Typical design practices for rotodynamic fluid pump configurations, axial or centrifugal, are centralized around a specific speed for a desired pressure and flow.1,2 Classically, axial-flow pumps tend to be used under high flow rate and low head pressure conditions, whereas centrifugal-flow pumps are designed for lower flow rate and higher head conditions. Many rotodynamic pumps used around the world are used under stable fluid pressure conditions that do not exhibit continuous variation. Unfortunately, this is not the case with ventricular assist devices (VADs) placed within the dynamic environment of the human heart. VADs are exposed to broad ranges of preload (left ventricular pressure [LVP]) and afterload (aortic pressure [AoP]) when implanted in the circulatory system. Typical blood pressures are 120/80 mm Hg (systolic/diastolic), and flows are 5.5 L/min for healthy adults.3 In this configuration, the transaortic pressure gradient (AoP–LVP) can have an impact on the output of the device.4 The transaortic pressure gradient is greatest during end systole and early diastole, where high arterial and decreasing ventricular pressures exist, and approaches zero during systole when the aortic valve is open. Thus, the application of typical pump design parameters for ideal performance over the range of physiological pressures is not viable.5
Many reports have been published on the performance characteristics of continuous-flow VADs.6–10 Reports available in the published literature use a closed-loop hydraulic circuit to characterize device performance (Figure 1A), where pressures may be measured near the inlet and outlet of the pump, outflow is measured, and outflow pressure may be varied by a valve or other similar means. However, due to the physical, hydrodynamic limitations of the closed-loop systems that are used for device characterization, only a limited range of flow rate (Q) and pressure differentials (ΔP) are reported.11 The closed-loop hydraulic system is an acceptable tool used to collect a limited amount of data; however, because the outflow is directly connected to the inflow, ΔP down to a certain minimal threshold may be achieved and nothing lower. As such, current devices using this system are not actually tested over the full range of physiologically relevant pressure-flow conditions.
The study of flow characteristics of rotodynamic blood pumps can yield a wealth of information. Yet, few reports test and analyze multiple devices under the same conditions (system, resistance, temperature, viscosity, etc.).12 Few reports compare performance characteristics and design constants of both axial- and centrifugal-flow VADs with one another.9,10 Functionality of axial- and centrifugal-flow devices can be nondimensionally compared with one another through the pump affinity laws.1 Dimensional analysis of device performance yields details on specific speed and general performance, which further show the hydraulic losses and efficiency of each device.
The comprehensive work of Smith et al.9 has supplied blood pump developers with a database of information for comparison and analyses of VADs. Although extremely valuable, the data were acquired under a variety of conditions in closed-loop systems. In our study, pressure-flow characteristics for two axial- and two centrifugal-flow VADs are measured over a wide range of uniform physiologically relevant conditions, by means of a novel, open-loop flow system.
Materials and Methods
A novel mock circulatory loop (Figure 1B) was designed to measure pump preload, afterload, and output flow rate under different operating conditions. The loop consisted of an upper reservoir and weir filled with a blood-analog fluid (~40% glycerin in water; Hi-Valley Chemical, Centerville, UT). The adjustable weir was used to maintain a steady inflow pressure to the VAD, which was connected to both upper and lower reservoirs by Tygon tubing (Saint-Gobain, Courbevoie, France). A manual gate valve was placed in series with the VAD to adjust the resistance (afterload). Four continuous-flow rotary blood pumps were tested, two axial flow and two centrifugal flow. Selected loop specifications are listed in Table 1.
Pump preload, or inflow pressure (P i), and pump afterload, or outflow pressure (P o) were measured with fluid-filled transducers (Edwards LifeSciences, Irvine, CA) and a pressure meter (Living Systems Instrumentation, St. Albans, VT). The pump flow rate (Q) was measured with an ultrasonic flow meter and flow probe (Transonic, Ithaca, NY). Acquisition of flow meter and pressure meter data signals was performed at 40 Hz with a custom system (National Instruments, Austin, TX).
The four devices analyzed have been or are part of clinical trials, and will be referred to hereafter as axial 1 (A1), axial 2 (A2), centrifugal 1 (C1), and centrifugal 2 (C2). A1 was operated between 7,000 and 13,000 rpm at 200 rpm increments. A2 was operated between 8,000 and 12,000 rpm in 1000 rpm increments. C1 was operated between 800 and 3,000 rpm, and C2 was operated between 1,800 and 3,000 rpm, both at 200 rpm increments. The resistance was varied from minimal to maximal with the manual gate valve at each pump speed. Flow rate was allowed to stabilize in 0.25 L/min increments. Pressure differential across the pump (ΔP = P o− P i) was recorded manually in increments of 1 L/min to ensure the integrity of the data-acquisition system. Each test was repeated three times, and the results were averaged; the mean values are reported.
