Large eddy simulation in a rotary blood pump: Viscous shear stress computation and comparison with unsteady Reynolds-averaged Navier-Stokes simulation

Transient Performance Analysis of Centrifugal Left Ventricular Assist Devices Coupled With Windkessel Model: Large Eddy Simulations Study on Continuous and Pulsatile Flow Operation

Computational fluid dynamics (CFD) simulations are widely used to develop and analyze blood-contacting medical devices such as left ventricular assist devices (LVADs). This work presents an analysis of the transient behavior of two centrifugal LVADs with different designs: HeartWare VAD and HeartMate3. A scale-resolving methodology is followed through Large Eddy Simulations, which allows for the visualization of turbulent structures. The three-dimensional (3D) LVAD models are coupled to a zero-dimensional (0D) 2-element Windkessel model, which accounts for the vascular resistance and compliance of the arterial system downstream of the device. Furthermore, both continuous- and pulsatile-flow operation modes are analyzed. For the pulsatile conditions, the artificial pulse of HeartMate3 is imposed, leading to a larger variation of performance variables in HeartWare VAD than in HeartMate3. Moreover, CFD results of pulsatile-flow simulations are compared to those obtained by accessing the quasi-steady maps of the pumps. The quasi-steady approach is a predictive tool used to provide a preliminary approximation of the pulsatile evolution of flow rate, pressure head, and power, by only imposing a speed pulse and vascular parameters. This preliminary quasi-steady solution can be useful for deciding the characteristics of the pulsatile speed law before running a transient CFD simulation, as the former entails a significant reduction in computational cost in comparison to the latter.

Viscosity Modeling for Blood and Blood Analog Fluids in Narrow Gap and High Reynolds Numbers Flows

For the optimization of ventricular assist devices (VADs), flow simulations are crucial. Typically, these simulations assume single-phase flow to represent blood flow. However, blood consists of plasma and blood cells, making it a multiphase flow. Cell migration in such flows leads to a heterogeneous cell distribution, significantly impacting flow dynamics, especially in narrow gaps of less than 300 μm found in VADs. In these areas, cells migrate away from the walls, forming a cell-free layer, a phenomenon not usually considered in current VAD simulations. This paper addresses this gap by introducing a viscosity model that accounts for cell migration in microchannels under VAD-relevant conditions. The model is based on local particle distributions measured in a microchannels with a blood analog fluid. We developed a local viscosity distribution for flows with particles/cells and a cell-free layer, applicable to both blood and analog fluids, with particle volume fractions of up to 5%, gap heights of 150 μm, and Reynolds numbers around 100. The model was validated by comparing simulation results with experimental data of blood and blood analog fluid flow on wall shear stresses and pressure losses, showing strong agreement. This model improves the accuracy of simulations by considering local viscosity changes rather than assuming a single-phase fluid. Future developments will extend the model to physiological volume fractions up to 40%.

Incorporating Unresolved Stresses in Blood Damage Modeling: Energy Dissipation More Accurate Than Reynolds Stress Formulation

OBJECTIVE

Reynolds Averaged Navier Stokes (RANS) models are often used as the basis for modeling blood damage in turbulent flows. To predict blood damage by turbulence stresses that are not resolved in RANS, a stress formulation that represents the corresponding scales is required. Here, we compare two commonly employed stress formulations: a scalar stress representation that uses Reynolds stresses as a surrogate for unresolved fluid stresses, and an effective stress formulation based on energy dissipation.

METHODS

We conducted unsteady RANS simulations of the CentriMag blood pump with three different closure models and a Large Eddy Simulation (LES) for reference. We implemented both stress representations in all models and compared the resulting total stress distributions in Eulerian and Lagrangian frameworks.

RESULTS

The Reynolds-stress-based approach overestimated the contribution of unresolved stresses in RANS, with differences between closure models of up to several orders of magnitude. With the dissipation-based approach, the total stresses predicted with RANS deviated by about 50% from the LES reference, which was more accurate than only considering resolved stresses.

CONCLUSION

The Reynolds-stress-based formulation proved unreliable for estimating scalar stresses in our RANS simulations, while the dissipation-based approach provided an accuracy improvement over simply neglecting unresolved stresses.

SIGNIFICANCE

Our results suggest that dissipation-based inclusion of unresolved stresses should be the preferred choice for blood damage modeling in RANS.

