In the United States, very few mechanical circulatory support (MCS) options exist for infants and children with myocardial dysfunction or heart failure.1 Ventricular assist devices (VADs) or artificial blood pumps are valid MCS alternatives for cardiac support in pediatric patients.1–3 In Europe, initial successes with VAD use in infants and children have proven the viability of blood pumps to support this population. More recently, in the United States, the MicroMed-DeBakey Child VAD and the Berlin Heart have been effectively used in pediatric patients older than 5 years of age and in infants, respectively.4–6
Our multidisciplinary research team at the University of Virginia, including the School of Engineering and Applied Science and the School of Medicine at the Children's Hospital, set out to better qualify and quantify the local need for a viable PVAD by establishing a database. This database tracked potential PVAD candidates seen at the University of Virginia Children's Hospital. This information provides insight into design parameters during optimization stages and the motivation for continuing to move forward with pump development.
The design objective for the PVAD is a compact pump with a streamlined blood flow path including minimal irregular flow patterns.3 Unique in design, the rotor of this PVAD is suspended entirely by magnetic bearings, not conventional mechanical bearings.7–10 This suspension prevents the impeller from any contact wear with the pump's internal surfaces. It also reduces regions of stagnant and high shear flow by enabling larger clearances (approximately five times wider) between the rotor and stationary housing. Numerical results for the first round of design (PVAD1) demonstrated an acceptable hydraulic performance for the blood pump. Several enhancements were incorporated into the PVAD1's design to facilitate prototype manufacturing.
Specifically, this research presents the findings from a database tracking potential PVAD candidates seen at the University of Virginia Children's Hospital (Charlottesville, VA), a numerical analysis of the optimized PVAD1 design (PVAD2 model), the selected technique for manufacturing of a plastic prototype for experimental flow testing, and preliminary hydraulic performance results. Figure 1 illustrates the PVAD2 design with hydraulic regions identified: inducer, impeller, diffuser, and flow straightener.
Materials and Methods
The database was established as a collaborative effort between the School of Engineering and Children's Hospital. It complies with confidentiality regulations per the Health Insurance Portability and Accountability Act and was approved by the University of Virginia's Human Investigations Committee of the Institutional Review Board. The inclusion of patients in the database was dependent on the patient's short life expectancy and consideration of PVAD use at the time of examination. The database included recordings of demographic variables: age, sex, height, weight, body surface area, and status variables (transplant status, extracorporeal membrane oxygenation implementation). The age of the patient was recorded at the time of the cardiac catheterization. Brief statements regarding the pediatric patient's surgical history (number of thoracotomies and sternotomies) were also included, because they would affect the implantation of the PVAD. The database contains hemodynamic variables, including pulmonary capillary wedge pressure, cardiac output, pulmonary resistance, and systemic vascular resistance at the time of their cardiac catheterization. The creation of this candidate database provided vital information for understanding our target patient base and in assessing the adequacy of the pump's design.
After optimizing the PVAD1 design accordingly, a model of the PVAD2 was created for numerical analysis. The computational grid was constructed using the software GridPro (Program Development Company, White Plains, NY), which produces high-quality structured elements accommodating various complex geometries. The computational flow model was implemented in TascFlow (ANSYS Incorporated, Canonsburg, PA), a state-of-the-art computational fluid dynamics (CFD) solver of the Reynolds Averaged Navier Stokes (RANS) equations. The numerical analysis included extensive steady flow simulations with pressure-flow and efficiency predictions, as well as fluid force estimations for the magnetic suspension design. Additionally, a blood damage analysis was completed using particle streamlines to assess potential levels of hemolysis and possible conditions giving rise to thrombosis.
