A physical description of the adhesion and aggregation of platelets

Abstract

The early stages of clot formation in blood vessels involve platelet adhesion-aggregation. Although these mechanisms have been extensively studied, gaps in their understanding still persist. We have performed detailed in vitro experiments, using the well-known Impact-R device, and developed a numerical model to better describe and understand this phenomenon. Unlike previous studies, we took into account the differential role of pre-activated and non-activated platelets, as well as the three-dimensional nature of the aggregation process. Our investigation reveals that blood albumin is a major parameter limiting platelet aggregate formation in our experiment. Simulations are in very good agreement with observations and provide quantitative estimates of the adhesion and aggregation rates that are hard to measure experimentally. They also provide a value of the effective diffusion of platelets in blood subject to the shear rate produced by the Impact-R.

Keywords: adhesion and aggregation rates; mathematical model; platelet deposition; shear-induced diffusion; whole blood in vitro experiments.

Figure 1.

(a) Platelet deposition as observed on the Impact-R 1×1 mm deposition window, after 300 s. (b) Result of the numerical simulation, obtained with the parameters of table 1.

Figure 2.

(a) Scanning electron microscopy image (magnification 12 000×) of platelet aggregates in the well. (b) The three-dimensional shape of a platelet aggregate based on the optical height obtained by digital holographic microscopy. The vertical scale bar unit is 5.2 nm and the field of view 12.8 ×12.8 μm. Scale bar, 20 μm.

Figure 3.

Sketch of the deposition substrate, discretized in cells of area ΔS, corresponding to the surface of a platelet. The grey levels indicate the density of albumin already deposited in each cell. The picture also illustrates the adhesion, aggregation and deposition along the z-axis. On the left panel, activated platelets (grey side discs) deposit first. Then in the right panel, non-activated platelets (white side discs) aggregate next to an already formed cluster.

Figure 4.

Number of particles adsorbed after 20 s, in the random walk model.

Figure 5.

Platelet velocity distribution in a two-dimensional blood shear flow, with fully resolved RBC and platelets.

Figure 6.

The result of the adhesion and aggregation model (continuous and dashed lines) and the experimental data (points). The parameters used in the simulation are given in table 1.

Figure 7.

Same as figure 6, but with p_add=120 s⁻¹ and p_agg= 14 s⁻¹. The size of the aggregates is very sensitive to this reduction of p_agg. The curves describing the time evolution of the number of pre-activated or non-activated platelets are very similar to those of figure 6, and not repeated here.

Figure 8.

(a) Distribution of the size of clusters at t=300 s. The area is given in square micrometres. (b) Distribution of cluster volumes at t= 300 s. The data suggest a power law with exponent −2.8. Simulation parameters are given in table 1.