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Technical Brief

# Verification Benchmarks to Assess the Implementation of Computational Fluid Dynamics Based Hemolysis Prediction Models

[+] Author and Article Information
Prasanna Hariharan

10903 New Hampshire Avenue,
Silver Spring, MD 20993
e-mail: Prasanna.hariharan@fda.hhs.gov

Gavin D’Souza, Richard A. Malinauskas

Silver Spring, MD 20993

Marc Horner

ANSYS, Inc.,
Evanston, IL 60201

Matthew R. Myers

Silver Spring, MD 20993

1Corresponding author.

Manuscript received July 15, 2014; final manuscript received June 05, 2015; published online July 9, 2015. Assoc. Editor: Francis Loth.This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited.

J Biomech Eng 137(9), 094501 (Jul 09, 2015) (10 pages) Paper No: BIO-14-1328; doi: 10.1115/1.4030823 History: Received July 15, 2014

## Abstract

As part of an ongoing effort to develop verification and validation (V&V) standards for using computational fluid dynamics (CFD) in the evaluation of medical devices, we have developed idealized flow-based verification benchmarks to assess the implementation of commonly cited power-law based hemolysis models in CFD. The verification process ensures that all governing equations are solved correctly and the model is free of user and numerical errors. To perform verification for power-law based hemolysis modeling, analytical solutions for the Eulerian power-law blood damage model (which estimates hemolysis index (HI) as a function of shear stress and exposure time) were obtained for Couette and inclined Couette flow models, and for Newtonian and non-Newtonian pipe flow models. Subsequently, CFD simulations of fluid flow and HI were performed using Eulerian and three different Lagrangian-based hemolysis models and compared with the analytical solutions. For all the geometries, the blood damage results from the Eulerian-based CFD simulations matched the Eulerian analytical solutions within ∼1%, which indicates successful implementation of the Eulerian hemolysis model. Agreement between the Lagrangian and Eulerian models depended upon the choice of the hemolysis power-law constants. For the commonly used values of power-law constants ($α$  = 1.9–2.42 and $β$  = 0.65–0.80), in the absence of flow acceleration, most of the Lagrangian models matched the Eulerian results within 5%. In the presence of flow acceleration (inclined Couette flow), moderate differences (∼10%) were observed between the Lagrangian and Eulerian models. This difference increased to greater than 100% as the beta exponent decreased. These simplified flow problems can be used as standard benchmarks for verifying the implementation of blood damage predictive models in commercial and open-source CFD codes. The current study used only a power-law model as an illustrative example to emphasize the need for model verification. Similar verification problems could be developed for other types of hemolysis models (such as strain-based and energy dissipation-based methods). And since the current study did not include experimental validation, the results from the verified models do not guarantee accurate hemolysis predictions. This verification step must be followed by experimental validation before the hemolysis models can be used for actual device safety evaluations.

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## Figures

Fig. 1

Flow between inclined plane surfaces in relative motion (inclined Couette flow). The figure is not drawn to scale.

Fig. 2

HI versus radial distance at the model exit for Newtonian (a) pipe and (b) Couette flow

Fig. 3

Comparison of HIout values (from Eq. (20)) from the analytical and Eulerian CFD solutions for different Reynolds numbers (Newtonian and Casson pipe flow). For the Newtonian model, both fluent and cfx simulations were performed for Re = 200, 800, 1200, and 1800. For the Casson model, both fluent and cfx simulations were performed for Re = 200, 1200, and 1800. An additional Newtonian model simulation was performed at Re = 100 for cfx. The Reynolds number for both Newtonian and Casson models was calculated using viscosity of 3.5 cP.

Fig. 4

Casson fluid flow in a pipe model (Re = 200): (a) velocity, (b) HI, (c) velocity-weighted HI, and (d) velocity-weighted HI integral

Fig. 5

Inclined Couette flow (a) longitudinal velocity, (b) transverse velocity, (c) HI, and (d) velocity-weighted HI integral as a function of radial distance at midplane and exit. Except for the HI1 model, results from the Eulerian and rest of the Lagrangian models compare well with the analytical data.

Fig. 6

Effect of mesh refinement for inclined Couette flow problem. The working mesh has a node ratio = 1.

Fig. 7

Sensitivity of HI models to power-law constants (α and β) for non-Newtonian fully developed pipe flow

Fig. 8

Sensitivity of HI models to power-law constants (α and β) for inclined Couette flow

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