Even when continuous-flow left ventricular assist devices (cf-LVADs) become the standard for bridging end-stage heart failure patients to heart transplantation, this development will not offer relief due to the long-term shortage of available donor hearts.1 Therefore, recovery of the failing heart and destination therapy will be long-term and sustainable treatment goals based on implantable cf-LVADs that provide long-term mechanical circulatory support (MCS).
For both strategies, the balance between naturally generated circulation and MCS is the key factor for survival and quality of life. Therefore, control strategies that ensure physiologic adaptation to MCS are as important as biocompatible pumps. Besides circulatory support, to preserve organ function, the degree of unloading the heart determines the interruption of the myocardial functional and structural breakdown and stimulation of myocardial recovery.
The only way to mimic a physiologic circulatory state is to change the level of LVAD support over time to meet patient-specific requirements at varying levels of perfusion demand such as during exercise or sleep.
For the implementation of these control strategies in cf-LVAD patients, accurate estimation of pump flow is necessary to give an estimation of native left ventricular function2 and the total perfusion in cf-LVAD patients. During LVAD support, the left ventricle is unloaded which results in adjusted intraventricular hemodynamic conditions. Therefore, estimation of left ventricular function based on changes in left ventricular dimensions alone is not reliable during LVAD support. In addition, the contribution of a cf-LVAD to the total cardiac output is hard to estimate when pump flow measurements are lacking.
Inclusion of sensors to measure pump flow in the outflow graft or pressure head may be useful. However, this addition may increase costs and the complexity may decrease reliability due to problems associated with biocompatibility and sensor failure.3 Therefore, it would be advantageous to estimate pump flow from pump parameters already known to the controller. Many pump models have been developed to estimate pump flow from power uptake and rotational pump speed under steady state conditions.3–5 These models mostly use a polynomial function to describe the relation between flow rate and power consumption.
In vivo measurements performed on the CentriMag RBP (Levitronix GmbH, Zürich, Switzerland) by Pirbodaghi et al.6 resulted in pressure-flow curves (H-Q curves) exhibiting a form of hysteresis. They concluded that the benefit of the addition of the derivative of flow with respect to speed of a pump model was minimal. Development of more physiologic control strategies will, however, require dynamic estimation models. Pump parameter estimation based on static pump characteristics provides a basis for the development of these models. Therefore, in this study, two types of pump models will be developed estimating static pump flow from pump speed and differential pressure or power uptake. These models will be compared for two axial-flow pumps, the HeartAssist5 (MicroMed, Houston, TX), the HeartMate II LVAD (Thoratec Corp., Pleasanton, CA) and for a centrifugal pump, the HeartWare (HeartWare, Framingham, MA), abbreviated as HA5, HMII, and HW, respectively. Coefficients of the models will be based on static characterization in which pump flow, pressure head, and power uptake are measured at different pump speeds under various loading conditions. It is hypothesized that models based on pressure head are more accurate in estimating pump flow than models based on power consumption.
Materials and Methods
Under static conditions, pump flow (Qlvad [L/min]), pressure head (Δplvad [mmHg]), and power uptake (P [W]) were determined at varying levels of pump speed (n [krpm]) and loading conditions.
Static characterization was done using heparinized porcine blood obtained from the slaughterhouse (hematocrit [Ht]: 40% for HMII and HW and 30% for HA5). The blood was circulated using a simple loop to control pump flow (Figure 1).
The loop consisted of a fluid reservoir connected to the inlet and outlet of the pump with tubes, providing a constant preload to the pump. The afterload was made variable by clamping the outflow tract of the pump.
Pump flow was measured with a flow sensor (type ME13PXN; Transonic Systems Inc, Ithaca, NY). Pressure sensors (P10EZ-1; Becton Dickinson, St. Niklaas, Belgium) were placed at the inlet and outlet of the pump to measure pressure head. The flow sensor was factory-calibrated for use with blood. Furthermore, power uptake and estimated pump flow as displayed on the controller (Qclinic [L/min]) were recorded. For the HMII and HW, pump flow as displayed on the controller is estimated from power uptake, while in case of the HA5 it is measured with an incorporated flow sensor. For the estimation of pump flow for the HW as displayed on the console, viscosity, derived from Ht, was taken into account.7
For the HMII and HA5, pump speed was increased from 6 to 12 krpm and 7.5 to 11.5 krpm, respectively, in 1 krpm increments. For the HW, the speed ranged from 1.8 to 3.6 krpm in 300 rpm steps. For every fixed speed, the afterload was gradually increased, by clamping the pump’s outflow tract, decreasing Qlvad to 0 L/min in 1 L/min steps.
