Study on the optimal elastic modulus of flexible blades for right heart assist device supporting patients with single-ventricle physiologies

Background Patients with single-ventricle physiologies continue to experience insufficient circulatory power after undergoing palliative surgeries. This paper proposed a right heart assist device equipped with flexible blades to provide circulatory assistance for these patients. The optimal elastic modulus of the flexible blades was investigated through numerical simulation. Methods A one-way fluid-structure interaction (FSI) simulation was employed to study the deformation of flexible blades during rotation and its impact on device performance. The process began with a computational fluid dynamics (CFD) simulation to calculate the blood pressure rise and the pressure on the blades’ surface. Subsequently, these pressure data were exported for finite element analysis (FEA) to compute the deformation of the blades. The fluid domain was then recreated based on the deformed blades’ shape. Iterative CFD and FEA simulations were performed until both the blood pressure rise and the blades’ shape stabilized. The blood pressure rise, hemolysis risk, and thrombosis risk corresponding to blades with different elastic moduli were exhaustively evaluated to determine the optimal elastic modulus. Results Except for the case at 8,000 rpm with a blade elastic modulus of 40 MPa, the pressure rise associated with flexible blades within the studied range (rotational speeds of 4,000 rpm and 8,000 rpm, elastic modulus between 10 MPa and 200 MPa) was lower than that of rigid blades. It was observed that the pressure rise corresponding to flexible blades increased as the elastic modulus increased. Additionally, no significant difference was found in the hemolysis risk and thrombus risk between flexible blades of various elastic moduli and rigid blades. Conclusion Except for one specific case, deformation of the flexible blades within the studied range led to a decrease in the impeller’s functionality. Notably, rotational speed had a more significant impact on hemolysis risk and thrombus risk compared to blade deformation. After a comprehensive analysis of blade compressibility, blood pressure rise, hemolysis risk, and thrombus risk, the optimal elastic modulus for the flexible blades was determined to be between 40 MPa and 50 MPa.


Supplementary Material
In this supplementary document, a CFD simulation was conducted on the centrifugal blood pump provided by the FDA for six different operating conditions [1] .Based on the obtained flow field information, Equations 5 and 6 in the main text were used to assess the hemolysis risk for each condition.These simulation results, combined with experimental data, facilitated the determination and verification of parameter B. The specific process included the following steps: Firstly, the simulated flow field data for condition 5 were compared with the measured data to validate the accuracy of the simulation methods (as the literature only provided flow field data for condition 5 [1] ).Secondly, the relationship between the simulation NIH value for condition 5 and parameter B was established.Then, the value of parameter B was determined using the experimental NIH value of condition 5. Finally, the determined value of parameter B was used to calculate the hemolysis risk for the remaining conditions.These calculations were then compared with experimental hemolysis risk results to verify the reliability of the chosen value.
The assembly diagram, detailed view, computational model, and extracted fluid domain of the centrifugal blood pump are shown in Supplementary Figure 1 [2] .The six operating conditions involved in this analysis are presented in Supplementary Table 1.In CFD simulation, the velocity distribution at the pump inlet was set according to the measured results.Supplementary Figures 2A and 2B illustrate the measured data and simulation setting of inlet velocity for an example flow rate of 6 L/min [2] .The pump outlet was set as a zero-pressure boundary condition.Blood was modeled as a Newtonian fluid with a density of 1060 kg/m 3 and a dynamic viscosity of 3.5 cP.Additionally, the SST k-ω model was used in the simulation as the Reynolds numbers for all operating conditions were far greater than 4000.The fluid domain was meshed as a polyhedral grid using Fluent Meshing 2020R2 (Canonsburg, USA).After a grid independence study, the fluid mesh consisting of approximately 15.3 million elements was used for simulation.Supplementary Figure 3 presents the measured and simulated results of two-dimensional velocities on a cross-section under condition 5 [1] .This cross-section is 1.2mm from the top of the impeller, aligning with the mid-axial plane of the diffuser.Comparing Supplementary Figures 3A and 3B, it is evident that the simulation results closely match the measured data.In the blade-passage, as the radial distance increases, the velocity initially increases and then decreases, with the maximum velocity values occurring near the edges of the blades.Furthermore, the jets in the diffuser area are all skewed towards the outer walls.Supplementary Figure 4 illustrates the variation of two-dimensional velocities along two paths within the cross-section [1] .The comparison between Supplementary Figures 4A1 and 4A2 shows that the CFD simulation accurately captures the trend and absolute values of velocity along the radial path.Observing Supplementary Figures 4B1 and 4B2, it is evident that the CFD simulation also accurately captures the trend of velocity along the horizontal path, although there is a certain deviation in the peak velocity values compared to the experimental data.These results validate that the CFD simulation has obtained an accurate flow field, which can be further utilized for identifying parameter B.
In this equation, ∆ represents the measured increase in plasma-free hemoglobin () during the test period (g/L),  is the blood volume in the test circuit (L),  denotes the hematocrit (%), ∆t is the duration of the test (minutes), and  signifies the flow rate (L/min).For condition 5, the measured data of the above parameters are as follows: ∆ = 0.41g/L， = 0.24L， = 36%, ∆ = 120 min,  = 6L/min [2] .Based on these data, the   corresponding to condition 5 was calculated to be 0.008747 g/100L.
The simulation NIH value was calculated according to Equations 5 and 6 in the main text.After completing the streamline number independence test, 2000 streamlines were released at the pump inlet.
The NIH values for each streamline were calculated, and the average value was used to represent the overall hemolysis risk.Supplementary Figure 5 illustrates the relationship between the simulation NIH value and parameter B, corresponding to condition 5.It is observed that when B is set to 0.55, the simulation NIH value is 0.008816 g/100L, differing only by 0.79% from the experimental NIH value.Furthermore, the simulation NIH values for the remaining operating conditions were also calculated, with B set to 0.55.The relative hemolysis index (RHI) for each operating condition was obtained by normalizing their respective simulation NIH values relative to the simulation NIH value of condition 5, as shown in Supplementary Figure 6 [1] .It is indicated that for conditions 1-4, the RHIs obtained in this study closely match the experimental results.For condition 6, however, the RHI obtained shows some differences from the experimental data, yet it aligns with the calculation results of most other research groups.Above comparison proves that selecting a value of 0.55 for B allows for a relatively accurate assessment of the hemolysis risk in centrifugal blood pumps or rotary devices with similar operating principles.
Supplementary Figure 5. Relationship between simulation NIH and parameter B (Corresponding to operating condition5)

2 .
Measured data and simulation settings of inlet velocity (Corresponding to a flow rate of 6 L/min.(A) Measured data; (B) Simulation settings)