Image-based flow simulation of platelet aggregates under different shear rates

Abstract

Hemodynamics is crucial for the activation and aggregation of platelets in response to flow-induced shear. In this paper, a novel image-based computational model simulating blood flow through and around platelet aggregates is presented. The microstructure of aggregates was captured by two different modalities of microscopy images of in vitro whole blood perfusion experiments in microfluidic chambers coated with collagen. One set of images captured the geometry of the aggregate outline, while the other employed platelet labelling to infer the internal density. The platelet aggregates were modelled as a porous medium, the permeability of which was calculated with the Kozeny-Carman equation. The computational model was subsequently applied to study hemodynamics inside and around the platelet aggregates. The blood flow velocity, shear stress and kinetic force exerted on the aggregates were investigated and compared under 800 s-1, 1600 s-1 and 4000 s-1 wall shear rates. The advection-diffusion balance of agonist transport inside the platelet aggregates was also evaluated by local Péclet number. The findings show that the transport of agonists is not only affected by the shear rate but also significantly influenced by the microstructure of the aggregates. Moreover, large kinetic forces were found at the transition zone from shell to core of the aggregates, which could contribute to identifying the boundary between the shell and the core. The shear rate and the rate of elongation flow were investigated as well. The results imply that the emerging shapes of aggregates are highly correlated to the shear rate and the rate of elongation. The framework provides a way to incorporate the internal microstructure of the aggregates into the computational model and yields a better understanding of the hemodynamics and physiology of platelet aggregates, hence laying the foundation for predicting aggregation and deformation under different flow conditions.

Fig 1. The schematic of the experiment set-up.

The width and the height of the chamber is 1 mm and 100 μm, respectively. The dimension of the recorded experimental domain is 125 μm × 100 μm × 100 μm.

Fig 2. Flow diagram for the image-based modelling methodology implemented in this work.

Experiment: microscopy images of platelet aggregates with labelled and non-labelled platelets caught by differential interference contrast microscopy with 100x magnification. Extracted information: reconstructed platelet aggregate geometry and permeability distribution over the aggregate. Computational modelling: the simulated domain for blood flow.

Fig 3. Fluorescence intensity (arbitrary units)—Density relation inside platelet aggregates.

(a) 800 s⁻¹ WSR. Slope = 0.0027. Intercept = -0.19. (b) 1600 s⁻¹ WSR. Slope = 0.0014. Intercept = 0.28. (c) 4000 s⁻¹ WSR. Slope = 0.0004. Intercept = -0.23. The unit in each subfigure is different due to the influence of external environment such as exposure level and labelling time.

Fig 4. Schematic diagram of the simulation domain.

(a) Blood perfusion channel and the location of the simulated domain. (b) Top view of the blood perfusion channel. (c) Domain of the blood flow simulation including the position of the platelet aggregate.

Fig 5. Distribution of fluorescence intensity, distribution of platelet aggregates density and permeability under 800 s⁻¹, 1600 s⁻¹ and 4000 s⁻¹ WSRs.

(a)-(c) Distributions of fluorescence intensity inside the platelet aggregates. (d) Average volume fraction of platelets of the platelet aggregates. (e) Distribution of volume fraction of platelets inside the platelet aggregates. (f) Distribution of permeability inside the platelet aggregates in log-scale.

Fig 6. Intensity of the fluorescence, corresponding porosity and the permeability of the platelet aggregate under 1600 s⁻¹ WSR.

(a) Intensity of the fluorescence obtained from the experimental data. (b) Corresponding porosity of the platelet aggregate. (c) Permeability of the platelet aggregate on the cross-sections of the aggregate obtained from the Kozeny-Carman equation. The results inside the platelet aggregates formed under 800 s⁻¹ and 4000 s⁻¹ WSRs are demonstrated in S1 Fig.

Fig 7. Flow field at WSR of 1600 s⁻¹.

(a) The velocity field of the blood flow on a cross-section of the flow domain. The red arrow indicates the direction of blood flow. (b) The velocity field of the blood flow inside the platelet aggregate on the cross-sections. The orange arrow points out the high flow velocity area between the shell and the core.

Fig 8. Stress analysis of the blood flow and the platelet aggregate under 1600 s⁻¹ WSR.

(a) The kinetic force exerted on the platelet aggregate. (b) The fluid shear stress on the surface of the platelet aggregate. The simulation results inside the platelet aggregates formed under 800 s⁻¹ and 4000 s⁻¹ WSRs are shown in S2 Fig.

Fig 9. Advection-diffusion balance.

Advection-diffusion balance of (a) Ca²⁺, (b) ADP and (c) Factor X on cross-sections inside the platelet aggregate under 1600 s⁻¹ WSR. The upper end of the color scale is set to 1. Therefore, areas with red color correspond to advection-dominated regions, while colors towards the lower end of the scale denote diffusion-dominated regions.

Fig 10. Platelet aggregates geometries, shear rates and the rate of elongation.

(a)-(c) Geometries of the platelet aggregates under 800 s⁻¹, 1600 s⁻¹ and 4000 s⁻¹ WSRs flow condition. (d)-(f) Cross-sectional shear rate profile under 800 s⁻¹, 1600 s⁻¹ and 4000 s⁻¹ WSRs flow condition. (g)-(i) Cross-sectional elongation rate profile under 800 s⁻¹, 1600 s⁻¹ and 4000 s⁻¹ WSRs flow condition.

Fig 11. Comparison of intrathrombus condition for different porosity values.

(a) Average blood flow velocity inside the platelet aggregates under various shear flow conditions. (b) Advection-dominated volume of ADP inside the platelet aggregates under various shear flow conditions. (c) Advection-dominated volume of Ca²⁺, ADP and Factor X inside the platelet aggregates under WSR of 1600 s⁻¹.

Fig 12. Comparison of intrathrombus condition for different porosity ranges.

(a) Average blood flow velocity inside the platelet aggregates under various shear flow conditions. (b) Advection-dominated volume of ADP inside the platelet aggregates under various shear flow conditions. (c) Advection-dominated volume of Ca²⁺, ADP and Factor X inside the platelet aggregates under WSR of 1600 s⁻¹.

Fig 13. Velocity magnitude of the blood flow inside the platelet aggregates under three WSRs.

(a) 800 s⁻¹, (b) 1600 s⁻¹ and (c) 4000 s⁻¹. The arrows point out the high flow velocity area between the shell and the core.