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Adult Circulatory Support

Numerical and In Vitro Experimental Investigation of the Hemolytic Performance at the Off-Design Point of an Axial Ventricular Assist Pump

Liu, Guang-Mao*; Jin, Dong-Hai; Jiang, Xi-Hang; Zhou, Jian-Ye*; Zhang, Yan*; Chen, Hai-Bo*; Hu, Sheng-Shou*; Gui, Xing-Min

Author Information
doi: 10.1097/MAT.0000000000000429
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Abstract

Left ventricular assist pumps have been used successfully to treat heart failure patients as destination therapy. Such devices include the HeartMate II, Micromed DeBakey VAD, Heartware HVAD, Jarvik 2000, etc.1–5 Continuous-flow ventricular assist pumps with greater durability and simpler design have been proven to be safe and effective with patients.6 However, blood damage, such as hemolysis and thrombosis, remains the most significant challenge when designing or improving a ventricular assist pump.7 Previous studies indicated that the hemolysis in ventricular assist pumps was primarily caused by the strong sheer stress, the blood exposure time,8,9 and the irregular flow, such as vortexes.10 Then, models concerning the scaled sheer stress and the hemolysis index were built to predict the hemolytic properties of the pumps using numerical simulation.11–13 Numerical simulation has been widely used in ventricular assist pump design and in the evaluation of hydraulic performance, shear stress distribution, and the hemolysis index within an assist pump.

In recent years, our study group has developed an axial ventricular assist pump meeting the hydraulic and hemolytic criteria, and this pump is currently undergoing clinical trials.14,15 This axial ventricular assist pump was developed at the design point flow rate of 5 L/min and 100 mm Hg pressure increase according to the clinical use at the Fuwai Hospital of the Chinese Academy of Medical Sciences. Oriental patients sometimes require a lower blood flow rate of 1 to 4 L/min, which means that the assist pump would work at off-design points. Therefore, it is necessary to evaluate the hydraulic and hemolytic performance of the axial ventricular assist pump at off-design points. The hemolytic characteristics at flow rates far from the design point were investigated in this study.

The purpose of the current study was to analyze the hemolytic properties both at the design point and at off-design points of the pump previously designed by our research group.16 A numerical simulation method was used to calculate the flow distribution of the pump. The shear stress, exposure time, and hemolysis index parameters were calculated as well. An in vitro hemolysis test was conducted both at the design point and at off-design points to verify the numerical results. The simulation and the in vitro test results indicate that the hemolysis performance is poor when the flow rate decreases. Specifically, at a flow rate of 1 L/min, the pump is not suitable for clinical use. The central objective was to ensure that the blood pump would work in a safe flow rate range and to develop guidelines for future blood pump design.

Materials and Methods

Geometry Model

The structure of the axial blood pump, which is referred to as FW-2 and is illustrated in Figure 1, includes three parts: three inlet guide vanes (IGV), four rotor blades, and six outlet guide vanes (OGV).16 The rotational speed of the pump is 8,000 rpm at the design point of 5 L/min and 100 mm Hg.

Figure 1.
Figure 1.:
Structure of the FW-2.

Computational Fluid Dynamics Simulation Model

A commercial computational fluid dynamics (CFD) package (CFX 14.0, ANSYS, Inc., Canonsburg, PA) was used to create the mesh. The Reynolds averaged Navier–Stokes equations were used to simulate the flow of the FW-2. A grid convergence study was completed to evaluate the influence of the number of grid elements on the accuracy of the CFD results and the computational convergence times. A grid with 49 blocks was used for the FW-2, as shown in Figure 2, and the entire mesh had approximately 220 million nodes without negative cells. Greater than 96% of the nodes’ skew angles ranged from 15 to 90°. The outlet region far from the stator blades was extended flatly to improve the computational convergence stability. The O grids generated at the zones near the blades and the more refined grids near walls were specified to obtain the properties of the boundary layers.

Figure 2.
Figure 2.:
Mesh used for the calculation.

The calculations were performed on a PC workstation with two Intel Xeon six core 2.0 GHz processors and 32 GB of RAM. Each calculation was run in parallel on six of the processors and took approximately 4 h to converge.

