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

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.

Machine learning based on computational fluid dynamics enables geometric design optimisation of the NeoVAD blades

The NeoVAD is a proposed paediatric axial-flow Left Ventricular Assist Device (LVAD), small enough to be implanted in infants. The design of the impeller and diffuser blades is important for hydrodynamic performance and haemocompatibility of the pump. This study aimed to optimise the blades for pump efficiency using Computational Fluid Dynamics (CFD), machine learning and global optimisation. Meshing of each design typically included 6 million hexahedral elements and a Shear Stress Transport turbulence model was used to close the Reynolds Averaged Navier-Stokes equations. CFD models of 32 base geometries, operating at 8 flow rates between 0.5 and 4 L/min, were created to match experimental studies. These were validated by comparison of the pressure-flow and efficiency-flow curves with those experimentally measured for all base prototype pumps. A surrogate model was required to allow the optimisation routine to conduct an efficient search; a multi-linear regression, Gaussian Process Regression and a Bayesian Regularised Artificial Neural Network predicted the optimisation objective at design points not explicitly simulated. A Genetic Algorithm was used to search for an optimal design. The optimised design offered a 5.51% increase in efficiency at design point (a 20.9% performance increase) as compared to the best performing pump from the 32 base designs. An optimisation method for the blade design of LVADs has been shown to work for a single objective function and future work will consider multi-objective optimisation.

Flow simulation-based particle swarm optimization for developing improved hemolysis models

The improvement and development of blood-contacting devices, such as mechanical circulatory support systems, is a life saving endeavor. These devices must be designed in such a way that they ensure the highest hemocompatibility. Therefore, in-silico trials (flow simulations) offer a quick and cost-effective way to analyze and optimize the hemocompatibility and performance of medical devices. In that regard, the prediction of blood trauma, such as hemolysis, is the key element to ensure the hemocompatibility of a device. But, despite decades of research related to numerical hemolysis models, their accuracy and reliability leaves much to be desired. This study proposes a novel optimization path, which is capable of improving existing models and aid in the development of future hemolysis models. First, flow simulations of three, turbulent blood flow test cases (capillary tube, FDA nozzle, FDA pump) were performed and hemolysis was numerically predicted by the widely-applied stress-based hemolysis models. Afterward, a multiple-objective particles swarm optimization (MOPSO) was performed to tie the physiological stresses of the simulated flow field to the measured hemolysis using an equivalent of over one million numerically determined hemolysis predictions. The results show that our optimization is capable of improving upon existing hemolysis models. However, it also unveils some deficiencies and limits of hemolysis prediction with stress-based models, which will need to be addressed in order to improve its reliability.

A Continuum Model for the Unfolding of von Willebrand Factor

von Willebrand Factor is a mechano-sensitive protein circulating in blood that mediates platelet adhesion to subendothelial collagen and platelet aggregation at high shear rates. Its hemostatic function and thrombogenic effect, as well as susceptibility to enzymatic cleavage, are regulated by a conformational change from a collapsed globular state to a stretched state. Therefore, it is essential to account for the conformation of the vWF multimers when modeling vWF-mediated thrombosis or vWF degradation. We introduce a continuum model of vWF unfolding that is developed within the framework of our multi-constituent model of platelet-mediated thrombosis. The model considers two interconvertible vWF species corresponding to the collapsed and stretched conformational states. vWF unfolding takes place via two regimes: tumbling in simple shear and strong unfolding in flows with dominant extensional component. These two regimes were demonstrated in a Couette flow between parallel plates and an extensional flow in a cross-slot geometry. The vWF unfolding model was then verified in several microfluidic systems designed for inducing high-shear vWF-mediated thrombosis and screening for von Willebrand Disease. The model predicted high concentration of stretched vWF in key regions where occlusive thrombosis was observed experimentally. Strong unfolding caused by the extensional flow was limited to the center axis or middle plane of the channels, whereas vWF unfolding near the channel walls relied upon the shear tumbling mechanism. The continuum model of vWF unfolding presented in this work can be employed in numerical simulations of vWF-mediated thrombosis or vWF degradation in complex geometries. However, extending the model to 3-D arbitrary flows and turbulent flows will pose considerable challenges.