Non-parametric dynamical estimation of blood flow rate,pressure difference and viscosity for a miniaturized blood pump

Abstract

Blood pumps are becoming increasingly important for medical devices. They are used to assist and control the blood flow and blood pressure in the patient’s body. To accurately control blood pumps, information about important hydrodynamic parameters such as blood flow rate, pressure difference and viscosity is needed. These parameters are difficult to measure online. Therefore, an accurate estimation of these parameters is crucial for the effective operation of implantable blood pumps. In this study, in vitro tests with bovine blood were conducted to collect data about the non-linear dependency of blood flow rate, flow resistance (pressure difference) and whole blood viscosity on motor current and rotation speed of a prototype blood pump. Gaussian process regression models are then used to model the non-linear mappings from motor current and rotation speed to the hydrodynamic variables of interest. The performance of the estimation is evaluated for all three variables and shows very high accuracy. For blood flow rate – correlation coefficient ( $r^2)$  = 1, root mean squared error ( $\mathrm{RMSE}$ ) = 0.31 ml min⁻¹, maximal error ( $ER{R}_{max}$ ) = 9.31 ml min⁻¹; for pressure $r^2$  = 1, $\mathrm{RMSE}$  = 0.09 mmHg, $ER{R}_{max}$  = 8.34 mmHg; and for viscosity $r^2$  = 1, $\mathrm{RMSE}$  = 0.09 mPa.s, $ER{R}_{max}$  = 0.31 mPa⋅s. The current findings suggest that this method can be employed for highly accurate online estimation of essential hydrodynamic parameters for implantable blood pumps.