The methods of mathematical modeling and digital computer simulation can be beneficially applied to the development and testing of cardiac assist devices. Such methods, used in conjunction with other investigative techniques, provide the researcher with a powerful tool for approaching the many difficult problems associated with operation and control of assist devices. Of utmost priority in this modeling application is the availability of a left-heart model which is responsive to variations in left-heart operating conditions. A left-heart model capable of realistically adapting to variations in operating conditions is necessary for evaluation of the effects which an assist device may have on the left-heart. For this purpose a left-heart model is formulated which is responsive to variations in heart rate, left-atrial filling pressure, left-ventricular end-diastolic volume, left-ventricular end-systolic volume and aortic load. The operation of this left-heart model is demonstrated by use of a simple aortic model in computer simulations. The potential of the modeling technique in general (and of the adaptive left-heart model in particular) for use as a research tool is exhibited by the development and use in simulations of a model for an intra-aortic balloon pump assist device. Suggested enhancements to the models for research application are presented.