A three-dimensional shear dependent continuum model of platelet aggregation under flow

Fig 1. vWF-mediated platelet aggregation. Upon vascular injury, vWF present in the subendothelium uncoils due to shear stress and binds transiently to a platelet’s GPIb receptor, effectively decelerating the platelet near the injury. The platelet subsequently adheres to subendothelial-bound collagen through its GPVI receptor. vWF in the plasma then binds to the subendothelial-bound platelet, enabling cohesion between bound and fluid-phase platelets. After vWF-mediated cohesion occurs, the recently bound platelet can be activated through shear stress, ADP, thrombin, or thromboxane, stimulating the αIIbβ3 integrin and enabling binding through fibrinogen.

Fig 2. Schematic of platelet model. Transition with dotted lines represent transient binding via vWF, while solid lines depict irreversible state changes. Arrows show the direction of the state change.

Fig 3. The computational domain. The microfluidic device has dimensions (ℓ,w,h)= (8000, 500, 50) μm. Blood is perfused over a 250×500μm2 collagen strip. The leading edge of the collagen strip is located approximately 5250 μm from the inlet of the microfluidic device. For the sake of computational efficiency, the computational domain represents a fraction of the microfluidic device with dimensions (ℓ,w,h)= (160, 150, 50) μm. The computational adhesion region is centered in the computational domain with‌‌ dimensions 100 × 100 μm2.

Fig 4. Shear-rate dependent functional forms of adhesion and cohesion. Functional forms for the on-rates k+(γ˙) (left) and off-rates k−(γ˙) (right) used to extend shear dependence beyond 2000/s. Piecewise-linear functions were tested for both on- and off-rates. Nonlinear forms include a hyperbolic tangent function for the on-rate, representing a faster-than-linear increase for intermediate shear rates, and an exponential relationship for the off-rate, reflecting reduced bond lifetimes as shear increases.

Fig 5. 3D reconstruction of platelet aggregates from confocal microscopy. Results at 5 minutes of perfusion over collagen related peptides at 300/s (A,B) and 1500/s (C,D) with a vehicle control (A,C) or inhibition (B,D) of amplification loops (indomethacin, 2Me-SAMP, MRS2719). DiOC6 labels all platelets and anti-CD62P labels activated platelets that have secreted α-granules. Flow is from upper-left to lower-right. Dimensions of box is length = 333 μm, width = 330 μm, and height = 30 μm.

Fig 6. Platelet aggregate volumes in experiments and simulations. Model predictions of aggregate volume in time compared with the mean experimental data with shear rate 300/s (top row) and 1500/s (bottom row), respectively and in the absence (left column) and presence (right column) of platelet inhibitors. Darkly shaded regions consist of 50% of the data and light shaded regions plus dark regions contain 100% of the data. Open circles are the experimental data (n = 14 for shear 300/s and n = 8 for shear 1500/s) and solid lines are simulations.

Fig 7. 3D rendering of numerically simulated clots and experiment comparisons. Each row shows a side view (left) and a top-down view (right) of simulated (left two columns) and experimental (right two columns) vWF-mediated platelet aggregation after 450 seconds. Rows A and B correspond to simulations with an initial wall shear rate of 300 s-1, with and without activation by ADP, respectively. Rows C and D correspond to simulations with an initial wall shear rate of 1500 s-1, with and without activation by ADP, respectively. Red in the simulations represents the sum of all activated platelets and the green are bound unactivated platelets. Red and green in the experiments is as before, DiOC6 labeled and anti-CD62P (marked for granule secretion), respectively.

Fig 8. 3D rendering of numerically simulated clots and intrathrombus platelet species distributions. Left column: shear rate of 300/s; right column: 1500/s. (A) Isovolume of subendothelial platelets (red) and bound unactivated platelets (green). (B) Same as in (A), with the addition of activated platelets bound via vWF (red). (C) Same as in (B), with an additional isovolume (blue) representing activated platelets bound via fibrinogen. Isovolumes are sliced along the channel centerline to enhance visualization. Together, these renderings illustrate how shear rate influences the spatial organization and composition of platelet populations within simulated thrombi.

Fig 9. Extravascular injury geometry. Snapshots of clot formation in the bleeding chip within the injury channel: (A) after 1 minute and (B) after 3 minutes and 25 seconds. Panel (C) shows occlusion time measurements (n = 13) in the bleeding chip, using three different metrics [46].

Fig 10. Shear-dependent adhesion and cohesion rates. Functional forms of the shear dependence for adhesion and cohesion rates involving vWF, along with the corresponding flow rates over time, measured at the end of the injury channel. The blue shaded bar indicates the interquartile range of experimental values shown in Fig 9. Flow rates below the experimentally defined occlusion threshold are shown in gray. In the legend, Trunc and Hyp denote truncated and hyperbolic functional forms, respectively, and on/off indicate whether the form was applied to the associated on- or off-rate. Exp denotes exponential.

Fig 11. 3D visualization of shear-dependent clot morphology and bound platelet distribution. Clot formation at early (left) and late (right) times without shear dependence (A) and with shear-dependent kinetics (B–C). Each clot is shown as an isovolume of bound platelet fraction, sliced along the geometry centerline to enhance visualization. Color contours on the clot surface indicate bound platelet fraction. (B) Off-rate truncated at 8000/s. (C) Exponential off-rate beginning at 2000/s. Time points are labeled.

Fig 12. 3D visualization of clot internal structure at occlusion. Clot structure at occlusion is visualized using species-resolved isovolumes, as in Fig 8. (A) Isovolumes of subendothelial platelets (red) and bound unactivated platelets (green). (B) Same as in (A), with the addition of activated platelets bound via vWF (red). (C) Same as in (B), with an additional isovolume (blue) representing activated platelets bound via fibrinogen. All isovolumes are sliced along the geometry centerline to enhance visualization. Together, these renderings illustrate the spatial organization and composition of platelet populations within the occlusion.