Deformation of human red blood cells in extensional flow through a hyperbolic contraction

Analysis of the Suitability of an Effective Viscosity to Represent Interactions Between Red Blood Cells in Shear Flow

Many methods to computationally predict red blood cell damage have been introduced, and among these are Lagrangian methods that track the cells along their pathlines. Such methods typically do not explicitly include cell-cell interactions. Due to the high volume fraction of red blood cells (RBCs) in blood, these interactions could impact cell mechanics and thus the amount of damage caused by the flow. To investigate this question, cell-resolved simulations of red blood cells in shear flow were performed for multiple interacting cells, as well as for single cells in unbounded flow at an effective viscosity. Simulations run without adjusting the bulk viscosity produced larger errors unilaterally and were not considered further for comparison. We show that a periodic box containing at least 8 cells and a spherical harmonic of degree larger than 10 are necessary to produce converged higher-order statistics. The maximum difference between the single-cell and multiple-cell cases in terms of peak strain was 3.7%. To achieve this, one must use the whole blood viscosity and average over multiple cell orientations when adopting a single-cell simulation approach. The differences between the models in terms of average strain were slightly larger (maximum difference of 6.9%). However, given the accuracy of the single-cell approach in predicting the maximum strain, which is useful in hemolysis prediction, and its computational cost that is orders of magnitude less than the multiple-cell approach, one may use it as an affordable cell-resolved approach for hemolysis prediction.

Resistance valves in circulatory loops have a significant impact on in vitro evaluation of blood damage caused by blood pumps: a computational study

Background: Hemolysis and its complications are major concerns during the clinical application of blood pumps. In-vitro circulatory testing loops have been employed as the key procedure to evaluate the hemolytic and thrombogenic performance of blood pumps during the development phase and before preclinical in-vivo animal studies. Except for the blood damage induced by the pump under test, blood damage induced by loop components such as the resistance valve may affect the accuracy, reproducibility, and intercomparability of test results. Methods: This study quantitatively investigated the impact of the resistance valve on in vitro evaluation of blood damage caused by blood pumps under different operating points. A series of idealized tubing models under the resistance valve with different openings were created. Three pumps - the FDA benchmark pump, the HeartMate 3 LVAD, and the CH-VAD - were involved in hypothetical tests. Eight operating points were chosen to cover a relatively wide spectrum of testing scenarios. Computational fluid dynamics (CFD) simulations of the tubing and pump models were conducted at the same operating points. Results and Conclusion: Overall, hemolysis and platelet activation induced by a typical resistance valve are equivalent to 17%-45% and 14%-60%, respectively, of those induced by the pump itself. Both ratios varied greatly with flow rate, valve opening and pump models. Differences in blood damage levels between different blood pumps or working conditions can be attenuated by up to 45%. Thus, hemolysis and platelet activation induced by the resistance valve significantly affect the accuracy of in-vitro hemocompatibility evaluations of blood pumps. A more accurate and credible method for hemocompatibility evaluations of blood pumps will benefit from these findings.

Practical implications of the erroneous treatment of exposure time in the Eulerian hemolysis power law model

BACKGROUND

Eulerian and Lagrangian power-law formulations are both widely used for computational fluid dynamics (CFD) to predict flow-induced hemolysis in blood-contacting medical devices. Both are based on the same empirical power-law correlation between hemolysis and the shear stress and exposure time. In the Lagrangian approach, blood damage is predicted by tracking both the stress and exposure time along a finite number of pathlines in the domain. In the Eulerian approach, a scalar transport equation is solved for a time-linearized damage index within the entire domain. Previous analytical work has demonstrated that there is a fundamental problem with the treatment of exposure time in the Eulerian model formulation such that the only condition under which the model correctly represents the true exposure time is in a flow field with no streamwise velocity variation. However, the practical implications of this limitation have yet to be thoroughly investigated.

METHODS

In this study, we demonstrate the inaccuracy of Eulerian hemolysis power-law model predictions due to the erroneous treatment of exposure time by systematically considering four benchmark test cases with increasing degrees of flow acceleration: Poiseuille flow through a straight tube, inclined Couette flow, and flow through a converging tube with two different convergence ratios.

RESULTS

Compared with Lagrangian predictions, we show that, as flow acceleration becomes more pronounced, the resultant inaccuracy in the Eulerian predictions increases. For the inclined Couette flow case, there is a small degree of flow acceleration that yields a discrepancy in the range of 10% between Lagrangian and Eulerian predictions. For flows with a larger degree of acceleration, as occurs in the converging tube flow cases, the discrepancy is considerably larger (up to 257%).

CONCLUSION

The inaccuracy of hemolysis predictions due to the erroneous treatment of exposure time in the Eulerian power-law model can be significant when there is streamwise velocity variation in the flow field. These results may partially explain the extremely large variability in CFD hemolysis predictions reported in the literature between Lagrangian and Eulerian models.

