Sensorless flow and head estimation in the VentrAssist rotary blood pump

Flow rate and pressure difference (or head) are key variables needed in the control of implantable rotary blood pumps. However, use of flow and/or pressure probes can decrease reliability and increase system power consumption and expense. For a given fluid viscosity, the flow state is determined by any 2 of the 4 pump variables: Flow, pressure difference, speed, and motor input power can be used. Thus, if viscosity is known or if its influence is sufficiently small, flow rate and pressure difference can be estimated from the motor speed and motor input power. For the VentrAssist centrifugal blood pump, which uses a hydrodynamic bearing, sensorless flow and pressure head estimation accuracy of 2 of our impeller designs were compared for a viscosity range of 1.2 to 4.5 mPas. This showed impeller design optimization can improve estimation accuracy. We also compared estimation accuracy using 2 blood analogues used in vitro, aqueous glycerol and red blood cells suspended in Haemaccel. The nature of the blood analogue and not only the viscosity of the fluid seems to influence estimation accuracy in our pump.     

Use of Motor Current in Flow Rate Measurement for the Magnetically Suspended Centrifugal Blood Pump

Abstract: Indirect measurement of the flow rate of a centrifugal blood pump using the driving motor current was studied. The pump flow rate can be expressed as a function of the motor current under a given motor speed in the absence of energy loss resulting from uncertain mechanical contact friction. The magnetically suspended centrifugal blood pump (MSCP), developed by the collaboration of Kyoto University and NTN Inc., was suitable for the application of this measuring method because the impeller is suspended magnetically inside the pump housing without any mechanical contact. The effect of fluid viscosity on the pump performance was investigated in detail, and it was possible to estimate the pump flow rate and the pressure difference through the pump (from inlet port to outlet port) accurately by monitoring the motor current and speed when the kinematic viscosity of working fluids was known. The kinematic viscosity of working fluids can also be measured with the MSCP. The motor current and motor speed were monitored in a chronic animal experiment, and the estimated flow rate and pressure difference showed good correlation with directly measured data.     

Calculus of variations approach for state and parameter estimation in switched 1D hyperbolic PDEs

This paper proposes the use of calculus of variations to solve the problem of state and parameter estimation for a class of switched 1‐dimensional hyperbolic partial differential equations coupled with an ordinary differential equation. The term “switched” here refers to a system changing its characteristics according to a switching rule, which may depend on time, parameters of the system, and/or state of the system. The estimation method is based on a smooth approximation of the system dynamics and the use of variational calculus on an augmented Lagrangian cost functional to get the sensitivity with respect to the initial state and some (possibly distributed) parameters of the system. Those sensitivities or variations, together with related adjoint systems, are used as inputs for an optimization algorithm to identify the values of the variables to be estimated. Two examples are provided to demonstrate the effectiveness of the proposed method. The first one is concerned with a switched overland flow model, developed from Saint‐Venant equations and Green‐Ampt law; the second example deals with a switched free traffic flow model based on the Lighthill‐Whitham‐Richards representation, modified by the presence of a relief route.     

Physiological control of blood pumps using intrinsic pump parameters: a computer simulation study

Implantable flow and pressure sensors, used to control rotary blood pumps, are unreliable in the long term. It is, therefore, desirable to develop a physiological control system that depends only on readily available measurements of the intrinsic pump parameters, such as measurements of the pump current, voltage, and speed (in revolutions per minute). A previously proposed DeltaP control method of ventricular assist devices (VADs) requires the implantation of two pressure sensors to measure the pressure difference between the left ventricle and aorta. In this article, we propose a model-based method for estimating DeltaP, which eliminates the need for implantable pressure sensors. The developed estimator consists of the extended Kalman filter in conjunction with the Golay-Savitzky filter. The performance of the combined estimator-VAD controller system was evaluated in computer simulations for a broad range of physical activities and varying cardiac conditions. The results show that there was no appreciable performance degradation of the estimator-controller system compared to the case when DeltaP is measured directly. The proposed approach effectively utilizes a VAD as both a pump and a differential pressure sensor, thus eliminating the need for dedicated implantable pressure and flow sensors. The simulation results show that different pump designs may not be equally effective at playing a dual role of a flow actuator and DeltaP sensor.     