In-Vitro Flow Validation of Third-Generation Ventricular Assist Devices: Feasibility and Challenges

Computational fluid dynamics (CFD) is a powerful tool for the in-silico evaluation of rotodynamic blood pumps (RBPs). Corresponding validation, however, is typically restricted to easily accessible, global flow quantities. This study showcased the HeartMate 3 (HM3) to identify feasibility and challenges of enhanced in-vitro validation in third-generation RBPs. To enable high-precision acquisition of impeller torques and grant access for optical flow measurements, the HM3 testbench geometry was geometrically modified. These modifications were reproduced in silico , and global flow computations validated along 15 operating conditions. The globally validated flow in the testbench geometry was compared with CFD-simulated flows in the original geometry to assess the impact of the necessary modifications on global and local hydraulic properties. Global hydraulic properties in the testbench geometry were successfully validated (pressure head: r = 0.999, root mean square error [RMSE] = 2.92 mmHg; torque: r = 0.996, RMSE = 0.134 mNm). In-silico comparison with the original geometry demonstrated good agreement ( r > 0.999, relative errors < 11.97%) of global hydraulic properties. Local hydraulic properties (errors up to 81.78%) and hemocopatibility predictions (deviations up to 21.03%), however, were substantially affected by the geometric modifications. Transferability of local flow measures derived on advanced in-vitro testbenches toward original pump designs is challenged by significant local effects associated with the necessary geometrical modifications.

The influence of non-conformal grid interfaces on the results of large eddy simulation of centrifugal blood pumps

BACKGROUND

Computational fluid dynamics has been widely used to assist the design and evaluation of blood pumps. Discretization errors associated with computational grid may influence the credibility of numerical simulations. Non-conformal grid interfaces commonly exist in rotary machines, including rotary blood pumps. Should grid size across the interface differ greatly, large errors may occur.

METHODS

This study explored the effects of non-conformal grid interface on the prediction of the flow field and hemolysis in blood pumps using large eddy simulation (LES). Two benchmarks, a nozzle model and a centrifugal blood pump were chosen as test cases.

RESULTS

This study found that non-conformal grid interfaces with considerable change of grid sizes led to discontinuities of flow variables and brought errors to metrics such as pressure head (7%) and hemolysis (up to 14%).

CONCLUSIONS

The results on the full unstructured grid are more accurate with negligible changes of flow variables across the non-conformal grid interface. A full unstructured grid should be employed for centrifugal blood pumps to minimize the influence of non-conformal grid interfaces for LES simulations.

Validation of Numerically Predicted Shear Stress-dependent Dissipative Losses Within a Rotary Blood Pump

Computational fluid dynamics find widespread application in the development of rotary blood pumps (RBPs). Yet, corresponding simulations rely on shear stress computations that are afflicted with limited resolution while lacking validation. This study aimed at the experimental validation of integral hydraulic properties to analyze global shear stress resolution across the operational range of a novel RBP. Pressure head and impeller torque were numerically predicted based on Unsteady Reynolds-averaged Navier-Stokes (URANS) simulations and validated on a testbench with integrated sensor modalities (flow, pressure, and torque). Validation was performed by linear regression and Bland-Altman analysis across nine operating conditions. In power loss analysis (PLA), in silico hydraulic power losses were derived based on the validated hydraulic quantities and balanced with in silico shear-dependent dissipative power losses. Discrepancies among both terms provided a measure of in silico shear stress resolution. In silico and in vitro data correlated with low discordance in pressure (r = 0.992, RMSE = 1.02 mmHg), torque (r = 0.999, RMSE = 0.034 mNm), and hydraulic power losses (r = 0.990, RMSE = 0.015W). PLA revealed numerically predicted dissipative losses to be up to 34.4% smaller than validated computations of hydraulic losses. This study confirmed the suitability of URANS settings to predict integral hydraulic properties. However, numerical credibility was hampered by lacking resolution of shear-dependent dissipative losses.

Large eddy simulation as a fast and accurate engineering approach for the simulation of rotary blood pumps

An accurate representation of the flow field in blood pumps is important for the design and optimization of blood pumps. The primary turbulence modeling methods applied to blood pumps have been the Reynolds-averaged Navier-Stokes (RANS) or URANS (unsteady RANS) method. Large eddy simulation (LES) method has been introduced to simulate blood pumps. Nonetheless, LES has not been widely used to assist in the design and optimization of blood pumps to date due to its formidable computational cost. The purpose of this study is to explore the potential of the LES technique as a fast and accurate engineering approach for the simulation of rotary blood pumps. The performance of "Light LES" (using the same time and spatial resolutions as the URANS) and LES in two rotary blood pumps was evaluated by comparing the results with the URANS and extensive experimental results. This study showed that the results of both "Light LES" and LES are superior to URANS, in terms of both performance curves and key flow features. URANS could not predict the flow separation and recirculation in diffusers for both pumps. In contrast, LES is superior to URANS in capturing these flows, performing well for both design and off-design conditions. The differences between the "Light LES" and LES results were relatively small. This study shows that with less computational cost than URANS, "Light LES" can be considered as a cost-effective engineering approach to assist in the design and optimization of rotary blood pumps.

