Application of CFX to Implantable Rotary Blood Pumps Suspended by Magnetic Bearings

Application of CFX to Implantable Rotary Blood Pumps Suspended by Magnetic Bearings Xinwei Song University of Virginia Houston G. Wood University of Virginia Abstract The University of Virginia has been utilizing CFX series software to design and analyze implantable rotary blood pumps for several years. Besides the basic computational fluid dynamics (CFD) calculations and simulations of fluid field for blood pumps, several advanced CFD models were used which were relevant to the analysis of blood pumps or magnetic bearings. A Lagrangian Particle Tracking study allowed quantitative predictions of the hemolysis (breakup of red blood cells) due to the relative high shear stress. Fluid forces and moments were calculated for the magnetic bearing design. A heat transfer study was performed to investigate the temperature rises in the blood through the pumps and surrounding tissues. A transient simulation was used to study the effects of pulsatile blood flow due to the heartbeat. The microsized geometry of the pump made the choice of turbulence models significant for the accuracy of calculation. CFD results for different turbulence models were compared with Particle Image Velocimetry (PIV) experimental data. The comparison showed that the k-ω model gave better predictions of the shear level within the near wall regions than the k-ε model. Introduction In the United States, approximately 40,000 new cardiac failure patients each year await a healthy donor heart for transplantation. Unfortunately, only approximately 2300 donor hearts become available each year. Recent statistics indicate that only 1 in 24 cardiac patients who desperately need a transplant actually receive a donor heart. Because of this shortage of healthy donor hearts, cardiac failure patients must rely on alternative means of circulatory support, such as using a mechanical artificial heart pump or left ventricular assist device (LVAD). The LVAD is designed to complement the heart s natural pumping action (1,2). Computational Fluid Dynamics (CFD) is an important design tool that is being used by many artificial heart researchers to design the blood flow paths through pumps (3,4). For some time, the Virginia Artificial Heart Institute (VAHI) has been developing a centrifugal pump for use as a continuous LVAD. This centrifugal pump has been named HeartQuest TM. HeartQuest TM has a magnetically levitated impeller design in order to increase its lifetime from 3-5 years to 15 years or more. From fluid dynamics point of view, HeartQuest TM includes 4 parts: the inlet elbow, the impeller, the back clearance, and the exit volute. The inlet elbow is a bent pipe specially designed to link to the impeller eye and feed the impeller with a wash of vertical and spatially uniform flow. The impeller has 5 blades and is fed by the inlet elbow and pumps the blood into the exit volute. The exit volute is the pump component that collects blood at the impeller outer radius and directs flow toward the pump discharge. The blood leaks back to the center of pump through a clearance gap between the impeller and lower housing. The thickness of the clearance gap is designed to be small enough to allow only a small fraction of blood to flow back, but large enough to prevent high shears and blood clots from occurring. The purpose of this paper is to predict the flow behavior in HeartQuest TM. Several advanced CFD features, including conjugate heat transfer, transient simulation, Lagrangian particle tracking, fluid force and moment calculation, and turbulence models, are executed for the special concerns of the blood pump. CFD Applications for Implantable Heart Pump The CFD model of HeartQuest TM is shown in Figure 1. The impeller has 5 open blades and is fed by the inlet elbow and pumps the fluid into the exit volute. The inlet elbow is a bent pipe specially designed to

link to the impeller eye and feed the impeller with a wash of vertical and spatially uniform flow. The exit volute is the pump component that collects fluid at the impeller outer radius and directs flow toward the pump discharge. A clearance is created between the impeller and lower housing by the magnetic levitation design. This clearance behaves as a reverse flow channel, allowing the fluid to leak back toward the center of pump due to the pressure difference. The thickness of the back clearance gap is designed to be small enough to allow only a small fraction of fluid to flow back, but large enough to prevent high hemolyzing shears and blood clots from occurring, and to keep the impeller from touching the housing during fluid disturbances. Figure 1. CFD Model and Grid Configuration of HeartQuest TM The 3D geometry of the pump is used to build the volume mesh, which represents the actual physical space that is simulated. Hexahedral