Prediction of mechanical hemolysis in medical devices via a Lagrangian strain-based multiscale model

Abstract

This work introduces a new Lagrangian strain-based model to predict the shear-induced hemolysis in biomedical devices. Current computational models for device-induced hemolysis usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged red blood cells (RBCs). These empirical correlations contain parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis in a general device. The proposed algorithm does not have any empirical parameters, thus can presumably be used for hemolysis prediction in various blood-wetting medical devices. In contrast to empirical correlations in which the Hb release is related to the shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and Hb release. In this approach, once the steady-state numerical solution of blood flow in the device is obtained under a prescribed operating condition, sample path lines are traced from the inlet of the device to the outlet to calculate the history of the shear stress tensor. In solving the fluid flow, it is assumed that RBCs do not have any influence on the flow pattern. Along each path line, shear stress tensor will be input into a coarse-grained (CG) RBC model to calculate the RBC deformation. Then the correlations obtained from molecular dynamics (MD) simulations are applied to relate the local areal RBC deformation to the perforated area on the RBC membrane. Finally, Hb released out of transient pores is calculated over each path line via a diffusion equation considering the effects of the steric hindrance and increased hydrodynamic drag due to the size of the Hb molecule. The total index of hemolysis (IH) is calculated by integration of released Hb over all the path lines in the computational domain. Hemolysis generated in the Food and Drug Administration (FDA) nozzle and two blood pumps, that is, a CentriMag blood pump (a centrifugal pump) and HeartMate II (an axial pump), for different flow regimes including the laminar and turbulent flows are calculated via the proposed algorithm. In all the simulations, the numerical predicted IH is close to the range of experimental data. The results promisingly indicate that this multiscale approach can be used as a tool for predicting hemolysis and optimizing the hematologic design of other types of blood-wetting devices.

Keywords: FDA nozzle; Lagrangian strain-based model; axial pump; centrifugal pump; mechanical hemolysis; multiscale modeling.

Figure 1:

Flowchart of the numerical algorithm.

Figure 2:

The summary of multiscale cell damage model: (a) A sample pathline obtained from solving blood flow in a medical device without considering the RBCs, (b) local strain distribution and nanopore formation on the RBC surface as a result of applying blood flow forces, (c) Hb diffusion out of porated regions.

Figure 3:

(a) computational grid and sample local normal vectors for triangular patches, (b) 2D illustration of kinematics for stretching and bending in spring connected network.

Figure 4:

Distribution of fluid froce on the pathline at a specific point on a triangluated element in the RBC model.

Figure 5:

RBC model validation: (a) stretch test, (b) relaxation test at 7 pN.

Figure 6:

FDA nozzle: (a) geometry and boundary conditions, (b) computational grid (1,393,562 elements).

Figure 7:

Grid independency study for the FDA nozzle at Re = 6500.

Figure 8:

1635 pathlines in FDA nozzle for different flow regimes.

Figure 9:

Comparison between CFD simulation and experimental studies for FDA nozzle at different throat Reynolds number.

Figure 10:

Different velocity gradients over the shown pathline in FDA nozzle at Re = 6500.

Figure 11:

(a) RBC shapes along a pathline in FDA nozzle, (b) instantaneous IH and strain rate magnitude.

Figure 12:

Comparison of numerical relative IH in FDA nozzle with the results published in [64], [67], [68].

Figure 13:

Variation in Relative IH estimation with number of pathlines in FDA nozzle.

Figure 14:

(a) Model of the CentriMag blood pump (D₂ = 0.009 m), (b) computational mesh (7.34 million elements).

Figure 15:

Different velocity gradients over the shown pathline in CentriMag blood pump at Re = 4000 rpm (350 mmHg).

Figure 16:

(a) RBC shapes along a pathline in CentriMag blood pump, (b) instantaneous IH and strain rate magnitude.

Figure 17:

Picture of the small volume loop experiment with a CentriMag pump.

Figure 18:

Numerical and experimental results for NIH in CentriMag at different pressure heads.

Figure 19:

Variation in NIH estimation with number of pathlines in CentriMag.

Figure 20:

(a) Schematic view of HeartMate II; (b) computational mesh (4.86 million elements)

Figure 21:

(a) Numerical and experimental results for NIH in HM II; (b) Variation in NIH estimation with number of pathlines in HM II.