The speed of the rotational part in the FW-2 pump was specified to be 8,000 rpm. The flow was defined as an axial flow in the inlet region, and a static pressure of 10 mm Hg was defined. The rotor–stator interfaces were defined both in the interfaces of the IGV to the rotor and the rotor to the stator. In the outlet region, specific flow rates of 5 (design point), 4, 3, 2, and 1 L/min were given in the simulation. The blood behavior could be treated as Newtonian in most regions of the blood pump, where the shear rate was greater than 100/s17. The incompressible blood fluid parameters are listed as follows: specific heat capacity, Cp, of 3,640 J/kg·K; density, ρ, of 1,055 kg/m3; and dynamic viscosity of 3.5 × 10−3 Pa·s.

The Reynolds number is defined as follows:

where the characteristic velocity U (m/s) is the tangential speed at the rotor blade tip, the characteristic length L (m) is the rotor blade tip diameter, and μ (m2/s) is the kinematic viscosity. The Reynolds number was then calculated to be approximately 1 × 104, which means that turbulent flow dominated the entire flow status. In this study, the k (turbulent kinetic energy) − ε (viscous dissipation rate) turbulence model was selected to solve the additional Reynolds stress terms from the time averaging procedure for the Navier–Stokes equations. This turbulence model has been wildly used in simulations of ventricular assist pumps; however, it also has limitations, such as inferior accuracy for low Reynolds numbers or in capturing the fluid characteristics during the flow separation along boundaries.1 Because of the low Reynolds number character of the FW-2 flow (Re ≈ 1 × 104), a logarithmic wall function was selected to characterize and resolve the near-wall flow conditions.

Hemolysis

The stress damage and residence time of the blood determine the hemolytic properties of the ventricular assist pump. Model by Heuser and Opitz13 has been widely used for the computational preliminary estimation of hemolysis in a blood pump and has been adopted in many other studies; therefore, the hemolysis estimated model was defined using the following equation:

where Hb is the total hemoglobin concentration, ΔHb is the released hemoglobin concentration, t (s) is the exposure time, and τ (Pa) is the scalar shear stress.

In 1995, Bludszuweit11 proposed a computational method for 1D scalar sheer stress (SSS). In this model, the six tensors of stress are integrated into one stress with all characteristics of those tensors, and this is conveniently calculated.11 The 1D SSS (Pa) is defined using the following equation:

The calculation should consider both the viscous stress and the Reynolds stress,12 so the final SSS is the sum of these two types of stresses.

Hemolysis is related to not only the SSS but also to the exposure time. In this study, method by Apel et al.17 was selected to calculate the exposure time. The exposure time is defined using the following equations:

The final hemolysis index with model by Heuser and Opitz13 is defined in the following equation:

where P is the number of path lines, τ is the SSS, and is the exposure time step.12 The computational method of hemolysis proposed above certainly would be influenced by the selections of the path lines and time steps.

In Vitro Hemolysis Test

An in vitro hemolysis test was performed in a mock circulatory loop consisting of a reservoir bag, PVC tubing, a pressure transducer, a flow transducer, and the blood pump. The mock loop was filled with 500 ml of fresh sodium citrate anticoagulant (1:9) and filtered citrated ovine blood collected from a local slaughterhouse. Blood hematocrit for each test point was adjusted to 30% before filling the loop. The loop was operated for 4 h at each of five flow rates sequentially (1, 2, 3, 4, and 5 L/min) against a 100 mm Hg pressure increase. The pressure, flow rate, and temperature were recorded throughout each experiment. Blood samples (2 ml) were obtained when each test began to establish the baseline plasma-free hemoglobin (PfHb). Subsequent samples were taken every half hour for each test to measure the PfHb. The PfHb values were used to calculate the normalized index of hemolysis (NIH) according to the following equation:

where △PfHb is the difference in the measurement PfHb between the current time point and the baseline for that flow rate (g/L), Hct is the hematocrit value of the blood in %, V is the loop volume (L), Q is the flow rate (L/min), and T is the test time (min) at that flow rate.

Results

Fluid Field

The simulated fluid fields at the design point (5 L/min) are presented in Figure 3. The blood fluid flows smoothly along the blades without flow separation in the pump passages. No return or vortex flows were found in the pump passages.

Figure 3.
Figure 3.:
Velocity vector at 5 L/min.