mesh elements were used in this model. The skew angle of the mesh elements were kept above 20 degrees and the aspect ratio under 150. The mesh element size and shape were adapted to the local geometric scale and expected flow features. The mesh therefore included more elements in areas where vortices or complex flow features were expected to occur. The mesh element sizes at the boundary layer were also important because of their effect on the performance of turbulence models; turbulence models require certain y+ values dependent on the boundary layer thickness. The y+ criteria were met for the turbulence model used in this simulation, resulting in average y+ values on the shroud and hub of 1.038 and 0.639 respectively. The full pump computational model mesh has about 350,000 elements. The mesh is composed of 29 blocks, which resulted from the different methods and software used to build it. A grid study of a single blade passage showed that a 40,000 element model was sufficient to capture the flow characteristics in the impeller region. Increasing the number of elements in the blade passage to 50,000 produced only minor changes in the flow solution and increased computation times by 20 percent. The final volume mesh for the five-blade impeller contained 200,000 elements. The numbers of elements in the back clearance gap, inlet elbow and exit volute were optimized by the same method. A final mesh size of 350,000 elements for the full computational model was deemed sufficient to provide an accurate simulation of the pump. CFD boundary conditions were specified to define the pump inlet and outlet as well as impeller rotation. The pump inlet was specified as a constant flow rate of 6L/min; the outlet was specified as a constant pressure outlet of 100 mm Hg. The rotational speed of the impeller was 2100 RPM. These boundary conditions were selected as the best representation of common physiological conditions and have been verified in bench-scale testing.

The simulation was run at a timestep of 0.001 s and was treated as being converged when the solution residuals had fallen below 1 10-4. Transient simulations were run with a timestep of 0.005 s, 5 iterations per time step and a timestep residual of 0.005. A pressure rise is the main output of a blood pump, and acts to reduce the load on the patient s native heart. The pressure rise created by the pump is presented in Figure 2 (5). Such data can only be obtained with a complete pump model. Although the pressure rise generated by the impeller is accurately calculated with a simple CFD model of one blade passage, the pressure losses in the exit volute can only be modeled with a full pump model. The latter allows simulating and taking into account the complex interaction between the impeller and the exit volute that may result in an important pressure difference across the volute. The pressure rise is decreasing as the flow rate is increasing, or as the rotational speed is decreasing, which directly corresponds with pump theory. The relation between flow rate and pressure rise exhibits nonlinearity: the slopes become more negative with increased flow rate. For some operating ranges, the pump produced a negative net pressure rise, which was related to the rapid increase of pressure drop through the exit volute at high flow rate. When the pressure lost in the exit volute exceeded the pressure rise through the impeller, the pump produced a negative net pressure rise. This indicated that HeartQuest TM was not suitable for use in this range, and that the exit volute needed further design improvement for wider operation range. As a result of the impeller action, blood leaves the impeller at a higher pressure and higher velocity than it enters the impeller. The velocity is partly converted into pressure in the volute and discharge pipe, both of which are unidirectional channels with gradually increasing area, before blood leaves the pump. The advanced CFD models that were used will be covered in subsequent sections of this paper. Figure 2. Pump Pressure Rise vs. Volume Flow Rate Blood Damage Evaluation The medium that the heart pump works with is blood. Blood consists of a suspension of cells, primarily erythrocytes, or red blood cells, in a Newtonian medium, plasma. The volume percentage of erythrocytes to plasma is approximately 45%, while platelets comprise 1%. For this study, blood is modeled as an incompressible, continuous medium having Newtonian rheological properties, instead of a suspension of cells. Blood behaves as a Newtonian fluid for shear rates greater than 100s -1. Preliminary studies and their comparison with experimental data have shown that the assumption of Newtonian behavior holds within the range of shear rates found in this study. Therefore, a constant viscosity of 0.0035 Pa-s and density of 1050 Kg/m 3 were used for each CFD simulation.