Noninvasive average flow estimation for an implantable rotary blood pump: a new algorithm incorporating the role of blood viscosity

The effect of blood hematocrit (HCT) on a noninvasive flow estimation algorithm was examined in a centrifugal implantable rotary blood pump (iRBP) used for ventricular assistance. An average flow estimator, based on three parameters, input electrical power, pump speed, and HCT, was developed. Data were collected in a mock loop under steady flow conditions for a variety of pump operating points and for various HCT levels. Analysis was performed using three-dimensional polynomial surfaces to fit the collected data for each different HCT level. The polynomial coefficients of the surfaces were then analyzed as a function of HCT. Linear correlations between estimated and measured pump flow over a flow range from 1.0 to 7.5 L/min resulted in a slope of 1.024 L/min (R2=0.9805). Early patient data tested against the estimator have shown promising consistency, suggesting that consideration of HCT can improve the accuracy of existing flow estimation algorithms.     

In vivo test of pressure head and flow rate estimation in a continuous-flow artificial heart

To avoid using sensors with low biocompatibility and low durability in implantable total artificial heart (TAH) systems, the authors previously proposed a new method for estimating instantaneous values of flow rate and pressure head on the basis of voltage, current, and rotational speed in a motor driven centrifugal pump. The previous in vitro experiments showed that the proposed estimator could automatically compensate for the effect of the change in blood viscosity on the estimation accuracy by employing two kinds of autoregressive exogenous models. In this study, validity and reliability of this estimation method were ascertained in an acute animal experiment. In the experiment, two centrifugal blood pumps were implanted into an adult goat as a total artificial heart. Results of estimation were compared with true values when blood viscosity was changed by injecting physiological saline. The results indicated that the system could successfully estimate pressure head by compensating the change of viscosity, although the estimation accuracy of the in vivo estimation was not so high as that of the previous in vitro tests.     

A navigation algorithm using measurement-based extrapolation

An element in the guidance loop of any aircraft is the navigation system. This system derives position (and sometimes velocity) information by combining data from various on-board and external measurement devices and transmits it to the guidance algorithm. In this paper a navigation algorithm is designed for an aircraft which has on-board inertial measurements, range measurements from a TACAN station, and range, elevation and azimuth measurements from a ground-based radar. The basic design philosophy is the predictor-corrector form for a recursive estimator. State prediction is accomplished by extrapolation of the inertial measurements rather than from Newton's second law. This eliminates major modelling problems caused by the aircraft's aerodynamics. State correction is accomplished using optimal linear stochastic estimation methods. The resulting estimator (navigation algorithm) is essentially an ‘extended Kalman filter’ which processes the above-mentioned inputs and generates optimal (in a linearized sense) estimates of the aircraft's latitude, longitude and altitude.     

Motor Feedback Physiological Control for a Continuous Flow Ventricular Assist Device

The response of a continuous flow magnetic bearing supported ventricular assist device, the CFVAD3 (CF3) to human physiologic pressure and flow needs is varied by adjustment of the motor speed. This paper discusses a model of the automatic feedback controller designed to develop the required pump performance. The major human circulatory, mechanical, and electrical systems were evaluated using experimental data from the CF3 and linearized models developed. An open-loop model of the human circulatory system was constructed with a human heart and a VAD included. A feedback loop was then closed to maintain a desired reference differential pressure across the system. A proportional-integral (PI) controller was developed to adjust the motor speed and maintain the system reference differential pressure when changes occur in the natural heart. The effects of natural heart pulsatility on the control system show that the reference blood differential pressure is maintained without requiring CF3 motor pulsatility.     