Figure 4 presents the simulated fluid field at the off-design points of the blood pump. Near the blade root region, the return and vortex flows existed both in the rotor and stator regions when the flow rate was less than 4 L/min. The flow separation first occurred at the suction surface of the trailing edge near the rotor blade root region at the 4 L/min flow rate (Figure 4A) and then expanded to the entire blade passages (Figure 4B). In the stator region, the area of flow separation increased when the flow rate decreased from 4 to 1 L/min. Near the middle region of the stator blades, the flow separation increased for the 3 (Figure 4C) and 1 L/min flow rate, and the area of this flow separation increased (Figure 4D). Near the blade tip region, there was no obvious flow separation in the rotor region, whereas backflow occurred at the suction surface of the trailing edge and extended to the stator region (Figure 4E). When the flow rate decreased to 1 L/min, the backflow expanded (Figure 4F).

Figure 4.
Figure 4.:
Velocity vectors at different flow rates. A: Near the blade root region at 4 L/min; B: near the blade root region at 1 L/min; C: near the blade middle region at 3 L/min; D: near the blade middle region at 1 L/min; E: near the blade tip region at 3 L/min; and F: near the blade tip region at 1 L/min.

The velocity distribution near the rotor blade root region was uneven at the off-design point of 1 L/min. The blood velocity near the inlet of the rotor is approximately 5.7 m/s and decreased rapidly to approximately 1 m/s at the 20% chord length of the rotor blade. At the outlet of the passages, the blood accelerated to 3 m/s to flow out. Near the middle region of the rotor blades, the velocity changed from 5 m/s to approximately 1 m/s, but this only occurred over approximately 5% of the chord length of the rotor at the 1 L/min off-design point. The quicker changes in the velocity will generate a greater velocity gradient and result in greater sheer stress.

Sheer Stress

Paul et al.18 proposed the blood damage standard as follows: whether the SSS is less than 425 Pa and the exposure time is less than 620 ms, the blood damage is small.

Figure 5 illustrates the SSS of FW-2 at 5, 3, and 1 L/min. At the design point of 5 L/min, the SSS in the entire meridional plane is less than 425 Pa. At the 1 L/min off-design point, the SSS at the middle of the leading edge of both the rotor and stator is greater than 425 Pa.

Figure 5.
Figure 5.:
The SSS at different flow rates. A: 5 L/min; B: 3 L/min; and C: 1 L/min. SSS, scalar sheer stress.

Exposure Time

Figures 6 and 7 demonstrate the streamline and the circumferentially averaged outlet flow angle (angle between the outlet velocity and the outlet axial velocity) of FW-2 at different flow rates, respectively. At the design point, the flow direction at the outlet is the same as the axial direction, whereas the exposure time is shorter. When the flow rate decreases, the outlet flow angle increases, and a whirl flow occurs at the outlet of the pump. The tangential outlet velocity has a greater influence on the outlet flow than the axial outlet velocity when the outlet flow angle is greater than 45°, and this results in a stronger whirl flow and a longer exposure time.

Figure 6.
Figure 6.:
Streamlines at different flow rates. A: 5 L/min; B: 3 L/min; and C: 1 L/min.
Figure 7.
Figure 7.:
Circumferentially averaged outlet flow angle at different flow rates. A: 5 L/min; B: 3 L/min; and C: 1 L/min.

This study adopted 290, 350, 400, and 500 path lines, respectively, to calculate the averaged exposure time of each sample at each calculated flow rate. The final averaged exposure time was the arithmetic average of those samples’ exposure times (Figure 8). Figure 8 shows that the exposure time increased slowly from the flow rate of 5 down to 2 L/min but increased rapidly from the flow rate of 2 down to 1 L/min. The averaged exposure time at the 1 L/min off-design point was 4.6 times the averaged exposure time at the 5 L/min design point.

Figure 8.
Figure 8.:
Averaged exposure time at different flow rates.

Hemolysis Index

The calculation method for the hemolysis index of FW-2 is the same as the exposure time, and the final result is the arithmetic averaged values. Figure 9 shows that the averaged hemolysis index was less than 1% between 5 and 3 L/min but greater than 1% between 3 and 1 L/min. The hemolysis index at the 1 L/min off-design point increased to 3.6 times greater than at the design point. Figure 9 demonstrates that the hemolysis index decreases from the flow rate of 5 to 4 L/min but increases from the flow rate of 4 to 1 L/min.