Cell-scale hemolysis evaluation of intervenient ventricular assist device based on dissipative particle dynamics

Most of the existing hemolysis mechanism studies are carried out on the macro flow scale. They assume that the erythrocyte membranes with different loads will suffer the same damage, which obviously has limitations. Thus, exploring the hemolysis mechanism through the macroscopic flow field information is a tough challenge. In order to further understand the non-physiological shear hemolysis phenomenon at the cell scale, this study used the coarse-grained erythrocytes damage model at the mesoscopic scale based on the transport dissipative particle dynamics (tDPD) method. Combined with computational fluid dynamics the hemolysis of scalarized shear stress (τ) in the clearance of "Impella 5.0" was evaluated under the Lagrange perspective and Euler perspective. The results from the Lagrange perspective showed that the change rate of scaled shear stress (τ˙) was the most critical factor in damaging RBCs in the rotor region of "Impella 5.0"and other transvalvular micro-axial blood pumps. Then, we propose a dimensionless number Dk with time integration based on τ˙ to evaluate hemolysis. The Dissipative particle dynamics simulation results are consistent with the Dk evaluation results, so τ˙ may be an important factor in the hemolysis of VADs. Finally, we tested the hemolysis of 30% hematocrit whole blood in the "Impella 5.0" shroud clearance from the Euler perspective. Relevant results indicate that because of the wall effect, the RBCs near the impeller side are more prone to damage, and most of the cytoplasm is also gathered at the rotor side.

Microfluidic techniques for mechanical measurements of biological samples

The use of microfluidics to make mechanical property measurements is increasingly common. Fabrication of microfluidic devices has enabled various types of flow control and sensor integration at micrometer length scales to interrogate biological materials. For rheological measurements of biofluids, the small length scales are well suited to reach high rates, and measurements can be made on droplet-sized samples. The control of flow fields, constrictions, and external fields can be used in microfluidics to make mechanical measurements of individual bioparticle properties, often at high sampling rates for high-throughput measurements. Microfluidics also enables the measurement of bio-surfaces, such as the elasticity and permeability properties of layers of cells cultured in microfluidic devices. Recent progress on these topics is reviewed, and future directions are discussed.

Examining the universality of the hemolysis power law model from simulations of the FDA nozzle using calibrated model coefficients

Computational fluid dynamics (CFD) is widely used to predict mechanical hemolysis in medical devices. The most popular hemolysis model is the stress-based power law model that is based on an empirical correlation between hemoglobin release from red blood cells (RBCs) and the magnitude of flow-induced stress and exposure time. Empirical coefficients are traditionally calibrated using data from experiments in simplified Couette-type blood-shearing devices with uniform-shear laminar flow and well-defined exposure times. Use of such idealized coefficients in simulations of real medical devices with complex hemodynamics is thought to be a primary reason for the historical inaccuracy of absolute hemolysis predictions using the power law model. Craven et al. (Biomech Model Mechanobiol 18:1005-1030, 2019) recently developed a CFD-based Kriging surrogate modeling approach for calibrating empirical coefficients in real devices that could potentially be used to more accurately predict absolute hemolysis. In this study, we use the FDA benchmark nozzle to investigate whether utilizing such calibrated coefficients improves the predictive accuracy of the standard Eulerian power law model. We first demonstrate the credibility of our CFD flow simulations by comparing with particle image velocimetry measurements. We then perform hemolysis simulations and compare the results with in vitro experiments. Importantly, the simulations use coefficients calibrated for the flow of a suspension of bovine RBCs through a small capillary tube, which is relatively comparable to the flow of bovine blood through the FDA nozzle. The results show that the CFD predictions of relative hemolysis in the FDA nozzle are reasonably accurate. The absolute predictions are, however, highly inaccurate with modified index of hemolysis values from CFD in error by roughly three orders of magnitude compared with the experiments, despite using calibrated model coefficients from a relatively similar geometry. We rigorously examine the reasons for the inaccuracy that include differences in the flow conditions in the hemolytic regions of each device and the lack of universality of the hemolysis power law model that is entirely empirical. Thus, while the capability to predict relative hemolysis is valuable for product development, further improvements are needed before the power law model can be relied upon to accurately predict the absolute hemolytic potential of a medical device.

Fire-Shaped Nozzles to Produce a Stress Peak for Deformability Studies

Fire-shaped nozzles can be used to study the deformability of microcapsules, particles, or cells traveling in a flow. Though their geometry depends on the dimensions of the original glass capillary and the heating conditions, they all produce a strain rate peak approximately at the section where the diameter is 1.5 times the minimum. The intensity of this peak and the time from its position to the neck can be easily estimated from the flow rate and three geometrical parameters, without the need for any simulation. In the convergent region of these nozzles, it is possible to observe the evolution of the deformation. It is necessary to use a sufficiently long nozzle to produce the maximum deformation before the neck.