Equivalent Scalar Stress Formulation Taking into Account Non-Resolved Turbulent Scales

PURPOSE

Cardiovascular engineering includes flows with fluid-dynamical stresses as a parameter of interest. Mechanical stresses are high-risk factors for blood damage and can be assessed by computational fluid dynamics. By now, it is not described how to calculate an adequate scalar stress out of turbulent flow regimes when the whole share of turbulence is not resolved by the simulation method and how this impacts the stress calculation.

METHODS

We conducted direct numerical simulations (DNS) of test cases (a turbulent channel flow and the FDA nozzle) in order to access all scales of flow movement. After validation of both DNS with literature und experimental data using magnetic resonance imaging, the mechanical stress is calculated as a baseline. Afterwards, same flows are calculated using state-of-the-art turbulence models. The stresses are computed for every result using our definition of an equivalent scalar stress, which includes the influence from respective turbulence model, by using the parameter dissipation. Afterwards, the results are compared with the baseline data.

RESULTS

The results show a good agreement regarding the computed stress. Even when no turbulence is resolved by the simulation method, the results agree well with DNS data. When the influence of non-resolved motion is neglected in the stress calculation, it is underpredicted in all cases.

CONCLUSION

With the used scalar stress formulation, it is possible to include information about the turbulence of the flow into the mechanical stress calculation even when the used simulation method does not resolve any turbulence.

Turbulence and turbulent flow structures in a ventricular assist device-A numerical study using the large-eddy simulation

Numerical flow simulations that analyze the turbulent flow characteristics within a turbopump are important for optimizing the efficiency of such machines. In the case of ventricular assist devices (VADs), turbulent flow characteristics must be also examined in order to improve hemocompatibility. Turbulence increases the shear stresses in the VAD flow, which can lead to an increased damage to the transported blood components. Therefore, an understanding of the turbulent flow patterns and their significance for the numerical blood damage prediction is particularly important for flow optimizations in VADs in order to identify and thus minimize flow regions where blood could be damaged due to high turbulent stresses. Nevertheless, the turbulence occurring in VADs and the local turbulent structures that lead to increased turbulent stresses have not yet been analyzed in detail in these machines. Therefore, this study aims to investigate the turbulence in an axial VAD in a comprehensive and double tracked way. First, the flow in an axial VAD was computed using the large-eddy simulation method, and it was verified that the majority of the turbulence was directly resolved by the simulation. Then, the turbulent flow state of the VAD was quantified globally. For this purpose, a self-designed evaluation method, the power loss analysis, was used. Subsequently, local flow regions and flow structures were identified where significant turbulent stresses prevail. It will be shown that the identified regions are universal and will also occur in other axial blood pumps as well, for example, in the HeartMate II.

Computational fluid dynamics simulation of time-resolved blood flow in Budd-Chiari syndrome with inferior vena cava stenosis and its implication for postoperative efficacy assessment

BACKGROUND

This study aimed to adopt computational fluid dynamics to simulate the blood flow dynamics in inferior vena cava stenosis based on time-dependent patient-specific models of Budd-Chiari syndrome as well as a normal model. It could offer valuable references for a retrospective insight into the underlying mechanisms of Budd-Chiari syndrome pathogenesis as well as more accurate evaluation of postoperative efficacy.

METHODS

Three-dimensional inferior vena cava models of Budd-Chiari syndrome patient-specific (preoperative and postoperative) and normal morphology model were reconstructed as per magnetic resonance images using Simpleware. Moreover, computational fluid dynamics of time-resolved inferior vena cava blood flow were simulated using actual patient-specific measurements to reflect time-dependent flow rates.

FINDINGS

The assessment of the preoperative model revealed the dramatic variations of hemodynamic parameters of the stenotic inferior vena cava. Moreover, the comparison of the preoperative and postoperative models with the normal model as benchmark showed that postoperative hemodynamic parameters were markedly ameliorated via stenting, with the attenuation of overall velocity and wall shear stress, and the increase of pressure. However, the comparative analysis of the patient-specific simulations revealed that some postoperative hemodynamic profiles still bore some resemblance to the preoperative ones, indicating potential risks of restenosis.

INTERPRETATION

Computational fluid dynamics simulation of time-resolved blood flow could reveal the tight correlation between the hemodynamic characteristics and the pathological mechanisms of inferior vena cava stenosis. Furthermore, such time-resolved hemodynamic profiles could provide a quantitative approach to diagnosis, operative regimen and postoperative evaluation of Budd-Chiari syndrome with inferior vena cava stenosis.