Pump flow was modeled as a function of pump speed and pressure head or power uptake. All models were chosen to be phenomenological, describing the relation between the pump parameters measured during static characterization.
Static Pump Flow Estimation From Pressure Head
Because of the differences in construction, axial and centrifugal pumps have differently shaped pressure-flow characteristics or H-Q curves. The shape of these curves, however, is not dependent on pump speed, and thus enables scaling.
For an axial-flow pump, the H-Q curve is typically S-shaped, while Δplvad is quadratically dependent on flow rate in a centrifugal pump (Figure 2). For inertia-dominated flow, pressure can be scaled with fluid density (ρ) and velocity (V). The scaling factor is ρ·V2. Pump flow can be scaled with respect to velocity and area (V·A). Consequently, Δplvad and Qlvad were scaled with n2 and n, respectively (Pirbodaghi et al.6), Equations 1 and 2, to exclude the influence of pump speed on the relation between flow rate and differential pressure.
Moreover, pump flow and pressure head can be scaled with ρ and inner diameter (d) to make the pump parameters dimensionless. However, because fluid density and inner diameter did not change for the individual pumps during static characterization, validation of scaling with these parameters was not possible and therefore not used in this study.
After normalization, the relation between Qs (L) and Δps (kg/m) is no longer dependent on pump speed. Because of the differently shaped characteristic H-Q curves, for each pump type a separate model was required to describe the relation between scaled pump flow and scaled pressure head. With these models, static pump flow could be estimated for each pump speed and pressure head, within the range as measured during static characterization. Therefore, experiments for characterizing the pump at an intermediate speed are not required.
Model for the axial pumps.
For the axial-flow pumps, the relation between Qs and Δps was modeled with a sigmoid function (Equation 3) to describe the H-Q curves. In this function, the coefficients, a1, a2, and a3, give an indication of pump flow at low Δplvad, the decrease in pump flow for increasing Δplvad, and pump flow at high Δplvad, respectively.
with coefficients a1 (L), a2 (-), and a3 (kg/m).
Insertion of Equations 1 and 2 into Equation 3 leads to an estimation of real pump flow:
Model for the centrifugal pump.
For the HW centrifugal pump, however, the relation between Qs and Δps was modeled using a quadratic function (Equation 5).
with coefficients b1 (kg/[m·L2]), b2 (kg/[m·L]), and b3 (kg/m).
Pump flow was therefore estimated by solving Equation 5 for a known Δps. Only positive pump flow was considered. Because constant b1 was negative in the pump model (decreasing Qlvad with increasing Δplvad), positive pump flow was estimated with the following equation:
Besides these pump models based on pump speed and pressure head, a pump model based on pump speed and power uptake was used to estimate static pump flow rate.
Static Pump Flow Estimation From Power Uptake
For axial and centrifugal pumps, the relation between flow and power is essentially linear (Figure 3). At low pump flows, internal energy losses or other factors may influence pump behavior of an axial pump, such that the flow-power relation becomes nonlinear and even nonmonotonous. In that case, minimum power uptake is not found at zero pump flow. The increase in power consumption for pump flows below this local minimum may be caused by an increase in friction on the bearings due to an increase in pressure head. For all pumps, flow was modeled as a linear function of power P (Equation 7).
with c1 in L/(min·W), c2 in L/W, c3 in L, and c4 in L/min.
For the axial pumps, however, pump characteristics were split into two linear parts (Figure 4). The coefficients c1–c4 were different for these two parts: one set of coefficients holding for power uptake higher than power uptake measured at zero pump flow (P0[W]) and another set holding for lower power consumption. For power uptake below P0, actually two solutions of pump flow are possible, resulting in an overestimation of pump flow below the flow rate at minimum power uptake.
