Responses of four rotary blood pumps (Incor, Heartmate II, Heartware, and Duraheart) at a single speed setting to changes in preload and afterload were assessed using the human left ventricle as a benchmark for comparison. Data for the rotary pumps were derived from pressure flow relations reported in the literature while the natural heart was characterized by the Frank-Starling curve adjusted to fit outputs at different afterloads reported in the literature. Preload sensitivity (mean ± SD) for all pumps at all afterloads tested was 0.105 ± 0.092 L/min/mm Hg, while afterload sensitivity was 0.09 ± 0.034 L/min/mm Hg-values that were not significantly different (t-test, P = 0.56). By contrast, preload sensitivity of the natural heart was over twice as high (0.213 ± 0.03 L/min/mm Hg) and afterload sensitivity about one-third (0.03 ± 0.01 L/min/mm Hg) the values recorded for rotary pumps (t-test, P < 0.001). Maximum preload sensitivity and minimum afterload sensitivity allow the right and left ventricles to synchronize outputs without neural or humoral intervention. This theoretical study reinforces the need to provide preload sensitive control mechanisms of sufficient power to enable the pump and left ventricle in combination to adapt to changes in right ventricular output automatically.

Abstract:In a clinical setting it is necessary to control the speed of rotary blood pumps used as left ventricular assist devices to prevent possible severe complications associated with over-or underpumping. The hypothesis is that by using only the noninvasive measure of instantaneous pump impeller speed to assess flow dynamics, it is possible to detect physiologically significant pumping states (without the need for additional implantable sensors). By varying pump speed in an animal model, five such states were identified: regurgitant pump flow, ventricular ejection (VE), nonopening of the aortic valve over the cardiac cycle (ANO), and partial collapse (intermittent and continuous) of the ventricle wall (PVC-I and PVC-C). These states are described in detail and a strategy for their noninvasive detection has been developed and validated using (n = 6) ex vivo porcine experiments. Employing a classification and regression tree, the strategy was able to detect pumping states with a high degree of sensitivity and specificity: state VE-99.2/100.0% (sensitivity/specificity); state ANO-100.0/100.0%; state PVC-I-95.7/91.2%; state PVC-C-69.7/98.7%. With a simplified binary scheme differentiating suction (PVC-I, PVC-C) and nonsuction (VE, ANO) states, both such states were detected with 100% sensitivity. Current commercially used implantable rotary blood pumps (iRBPs) make little or no attempt to automatically control pump speed to optimize ventricular assistance. In order to achieve such a control strategy, a major design goal for iRBPs is the ability to reliably and accurately detect pumping states that cause such deleterious effects as ventricular collapse due to overpumping, or pump backflow (regurgitation) as a result of underpumping (1). Naturally, the ideal control set point is where left ventricular (LV) ejection is occurring and there is a net positive flow through both the aortic valve (AV) and the pump.A state that would be of long-term concern to a patient would occur at higher relative pump speeds when there is insufficient blood in the ventricle to sustain normal LV ejection and the AV remains closed throughout the entire cardiac cycle. In this instance there is no flow through the AV and the possibility of blood stasis distal to the AV, which could lead to significant patient complications due to clotting. However, it has been recognized (2,3) that the aim of ensuring AV opening is often infeasible in patients with LV failure. The lack of native heart contractility in such patients means that in order to attain a level of pump flow which adequately perfuses the body, a pump speed which produces the state of full AV closure is often required. Even higher speeds would result in partial or total ventricular collapse as the volume of blood drawn from the ventricle chamber is increased to a level at which pulmonary supply cannot meet pump demand. Deleterious outcomes could also occur at lower relative pump speeds where there is regurgitant flow through the pump.Experimentation in the transition of pumping stat...

Abstract: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 (R 2 = 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. Key Words: Implantable rotary blood pump-Noninvasive flow estimation-Control strategyLeft ventricular assist device-Hematocrit-Rotary blood pump.

Let A be a random m × n matrix over the finite field F q with precisely k non-zero entries per row and let y ∈ F m q be a random vector chosen independently of A. We identify the threshold m/n up to which the linear system Ax = y has a solution with high probability and analyse the geometry of the set of solutions. In the special case q = 2, known as the random k-XORSAT problem, the threshold was determined by [Dubois and Mandler 2002 for k = 3, Pittel and Sorkin 2016 for k > 3], and the proof technique was subsequently extended to the cases q = 3,4 [Falke and Goerdt 2012]. But the argument depends on technically demanding second moment calculations that do not generalise to q > 3. Here we approach the problem from the viewpoint of a decoding task, which leads to a transparent combinatorial proof.

Non-invasive estimation of flow was investigated in an implantable rotary blood pump (iRBP) with a hydrodynamic bearing. The effects of non-pulsatile and pulsatile flows were studied using in vitro mock loops, and acute (N = 3) and chronic (N = 6) ovine experiments. Using the non-pulsatile and pulsatile mock loops an average flow estimation algorithm was derived from root mean square (RMS) pump impeller speed and RMS input power. These algorithms were programmed into the iRBP controller for subsequent validation in vivo. In the acute experiments, venous return and systemic vascular resistance were adjusted through pharmacological intervention and exsanguination to produce an average range of pump flows from 0.0 to 2.6 l min(-1). Over this range the RMS estimation error was 88 +/- 12 ml, with a linear correlation slope of 0.992 +/- 0.006 (R2 = 0.986 +/- 0.004). In the chronic experiments, animals were monitored daily for up to three months and an average range of flows from 2.8 to 4.8 l min(-1) recorded. A linear correlation between the estimated and measured pump flows yielded a slope of 1.005 +/- 0.006 (R2 = 0.966 +/- 0.004). The RMS estimation error was 120 +/- 11 ml. Using this algorithm it is possible to effectively estimate flow in a rotary blood pump without implanting additional invasive sensors.

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.

An integral component in the development of a control strategy for implantable rotary blood pumps is the task of reliably detecting the occurrence of left ventricular collapse due to overpumping of the native heart. Using the noninvasive pump feedback signal of impeller speed, an approach to distinguish between overpumping (or ventricular collapse) and the normal pumping state has been developed. Noninvasive pump signals from 10 human pump recipients were collected, and the pumping state was categorized as either normal or suction, based on expert opinion aided by transesophageal echocardiographic images. A number of indices derived from the pump speed waveform were incorporated into a classification and regression tree model, which acted as the pumping state classifier. When validating the model on 12,990 segments of unseen data, this methodology yielded a peak sensitivity/specificity for detecting suction of 99.11%/98.76%. After performing a 10-fold cross-validation on all of the available data, a minimum estimated error of 0.53% was achieved. The results presented suggest that techniques for pumping state detection, previously investigated in preliminary in vivo studies, are applicable and sufficient for use in the clinical environment.

We develop a Lipschitz estimate for unitary operators. More specifically, we show that for each p ∈ ( 1 , ∞ ) p\in (1,\infty ) there exists a constant d p d_p such that ‖ f ( U ) − f ( V ) ‖ p ≤ d p ‖ U − V ‖ p \left \Vert f(U) - f(V)\right \Vert _p \leq d_p \left \Vert U - V\right \Vert _p for all Lipschitz functions f : T → C f: \mathbb {T} \to \mathbb {C} and unitary operators U U and V V .