A mathematical model for estimating physiological parameters of blood flow through rotary blood pumps has been developed. The model is based on the flow–pressure head characteristics of the Sputnik pediatric rotary blood pump measured under static and dynamic conditions, which allows it to cover a wide range of states of the cardiovascular system. The model provides sensorless estimation of the flow–pressure head characteristics. For the Sputnik pediatric rotary blood pump, the accuracy of estimation of the flow and the pressure head averaged over a single cardiac cycle is R2 = 0.998 and R2 = 0.976, respectively. A ViVitro Pulse Duplicator SD2001-1 bench (ViVitro Inc., Victoria, Canada) has been used to verify the developed mathematical model. The verification yielded the following values of accuracy of estimation of parameters averaged over a single cardiac cycle: flow rate, R2 = 0.993; pressure head, R2 = 0.994.
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References
Giridharan et al., “Miniaturization of mechanical circulatory support systems,” Artif. Org., 36, No. 8, 731-758 (2012).
Kirklin, J. K., Pagani, F. D., Kormos, R. L., et al., “Eighth annual INTERMACS report: Special focus on framing the impact of adverse events,” J. Heart Lung Transplant., 36, 1080-1086 (2017).
Selishchev, S. V. and Telyshev, D. V., “Optimisation of the Sputnik-VAD design,” Int. J. Artif. Org., 39, No. 8, 407-414 (2016).
Slaughter, M. S., Bartoli, C. R., Sobieski, M. A., et al., “Intraoperative evaluation of the Heartmate II flow estimator,” J. Heart Lung Transplant., 28, No. 1, 39-43 (2009).
Wakisaka, Y., Okuzono, Y., Taenaka, Y., et al., “Noninvasive pump flow estimation of a centrifugal blood pump,” Artif. Org., 21, No. 7, 651-654 (1997).
Lim, E., Karantonis, D. M., Reizes, J. A., et al., “Noninvasive average flow and differential pressure estimation for an implantable rotary blood pump using dimensional analysis,” IEEE Trans. Biomed. Eng., 55, No. 8, 2094-2101 (2008).
Pektok, E. et al., “Remote monitoring of left ventricular assist device parameters after HeartAssist-5 implantation,” Artif. Org., 37, No. 9, 820-825 (2013).
Pennings, K. A., Martina, J. R., Rodermans, B. F., et al., “Pump flow estimation from pressure head and power uptake for the HeartAssist5, HeartMate II, and HeartWare VADs,” ASAIO J., 59, No. 4, 420-426 (2013).
Schmid, D. M., Kaufmann, F., Amacher, R., et al., “Left ventricular assist devices: Challenges toward sustaining long-term patient care,” Ann. Biomed. Eng., 45, No. 8, 1836-1851 (2017).
Telyshev, D., Denisov, M., Pugovkin, A., et al., “The progress in the novel pediatric rotary blood pump Sputnik development,” Artif. Org., 42, No. 4, 432-443 (2018).
Telyshev, D. V., Denisov, M. V., and Selishchev, S. V., “The effect of rotor geometry on the H–Q curves of the Sputnik implantable pediatric rotary blood pump,” Biomed. Eng., 50, No. 6, 420-424 (2017).
Denisov, M. V., Selishchev, S. V., Telyshev, D. V., et al., “Development of medical and technical requirements and simulation of the flow–pressure characteristics of the Sputnik pediatric rotary blood pump,” Biomed. Eng., 50, No. 5, 296-299 (2017).
Ayre, P. J., Lovell, N. H., and Woodard, J. C., “Non-invasive flow estimation in an implantable rotary blood pump: A study considering nonpulsatile and pulsatile flows,” Physiol. Meas., 24, No. 1, 179-189 (2003).
AlOmari, A. H., Savkin, A. V., Karantonis, D. M., et al., “Non-invasive estimation of pulsatile flow and differential pressure in an implantable rotary blood pump for heart failure patients,” Physiol. Meas., 30, No. 4, 371-386 (2009).
Malagutti, N., Karantonis, D. M., Cloherty, S. L., et al., “Non-invasive average flow estimation for an implantable rotary blood pump: A new algorithm incorporating the role of blood viscosity,” Artif. Org., 31, No. 1, 45-52 (2007).
Granegger, M., Moscato, F., Casas, F., et al., “Development of a pump flow estimator for rotary blood pumps to enhance monitoring of ventricular function,” Artif. Org., 36, No. 8, 691-699 (2012).
Pirbodaghi, T., “Mathematical modeling of rotary blood pumps in a pulsatile in vitro flow environment,” Artif. Org., 41, No. 8, 711-716 (2017).
Stepanoff, A. J., Centrifugal and Axial Flow Pumps: Theory, Design, and Application, J. Wiley, New York (1948).
Nelik, L., Centrifugal and Rotary Pumps: Fundamentals with Applications, Boca Raton, Florida (1999).
Pillay, P. and Krishnan, R., “Modeling, simulation and analysis of permanent magnet motor drives. I. The brushless DC motor drives,” IEEE Trans. Ind. Appl., 25, No. 2, 263-273 (1989).
Choi, S., Boston, J. R., Thomas, D., et al., “Modeling and identification of an axial flow blood pump,” Proc. Amer. Control Conf., 6, 3714-3715 (1997).
Yoshizawa, M., Sato, T., Tanaka, A., et al., “Sensorless estimation of pressure head and flow of a continuous flow artificial heart based on input power and rotational speed,” ASAIO J., 48, No. 4, 443-448 (2002).
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Translated from Meditsinskaya Tekhnika, Vol. 54, No. 3, May-Jun., 2020, pp. 7-10.
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Telyshev, D.V. A Mathematical Model for Estimating Physiological Parameters of Blood Flow through Rotary Blood Pumps. Biomed Eng 54, 163–168 (2020). https://doi.org/10.1007/s10527-020-09996-0
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DOI: https://doi.org/10.1007/s10527-020-09996-0