Fig 1.
Geometry of the vessel fragment.
Lx, Ly and H correspond to vessel length, cross section diameter and plaque height. Γin and Γout denote inlet and outlet boundaries respectively. Γ+ and Γ− refer to upper and lower vessel walls respectively.
Table 1.
Parameter values.
Fig 2.
Parametric diagram of blood coagulation system regimes in the parameter space.
Re is the Reynolds number and is the non-dimensional vessel wall permeability. Label “I” is used to denote stationary regimes with no coagulation in the vessel while “II” marks the regimes with thrombi formation. Also shown are two typical values Re1, Re2 marking the boundary of the coagulation regime for a given
and
—the permeability of the vessel wall below which clotting does not occur under any hydrodynamic conditions. Finally, Re = Reτ2 indicates the lowest Reynolds number at which the shear stress reaches τ2 and the local permeability of the vessel reaches
. h = 0.6, d = 0.4.
Fig 3.
Parametric diagrams of blood coagulation regimes in the (h, Re) parameter space for two different values of , the non-dimensional plaque diameter.
Region “I” denotes regimes in which there is no coagulation, region “II” represents regimes of macroscopic thrombus formation. (a): ,
; (b):
,
.
Fig 4.
Successive stages of a solid thrombus formation.
a—thrombus nucleation, b—formation of fibre-like fibrin structure, c—fibre-like structure thickening, d—solid thrombus. Shown are the color maps of Nw—the weight-average number of monomers in fibrin-polymer in the vessel, with red areas representing regions of fibrin gel formation (). Streamlines are plotted to visualize the flow, and the separatrix, which divides the core of the flow from the recirculation zone, is shown with a dashed line. Parameters used in the simulations are: Re = 130, h = 0.5,
,
. Note that only a fragment of the vessel closest to the plaque is depicted.
Fig 5.
Successive stages of a friable floating fibrin structure formation.
a—thrombus nucleation, b—formation of fibre-like fibrin structure, c—thick and friable floating fibrin structure. Shown are the color maps of Nw—the weight-average number of monomers in fibrin-polymer in the vessel, with red areas representing regions of fibrin gel formation (). Streamlines are plotted to visualize the flow, and the separatrix is shown with a dashed line. Parameters used in these simulations are: Re = 180, h = 0.6,
,
. Note that only a fragment of the vessel closest to the plaque is depicted.