Input power was measured by a power analyzer (Valhalla Scientific, Poway, CA). For data analysis and plotting, MATLAB (v6.5; MathWorks, Natick, MA) and a spreadsheet program (Excel 2007, Microsoft, Redmond, WA) were used. The relationship between pump flow rate and differential pressure was extracted from the original 40 Hz files and tabulated in another file at 0.25 L/min increments for all applicable speeds.
Dimensionless quantities for pump flow or the so-called pump affinity laws have been well established for fluid dynamic analysis and comparison of pumps.1 The analysis here includes nondimensional performance parameters such as specific speed (N), head coefficient (ψ), flow coefficient (φ), pump Reynolds number (R e), and hydraulic efficiency (ηh). Specific speed is calculated using Equation 1, where Ω is the rotational speed of the impeller [rad/s], Q is the flow rate [m3/s], H is the head [Pa], and g is the acceleration due to gravity [m/s2]. Using consistent metric units will yield a dimensionless N.
Performance curves for any given impeller speed are unified into a single curve via the nondimensionalization of pressure (or head) and flow rate. Equations 2 and 3 are used to gauge characteristic coefficients for head (ψ) and flow (φ), where R is the radius of impeller [m], and A is the area of inlet or outlet [m2]. Table 2 shows the radius of each impeller and the inlet area for each device in this study. Pump Reynolds number is defined by Equation 4. Hydraulic efficiency is the ratio of power imparted to the fluid to the power input to the impeller13 and can be calculated with Equation 5,
where ρ is the fluid density, µ is the dynamic viscosity, and T is the torque applied by the impeller to the fluid. Torque is approximated by T = IΩ2, where I is the impeller mass moment of inertia. The format of Equation 5 is relevant because pressures were measured at the same height, and inlet and outlet diameters are the same for a single device.
Another point of interest for pump designers is the pump resistance (R p), which is commonly defined by the slope of the performance curve. Equation 6 characterizes the pump resistance function in nondimensional terms. Finally (Equation 7), pump sensitivity (S p) is hereby described as the inverse of pump resistance.
Using our open-loop configuration, pressure-flow performance curves were generated for each LVAD (Figure 2). ΔP values down to zero were obtained for all devices. The range of data for ΔP = 0 is crucial because the physiological system (AoP – LVP) can reach this region during systole.4 Q continues to increase as ΔP decreases, for all values that were measured here. The performance curves for axial- and centrifugal-flow pumps are relatively typical in that the pressure for centrifugal-flow pumps is reasonably flat and the pressure gradually decreases as flow increases, and the curves for axial flow are much steeper and comparatively linear.2 With the pressure-flow data taken on the continuous-flow mock loop, shown here, theoretical pump design parameters are analyzed and compared.
The Reynolds number, a dimensionless ratio of inertial to viscous forces, has been defined by Equation 4, and although similar to the form for uniform flow within a pipe, does not have the same connotation associated with laminar or turbulent flows. Pump Reynolds numbers are dependent on pump geometry, and thus are related to hydraulic efficiency.14 Evaluation of Reynolds number under typical operational ranges is significant because it establishes a metric for the flow regime and can be used to assess drag at a device–fluid interface. Table 2 contains pump Reynolds numbers over which each device was operated. Furthermore, hydraulic efficiencies (Equation 5) for each device for the various operational R e are plotted against flow coefficient in Figure 3. Of the four, C2 achieves the highest ηh over the broadest range of φ, and A2 reaches the lowest peak ηh this time over the smallest range of φ.
Performance curves for any given impeller speed are unified into a single curve via the dimensional analysis for head and flow coefficients. The nondimensional performance curves for each device are shown in Figure 4A. The A1 and C1 devices show corresponding head versus flow properties, especially for the 0.5<φ<1.5 regime. Shut off ψ values are 0.45, 0.29, 0.37, and 0.57 for A1, A2, C1, and C2, respectively. Similarly, maximum φ values, where ψ = 0, are 0.22, 0.13, 0.20, and 0.50 for A1, A2, C1, and C2, respectively.