The PVAD2 model was the basis for the computer-aided design (CAD) drawings, created using Solidworks (Solidworks, Concord, MA), a three-dimensional solid modeling software most often used for prototype manufacturing. A few minor modifications were made to the PVAD2 design to facilitate rapid prototyping. Paramount Industries (Langhorne, PA) applied stereolithography, one of the most popular and innovative rapid prototyping techniques, to produce the plastic pump prototype (WaterShed resin material) with acceptable manufacturing tolerances. Stereolithography uses laser technology to photochemically harden liquid resins, layer by layer, into a solid plastic form according to manufacturing CAD drawings. The plastic prototype was then hydraulically tested in an experimental test-rig. In this study, the test prototype had a mechanical suspension, rather than a magnetic suspension, to enable the accurate location of the impeller within the pump housing. These preliminary hydraulic tests provided data to validate the pump's design by characterizing the pressure-flow performance for various operating conditions.
One of the major alterations to the PVAD1 design included the division of the diffuser region into two sections: the first part capturing 90% of the blade curvature (new diffuser), and the second section capturing the remaining straight portion of the blades at the pump's outlet (flow straightener). This alteration improved manufacturing of the complex diffuser region and postprocessing or machining. Figure 2 displays the specific design enhancements to the PVAD1, producing the PVAD2 design. The internal fluid regions of the PVAD2 model include: 1) an inducer region with six stationary blades to reduce flow irregularities entering the pump and to house active magnetic bearing components; 2) a rotating impeller with four blades to impart kinetic energy to the fluid; 3) a stationary diffuser section with five curved blades specifically designed to convert the kinetic energy to potential energy (increase in pressure); and, 4) a flow-straightener region with three stationary blades mounted to the outlet pump housing. The pump is designed to deliver 0.5–3 l/min with pressure rises of 50–95 mm Hg for pediatric patients.11,12 These pressures correspond to average systolic-diastolic values for pediatric patients. Projected final dimensions of the pump with magnetic bearing and motor components in place are 35 mm in diameter by 65 mm in length (Figure 1).
CFD Approach and Analysis
The flow conditions within the PVAD2 are expected to be turbulent, thus the k-ε turbulence model was selected for initial CFD simulations. This model selection will be re-evaluated after completing an extensive turbulence model study with comparison to hydraulic testing results. A constant viscosity value of 0.0035 kg/m*s was employed for each CFD simulation, corresponding to a hematocrit of approximately 33%, which is reasonable for PVAD candidates.3 Likewise, a constant density fluid was applied with a value of 1,050 kg/m3.3
Grid Quality and Convergence Study
Each region of the PVAD2 was created separately and then linked together via interfaces. Grid convergence studies were completed to determine regional mesh densities and to ensure an adequate number of elements for successful physical representation. The full computational model of the axial PVAD consists of approximately 397,000 elements. Table 1 shows the final grid densities for each region of the pump. In a maximum convergence cutoff study, hydraulic performance parameters and velocities at selected grid points varied less than 5% for convergence cutoff levels ranging from 1 × 10−3 to 1 × 10−4. Therefore, a maximum residual convergence criterion of 5 × 10−4 was deemed acceptable for each CFD simulation. Additionally, grid aspect ratios of less than 200 were maintained, and no negative volumes existed throughout the mesh.
Steady flow was assumed through the pump model with constant boundary conditions and velocities for these CFD simulations. The no-slip boundary condition was applied to stationary walls, ensuring the fluid velocity values along the boundary would equal zero. A stationary wall boundary was applied to the internal housing regions of the pump. The rotor, however, was specified as rotating walls in the counterclockwise direction according to the blade orientation. The frozen rotor interface linked regions of different reference frames and maintained flow properties without circumferential averaging. An inflow rate and rotational speed were specified for each simulation. The outflow pressure was specified to be constant at 20,000 Pa to establish the outlet boundary condition. Flow rates of 0.5–3 l/min for 7,000–9,000 rpm were simulated.