Investigation of the flow performance of a nutating blood pump by computational fluid dynamics

In centrifugal blood pumps, blood is moved into a circular path with the help of an impeller. In a nutating pump, the nutating body takes over the role of the impeller. Since the nutating body itself does not rotate, this pump needs no seal, no blood contacting, and no magnetic bearings. To examine the suitability of the nutating pump principle for mechanical heart assist, the flow performance of different nutating pump models was investigated by computational fluid dynamics. The geometrical parameters of the pump were varied and flow-pressure curves were calculated for 12 models at different rotation frequencies. All models showed satisfactory flow-pressure curves. One model was computed minutely at 1 flow configuration to examine shear stresses within the fluid. A flow of 5 L/min and a frequency of 3,300 rotations per min (rpm) resulted in a differential pressure of 85 mm Hg. The maximum shear stress in the fluid at this flow was estimated to be 193 Pa which is considered to be an acceptable value for a blood pump.     

Effect of pulsatility on the mathematical modeling of rotary blood pumps

In this study, the effect of time derivatives of flow rate and rotational speed was investigated on the mathematical modeling of a rotary blood pump (RBP). The basic model estimates the pressure head of the pump as a dependent variable using measured flow and speed as predictive variables. Performance of the model was evaluated by adding time derivative terms for flow and speed. First, to create a realistic working condition, the Levitronix CentriMag RBP was implanted in a sheep. All parameters from the model were physically measured and digitally acquired over a wide range of conditions, including pulsatile speed. Second, a statistical analysis of the different variables (flow, speed, and their time derivatives) based on multiple regression analysis was performed to determine the significant variables for pressure head estimation. Finally, different mathematical models were used to show the effect of time derivative terms on the performance of the models. In order to evaluate how well the estimated pressure head using different models fits the measured pressure head, root mean square error and correlation coefficient were used. The results indicate that inclusion of time derivatives of flow and speed can improve model accuracy, but only minimally.     

A method for control of an implantable rotary blood pump for heart failure patients using noninvasive measurements

We propose a deadbeat controller for the control of pulsatile pump flow (Q(p) ) in an implantable rotary blood pump (IRBP). Noninvasive measurements of pump speed and current are used as inputs to a dynamical model of Q(p) estimation, previously developed and verified in our laboratory. The controller was tested using a lumped parameter model of the cardiovascular system (CVS), in combination with the stable dynamical models of Q(p) and differential pressure (head) estimation for the IRBP. The control algorithm was tested with both constant and sinusoidal reference Q(p) as input to the CVS model. Results showed that the controller was able to track the reference input with minimal error in the presence of model uncertainty. Furthermore, Q(p) was shown to settle to the desired reference value within a finite number of sampling periods. Our results also indicated that counterpulsation yields the minimum left ventricular stroke work, left ventricular end diastolic volume, and aortic pulse pressure, without significantly affecting mean cardiac output and aortic pressure.     

Mathematical Modeling of Rotary Blood Pumps in a Pulsatile In Vitro Flow Environment

Nowadays, sacrificing animals to develop medical devices and receive regulatory approval has become more common, which increases ethical concerns. Although in vivo tests are necessary for development and evaluation of new devices, nonetheless, with appropriate in vitro setups and mathematical models, a part of the validation process can be performed using these models to reduce the number of sacrificed animals. The main aim of this study is to present a mathematical model simulating the hydrodynamic function of a rotary blood pump (RBP) in a pulsatile in vitro flow environment. This model relates the pressure head of the RBP to the flow rate, rotational speed, and time derivatives of flow rate and rotational speed. To identify the model parameters, an in vitro setup was constructed consisting of a piston pump, a compliance chamber, a throttle, a buffer reservoir, and the CentriMag RBP. A 40% glycerin–water mixture as a blood analog fluid and deionized water were used in the hydraulic circuit to investigate the effect of viscosity and density of the working fluid on the model parameters. First, model variables were physically measured and digitally acquired. Second, an identification algorithm based on regression analysis was used to derive the model parameters. Third, the completed model was validated with a totally different set of in vitro data. The model is usable for both mathematical simulations of the interaction between the pump and heart and indirect pressure measurement in a clinical context.     

