Platelet activation via dynamic conformational changes of von Willebrand factor under shear.

Shear-induced conformational changes of von Willebrand factor (VWF) play an important role in platelet activation. A novel approach describing VWF unfolding on the platelet surface under dynamic shear stress is proposed. Cumulative effect of dynamic shear on platelet activation via conformational changes of VWF is analysed. The critical condition of shear-induced platelet activation is formulated. The explicit expression for the threshold value of cumulative shear stress as a function of VWF multimer size is derived. The results open novel prospects for pharmacological regulation of shear-induced platelet activation through control of VWF multimers size distribution

Parametric diagrams of blood coagulation regimes in the (<i>h</i>, <i>Re</i>) parameter space for two different values of d~, the non-dimensional plaque diameter.

<p>Region “I” denotes regimes in which there is no coagulation, region “II” represents regimes of macroscopic thrombus formation. (a): </p><p></p><p></p><p></p><p><mi>d</mi><mo>~</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>3</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><mn>2</mn><p></p><mo>=</mo><mn>7</mn><p></p><p></p><p></p>; (b): <p></p><p></p><p></p><p><mi>d</mi><mo>~</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><mn>2</mn><p></p><mo>=</mo><mn>7</mn><p></p><p></p><p></p>.<p></p

Successive stages of a solid thrombus formation.

<p>a—thrombus nucleation, b—formation of fibre-like fibrin structure, c—fibre-like structure thickening, d—solid thrombus. Shown are the color maps of <i>N</i>_<i>w</i>—the weight-average number of monomers in fibrin-polymer in the vessel, with red areas representing regions of fibrin gel formation (</p><p></p><p></p><p></p><p><mi>N</mi><mi>w</mi></p><mo>≥</mo><p><mi>N</mi><mi>w</mi><mi>s</mi></p><p></p><p></p><p></p>). 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: <i>Re</i> = 130, <i>h</i> = 0.5, <p></p><p></p><p></p><p><mi>d</mi><mo>~</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><mn>2</mn><p></p><mo>=</mo><mn>9</mn><mo>.</mo><mn>5</mn><p></p><p></p><p></p>. Note that only a fragment of the vessel closest to the plaque is depicted.<p></p

Parametric diagram of blood coagulation system regimes in the (Re,μ~2) parameter space.

<p><i>Re</i> is the Reynolds number and </p><p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><mn>2</mn><p></p><p></p><p></p><p></p> 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 <i>Re</i>₁, <i>Re</i>₂ marking the boundary of the coagulation regime for a given <p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><mn>2</mn><p></p><p></p><p></p><p></p> and <p></p><p></p><p></p><p></p><p><mi>μ</mi><mo>~</mo></p><p><mi>m</mi><mi>i</mi><mi>n</mi></p><p></p><p></p><p></p><p></p>—the permeability of the vessel wall below which clotting does not occur under any hydrodynamic conditions. Finally, <i>Re</i> = <i>Re</i>_<i>τ</i>2 indicates the lowest Reynolds number at which the shear stress reaches <i>τ</i>₂ and the local permeability of the vessel reaches <p></p><p></p><p></p><p></p><p><mi>μ</mi><mn>2</mn></p><mo>~</mo><p></p><p></p><p></p><p></p>. <i>h</i> = 0.6, <i>d</i> = 0.4.<p></p

Successive stages of a friable floating fibrin structure formation.

<p>a—thrombus nucleation, b—formation of fibre-like fibrin structure, c—thick and friable floating fibrin structure. Shown are the color maps of <i>N</i>_<i>w</i>—the weight-average number of monomers in fibrin-polymer in the vessel, with red areas representing regions of fibrin gel formation (</p><p></p><p></p><p></p><p><mi>N</mi><mi>w</mi></p><mo>≥</mo><p><mi>N</mi><mi>w</mi><mi>s</mi></p><p></p><p></p><p></p>). Streamlines are plotted to visualize the flow, and the separatrix is shown with a dashed line. Parameters used in these simulations are: <i>Re</i> = 180, <i>h</i> = 0.6, <p></p><p></p><p></p><p><mi>d</mi><mo>~</mo></p><mo>=</mo><mn>0</mn><mo>.</mo><mn>4</mn><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>d</mi><mo>~</mo></p><mo>=</mo><mn>12</mn><p></p><p></p><p></p>. Note that only a fragment of the vessel closest to the plaque is depicted.<p></p

Parameter values.

<p>Parameter values.</p

Geometry of the vessel fragment.

<p><i>L</i>_<i>x</i>, <i>L</i>_<i>y</i> and <i>H</i> correspond to vessel length, cross section diameter and plaque height. Γ_<i>in</i> and Γ_<i>out</i> denote inlet and outlet boundaries respectively. Γ₊ and Γ₋ refer to upper and lower vessel walls respectively.</p