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

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. 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 only used 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). However, 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.

On Eulerian versus Lagrangian models of mechanical blood damage and the linearized damage function

“…Hariharan, et al found dependence of the ratio of predicted hemolysis between the original and linearized methods on the exponent of duration of exposure for fully developed non‐Newtonian pipe flow, which satisfies issue 1. While they did not recognize the error in the Garon & Farinas source term, this dependence confirms the inconsistency (issue 2).…”

“…Some of these are based on a linearized damage function and, therefore, suffer from problems related to issues 1 and 2 identified here for the Eulerian approach. A common finding among Lagrangian and Eulerian models is that predicted hemolysis differs from measured hemolysis by orders of magnitude, thus additional modeling challenges beyond the mathematical validity issues raised in this article remain to be resolved by future research.…”

Multi‐Objective Genetic Algorithm Assisted by an Artificial Neural Network Metamodel for Shape Optimization of a Centrifugal Blood Pump

“…The simulated pipe has the radius and length of 2.5 and 400 mm, respectively (39). The pipe flow is investigated since it has an analytical solution for Eulerian-based hemolysis model in the laminar flow regime.…”

Modelagem matemática da fluidodinâmica não-newtoniana e bifásica simplificada da hemólise induzida mecanicamente em sistemas de bombeamento centrífugo de sangue

“…De um modo geral, em relação aos modelos para quantificação de hemólise, principalmente aos modelos baseados em lei de potências, haja visto que a grande maioria das publicações até o presente mostram simulações computacionais que ou os utilizam diretamente ou então utilizam modelos aperfeiçoados mas derivados deles, pode-se observar um ponto de deficiência que reside no fato de eles incorporarem relações empíricas construídas a partir de experimentos realizados em condições em que a tensão de cisalhamento é constante ao longo de uma linha de corrente (Hariharan et al, 2015). Os dados experimentais sobre os quais essas re-lações empíricas foram calculadas foram obtidas em viscosímetros com escoamento laminar e campo de tensões uniforme, portanto não capturando as características típicas de um escoamento em dispositivos médicos reais, com campo de tensões variável e exposições temporais mais curtas, e múltiplas, a tensões de cisalhamento relativamente altas em diversos pontos de um mesmo dispositivo.…”

“…A vantagem do modelo baseado em deformação é que ele pode modelar o processo de relaxamento da membrana viscoelástica da hemácia, o que não é possível usando um modelo baseado em tensão mecânica (Arora et al, 2004), (Chen e Sharp, 2011), (Arwatz e Smits, 2013), (Ezzeldin et al, 2015), (Hariharan et al, 2015).…”