Fig 1.
Illustration of the continuum model and its basic concepts.
A) A continuum model considers a 3D vessel with an ellipsoidal injury site (with a zone of thrombin generation characterized by the time-dependent thrombin flux). Brinkman approach is used to calculate flow inside the thrombus and in the vessel. Thrombus shell and core zones are represented as porous domains with different porosities. Their location depends on the local concentrations of platelet activators- thrombin and ADP and degree of degranulation, as thrombin also triggers platelet dense granule secretion, which results in ADP release. Transport of thrombin and ADP is described by the convection-diffusion equation. B) In a continuum model the local platelets’ state depends on the local concentration of thrombin and ADP. ADP induces reversible platelet activation; low concentration of thrombin induces irreversible platelet activation; high concentration of thrombin additionally induces release of platelet dense granules with ADP, and transformation of a shell platelet into a core platelet if the particular degranulation threshold has been reached.
Fig 2.
Comparison between the continuum model simulations and in vivo experiments on the laser-induced thrombosis in the wild type mice.
A) Model geometry. 3D computational domain consisted of a cylinder representing the vessel and an injury site zone. Vessel diameter was 36 microns, while vessel length was 3060 microns. Injury zone was represented as an oblate ellipsoid with semiaxes of 13.5, 13.5 and 6 microns. Center of the ellipsoid was located on the vessel wall. Blue color marks the zone of thrombin generation. B) Temporal dynamics of thrombus core area and total thrombus area in vivo (data from Movie A [20], orange and red dots) and in the model simulation (green and blue dots). C) Temporal dynamics of the thrombus core area in vivo and in the model simulation (high resolution). D) Images of thrombus showing the core and a shell in the model simulation (vessel lumen is brown, shell is blue, core is dark blue). Flow direction was from top to the bottom. On each image color bar shows the values of porosity corresponding to the colors on this image. Note that thrombus core efficiently occupied the injury site zone.
Fig 3.
Continuum model profiles of thrombin and ADP, dense granule density and platelet activation state.
On A)-D) color bar shows the values of concentration (units [nM]) corresponding to colors on this image. A), B)-Profiles of thrombin at 60 s and 130 s. C), D) - Profiles of ADP at 60 s and 130 s. Note the significant drop of ADP concentration in thrombus at 130 seconds. E), F)- Profiles of dense granule density inside the thrombus at 60 s and 130 s. Color bar shows the values of dense granule density (arbitrary units) corresponding to colors on the image. G), H)- Profiles of platelet activation state at 60 s and 130 s. Platelets reversibly activated by ADP are shown in green, platelets irreversibly activated by thrombin are shown in brown, vessel lumen is blue. Note the depletion of dense granules in a thrombus core at 130 s.
Fig 4.
Comparison between the continuum model simulations and in vivo experiments on laser-induced thrombosis in mice with Hermansky-Pudlak syndrome.
A) Temporal dynamics of thrombus core area and total thrombus area in vivo (light ear mouse, data from Movie D from [20], orange and red dots) and in the model simulation (green and blue dots). B) Upper image: image of a thrombus in the model simulation for HPS mouse at 130 s (vessel lumen is brown, shell is blue, core is dark blue). Flow direction was from top to the bottom. Color bar shows the values of porosity corresponding to colors on this image. Lower image: profile of thrombin in the model simulation for HPS mouse at 130 s. Color bar shows values of thrombin concentration (units [nM]) corresponding to colors on this image. Note the significant decrease of overall thrombus size and thrombus core size in HPS mouse compared to the wild type mouse. C) Overall data on temporal dynamics of thrombus core area and thrombus area in vivo (wild type mouse and mouse with Hermansky-Pudlak syndrome denoted as WT and HPS; data from Movie A (orange and red dots) and Movie D (light magenta and robin egg blue dots) from [20]; and in the model simulations (green and dark blue dots for WT mice; dark purple and dark olive dots for HPS mice).
Fig 5.
Mechanism of thrombus growth and occlusion in the in silico simulations of FeCl3-unduced thrombosis.