For a particular design, the maximum hydraulic efficiency, or best efficiency point (BEP), occurs at the same N, ψ, and φ, regardless of Reynolds number or impeller speed. The values of the nondimensional parameters for each device at BEP are also presented in Table 2. ψ and φ points at BEP are plotted graphically along with nondimensional performance curves in Figure 4A, whereas Figure 4B displays the pressure-flow regimes represented by the specific speeds at BEP for each pump. Specific speed for a pump impeller is used to show pump characteristics over a range of pressure and flow values. During design, specific speed is implemented to define physical properties and flow types for pumps. It is most intriguing to note that all four devices experience BEP at nearly the same point where the ψ/φ ratio is ~1.7. Although the ψ/φ ratio is similar for all four devices at BEP, the optimal operating flow regime for the A2 device is markedly different than that observed for the other three pumps.
Continual analysis of the dimensionless values from the pressure-flow performance curves can yield further insight to a pump’s functionality. Pump resistance is usually a positive value for design flow conditions, but can be negative at low flow rates.2 An additional quantity, pump sensitivity, can be related from ψ and φ, or R p. High sensitivity values indicate that a pump will have a large change in output for a small change in pressure (Equations 6 and 7).
Pump sensitivity and pump resistance are important quantities that provide an understanding of how a device will behave under fluctuating operating conditions. Quantification of the details may produce a metric related to hemo- and/or biocompatibility. Figure 5 presents R p and S p as a function of φ and as a function of ψ for each of the evaluated devices. Although the resistance and sensitivity functions for each pump vary, a general observation can be made that the continuous-flow pumps show increasing resistance with increasing flow and decreasing head, and conversely, increasing sensitivity with increasing head and decreasing flow. Minimum resistance and maximum sensitivity for both A2 and C1 occur where φ = 0, and correspondingly, maximum resistance and minimum sensitivity for both occur where ψ = 0. The other two devices exhibit similar behavior in general; however, upon closer inspection local minima and maxima can be found on the dimensionless functions of resistance and sensitivity. Minimum resistance and maximum sensitivity occur at (ψ, φ) = (0.28, 0.11) and (0.56, 0.08) for A1 and C2, respectively, whereas the maximum resistance and minimum sensitivity are found at (0.04, 0.21) and (0.10, 0.38), respectively.
Herein we discuss the effects and implications of our open-loop mock flow system. We analyze and compare theoretical pump design parameters using the pressure-flow data. We explore similarities between axial- and centrifugal-flow device hydraulic performance as well as pump resistance and pump sensitivity.
As displayed in Figure 2, our open-loop mock flow system effectively achieves extensive pressure-flow regimes across both axial- and centrifugal-flow implantable blood pumps, demonstrating the effectiveness and benefit of using a slightly more complex system for hydraulic analysis. The open-loop flow system is capable of achieving ΔP values that are scientifically relevant for a device that will be placed in parallel with the physiologic system. We recommend future analyses of such devices to be done under conditions that resemble our open-loop flow system.
Nondimensionalization of flow variables, by removing units that involve physical measures, can simplify and scale the hydrodynamic system. In addition, further information regarding the performance properties of a system can be revealed. The dimensionless values outlined previously are common practice in fluid flow analyses. For example, the nondimensionalization of pressure-flow performance curves taken over several rotational speeds for a given rotodynamic pump will yield a single performance curve. From the dimensionless performance curve, general observations can be made regarding hydraulic losses to which the device is subject.
Several conditions can contribute to pump loss, including hydraulic factors such as skin friction, turbulence, separation, cavitation and flow-path geometry, and mechanical factors such as bearings, disc friction, gaps, and more.14 The idealized pump will exhibit a straight line for the ψ–φ curve,1 because ψ and φ generally demonstrate an inversely proportional relationship. However, in reality all pumps are subject to losses, and thus will be somewhere below the ideal ψ–φ line. Consequently, the further a dimensionless performance curve lays below the ideal line, the stronger the implication that the pump has greater hydraulic losses.
The hydraulic efficiency is related to the ability of a pump to conduct fluid with minimal loss. Understanding of hydraulic energy losses, or efficiency, is key to evaluating the global design of the fluid flow path. Hydraulic efficiency is not to be confused with overall system efficiency. For example, VAD systems require power supplies and controllers. Each system controller is designed separately and, as such, has a unique way of operating the pump. The efficiencies of the motors and controllers contribute to the overall system efficiency, but are separate from the hydraulic efficiency.