The success of a heart pump is dependent on creating flow conditions that are extremely compatible with the working medium, blood. Therefore, it is essential to quantify the levels of blood trauma that occur in a working heart pump. Hemolysis, the breakdown or destruction of red blood cells, causes the contained protein hemoglobin (Hb) to be released into the surrounding medium. Continuous destruction of red cells reduces the blood s ability to transport oxygen. Experimental studies have revealed that both Reynolds turbulent and viscous shear stresses throughout the pump contribute to blood damage. Reynolds stresses occur as a result of momentum transfer due to the turbulent flow conditions. Viscous shear stresses, however, arise because of the intermolecular frictional forces within the fluid itself. In this study, these stresses are considered to describe the level of trauma experienced by the blood as it travels through the LVAD. An attempt to mathematically describe hemolysis induced the following relation between shear stress, exposure time and the extent of damage to erythrocytes as given by the power law: dhb α β / Hb = C τ T (1) Here, Hb is the hemoglobin content, dhb represents the damaged hemoglobin content, τ signifies the characteristic scalar stress, T is the stress exposure time, and C,α,β correspond to constants that can be obtained by regressing experimental data. Researchers obtain different values for the constants depending on experimental conditions. The values C=1.80e -6, α = 1. 991, and β = 0. 765 have been used in this study (6,7). An integral approach is used to cumulatively estimate the damage to red cells: outlet outlet 6 1.991 0.765 1.8 10 τ dt = 6 1.991 0.765 1.8 10 τ T (2) D = inlet inlet Where D symbolizes the blood damage index and is a measure of the possibility of erythrocytes being damaged. Inlet and outlet correspond to the entrance and exit faces of the blood pump in the computational model. A Lagrangian particle tracking technique was used to obtain the stress history of 388 representative particles along their streaklines in CFX-TASCflow. Figure 3 illustrates several representative streaklines, colored according to the exposure time. The Euler forward integration of the particle velocity was executed to determine the coordinates of particles. An integral computation made it possible to consider the damage history of each particle. Figure 3. Streaklines Colored by Exposure Time

Most, 322 of 388, blood particles took less than 0.19 seconds to travel completely through the pump. The mean residence time was 0.34 seconds with a maximum residence time of 5.3 seconds due to a possible vortex region. The mean value of the blood damage index was found to be 0.21% with a maximum value of approximately 2.04%. For 313 of 388 particles, the blood damage index remained less than 0.16%. This low blood damage index indicates that cells traveling along these streaklines are not likely to be ruptured. For the remaining 75 particles with damage index values ranging from 0.21% to 2.04%, there is a greater possibility of damage to the particles, especially at the higher end of the range. Fluid Force and Moment Calculations Knowledge of the forces and moments exerted on the impeller is essential in optimizing the magnetic suspension design. After the simulation was completed, the three vector components of the forces on the impeller were determined by summing the individual contributions at all element surfaces on the impeller s walls. Due to the axially symmetrical configuration of impeller, the radial forces were relatively small. Any variation resulted from the lack of symmetry of the inlet elbow and exit volute. The axial force of 3.8N is a critical parameter for magnetic suspension design. The direction of axial force is upward because the average pressure in the back clearance is larger than that in the blade passage. With a decrease in flow rate or an increase in rotational speed, both radial forces and axial force increased as expected. Figure 4 shows the results of axial fluid forces on the impeller. The radial moments, which generate rotation, can be determined in a similar manner. The radial moments exist because of the flow direction of the fluid through the inlet elbow. Larger flow rates caused the flushing forces and pressure differences along the exit volute to become larger. Therefore, the radial moments increased with larger flow rates. The radial moments were on the order of 10-3 N m. Figure 4. Axial Force on Impeller Heat Transfer Calculation The heat generated in motors results in a temperature rise in the pump materials, the blood through pump and the surrounding tissue. An investigation and evaluation of this kind of temperature rise was done in order to ensure there was no thermal damage to the blood. This is a kind of solid-fluid coupled problem: the boundary condition on the interfaces between solid and liquid were unknown and needed iterations during both temperature field calculations in the solid and fluid field calculations in the blood. The heat