Development of a pump flow estimator for rotary blood pumps to enhance monitoring of ventricular function

Estimation of instantaneous flow in rotary blood pumps (RBPs) is important for monitoring the interaction between heart and pump and eventually the ventricular function. Our group has reported an algorithm to derive ventricular contractility based on the maximum time derivative (dQ/dt_max as a substitute for ventricular dP/dt_max) and pulsatility of measured flow signals. However, in RBPs used clinically, flow is estimated with a bandwidth too low to determine dQ/dt_max in the case of improving heart function. The aim of this study was to develop a flow estimator for a centrifugal pump with bandwidth sufficient to provide noninvasive cardiac diagnostics. The new estimator is based on both static and dynamic properties of the brushless DC motor. An in vitro setup was employed to identify the performance of pump and motor up to 20 Hz. The algorithm was validated using physiological ventricular and arterial pressure waveforms in a mock loop which simulated different contractilities (dP/dt_max 600 to 2300 mm Hg/s), pump speeds (2 to 4 krpm), and fluid viscosities (2 to 4 mPa·s). The mathematically estimated pump flow data were then compared to the datasets measured in the mock loop for different variable combinations (flow ranging from 2.5 to 7 L/min, pulsatility from 3.5 to 6 L/min, dQ/dt_max from 15 to 60 L/min/s). Transfer function analysis showed that the developed algorithm could estimate the flow waveform with a bandwidth up to 15 Hz (±2 dB). The mean difference between the estimated and measured average flows was +0.06 ± 0.31 L/min and for the flow pulsatilities ?0.27 ± 0.2 L/min. Detection of dQ/dt_max was possible up to a dP/dt_max level of 2300 mm Hg/s. In conclusion, a flow estimator with sufficient frequency bandwidth and accuracy to allow determination of changes in ventricular contractility even in the case of improving heart function was developed.     

New blood volume monitoring method for hemodialysis: A-V pressure gradient measurement by synchronized one-point reading

Abstract:  During hemodialysis, rapid ultrafiltration often causes symptomatic hypotension. To predict the occurrence of volume-dependent hypotension as early as possible, continuous hematocrit monitoring with the Crit-Line noninvasive monitor has been widely used to measure blood volume changes during hemodialysis. As another potential method of monitoring blood volume variations, we studied blood viscosity, which is theoretically associated with the pressure gradient across the dialyzer. Blood viscosity (calculated by the Hugen-Poiseuille formula) is a major determinant of the blood flow rate and is associated with the pressure difference between the postpump arterial (A) and venous (V) pressures. The A-V pressure gradient fluctuates due to pump pulsation, so we minimized this noise by always reading the pressure gradient at the same point out of 1400 partitions on the rotary pump. To test this synchronized one-point reading method, the A-V pressure gradient was measured using 3 different xanthan gum solutions and was found to be linearly proportional to the model blood flow rate. In an experimental dialysis system using a xanthan gum solution (300 mg/L), the A-V pressure gradient showed a gradual linear increase along with the ultrafiltration rate up to 1 L/h as the viscosity slowly increased in the dialyzer. The changes of blood volume shown by this method were significantly correlated with data obtained using the Crit-Line in 8 patients undergoing hemodialysis. This simple and inexpensive method may allow monitoring of blood volume changes and thus provide data that are beneficial for fluid management in hemodialysis patients suffering from clinical dialysis intolerance.     

Noninvasive Pump Flow Estimation of a Centrifugal Blood Pump

Abstract: A flow rate estimating method was investigated for a centrifugal blood pump developed in our institute. The estimated flow rate was determined by the power consumption, the rotating speed of the motor, and the hematocrit value. The power consumption and the rotating speed of the motor were measured with a wattmeter. The examinations were performed in a closed mock loop filled with goat blood with hematocrit values of 21.5%. 28%, 34%, and 42%. Measured values of blood viscosity were 2.47, 3.09, 3.71, and 5.07 mPa. s at a share rate of 37.5/s, respectively. A linear correlation between the power consumption and the pump flow rate was observed in all hematocrit values. But variations in hematocrit caused a difference in the flow rate up to 1.1 L/min at the same power consumption and rotating speed. Effects of blood viscosity on the flow estimation were corrected by the hematocrit value. The value of the coefficient of determination, R², between the estimated flow rate and the measured flow rate was 0.988. These results may indicate that the flow estimating method calculated by the power consumption of the motor, the rotating speed, and the hematocrit value is useful in the clinical situation.     

