# Flow in a Ventricular Assist Device - Pump Performance & Blood Damage Prediction

## Key Fluid Physics

Flow Physics

The flow in a rotary blood pump is characterized by an interaction of the "idealized" primary flow (blade-congruent, uniform, on circular-cylindrical paths) with secondary flows in the rotor and stator blade channels . These secondary flows arise from rotational effects (Coriolis forces, centrifugal forces), from transient processes (e.g., rotor-stator interaction), in gaps, or in viscous boundary layers [35,36]. The processes lead to a complex, three-dimensional, vortical flow with physiologically significant turbulent stresses in the VAD (see sections Description and Evaluation)).

Fluid Physics

When calculating blood flow through complex medical devices, it should always be kept in mind that blood is a non-Newtonian, multiphase fluid. However, in simulations in rotary blood pumps, blood is always approximated as a Newtonian, single-phase fluid. The Newtonian assumption is justified because the viscosity reaches an asymptotic behaviour under high shear rates. For the simulations, a blood-analogous fluid is assumed, which has density and viscosity comparable to blood. This assumption is necessary because it is impossible with current computational technology to account for the multiphase character of blood in a VAD simulation. This is partly due to the fact that the dimensions of the blood components are much smaller than the vortex structures calculated by the simulation. Therefore, much larger computational grids than used in the current literature are needed to resolve the blood components (size order of erythrocytes of the order $10^{-6}~m$ ) in the simulation.

## Application Uncertainties

Numerical Uncertainties

In this KB wiki entry, the VAD flow is considered at fixed operating points (constant volume flow and constant speeds), which is typical for flow analysis in preclinical design of VADs. In reality, the VAD may be exposed to continously varying inflow conditions if the diseased heart has residual activity . Due to the continous acceleration and deceleration in the pulsatile flow, the flow and stress field in the VAD will also change in time . In recent years, there has been a trend towards performing numerical investigations with pulsatile inflow. However, the boundary conditions for the VAD must be accurately defined here, since the VAD interacts in a reciprocal manner with the cardiovascular system.

The numerical uncertainties due to the grid resolution with URANS in the calculation of fluid mechanical and hemodynamical parameters will be explained later.

Experimental Uncertainties

It is important that the validation experiments use a blood analogue fluid that adequately represents the simulated fluid properties. In this study, a mixture of glycerol-water is used, whose density is 5% greater than that of the numerical fluid. Despite the same dynamic viscosity, this has an impact on the VAD flow field, since the density in the conservation equations is coupled to the pressure of the fluid. The deviation for the head $H$ is estimated to be ≈ 3 mmHg for the present case.

## Computational Domain and Boundary Conditions

Certain conditions have to be considered for domain-size and boundary-condition assignment:

• For the analysis, straight inflow and outflow cannulas are included. These cannulas should extend sufficiently far (four and seven times the impeller diameter, respectively) from the guide vanes. Preliminary URANS studies in Ref.  have shown that the used distances are sufficient in order to prevent negative influences of the boundary conditions on the results.
• A constant flow rate $Q$ should be defined at the outlet - and not at the inlet - of the domain, to guarantee that eddies with non-uniform pressure distribution can pass the outlet.

## Discretisation and Grid Resolution

For LES:

• In order to guarantee that most of the turbulence within the VAD is directly resolved, special consideration must be given to the computational grid. This is especially the case for the near-wall resolution, since the energy-containing eddies, which need to be resolved by LES, scale linearly with the wall distance. In order to resolve these eddies, a high grid resolution in all spatial directions is necessary. Therefore, the grid characteristics should follow the literature recommendations for wall-resolving LES, with a near-wall grid, which observes the upper limits of $\Delta _{x}^{+}\leq 50$ and $\Delta _{z}^{+}\leq 20$ for the grid sizes in the flow and spanwise direction. Furthermore, the first wall-normal node should have a maximum dimensionless distance of $y_{1}^{+}\leq 1$ and the grid growth factor should not exceed $r_{g}=1.05$ near the wall. Additionally, further grid quality measures should be kept to minimize discretization errors and obtain a proper convergence behavior. Grid angles should be larger than 20°, aspect ratios smaller than 5 in the core flow region and the mesh expansion factor smaller than 20. Furthermore, the interfaces between the rotor-stator domains must be created as evenly as possible, in order to guarantee a smooth progression of the transported flow variables across the interfaces.
• An excellent overview about resolution and modeling evaluation for general LES application is given in Ref. . Some of these verification methods were applied in section CFD Simulations to the LES in the VAD flow.

For URANS:

• The extended grid convergence study shows that discretization errors are significant for blood damage prediction based on the effective stresses. Even when the similation indicates a small discretization error for the pump characteristics, the error can be significant for the blood damage prediction results.
• The generally coarser grid resolution - especially in the near-wall region - leads to lower values for blood damage compared to the results computed with LES.

## Physical Modelling

The fluid mechanical evaluation of the pump characteristics (head, efficiency) shows that the URANS can satisfactorily reproduce these quantities with the applied setup. However, for the hemodynamic evaluation, the discrepancies between URANS and LES are many times greater and the similarity in stresses depend on the operating point. At partial load, the stresses are similar and the blood damage prediction results differ not much between both methods. At the nominal operating point, the deviations in effective stresses are larger, which also leads to larger differences in the blood damage prediction.

It is important to note that $\varepsilon _{turb}$ obtained from a turbulence or a subgrid-scale model should always be included in the stress definition in Eq. (10). This term was often omitted in earlier URANS computations [5,33,34]. But preliminary calculations of the author and his co-workers [6,29] have shown that this leads to unrealistic results.

## Recommendations for Future Work

Three recommendations can be made on the experimental and numerical side:

• It would be worthwhile to have more experimental validation data, e.g., of the velocities or the turbulent kinetic energy, in order to perform a fluid mechanical investigation and validation of these quantities in the VAD as well.
• Hybrid RANS-LES models appear suitable to provide the trade-off between high accuracy (LES) and low computation time (RANS method). It would be interesting to see how a hybrid LES model computes the hemodynamical parameters compared to the presented methods.
• LES computations under pulsating conditions to study the occuring secondary flows and the subsequent (turbulent) stresses would be a step forward to better understand the VAD flow under realistic operation condition.

## Acknowledgements

The authors acknowledge the North-German Supercomputing Alliance (HLRN) for providing HPC resources that have contributed to the research reported in this KB Wiki entry.