source from the motor and the active bearings is 4.3 W. The boundary conditions were set as the normal human body temperature at the inlet and the surrounding tissue. The study revealed that 66% of the heat was removed by the blood flow, while the remaining 34% of the heat was transferred to the tissue. Due to the high specific heat of blood and tissue, the temperature rises within them were less than 0.1 C. Even in the motor, the temperature increase was less than 0.2 C. So, the thermal damage in HeartQuest TM was predicted to be insignificant. Turbulence Model Study Due to highly disturbed flow around the moving blades, flow in most regions inside the blood pump is turbulent. The choice of turbulence models is an important factor in the CFD simulation. However, determining the optimal turbulence model for miniature blood pumps can be difficult. The default turbulence model has to be reevaluated for the specific application of small size blood pumps. A second concern is the complicated geometry of blood pump and relatively low flows, which make wall effects more important. The different treatments of near-wall regions, their constraint for grid distribution, and their compatibility with turbulence models become a critical factor in ensuring the accuracy of CFD predictions. In CFX, the available turbulence models include k-ε model and k-ω model. Here k, ε, ω denote the turbulent kinetic energy, turbulent dissipation rate, turbulent frequency respectively. Both models utilize the eddy viscosity assumption to relate the Reynolds stress and turbulent terms to the mean flow variables. The near-wall treatment includes Log-law wall functions, k-ω combined low/high Re wall functions, and a two-layer turbulence model. Log-law wall functions employ a logarithmic function to bridge the viscous near-wall layer and eliminate the necessity of numerically resolving the large gradients in the thin near-wall region. The recommended Log-law wall function employed by k-ε model is scalable Log-law wall function, which artificially moves the virtual walls to the edge of the viscous sublayer in order to avoid the effects of fine grid inconsistencies. The two-layer turbulence model is another near-wall treatment developed for k-ε model. It implements a one-equation model to solve the near-wall region and uses the k- ε model for far-wall region. The two-layer model needs more computational resources, is less numerically stable, and is therefore impractical. The k-ω model is able to provide the analytical expression for ω in the viscous sublayer. This advantage is exploited to achieve an automatic, blended transition from the nearwall functions for coarse grids to the near wall formulation for fine grids. This blending is desirable for low Reynolds number flows because of the corresponding attenuation of the viscous sublayer. This feature makes k-ω model more suitable for low-re flows because most of the error arising from the thicker viscous sublayer is avoided. In order to compare the k-ε model and k-ω models, two grids were created. A fine grid system with the first near-wall grid point located y + <2, which satisfies the requirement of the k-ω model activated in both nearwall and far-wall regions, was generated for the k-ω model. A grid with the first near-wall grid point located y + =11, which is assumed to coincide the edge of viscous sublayer, was developed for the k-ε model. The process of determining the y + locations for the grids was iterative. A standard k-ε model with near wall function was run to obtain the best guess of the first near-wall grid location, characteristic velocity, and thickness of boundary layer for different regions. The centrifugal blood pump prototype is the HeartQuest TM VAD. The boundary layer thickness δ is estimated by Equation 3. 7 1 δ = 0.14LRe 6 / (3) Re L Re L is the Reynolds number in term of characteristic length, where L is the diameter of the impeller in this study. Equation 4 is employed to decide the first point location. + µ y / y = (4) τ ρ wall y is the distance of the first point to wall, τ wall is the wall shear stress, µ is the viscosity and ρ is the density of blood. τ wall was obtained from the preliminary results.