Fluid stresses that arise from the high rotational speeds and the narrow clearances between rotating and stationary parts may result in damage to red blood cells (RBCs) and the activation of the platelets, contributing to thrombus formations.13,14 Flow stagnation where blood pools in one location for an extended period while in contact with a foreign surface may also activate the body's coagulation cascade, potentially resulting in a clot formation. Turbulent flow and other irregular flow patterns may also contribute to both hemolysis (destruction of RBCs) and thrombosis. Reports indicate that fluid stresses on the order of 102 Pa may destroy red cells and damage platelets, while fluid stresses on the order of 10−2 Pa may result in platelet aggregation and initiation of coagulation and clot formation.15,16
In this study, scalar fluid stress values were numerically estimated, and blood damage indices were determined for the PVAD to predict flow conditions and to estimate the fluid stresses within the PVAD. TascFlow has the capability to estimate the fluid stresses at any nodal location in the computational flow field. Bludszuweit17,18 developed the scalar stress value, which contains the six components of the stress tensor and represents the level of stress experienced by the blood. We adopted this approach to account for the three-dimensional flow field and calculated the scalar stress (σ) according to Bludszuweit's stress formula:
A maximum stress value of 250 Pa has been widely accepted as the design criterion in the development of VADs.13 Not only is the magnitude of the stress critical to assessing the potential for hemolysis and thrombosis, but the exposure time to such levels of stress is also an important parameter to consider. We have developed a novel method for estimating a blood damage index,13 which corresponds to a ratio of the released hemoglobin to the total hemoglobin present in blood flowing through the pump. In this analysis, CFD tracks the stress history of the fluid via the particle streamlines. The particles with no mass or reactive properties and similar time/lengths scales to the flow conditions were released at the inflow of the CFD model and traveled along their corresponding streamlines. The surface conditions of the CFD model were defined as smooth and inert. The accumulation of stress and exposure time was integrated or, as in this discrete case, summed along the streamlines to evaluate the potential for blood damage.13 This cumulative approach, including viscous and turbulent stresses, provides a statistical estimate of possible damage to RBCs traveling through the PVAD:
where D represents the blood damage index and reflects the percentage of damaged RBCs, t is the stress exposure time, and inlet and outlet symbolize the entrance and exit faces of the PVAD2 in the CFD model, respectively. The numerical constants in Equation 2, relating the scalar stress to the exposure time, were obtained by regression of experimental data in a Couette viscometer with an exposure time of 0.0034 to 0.6 seconds for fluid stresses of 40–700 Pa. This range of investigation is comparable to the flow conditions and stress levels in blood pumps.13
Figure 3 illustrates a Solidworks CAD model of the test rig. The plastic pump's impeller is supported by a rear-mounted, stainless-steel drive shaft that passes through the outlet tank. The shaft is supported by two mechanical ball bearings and then connected to a high-speed DC motor. Motor electronics monitored and controlled the pump's rotational speed. The entire rotating assembly was mounted on linear bearings to allow for motion in the axial direction; similarly, a two-axis translational stage controlled the radial position of the impeller via manual micrometers. The axial motion of the entire assembly of bearings (motor and linear bearings) was constrained by a positional micrometer. Flow rates were measured using an ultrasonic flow meter (Transonic) clamped to the length of flexible tubing, connecting the inlet reservoir tank to the outlet tank. Pressures were determined within both tanks using a differential pressure transducer.
Data-collection software enabled the simultaneous measurements of pressure rise, rotational speed, and flow rate. A sampling rate of 25 Hz was deemed acceptable given the steady flow conditions being examined. At a specific rotational speed, the pressure rise between the inlet and outlet tank was recorded with the flow control valve fully opened to achieve a maximal flow rate. The valve in the flow loop was then incrementally closed to increase the flow resistance, resulting in flow rate reduction. Flow rates of 0.5 to 4.5 l/min were achieved for rotational speeds of 5,960 ± 18 rpm, 7,000 ± 20 rpm, 7,980 ± 23 rpm, 8,950 ± 24 rpm, and 9,975 ± 31 rpm. A water/glycerin mixture (60/40 solution by percent mass) was used as the fluid medium and blood analog solution. A Cannon-Fenske viscometer and hydrometer were used to verify the fluid properties of the water/glycerin mixture: a viscosity of 3.5 ± 0.17 cP and a specific gravity of 1.1 ± 0.002. Strict calibration of all experimental instruments was completed to ensure reproducibility and to minimize systematic errors. Figure 4 shows the plastic PVAD prototype as manufactured by stereolithography rapid prototyping techniques and used for the hydraulic testing.
