Modeling and simulation of a blood pump for the development of a left ventricular assist system controller. (English) Zbl 1274.93027

Summary: A mathematical model describing the pressure-volume relationship of the Novacor Left Ventricular Assist System (LVAS) is developed. The model consists of lumped resistance, capacitance, and inductance elements with one time-varying capacitor to simulate the cyclical pressure generation of the system. The ejection and filling portions of the pump cycle are modeled with two separate functions. The corresponding model parameters are estimated by least squares fit to experimental data obtained in the laboratory. The model performed well at simulating pump pressure of operation throughout the full cycle. Computer simulation of the pump with a cardiovascular model demonstrate the interaction between the LVAS and the cardiovascular system. This model can be used to incorporate on-line cardiovascular parameter estimation and to design a new controller for the LVAS.


93A30 Mathematical modelling of systems (MSC2010)
92C50 Medical applications (general)
Full Text: Link


[1] Co., Baxter Healthcare, Division, Novacor: Novacor N100 Left Ventricular Assist System Operator’s Manual. Corporation Internal Manual (Unpublished), 1991
[2] Breitenstein D. S.: Cardiovascular Modeling: The Mathematical Expression of Blood Circulation. M.S. Thesis, Univeristy of Pittsburgh, 1993
[3] Devore J. L.: Probability and Statistics for Engineering and Sciences. Third edition. Brooks/Cole Publishing Company, Pacific Grove, 1991, pp. 466-468
[4] Franklin G. F., Powell J. D., Emami-Naeini, Abbas: Feedback Control of Dynamic Systems. Addison-Wesley, New York 1988, pp. 49-68 · Zbl 0615.93001
[5] Hogness J. R., Antwerp M. Van: The Artificial Heart: Prototypes, Policies, and Patients. National Academy Press, Washington 1991
[6] Lewis F. L.: Optimal Control. Wiley, New York 1986, pp. 345-346
[7] More J. J.: The Levenburg-Marquardt algorithm: Implementation and theory. Numerical analysis (G. A. Watson, Lecture Notes in Mathematics 630). Springer-Verlag, Berlin pp. 269-312
[8] Oppenheim A. V., Schafer R. W.: Discrete-Time Signal Processing. Prentice-Hall, Englewood Cliffs, NJ 1989, pp. 203-204 · Zbl 0676.42001
[9] Portner P. M., LaForge D. H., Oyer P. E., Greene G. F., Jassawalla J. S., Ream A. K., Miller P. J., Shumway N. E., Chen H.: An alternative in end-stage heart disease: Long-term ventricular assistance. Heart Transplantation 3 (1983), 47-59
[10] Spyker D. A.: Simulation in the analysis and control of a cardio-circulatory assist device. Simulation 15 (1970), 196-205 · doi:10.1177/003754977001500503
[11] Unger F.: Assisted Circulation 2. Springer, New York 1984, pp. 115-141
[12] Williams J. L.: Load-sensitive Mock Circulatory System for Left Ventricular Assist Device Controller Development and Evaluation. M.S. Thesis, University of Pittsburgh, 1995
[13] Yu Y.-C., Antaki J. F., Boston J. R., Simaan M., Miller P. J.: Mathematical model of pulsatile blood pump for LVAS control. Proc. of American Control Conf., Albuquerque 1997, vol. 6, pp. 3709-3713
[14] Yu Y.-C., Boston J. R., Simaan M., Antaki J. F.: Identification scheme for cardiovascular parameter estimation. Preprints of IFAC 13th World Congress, San Francisco 1996, vol. B, pp. 417-422
[15] Yu Y.-C., Boston J. R., Simaan M., Antaki J. F.: Estimation of systemic vascular bed parameters for artificial heart control. IEEE Trans. Automat. Control 43 (1998), 765-778 · doi:10.1109/9.679017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.