The overall anatomic footprint of the centrifugal-flow pumps used here are not noticeably greater than those designed for axial flow, although anatomic placement may vary. Figure 4A shows the centrifugal devices that have greater pressure and flow capacity. The centrifugal and axial curves displayed in this figure demonstrate that in general, the centrifugal devices have greater (ψ,φ) values than that of the axial, a fact that correlates with the database presented by Smith et al.9 The A1 and C1 devices yield similar dimensionless flow characteristics and hydraulic efficiency, with the A2 and C2 pumps below and above, respectively, the region where A1 and C1 reside. Typical turbomachinery properties are illustrated by a comparison of Figures 3 and 4, where hydraulic efficiencies for each pump are roughly correlated with the location of dimensionless performance curves.1,2
The internal flow-path volumes of both axial-flow pumps are relatively similar. The flow-path volumes of C1 and C2 devices are two and three times greater than the axial pumps, respectively. Hydraulic efficiency is said to be related to pump size via the operating pump Reynolds number.14 Notably, in our results, each device exhibits a ηh dependence on R e that is unique to each.
A similar ψ/φ ratio for all four devices at BEP is of great significance and almost compels a conclusion that all pumps were independently designed to the same specification. However, upon examination of the operational range of the hydraulically efficient specific speeds, or design-specific speeds, it is noticeable that one of the axial-flow devices (A2) operates most efficiently in a pressure-flow regime considerably apart from the other three devices. This shows that at least one of the devices was designed for a slightly different functional environment. However, it is worthy to note that hydraulic efficiency is not, nor should it be, the primary concern when designing a continuous-flow blood pump. The primary objective for these devices is to move blood without causing hemolysis or thrombosis to the working fluid, so compromises in the fluid flow path are to be expected when dealing with a long-term life support device.
Generally, the continuous-flow pumps show increased resistance with high φ and low ψ, and conversely increased sensitivity with high ψ and low φ. This may be expected because, as previously stated, centrifugal pumps are typically designed for use in low-flow, high-pressure applications. Of particular interest is that C1 and C2 reveal much lower resistance, possibly due to the centrifugal flow path itself, than that within the realm of capability for A1 and A2.
The resulting analyses presented here position dimensionless values and equations as the center of attention. Particular interest has been given to hydraulic efficiency of the devices. Head and flow coefficients, pump resistance, and pump sensitivity have all been explored. Although these are routine concepts within the development of rotodynamic pumps, we show that added data can be collected and calculated by using an open-loop flow system. However, our results should be interpreted with several caveats.
First, the flow characteristics and physiological similarities for a mechanical pump, axial or centrifugal, when connected in parallel with a pulsating pump, such as the device configuration when implanted, is not evaluated here. Evaluation of pump performance under pulsating preload and afterload conditions could be highly beneficial when comparing devices with one another and with the native heart and is recommended for future work. Second, this study examines the flow characteristics of different VADs under continuous-flow conditions. Standard design practices for fluid-pumping systems have been set up for constant-flow relationships and do not consider pulsatile conditions.1,2 The difference in BEP flow regimes among devices can be explained by the need to operate the device under a wide range of preloads and afterloads because the intended use in parallel with a human heart is not only for an individual human system but also across a diverse array of the potential human population.
Third, fluid viscosity is directly related to fluid temperature. Although fluid viscosity and temperature were maintained in both upper and lower reservoirs, it was not possible to do so at all points in the circulation loop instantaneously. Thus, it is possible that the temperature and viscosity varied slightly at local points during device operation. Fourth, only four devices are evaluated here, which may not be sufficient to develop conclusions between axial- and centrifugal-flow pumps, generally. Finally, hemocompatibility assessment is not carried out here. Damage to cellular structures within the transported fluid and the tradeoffs that it may impart to hydraulic efficiency are other concerns that VAD design should consider. Only global performance of each device is assessed without consideration to local phenomenon such as backflow, turbulence, flow-path design, surge, and auto-oscillation.
The open-loop flow system was successfully able to generate pump pressure differential at levels equal to or less than zero, thus providing more data to formulate clinically relevant assessment of pump function. On the basis of the pumps investigated here, the centrifugal-flow devices exhibit greater efficiency than the axial, which agrees with the work of Smith et al.9 Further, the centrifugal-flow VADs demonstrate lower resistance, which implies greater sensitivity, than the axial-flow designs for low flow rates. Hemocompatibility, durability, and other factors must be considered when drawing conclusions regarding which device is most optimal in the human cardiovascular system. It is hoped that blood pump developers, clinicians, and others will use open-loop systems in future analyses for an increased understanding of pump performance under a wide range of conditions and also that future comparisons and data collection will be carried out under uniform operating conditions.