Investigation of the Characteristics of HeartWare HVAD and Thoratec HeartMate II Under Steady and Pulsatile Flow Conditions

The aim of this study was to elucidate the dynamic characteristics of the Thoratec HeartMate II (HMII) and the HeartWare HVAD (HVAD) left ventricular assist devices (LVADs) under clinically representative in vitro operating conditions. The performance of the two LVADs were compared in a normothermic, human blood‐filled mock circulation model under conditions of steady (nonpulsatile) flow and under simulated physiologic conditions. These experiments were repeated using 5% dextrose in order to determine its suitability as a blood analog. Under steady flow conditions, for the HMII, approximately linear inverse LVAD differential pressure (H) versus flow (Q) relationships were observed with good correspondence between the results of blood and 5% dextrose under all conditions except at a pump speed of 9000 rpm. For the HVAD, the corresponding relationships were inverse curvilinear and with good correspondence between the blood‐derived and 5% dextrose‐derived relationships in the flow rate range of 2–6 L/min and at pump speeds up to 3000 rpm. Under pulsatile operating conditions, for each LVAD operating at a particular pump speed, an counterclockwise loop was inscribed in the HQ domain during a simulated cardiac cycle (HQ loop); this showed that there was a variable phase relationship between LVAD differential pressure and LVAD flow. For both the HMII and HVAD, increasing pump speed was associated with a right‐hand and upward shift of the HQ loop and simulation of impairment of left ventricular function was associated with a decrease in loop area. During clinical use, not only does the pressure differential across the LVAD and its flow rate vary continuously, but their phase relationship is variable. This behavior is inadequately described by the widely accepted representation of a plot of pressure differential versus flow derived under steady conditions. We conclude that the dynamic HQ loop is a more meaningful representation of clinical operating conditions than the widely accepted steady flow HQ curve.     

Sensorless Viscosity Measurement in a Magnetically‐Levitated Rotary Blood Pump

Controlling the flow rate in an implantable rotary blood pump based on the physiological demand made by the body is important. Even though various methods to estimate the flow rate without using a flow meter have been proposed, no adequate method for measuring the blood viscosity, which is necessary for an accurate estimate of the flow rate, without using additional sensors or mechanisms in a noninvasive way, has yet been realized. We have developed a sensorless method for measuring viscosity in magnetically levitated rotary blood pumps, which requires no additional sensors or mechanisms. By applying vibrational excitation to the impeller using a magnetic bearing, we measured the viscosity of the working fluid by measuring the phase difference between the current in the magnetic bearing and the displacement of the impeller. The measured viscosity showed a high correlation (R² > 0.992) with respect to a reference viscosity. The mean absolute deviation of the measured viscosity was 0.12 mPa·s for several working fluids with viscosities ranging from 1.18 to 5.12 mPa·s. The proposed sensorless measurement method has the possibility of being utilized for estimating flow rate.     

Hemodynamic System Analysis of Intraarterial Microaxial Pumps In Vitro and In Vivo

