# A CFD-based Kriging surrogate modeling approach for predicting device-specific hemolysis power law coefficients in blood-contacting medical devices

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## Abstract

Most stress-based hemolysis models used in computational fluid dynamics (CFD) are based on an empirical power law correlation between hemolysis generation and the flow-induced stress and exposure time. Empirical model coefficients are typically determined by fitting global hemolysis measurements in simplified blood shearing devices under uniform shear conditions and with well-defined exposure times. CFD simulations using these idealized global empirical coefficients are then performed to predict hemolysis in a medical device with complex hemodynamics. The applicability, however, of this traditional approach of using idealized coefficients for a real device with varying exposure times and non-uniform shear is currently unknown. In this study, we propose a new approach for determining device- and species-specific hemolysis power law coefficients (*C*, *a*, and *b*). The approach consists of calculating multiple hemolysis solutions using different sets of coefficients to map the hemolysis response field in three-dimensional (*C*, *a*, *b*) parameter space. The resultant response field is then compared with experimental data in the same device to determine the coefficients that when incorporated into the locally defined power law model yield correct global hemolysis predictions. We first develop the generalized approach by deriving analytical solutions for simple uniform and non-uniform shear flows (planar Couette flow and circular Poiseuille flow, respectively) that allow us to continuously map the hemolysis solution in (*C*, *a*, *b*) parameter space. We then extend our approach to more practical cases relevant to blood-contacting medical devices by replacing the requirement for an analytical solution in our generalized approach with CFD and Kriging surrogate modeling. Finally, we apply our verified CFD-based Kriging surrogate modeling approach to predict the device- and species-specific power law coefficients for developing laminar flow in a small capillary tube. We show that the resultant coefficients are much different than traditional idealized coefficients obtained from simplified uniform shear experiments and that using such idealized coefficients yields a highly inaccurate prediction of hemolysis that is in error by more than 2000% compared to experiments. Our approach and surrogate modeling framework may be applied to more complex medical devices and readily extended to determine empirical coefficients for other continuum-based models of hemolysis and other forms of flow-induced blood damage (e.g., platelet activation and thrombosis).

## Keywords

Hemolysis Blood damage Power law model Kriging surrogate modeling## Notes

### Acknowledgements

The authors thank C. Paulson and P. Hariharan for helpful discussions. We also thank T. Zhang for clarifying the development of the power law coefficients for ovine blood that are provided in Table 1. Additionally, thanks to M. Myers and T. Morrison for reviewing the manuscript. This study used the computational resources of the high-performance computing clusters at the US Food and Drug Administration (FDA), Center for Devices and Radiological Health (CDRH). The findings and conclusions in this article have not been formally disseminated by the US FDA and should not be construed to represent any agency determination or policy. The mention of commercial products, their sources, or their use in connection with material reported herein is not to be construed as either an actual or implied endorsement of such products by the Department of Health and Human Services.

### Compliance with ethical standards

### Conflicts of interest

The authors declare that they have no conflicts of interest.

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