Results and Discussion
PVAD Candidate Database
Table 2 shows the database findings to date for potential PVAD recipients from March 2004 to 2005 at the University of Virginia Children's Hospital. These findings illustrate the diverse spectrum of diagnoses and pathophysiologies for potential PVAD recipients. The ages of possible candidates ranged from 6 months to 13 years with body surface areas of 0.35 to 1.56 m2. Unlike in the adult population, where left ventricular failure dominates, the complexity of pediatric pathophysiologies and vast capacity requirements for a VAD complicates the design of an effective blood pump for the entire pediatric population. Based on these database findings, the focus of our PVAD development has not changed and continues to be the development of a pump for infants and children, where the need seems to be the greatest according to this abbreviated study thus far.
CFD Hydraulic Performance Estimations
Figure 5 shows the pressure-flow performance for this computational PVAD2 model. Each data point corresponds to a steady-state simulation for a specific flow rate and rotational speed. The static pressure rise across the pediatric pump for a given rotational speed decreased with increasing flow rate, as expected due to flow losses. A pressure rise range of 50–95 mm Hg was achieved for this pump's design under these operating conditions. The pressure performance curves demonstrate the pump's ability to deliver adequate flow with the desired pressure rise.
The hydraulic efficiency for each CFD simulation was determined according to:
where η is the power efficiency, denotes the mass flow rate, ρ represents the fluid density, P2 symbolizes the total pressure at the pump's outlet, P1 represents the total pressure at the inlet, M corresponds to the applied mechanical torque, and ω signifies the rotational speed. CFD results estimated best efficiency points ranging from 20% to 30%, typical efficiencies for blood pumps.19
CFD Rotor Fluid Force Estimations
The forces exerted on the impeller must be estimated to ensure an effective magnetic bearing suspension design.20 A macro within TascFlow was used to calculate these forces exerted over the impeller's wetted surface area. Figure 6 displays the computed axial fluid forces on the pediatric pump's impeller for the centered impeller position. The direction of the force corresponds to the sign convention established in Figure 1 where the axial force acts in the direction opposite to the flow. For these operating conditions, the axial force reached a maximum force of 1.7 N in the positive axial direction. This force magnitude is well within the counter force generation capabilities of compact magnetic bearings. The increase in axial fluid force with an increase in rotational speed correlates with the change in axial pressure difference across the pump, as expected.21 Because of the centered position of the impeller and axi-symmetric flow during these CFD simulations, the radial forces exerted on the rotor were found to be less than 10−2 N.