A) Model geometry. 2D computational domain consisted of a rectangle representing the vessel and a segment representing the injury site zone. Vessel height was 0.5 mm, vessel length was 42.5 mm. Injury site length was 1 mm. Injury site zone coincided with the zone of thrombin generation. Green color marks the injury site zone. B)-F) show the data from the same simulation which ended in vessel occlusion at 248.6 second. Maximal thrombin flux was 2 pmol/(m2 ⋅ s). At all of the images flow direction was from top to the bottom. B) Image of the thrombus at the time of occlusion. Vessel lumen is brown, thrombus core is dark blue, while thrombus shell is blue. Color bar shows the values of porosity corresponding to colors on the image. C) Platelet activation state at the time of occlusion. Platelets reversibly activated by ADP are shown in green, platelets irreversibly activated by thrombin are shown in brown, vessel lumen is blue. D) The profile of thrombin at the time of occlusion. Color bar shows the values of concentration (unit [nM]) corresponding to colors on the image E) Profile of ADP at the time of occlusion. Color bar designations correspond to panel “D”. F) Profile of dense granule density inside the thrombus at the time of occlusion. Color bar shows the values of dense granule density (arbitrary units) corresponding to the colors on the image. G) Thrombus growth at intermediate value of maximal thrombin flux. Image of a non-occlusive thrombus at 600 seconds. Vessel lumen is brown, thrombus core is dark blue, while thrombus shell is blue. Maximal thrombin flux was 1.5 pmol/(m2 ⋅ s). Color bar designations correspond to panel “B”. H) The effect of turning off the ADP release from platelet dense granules on thrombus growth. Image of a thrombus at 600 seconds. Vessel lumen is brown, thrombus core is dark blue, while thrombus shell is blue. Maximal thrombin flux was 3 pmol/(m2 ⋅ s). Color bar designations correspond to panel “B”. I) Temporal dynamics of a blood flow in the vessel in silico. Red line: simulation with maximal thrombin flux of 3 pmol/(m2 ⋅ s). Orange line: simulation with maximal thrombin flux of 2 pmol/(m2 ⋅ s). Blue line: simulation with maximal thrombin flux of 1.5 pmol/(m2 ⋅ s). Green line: simulation with maximal thrombin flux of 3 pmol/(m2 ⋅ s), when the ADP release from platelet dense granules was turned off. J) Temporal dynamics of the thrombus area in the model simulations. Color designations correspond to panel “I”. K) Temporal dynamics of the thrombus core area in the model simulations. Color designations correspond to panel “I”.
Table 1.
Scenarios of FeCl3-induced thrombosis in 2D model simulations. * Simulations were stopped at the moment of occlusion or, if no occlusion was observed during 600 seconds, simulation lasted 600 seconds.
Fig 6.
Simulation of thrombus growth after the circular vessel injury in 3D.
A) Illustration of the idea suggesting the importance of the large thrombus shell for hemostasis in response to the penetrating injury. Top row: three stages of thrombus formation after the non-penetrating injury. Thrombus becomes smaller due to the decrease in ADP concentration. Thrombus shell is shown in orange, while the core is shown in green. Bottom row: three stages of the hemostatic plug formation upon complete vessel dissection: formation of a large shell allows the thrombus to reach itself from the opposite sides and thus completely occlude the injured vessel. B)-E) 2D axisymmetric computational domain consisted of a cylinder representing the vessel and the injury site zone. Vessel diameter was 36 microns, vessel length was 3060 microns. Injury zone was represented as a torus with an elliptic section with semiaxes of 13.5 and 6 microns. B), C)- Images of thrombus in the model simulation at 40 seconds and at the moment of occlusion (42.123 s). Vessel lumen is brown, shell is blue, while the core is dark blue. Flow direction was from top to the bottom. On each image color bar shows the values of porosity corresponding to colors on this image. D) 3D view of the thrombus at the moment of occlusion. Vessel lumen is brown, shell is blue, core is dark blue. E) Simulation where ADP release from platelet dense granules was turned off. Image of the thrombus in the model simulation at 200 seconds. Vessel lumen is brown, shell is blue, while the core is dark blue. Flow direction was from top to the bottom. Color bar shows values of porosity corresponding to colors on this image.
Table 2.
Model parameters. Designations: MPV - mean platelet volume, WSR - wall shear rate.