Figure 9.
Figure 9.:
Hemolysis index at different flow rates.

Normalized Index of Hemolysis

Figure 10 shows the NIH measured using an in vitro hemolysis test. The NIH was less than 0.02 g/100 L from 5 to 4 L/min and less than 0.05 g/100 L from 3 to 2 L/min. The NIH at the 1 L/min off-design point was 0.162 g/100 L, which is almost 10 times greater than at the design point.

Figure 10.
Figure 10.:
NIH at different flow rates. NIH, normalized index of hemolysis.

Discussion

The fluid field result shows that the incidence angle at the leading edge of the blade increased when the flow rate decreased from the design point. The increase in the incidence angle leads to an increase in the flow turning angle and a decrease in the relative velocity, which would result in a stronger adverse pressure gradient. The flow separates on the suction surface of the trailing edge of the blades first and then expands to the entire blade passages when the adverse pressure gradient expands. When the flow rate decreases, flow separation appears in the rotor and stator region. Flow separation in the rotor region is mainly at the suction surface of the trailing edge of the rotor blade. In the stator region, flow separation occurs over the entire suction surface of the stator blade. The adverse pressure gradient and flow separation appearing in these regions would aggravate the hemolysis of the blood pump.

The magnitude of the SSS is related to the magnitude of the velocity gradient. The outflow angle of the blood pump increased and resulted in a rotational flow in the outlet and a longer exposure time when the flow rate decreased. With a decrease in the flow rate, the incidence angle of the rotor increased and caused flow separation at the trailing edge of the rotor blades. Accordingly, a reduced flow rate results in a greater SSS. The scalar shear stress in the rotor region at the 1 L/min off-design point was 70% greater than at the design point because of the large incidence angle and flow separation.

For a ventricular assist pump, the calculated hemolysis is related to the comprehensive effect of the SSS and the exposure time. The main reasons for the increase in the hemolysis index of FW-2 at the lower flow rate are the greater averaged SSS in the rotor region and the longer exposure time. The hemolysis index is lower at 4L/min than at 5L/min, perhaps because the area of SSS greater than 425 Pa at 4 L/min flow rate was smaller than at 5 L/min. However, when changing from a flow rate of 4 to 2 L/min, a greater averaged SSS in the rotor region and a longer exposure time increased the hemolysis index, although the area of the SSS that was greater than 425 Pa was smaller. When the flow rate decreased from 2 L/min, the SSS in the rotor region increased rapidly, and the exposure time was longer. Consequently, the hemolysis index increased quickly. When the flow rate decreased to 1 L/min, the hemolysis performance became especially adverse.

The in vitro hemolysis results verified the calculated hemolysis results. The NIH increased when the flow rate decreased gradually from 5 to 2 L/min. The NIH increased rapidly to 0.162 g/100 L when the flow rate decreased from 2 to 1 L/min. The FW-2 should not be used at a flow rate of 1 L/min in the clinic because adverse hemolysis would occur.

The work to date does have limitations. The model by Heuser and Opitz13, which is widely used for the computational estimation of hemolysis in blood pumps, could not fully conform to the test results. The calculation could not simulate all of the flow details in the blood pump. The in vitro hemolysis test and animal experiments helped considerably.

When a blood pump is designed or improved, the design point is the most important and most commonly used working condition. The results have illustrated adverse hemolysis when the blood pump worked far away from the design point. Therefore, a more proper design point that should be selected may be 3 L/min because both 1 and 5 L/min are close to 3 L/min.

Conclusions

The adverse hemolytic performance at the 1 L/min off-design point was simulated numerically and tested in vitro in this study. The FW-2 blood pump should not be used at a flow rate of 1 L/min in the clinic. This study verified the severe hemolysis observed in animal experiments when the pump worked far away from the design point. In general, the study of FW-2 is beneficial for the future design of ventricular assist pumps in our research group. Further studies will be performed to optimize the structure of the ventricular assist pump with the goal of improving the biocompatibility of the pump by selecting 3 L/min as the design point for the flow rate. This research also demonstrated that perhaps using a flow rate of 3 L/min as the design point for ventricular assist pumps used for oriental patients is more suitable.

References

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Keywords:

ventricular assist pump; hemolysis index; normalized index of hemolysis; numerical simulation

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