Mechanisms of regulation of the hemostatic system • Platelet functioning (adhesion, activation, aggregation) – cell hemostasis • Blood clotting – plasma hemostasis • Blood flow – carrier Alexey Tokarev, PhD Federal Research and Clinical Centre of Pediatric Hematology, Oncology and Immunology, National Research Center for Hematology (Ministry of Health and Social Development of Russian Federation, Moscow) Hemostatic plug (health) and thrombus (disease) formation 1/ 3
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Mechanisms of regulation of the hemostatic system Platelet functioning (adhesion, activation, aggregation) – cell hemostasis Blood clotting – plasma hemostasis.
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Federal Research and Clinical Centre of Pediatric Hematology, Oncology and Immunology, National Research Center for Hematology
(Ministry of Health and Social Development of Russian Federation, Moscow)
Hemostatic plug (health) and thrombus (disease) formation
1/3
Platelet cross-flow distribution
Tokarev et al., Biophys. J., 2011b
wal
l wall
• Eulerian (PDEs)Modeling approach:
Tokarev et al. 2012. Rus. J Num. Anal. Math. Model.
• Lagrangian (particles)
Tosenberger et al. 2012. Rus. J Num. Anal. Math. Model.
Platelet adhesion
Tokarev et al., Biophys. J., 2011a
Plasma clotting
Fibrin mesh. SEM made by Jean-Claude Bordet (France).
Blood flow
Plug/ thrombus growth
Falati et al (2002)
plateletsplatelets+fibrin
fibrin
• Platelet activation, secretion, aggregation
Ohlmann (2000)
Some general questions:1.Biological: how plug/thrombus growth stops? Can this stopping result from the interaction between platelet and plasma subsystems?2.Methodological: How to mathematically model this complex system in a biology-adequate way? How to deal with platelet activation/signalling? How to connect intra-platelet signalling (detailed model of platelet activation) and changes in platelet properties (simple model of platelet activation)? 2/3
Some general questions:1.What is the mechanism of clotting propagation and stopping?2.How can we properly reduce the dimension of the large system of coupled PDEs (~30 eqs. down to 2-3 eqs.)?
Plasma clotting in non-stirring and slow-flow conditions
Reaction-diffusion PDEs (no flow) Reaction-diffusion-convection PDEs
Slow flow Boundary of fibrin clot (flow-resistant)
Injury
Dashkevich et al. Thrombin propagates in space during blood coagulation as a traveling wave: a new biological excitable medium. Submitted to PNAS.
0,001 2 3 40
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100 Experiment Theory
Thr
ombi
n ac
tivity
, nM
Distance from the activator, mm
Thrombin concentration wave
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Additional slides
Strong non-uniform platelet distribution across blood flow generally arises due to the finiteness of platelet own size
Tokarev et al., Biophys. J., 2011, 101 (8): 1835-1843.
Platelet
Erythrocyte
Excluded volume
wal
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Inflow hematocrit/100%, 0
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Inflow hematocrit/100%, 0
Platelet adhesion from blood flow is controlled by near-wall rebounding collisions with erythrocytes
Tokarev et al., Biophys. J., 2011, 100 (4): 799-808.