Evaluation of clinically relevant operating conditions for left ventricular assist device investigations

Standardized boundary conditions for flow rate and pressure difference are currently not available for the development and certification process of ventricular assist devices. Thus, interdisciplinary studies lack comparability and quantitative assessment. Universally valid boundary conditions could be used for the application of numerical and experimental investigations and the approval procedure of ventricular assist devices. In order to define such boundaries, physiological data from INCOR^® patients were evaluated. A total of 599 out of possible 627 ventricular assist device patients were analyzed regarding their cardiac demands of flow rate and pressure head. An analysis of long-term data was performed, in order to provide respective, static mean values for benchmark testing. Furthermore, the short-term data of 188 patients delivered field data-based dynamic flow and pressure curves. The results of the study revealed physiologically reasonable boundary conditions, which can be applied in numerical or experimental investigations of ventricular assist devices. For steady flow analysis, single values for flow rate (4.46 L/min) and pressure head (62 mmHg) are suggested. For the support of pulsatile and unsteady flow studies, seven typical patients and one representative dynamic curve for flow rate and pressure head are proposed.The standardized results provided in this article, can be used in favor of interdisciplinary comparability of future numerical computations or in vitro ventricular assist device tests in research, development, and approval.

Analysis of flow field and hemolysis index in axial flow blood pump by computational fluid dynamics-discrete element method

To fully study the relationship between the internal flow field and hemolysis index in an axial flow blood pump, a computational fluid dynamics-discrete element method coupled calculation method was used. Through numerical analysis under conditions of 6000, 8000, and 10,000 r/min, it was found that there was flow separation of blood cell particles in the tip of the impeller and the guide vane behind the impeller. The flow field has a larger pressure gradient distribution, which reduces the lift ratio of the blood pump and easily causes blood cell damage. The study shows that the hemolysis index obtained by the computational fluid dynamics-discrete element method is 4.75% higher than that from the traditional computational fluid dynamics method, which indicates the impact of microcollision between erythrocyte particles and walls on hemolysis index and also further verifies the validity of the computational fluid dynamics-discrete element coupling method. Through the hydraulic and particle image velocimetry experiments of the blood pump, the coincidence between numerical calculation and experiment is analyzed from macro and micro aspects, which shows that the numerical calculation method is feasible.

Influence of turbulent shear stresses on the numerical blood damage prediction in a ventricular assist device

The blood damage prediction in rotary blood pumps is an important procedure to evaluate the hemocompatibility of such systems. Blood damage is caused by shear stresses to the blood cells and their exposure times. The total impact of an equivalent shear stress can only be taken into account when turbulent stresses are included in the blood damage prediction. The aim of this article was to analyze the influence of the turbulent stresses on the damage prediction in a rotary blood pump's flow. Therefore, the flow in a research blood pump was computed using large eddy simulations. A highly turbulence-resolving setup was used in order to directly resolve most of the computed stresses. The simulations were performed at the design point and an operation point with lower flow rate. Blood damage was predicted using three damage models (volumetric analysis of exceeded stress thresholds, hemolysis transport equation, and hemolysis approximation via volume integral) and two shear stress definitions (with and without turbulent stresses). For both simulations, turbulent stresses are the dominant stresses away from the walls. Here, they act in a range between 9 and 50 Pa. Nonetheless, the mean stresses in the proximity of the walls reach levels, which are one order of magnitude higher. Due to this, the turbulent stresses have a small impact on the results of the hemolysis prediction. Yet, turbulent stresses should be included in the damage prediction, since they belong to the total equivalent stress definition and could impact the damage on proteins or platelets.

Grid-Induced Numerical Errors for Shear Stresses and Essential Flow Variables in a Ventricular Assist Device: Crucial for Blood Damage Prediction?

Adverse events due to flow-induced blood damage remain a serious problem for blood pumps as cardiac support systems. The numerical prediction of blood damage via computational fluid dynamics (CFD) is a helpful tool for the design and optimization of reliable pumps. Blood damage prediction models primarily are based on the acting shear stresses, which are calculated by solving the Navier–Stokes equations on computational grids. The purpose of this paper is to analyze the influence of the spatial discretization and the associated discretization error on the shear stress calculation in a blood pump in comparison to other important flow quantities like the pressure head of the pump. Therefore, CFD analysis using seven unsteady Reynolds-averaged Navier–Stokes (URANS) simulations was performed. Two simple stress calculation indicators were applied to estimate the influence of the discretization on the results using an approach to calculate numerical uncertainties, which indicates discretization errors. For the finest grid with 19 × 106 elements, numerical uncertainties up to 20% for shear stresses were determined, while the pressure heads show smaller uncertainties with a maximum of 4.8%. No grid-independent solution for velocity gradient-dependent variables could be obtained on a grid size that is comparable to mesh sizes in state-of-the-art blood pump studies. It can be concluded that the grid size has a major influence on the shear stress calculation, and therefore, the potential blood damage prediction, and that the quantification of this error should always be taken into account.