Measured static pump characteristics were used to estimate the coefficients in the pump models. Flow estimated with these models was also compared with the estimations of pump flows as used in the clinic (i.e., displayed on the consoles). In case of the HA5, this flow rate was measured with the incorporated flow sensor. The other two designs use an estimation algorithm for determining flow rate.
Estimation of Coefficients
Coefficients a1–a3 of the static pump model, estimating Qs from Δps for the axial-flow pumps, were determined using the Levenberg-Marquardt algorithm as implemented in MATLAB (release 2010b). All other coefficients were determined using a standard linear regression method.
Static Pump Characteristics
Static characterization of all three pumps was done using blood (Figure 5). For an increase in pump speed, both pump flow and pressure head increased. The shapes of the H-Q curves were similar at different pump speeds. This shape differed for an axial pump (HA5 and HMII) compared to a centrifugal pump (HW). For the HW VAD, the increase in pressure head became less with increasing pump flow and reached a maximum at zero pump flow, while it increased further for the axial-flow pumps.
Comparing the three pumps, the overall power uptake was found to be highest in the HA5 and lowest in the HW. In case of the HA5, for flow rates below 6 L/min, pump power uptake was independent of flow rate and only varied with pump speed. Accurate estimation of low pump flows from power uptake was therefore not possible for the HA5. The same was found for the HMII at low pump speeds (flow <4 L/min, n < 8 krpm).
Moreover, for the axial pumps, the relation between power uptake and pump flow was found to be nonmonotonous. Minimum power uptake was not measured at zero pump flow because a local minimum in pump flow exists. Above this minimum, pump flow increased with increasing power, while below this local minimum, pump flow decreased with an increase in power uptake. This leads to overestimation of pump flow below the minimum if an increase in pump flow is assumed with increasing power uptake. For the HA5 running at 12.5 krpm, the local minimum in power uptake was found at a pump flow of 3 L/min. At this pump speed, a power uptake of, e.g., 17.5 W was measured at zero pump flow and also at a flow rate of 10 L/min.
For the HW VAD, pump flow increased linearly with increasing power uptake. Based on the static characteristics, pump models were developed to estimate pump flow from the other pump parameters.
Static Pump Models
Estimation from pressure head.
Normalization with pump speed resulted in H-Q curves, which were no longer dependent on pump speed (Figure 6). For all three pumps, scaled flow Qs was modeled as a function of Δps. Coefficients a1, a2, and a3 were estimated for the axial pumps and b1, b2, and b3 for the HW VAD (Table 1). Constant a2 was higher for the HA5 compared with the HMII, which indicates a faster decay in pump flow for increasing pressure differences across the pump or higher afterload sensitivity in the HA5.
Estimation from power uptake.
For all pumps, pump flow was modeled as a linear function of power uptake and pump speed, rendering coefficients c1–c4 (Table 1). For both axial pumps, pump flow estimation was split into two parts, with power uptake either higher than P0 (power uptake at zero pump flow) or equal to or lower than P0.
Comparison with pump flow estimation.
Estimation of pump flow, using the static pump models developed in this study based on static characteristics, was compared with estimated pump flow, as used in the clinic, displayed on the consoles. For the HA5, pump flow as displayed on the console was measured with an incorporated flow sensor. For the HMII and HW, this pump flow estimation as displayed on the console was also based on power uptake and pump speed. For HW, pump flow estimation in the console was dependent on the Ht of the blood.7 Measured and estimated pump flows were compared for measurements performed on blood (Figure 7).
Using pressure head and pump speed, static pump flow was estimated accurately in all three pumps. The values of the coefficient of determination (R2) were 0.98, 0.99, and 0.98 for the HA5, HMII, and HW, respectively.
In the HA5 and HMII, use of power uptake and pump speed was not sufficient for pump flow estimation, and R2 was 0.71 and 0.93 for the HA5 and HMII, respectively. Pump flows below approximately 3 L/min for the HA5 and 2 L/min for the HMII were overestimated. For the HW, static pump flow estimation based on pump speed and power uptake was accurate (R2, 1.0).
