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Modeling and prediction of flow-induced hemolysis: a review

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Abstract

Despite decades of research related to hemolysis, the accuracy of prediction algorithms for complex flows leaves much to be desired. Fundamental questions remain about how different types of fluid stresses translate to red cell membrane failure. While cellular- and molecular-level simulations hold promise, spatial resolution to such small scales is computationally intensive. This review summarizes approaches to continuum-level modeling of hemolysis, a method that is likely to be useful well into the future for design of typical cardiovascular devices. Weaknesses are revealed for the Eulerian method of hemolysis prediction and for the linearized damage function. Wide variations in scaling of red cell membrane tension are demonstrated with different types of fluid stresses when the scalar fluid stress is the same, as well as when the energy dissipation rate is the same. New experimental data are needed for red cell damage in simple flows with controlled levels of different types of stresses, including laminar shear, laminar extension (normal), turbulent shear, and turbulent extension. Such data can be curve-fit to create more universal continuum-level models and can serve to validate numerical simulations.

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[adopted from Lux and Palek (1995)]

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Notes

  1. Technically, the distinction between turbulent and laminar flow depends on the stability of the flow. Turbulent flow is unstable to minor disturbances, which produce apparently chaotic motion that is self-perpetuating. “Apparently” is used because turbulent flow is not entirely chaotic. Rather, it can involve coherent structures that evolve with time, for instance, hairpin vortices in flow over flat surfaces, and structures that are not truly steady, but have characteristics with steady, long-term means, such as streaks in turbulent Couette flow. Turbulent flow is inherently unsteady, even though statistically steady means exist, for instance, mean velocity profiles in pipe flow. It is tempting to contrast laminar flow as steady, but this is also not true. Oscillatory (Womersley) flow in a pipe is an example of flow that is unsteady and laminar for certain conditions. While Womersley flow is driven by an oscillatory pressure gradient, unsteadiness can be triggered spontaneously in laminar flow that is steady upstream, for instance, the oscillating Karman vortex street downstream of a cylinder. Neither is laminar flow strictly stable. Laminar flow can switch between multiple states. For instance, for a range of divergence angles, the (bistable) jet in a diverging channel can be attached to either wall. The key feature that identifies turbulent flow is instability that results in velocity and fluid stress fluctuations across a spectrum of length and frequency scales that laminar flows lack. Laminar velocity fluctuations behind a prosthetic valve, for instance, begin decaying immediately downstream, but turbulent fluctuations are continuously reenergized. For steady state, turbulence production equals dissipation. The instantaneous fluctuations of velocity are largely unpredictable, but can be simulated by direct numerical simulation (DNS). The large computational cost of DNS typically leads to the use of statistical measures (e.g., Reynolds decomposition, see Sect. 3.2) to solve turbulent flow problems.

  2. The Deborah number is a ratio of the time constant of the breakup/reformation of the cell layer to the unsteady time constant for the flow, for instance, the time period of oscillatory flow. The Deborah number determines whether the structure reforms within the oscillatory time period. The Weissenberg number is the same time constant for the cell structure divided by a steady time constant for the flow, which is typically a characteristic length divided by the fluid velocity. The characteristic length may be the longitudinal distance between features that substantially change the fluid velocity in a complex geometry, such as the distance between peaks of a wavy wall, or may be the transverse distance in a simple geometry, e.g., the radius in a long straight pipe. In the first case, the Weissenberg number determines whether the structure has time to reform between peaks. In the second case, the characteristic time is the time it takes the flow to move longitudinally a distance equal to the radius, and the Weissenberg number determines how the entrance length for cell layer formation compares to the radius.

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Faghih, M.M., Sharp, M.K. Modeling and prediction of flow-induced hemolysis: a review. Biomech Model Mechanobiol 18, 845–881 (2019). https://doi.org/10.1007/s10237-019-01137-1

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