A Mathematical Model for Estimating Physiological Parameters of Blood Flow through Rotary Blood Pumps

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A Mathematical Model for Estimating Physiological Parameters of Blood Flow through Rotary Blood Pumps D. V. Telyshev1,2

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 SD20011 bench (ViVitro Inc., Victoria, Canada) has been used to verify the developed mathematical model. The verifi cation 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.

Introduction About one million cases of cardiac failure are annu ally diagnosed worldwide [1]. Donor heart transplanta tion or implantation of a ventricular assist device (VAD) is an effective way of treating cardiac failure. The rate of heart transplantations does not grow for objective rea sons, while there is a noticeable increase in the rate of VAD implantations [2]. Rotary blood pumps (RBP) are modern VADs with a single movable part, the impeller [3], operating on the principle of vector control of a synchronous DC electric machine. By controlling the rotor speed, it is possible to achieve the required physiological parameters of blood flow and pressure head in the pump. Blood flow through the pump and pressure at the pump inlet and outlet are the main physiological param eters that have to be estimated to assess the RBP opera tion.

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Institute of Biomedical Systems, National Research University of Electronic Technology (MIET), Zelenograd, Russia; Email: [email protected] Institute for Bionic Technologies and Engineering, I. M. Sechenov First Moscow State Medical University, Ministry of Health of the Russian Federation, Moscow, Russia.

At present, there are two main approaches to meas uring blood flow: direct measurement of blood flow and measurement by sensorless methods [46]. Sensorless methods use the fact that the power con sumption of the pump depends on the flow through it. This approach to estimation of blood flow holds considerable promise, because it does not require sensors to be built into RBPs (such builtin sensors increase the complexity of the pump design, reducing thereby its reliability). However, the sensorless measurement approach, when applied to VAD, meets the following difficulty: the efficiency of the system is rather low, which makes it dif ficult to assess the direct relationship between the electri cal and hydraulic parameters of the system. The maxi mum efficiency of an RBP does not exceed 20%. Figure 1 shows a diagram of power losses