Abstract: Because of the lack of a sophisticated pump management system, the performance of the Hemopump in patients cannot be assessed successfully. To clarify the interrelationship between an intravascular nonpulsatile pump and a pulsating ventricle, an in vitro study was set up under controlled conditions. Before these in vitro experiments, a series of in vivo experiments were performed in sheep using Hp31 cannulae. As anticipated, the resulting pulsatile pump flow was a function of the momentary pressure difference across the pump. This varying pump flow showed a significant flow loop hysteresis, indicating that the pressure difference across the pump is not the only parameter governing momentary pump flow of a rotary pump operating at constant speed in a pulsatile environment. Furthermore, flow in the Hp31 was significantly influenced by the inflow situation, blood supply, size of the ventricular cavity, and shape and position of the inflow cannula within the ventricle. Pulsatile flow conditions with good as well as impaired inflow into the pump were accordingly simulated in vitro to verify the in vivo measurements, to characterize the various inflow conditions, and to discuss methods of improved pump management. As a result of the in vivo and in vitro experiments, one can rely on the measurement of nonpulsatile in vitro flow and pressure differences across the pump to characterize the momentary pump flow for good inflow conditions into the pump. For these situations, the flow hysteresis produced, caused by fluid inertia within the pump and cannula, can be neglected. In contrast, for an impaired inflow situation, the calculated pump flow based on pressure difference measurements can be misleading. Consequently, an improved pump management system is required to adjust the pump speed, the pump performance, to any kind of impaired inflow.     

Effect of parameter variations on the hemodynamic response under rotary blood pump assistance

Numerical models, able to simulate the response of the human cardiovascular system (CVS) in the presence of an implantable rotary blood pump (IRBP), have been widely used as a predictive tool to investigate the interaction between the CVS and the IRBP under various operating conditions. The present study investigates the effect of alterations in the model parameter values, that is, cardiac contractility, systemic vascular resistance, and total blood volume on the efficiency of rotary pump assistance, using an optimized dynamic heart-pump interaction model previously developed in our laboratory based on animal experimental measurements obtained from five canines. The effect of mean pump speed and the circulatory perturbations on left and right ventricular pressure volume loops, mean aortic pressure, mean cardiac output, pump assistance ratio, and pump flow pulsatility from both the greyhound experiments and model simulations are demonstrated. Furthermore, the applicability of some of the previously proposed control parameters, that is, pulsatility index (PI), gradient of PI with respect to pump speed, pump differential pressure, and aortic pressure are discussed based on our observations from experimental and simulation results. It was found that previously proposed control strategies were not able to perform well under highly varying circulatory conditions. Among these, control algorithms which rely on the left ventricular filling pressure appear to be the most robust as they emulate the Frank-Starling mechanism of the heart.     

Bypass flow, mean arterial pressure, and cerebral perfusion during cardiopulmonary bypass in dogs

OBJECTIVE: To determine if normal cardiopulmonary bypass (CPB) pump flows maintain cerebral perfusion in the context of reduced mean arterial pressure at 33 degrees C. DESIGN: A prospective investigation. SETTING: Animal CPB research laboratory. PARTICIPANTS: Seven dogs that underwent CPB. INTERVENTIONS: Seven dogs underwent CPB at 33 degrees C using alpha-stat management and a halothane, fentanyl-midazolam anesthetic. Cerebral blood flow was measured using the sagittal sinus outflow technique. After control measurements at 70 mm Hg, cerebral physiologic values were determined under four conditions in random order: (1) mean arterial pressure of 60 mm Hg achieved by a reduction in pump flow, (2) mean arterial pressure of 60 mmHg determined by partial opening of a femoral arterial-to-venous reservoir shunt, (3) mean arterial pressure of 45 mm Hg by reduced pump flow, and (4) mean arterial pressure of 45 mm Hg by shunt. A 9F femoral arterial-to-venous reservoir shunt was controlled by a screw clamp. MEASUREMENTS AND MAIN RESULTS: Except for the controlled variables of mean arterial pressure and bypass flow, physiologic determinants of cerebral blood flow (temperature, PaCO2 and hematocrit) did not differ under any of the CPB conditions. Pump flow per se was not a determinant of cerebral perfusion. Cerebral blood flow and cerebral oxygen delivery did not differ with changes in pump flow if mean arterial pressure did not differ. Cerebral blood flow depended on mean arterial pressure under all pump flow conditions, however. CONCLUSIONS: Over the range of flows typical in adult CPB at 33 degrees C, pump flow does not have an effect on cerebral perfusion independent of its effect on mean arterial pressure. A targeted pump flow per se is not sufficient to maintain cerebral perfusion if mean arterial blood pressure is reduced.