For the HA5, measurements performed with the incorporated flow sensor were similar to pump flows measured with the Transonic flow sensor (R2, 1.0). The incorporated flow sensor has a range of 10 L/min, and therefore, the signal levels off above this flow rate.
Pump flows as displayed on the Thoratec console (for the HMII) were overestimated below 3 L/min (R2, 0.90). Pump flows were underestimated with approximately 1.5–2 L/min using the pump model as implemented in the console for the HW.
The static pump model proposed in this study, which estimates pump flow (Qlvad) from the pressure head (Δplvad), is capable of describing pump behavior under static conditions for all three pumps with the same acceptable level of accuracy (R2 was 0.98, 0.99, and 0.98 for the HA5, HMII, and HW, respectively). It is possible to scale Qlvad and Δplvad with n and n2, respectively, owing to the similarity in shape of the flow-pressure curves at different pump speeds. In the same way, it is possible to scale these pump parameters with fluid density and inner diameter of the pump, resulting in dimensionless flow Qs and pressure drop Δps. Because diameter and fluid density were not changed for the measurements of the pump, we did not use this option. Moreover, the coefficients in these models are still dependent on blood viscosity.
In a model estimating flow rate from pressure head, the coefficients are dependent on the position of the pressure measurements performed to calculate Δplvad. Therefore, with the use of Δplvad to estimate pump flow in patients, the measurement positions of inlet and outlet pressure of the pump need to be known and similar during static characterization to obtain coefficients for the pump models.
With a change in pump flow, changes in power are small for the axial pumps. Changes in power are smaller in the HA5 than in the HMII, which could explain the better results in pump flow estimation for the HMII based on power uptake (R2, 0.71 and 0.93 for the HA5 and HMII, respectively).
Furthermore, as a consequence of the nonmonotonous relation between flow and power uptake, low pump flows are overestimated when assuming an increase in pump flow for increasing power uptake. Overestimation of pump flow is a problem during critical situations in which pump flows are low or even zero (e.g., in cases of pump thrombosis), whereas the Thoratec console would display pump flows around 3–4 L/min in these situations. The console does not display any estimation of pump flow with pump speeds below 8 krpm and for pump flows lower than 4 L/min at 8 krpm.
For the HW centrifugal pump, flow increases linearly with power uptake. Therefore, for this pump, flow estimation from power uptake is accurate under static conditions. The pump flow as displayed on the HW console (which is based on power uptake, pump speed, and Ht), however, is underestimated compared to measured pump flow. This could be due to the dependency of the coefficients in the model on blood viscosity. Therefore, in the development of pump models, the influence of viscosity or the Ht of the blood on pump behavior needs to be considered in determination of the coefficients of the model.
During a pilot study, measurements were performed on the HMII with blood in a mock loop,8 simulating a patient on LVAD support (Figure 8). Dynamic pump behavior resulted in loop-shaped H-Q curves, indicating inertial effects due to acceleration/deceleration of the blood. Under dynamic conditions, estimation of mean pump flow from mean power uptake or mean pressure head, using static pump characteristics, should therefore be further investigated.
For the HA5, with the incorporated flow sensor, the model estimating pump flow from pressure difference could be used to derive left ventricular pressure. To do this, aortic pressure should be measured in LVAD patients. This can be performed with, e.g., a Nexfin monitor (BMEYE B.V., Amsterdam, The Netherlands), which uses a sensor wrapped around a patient’s finger to noninvasively measure continuous arterial blood pressure.9
Pump parameter estimation based on static pump characteristics provides a basis for the estimation of cf-LVAD flow. Nevertheless, a better measurement accuracy to assess dynamic, more physiologic conditions is still needed.
Estimation of pump flow based on power uptake alone is only accurate in the HW centrifugal pump. Additional measurement of cf-LVAD flow at the site of the exit cannula such as in HA5 is therefore rational and may enhance flow estimation under static conditions. In patients measured or estimated, pump flow can be used to estimate differential pressure across the cf-LVAD, and thus may provide diagnostic information about the patient’s LV condition.