patient image-based model that is implicitly coupled with a model of at least a portion of the remaining cardiovascular system. The 3-D patient image-based model includes at least a portion of the thoracic aorta and epicardial coronaries of the patient. The shape of one or more velocity profiles at the interface of the models is enforced to control complex flow features of recirculating or retrograde flow thereby minimizing model instabilities and resulting in patient-specific predictions of coronary flow rate and pressure. The invention allows for patient-specific predictions of the effect of different or varying physiological states and hemodynamic benefits of coronary medical interventions, percutaneous coronary interventions and surgical therapies.