Computational Fluid-Structure Interaction Study of a New Wave Membrane Blood Pump

PURPOSE

Wave membrane blood pumps (WMBP) are novel pump designs in which blood is propelled by means of wave propagation by an undulating membrane. In this paper, we computationally studied the performance of a new WMBP design (J-shaped) for different working conditions, in view of potential applications in human patients.

METHODS

Fluid-structure interaction (FSI) simulations were conducted in 3D pump geometries and numerically discretized by means of the extended finite element method (XFEM). A contact model was introduced to capture membrane-wall collisions in the pump head. Mean flow rate and membrane envelope were determined to evaluate hydraulic performance. A preliminary hemocompatibility analysis was performed via calculation of fluid shear stress.

RESULTS

Numerical results, validated against in vitro experimental data, showed that the hydraulic output increases when either the frequency or the amplitude of membrane oscillations were higher, with limited increase in the fluid stresses, suggesting good hemocompatibility properties. Also, we showed better performance in terms of hydraulic power with respect to a previous design of the pump. We finally studied an operating point which achieves physiologic flow rate target at diastolic head pressure of 80 mmHg.

CONCLUSION

A new design of WMBP was computationally studied. The proposed FSI model with contact was employed to predict the new pump hydraulic performance and it could help to properly select an operating point for the upcoming first-in-human trials.

Elongational Stresses and Cells

Fluid forces and their effects on cells have been researched for quite some time, especially in the realm of biology and medicine. Shear forces have been the primary emphasis, often attributed as being the main source of cell deformation/damage in devices like prosthetic heart valves and artificial organs. Less well understood and studied are extensional stresses which are often found in such devices, in bioreactors, and in normal blood circulation. Several microfluidic channels utilizing hyperbolic, abrupt, or tapered constrictions and cross-flow geometries, have been used to isolate the effects of extensional flow. Under such flow cell deformations, erythrocytes, leukocytes, and a variety of other cell types have been examined. Results suggest that extensional stresses cause larger deformation than shear stresses of the same magnitude. This has further implications in assessing cell injury from mechanical forces in artificial organs and bioreactors. The cells' greater sensitivity to extensional stress has found utility in mechanophenotyping devices, which have been successfully used to identify pathologies that affect cell deformability. Further application outside of biology includes disrupting cells for increased food product stability and harvesting macromolecules for biofuel. The effects of extensional stresses on cells remains an area meriting further study.

Hemolysis estimation in turbulent flow for the FDA critical path initiative centrifugal blood pump

Hemolysis in medical devices and implants has been a primary concern over the past fifty years. Turbulent flow in particular can cause cell trauma and hemolysis in such devices. In this work, the effects of turbulence on red blood cell (RBC) damage are examined by simulating the flow field through a centrifugal blood pump that has been identified as a case study through the critical path initiative of the US Food and Drug Administration (FDA). In this study, a new model was employed to predict hemolysis in the turbulent flow environment in the pump selected for the FDA critical path initiative. The operating conditions for a centrifugal blood pump were specified by the FDA for rotational speeds of 2500 and 3500 rpm. The model is based on the analysis of the smaller eddies within the turbulent flow field, since it is assumed that turbulent flow eddies with sizes comparable to the dimensions of the RBCs lead to cell trauma. The Kolmogorov length scale of the velocity field is used to identify such small eddies. Using model parameters obtained in prior work through comparisons to capillary and jet flow, it is found that hemolysis for the 2500-rpm pump was predicted well, while hemolysis for the 3500-rpm pump was overpredicted. Results indicate refinement of the model and empirical constants with better experimental data is needed.

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.

On the Discretization of the Power-Law Hemolysis Model

Flow-induced hemolysis remains a concern for blood-contacting devices, and computer-based prediction of hemolysis could facilitate faster and more economical refinement of such devices. While evaluation of convergence of velocity fields obtained by computational fluid dynamics (CFD) simulations has become conventional, convergence of hemolysis calculations is also essential. In this paper, convergence of the power-law hemolysis model is compared for simple flows, including pathlines with exponentially increasing and decreasing stress, in gradually expanding and contracting Couette flows, in a sudden radial expansion and in the Food and Drug Administration (FDA) channel. In the exponential cases, convergence along a pathline required from one to tens of thousands of timesteps, depending on the exponent. Greater timesteps were required for rapidly increasing (large exponent) stress and for rapidly decreasing (small exponent) stress. Example pathlines in the Couette flows could be fit with exponential curves, and convergence behavior followed the trends identified from the exponential cases. More complex flows, such as in the radial expansion and the FDA channel, increase the likelihood of encountering problematic pathlines. For the exponential cases, comparison of converged hemolysis values with analytical solutions demonstrated that the error of the converged solution may exceed 10% for both rapidly decreasing and rapidly increasing stress.