1. 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

2. Platelet cross-flow distribution Tokarev et al., Biophys. J., 2011b 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) platelets platelets+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

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. Thrombin concentration wave 3/3

4. Additional slides

5. 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 wall

6. Platelet adhesion from blood flow is controlled by near-wall rebounding collisions with erythrocytes Tokarev et al., Biophys. J., 2011, 100 (4): 799-808. Convection + shear-induced diffusion Translocation/ activation Detachment Firm adhesion Pushing out by RBC Capture Platelet activation time = const

7. Platelet activation - pathways

8. Platelet activation – phenomenological behaviour