Figure 5 shows the absolute speeds at axially mid-height span, near hub layer, and near shroud layer in the HeartQuest TM VAD. The results according to k-ε model with scalable near-wall function, the Particle Image Velocimetry (PIV) results, and k-ω model have been plotted from left to right in one row. The CFD boundary conditions are same as the testing condition: the inlet is specified as a constant flow rate of 6L/min, the outlet as a constant pressure of 100 mm Hg, and the rotational speed is 2100 RPM. The comparison shows that better agreement has been obtained with the k-ω model, especially around the nearwall region (8). Figure 5. Comparison of CFD and PIV Results (Left- k-ε model, Middle-PIV, Right-k-ω model) Transient Simulations The HeartQuest TM continuous flow left ventricle assist device (LVAD) operates under highly transient conditions. The inlet blood flow from the native left ventricle is pulsatile, and the pump s asymmetric circumferential configuration with five rotating blades forces blood intermittently through the great arteries. A study of the pump s performance under transient conditions is essential to ensure an effective and reliable design. A transient CFD simulation was performed for HeartQuest TM VAD. A pulsatile inlet mass flow rate was specified at the inlet. CFX-Tascflow was run with a transient boundary condition that was implemented using local source code, which included an equation to calculate the mass flow rate at the inlet. The equation used in the source code was determined from experimental physiologic control studies of a patient with a VAD implant suffering from end-stage heart failure. The volumetric flow rate varied between 4 and 7 L/min with a systolic period of 40% and a diastolic period of 60%. CFX-TASCflow s frozen rotor multireference-frame model was used in order to save the computational sources. The time step was set at 0.005 s to catch the variations of fluid field during a period of 0.8 seconds. The resulting velocity field, pressure distribution, and fluid forces and moments were time varying. The steady and transient results of pressureflow performance are plotted in Figure 6. The rotational speed for the simulation was 2100 RPM. The transient solution demonstrates characteristic hysterisis performance. The difference between the transient and steady results proved to be approximately 10%.

Figure 6. Comparison of Transient and Steady Studies Conclusion A fully magnetically suspended, small centrifugal blood pump was numerically simulated using CFD. The flow patterns in pump were modeled and a wide range of CFD studies were executed. The results show that HeartQuest TM has attractive performances and implantable dimensions. CFD simulation is a powerful tool in designing, demonstrating and optimizing small size pumps. References 1. DeBakey M. E., 2000, The Odyssey of the Artificial Heart, Artificial Organs, 24(6), pp. 405-11. 2. Olsen D. B., 2000, The History of Continuous-Flow Blood Pumps, Artificial Organs, 24(6), pp. 401-4. 3. Apel J., Neudel F., and Reul H., 2001, Computational Fluid Dynamics and Experimental Validation of a Microaxial Blood Pump, ASAIO Journal, 47(5), pp. 552-8. 4. Wood H. G., Anderson J. B., Allaire P. E., McDaniel J. C. and Bearnson G., 1999, Numerical Solution for Blood Flow in a Centrifugal Assist Device, International Journal of Artificial Organs, 22(12), pp. 827-36. 5. Song X., Wood H. G., Olsen D. B. CFD Study of the 4 th Generation Prototype of a Continuous Flow Ventricular Assist Device. ASME Journal of Biomechanical Engineering (Accepted) 6. Song X., Throckmorton A. L., Wood H. G., Antaki J. F., Olsen D. B., 2003, CFD Prediction of Blood Damage in a Centrifugal Pump. Artificial Organs 27(10), pp. 935-7. 7. Song X., Throckmorton A. L., Wood H. G., Antaki J. F., Olsen D. B., Quantitative Evaluation of Blood Damage in a Centrifugal VAD by Computational Fluid Dynamics. ASME Journal of Fluids Engineering. (Accepted) 8. Song X., Wood H., G., Day S. W., Olsen D. D., 2003, Studies of Turbulence Models in a CFD Model of a Blood Pump. Artificial Organs 27(10), pp. 938-41