Approximately 200 particles were released at the inlet port of the PVAD2 model; thus, a total of 200 streamlines were tracked and recorded. The blood damage index for each particle was computed according to Equation 2. As an example, Figure 7 illustrates the scalar stress and exposure time to such stress for two particles (#25 and #100) traveling through the pump. Figure 8 displays the particle distributions of the exposure or residence times within the pump. The mean residence time was 0.105 seconds with a maximum residence time of 0.224 seconds. Approximately 187 (93.5%) of the particles took less than 0.14 seconds to travel completely through the PVAD. Figure 9 shows the particle distributions of the blood damage indices. The mean value of the blood damage index was found to be approximately 0.09% with a maximum value of 0.35%. The blood damage index remained < 0.24% for 190 of the 200 particles. This low value indicates a low probability of trauma to these particles. For the remaining 10 particles, however, where the damage index values range from 0.26% to 0.35%, there is a higher probability of damage to the blood particles traveling through the pump. Even though the damage indices for these particles remained below 0.5%, an encouraging result, additional hematologic experiments must be completed to further explore the potential for blood trauma.13
Experimental Testing Results
Figure 10 demonstrates the preliminary results of the prototype's hydraulic testing. There are a couple of differences between the PVAD2 numerical model and prototype configuration for ease of manufacturing. The major differences between the PVAD2 CFD model and the final plastic prototype include an increase in outlet diameter and a reduction in the number of diffuser blades from five to four. As seen in Figure 10, an increase in the pump's pressure rise was measured over the rotational speeds and desired flow rates, as theoretically would be expected. The plastic prototype performed much better than expected given the lack of one diffuser blade to generate additional pressure rise. The effect of the reduction in diffuser blade number from numerical model to prototype configuration is evident in the loss of the pressure at the higher flow rates. Also, the pressure loss at higher flow rates can be attributed to operating at off-design conditions, as expected. Deviations between the numerical model and prototype performance were approximately 10–15% at the higher flow rates. Nevertheless, the plastic prototype produced pressure rises of 20–160 mm Hg for flow rates of 0.5–4.5 l/min over rotational speeds of approximately 6,000–10,000 rpm. These results represent a reasonable starting point for continuing with additional hydraulic experiments and possible blood bag experiments.
Thousands of pediatric patients with heart failure in the United States would benefit from the availability of an effective and reliable PVAD. The mechanical circulatory support options currently in place are intended for short-term use, only a few weeks at most, with many patients desperately in need of longer-term support while waiting for a donor heart. By adopting the latest technology in the field of artificial heart research, we have designed and developed an axial-flow PVAD (PVAD2) with a magnetically suspended impeller.
The PVAD2 represents the optimized design of the PVAD1. This optimized design demonstrated the potential of the PVAD to produce 1.5 l/min and 72 mm hg at 8,000 rpm, an improved performance of approximately 10% at the design point. Additionally, the pump is able to deliver a range of flows from 0.5 to 3 l/min with desired physiologic pressure rises. The axial and radial forces estimated from the computational results are well within a range for which the magnetic suspension and motor configuration can compensate for flow perturbations. Fluid efficiencies were also found to correlate well with expectations and the performance of rotary VADs. The blood damage estimations also demonstrated acceptable levels and ranges within the flow domain.
A plastic pump prototype was constructed via stereolithography rapid prototyping techniques within specified manufacturing tolerances. The experimental hydraulic testing revealed an acceptable range of operability and performance for the plastic PVAD prototype. Preliminary comparison of the numerical results to hydraulic testing demonstrated an approximate 10–15% deviation. This deviation may be a result of the inherent CFD model and prototype differences: 1) one less diffuser blade in the prototype, and 2) an increase in the outlet diameter for the prototype as compared to the CFD model of the PVAD2. Pressure rises of 20–160 mm Hg were achieved for rotational speeds of approximately 6,000–10,000 rpm over flows of 0.5 l/min to 4.5 l/min, as desired. These preliminary and positive results indicate an acceptable design for the PVAD and encourage further hydraulic testing with a focus on the fluid forces exerted on the impeller for the motor and magnetic suspension design.
In conclusion, the PVAD2 CFD analysis and prototype hydraulic testing represent a significant step in the design and optimization process for this blood pump. The next phase will include the creation of a CFD model (PVAD3) that is geometrically similar to the plastic pump prototype. Therefore, a direct and quantitative comparison of the experimental results to numerical predictions can be completed. This validation of the numerical modeling will give designers more confidence in the CFD results of future models. After another significant design evaluation, a magnetically suspended PVAD will be constructed for extensive hydraulic and animal testing. This detailed, thorough, and repetitive design approach for the PVAD will eventually produce an effective MCS option for thousands of infants and children.
Financial support for this work was provided by the Biomedical Engineering GAANN Fellowship for Research in Vascular Engineering, Andy Ford Research Award for Excellence and Innovation in the Field of Pediatric Cardiovascular Disease, and the University of Virginia Children's Medical Center Scholar's Award.
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