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Blood as a new type of active medium Blood as a new type of active medium

Spatial dynamic of clot formation and coagulation disorders Spatial dynamic of clot formation and coagulation disorders

F.I. Ataullakhanov F.I. Ataullakhanov, , M.A. Panteleev M.A. Panteleev

National Research Center for Hematology, Moscow, Russia National Research Center for Hematology, Moscow, Russia

The coagulation cascade: a simplified scheme

platelets tissue factor fibrin platelets + tissue factor tissue factor + fibrin platelets + fibrin platelets + fibrin + tissue factor

Real-time in vivo thrombus formation: confocal microscopy

Falati et al. Nature Medicine 2002; 8: 1175 - 1181

?

The problem of complexity

• 1. More than 50 proteins…
• 2. Interacting in more than 100 reactions…
• 3. With each other, with blood cells, vascular cells, and

extravascular cells…

• 4. In the presence of rapid blood flow…
• 5. And all components are free to diffuse thoughout the

vasculature…

The problems of complexity in coagulation: specification

Basic hypothesis

Such specific tasks for blood coagulation may include: 1) Activation threshold: not to function unless necessary 2) Spatial propagation: to create a 3D clot 3) Termination of propagation: to localize the process and thus avoid thrombosis 4) Coagulation in flow: to function normally or not to function at all.

Complex biochemical systems can be reduced to simpler subsystems, each performing a specific task

Objective of the study

To identify reactions of the coagulation cascade, which are responsible for the specific tasks

• 1. The model is composed of 28 partial differential equations
• 2. The variables include: active coagulation factors, their

inactive precursors, inhibitors, platelets

• 3. Model parameters were kinetic constants (>100) and

concentrations (>40), taken from experimental studies. No adjustment was performed.

• 4. Conditions: physiological temperature and ionic strength

(37ºC, pH 7.2–7.4, 2 Ca++, 150 NaCl)

• 5. In order to develop the model, a hierarchy of increasingly

complex systems was simulated; comparison with experiment was carried out at each step

• 6. The final version of the model was tested by comparison

with >100 experimental curves obtained under different conditions by several laboratories, including ours

Mathematical model

[ ]

t VIIIa

• 2

2

] [ x VIIIa DVIIIa

• =

[ ][

] [ ]

F IIa VIII M F IIa VIII cat

IIa K IIa VIII k +

• +

, ,

[ ]

VIIIa hVIIIa

• A typical model equation

(for a one-dimensional reaction-diffusion system)

Diffusion Production Inhibition

• 1. Reduction (control analysis, Tikhonov's theorem)
• 2. Stability analysis
• 3. Numerical experiments

Methods of model analysis

Task 1: Activation threshold

0.00 0.02 0.04 0.06 0.08 0.10 0.12 1 2 3 4 5 6 7

Fibrin Activation

0.00 0.02 0.04 0.06 0.08 0.10 0.12 1 2 3 4 5 6 7

Fibrin Activation

( )

1

• =

Bx

e A y Ax y =

Final clot density VS activation: model reduction

Factor V is activated No factor V activation

0.00 0.02 0.04 0.06 0.08 0.0 0.2 0.4 0.6 0.8 1.0

Fibrin clot density (a.u.) Activation (pM of TF)

Final clot density VS activation: the experiment

Activation threshold

Activation

Task 2: Spatial propagation

IN VITRO T I M E IN VIVO

The end

Normal Hemophilia A

Panteleev et al. Biophys J. 2006

Contribution of two pathways to factor X activation: the model

10 20 30 0.0 0.5 1.0 1.5 2.0

Factor VIII 0% 1% 5% 10% 20% 40% 100%

Theory

Clot size (mm) Time (min)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 40 30 20 10

Extrinsic

Time (min) Distance (mm) Factor Xa (nM)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 40 30 20 10

Intrinsic

T i m e ( m i n ) Distance (mm) Factor Xa (nM)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 0.0 0.1 0.2 0.3 0.4 0.5 0.6 40 30 20 10

Summary

Time (min) Distance (mm) Factor Xa (nM)

10 20 30 0.0 0.5 1.0 1.5 2.0

Experiment

Clot size (mm) Time (min)

Factor X activation in the reaction-diffusion system

Panteleev et al. Biophys J. 2006

Spatial propagation

Propagation

Task 3: Termination of propagation

20 40 60 0.0 0.5 1.0 1.5 2.0

100 nM thrombomodulin 10 nM thrombomodulin Control Clot size (mm) Time (min)

20 40 60 80 100 0.0 0.5 1.0 1.5 2.0

Final clot size (mm) Thrombomodulin (nM)

Clot localization by thrombumodulin

Model Model+Experiment

Panteleev et al. Biophys J. 2006

Clot localization by thrombumodulin

Panteleev et al. Biophys J. 2006

Termination of propagation

Termination

Task 4: Coagulation in flow

100 200 300 400 500 20 40 60

Lag time (min) Shear rate (min

• 1)

Normal plasma Factor VII activation by Xa is accelerated 10-fold Factor VII activation by Xa is slowed down 10-fold

Coagulation inhibition by blood flow: the model

Coagulation in flow

Flow control

Conclusions: decyphering the coagulation cascade

Propagation Termination Activation Flow control

Acknowledgements

National Research Center for Hematology, Moscow, Russia F.I. Ataullakhanov D.A. Kireev J.V. Krasotkina M.V. Ovanesov M.A. Panteleev A.V. Pokhilko V.I. Sarbash A.M. Shibeko E.I. Sinauridze A.A. Tokarev V.I. Zarnitsina Moscow State University, Moscow, Russia A.N. Balandina A.A. Butylin E.N. Lipets E.S. Lobanova University of Lyon-1, Lyon, France J.-C. Bordet

• C. Negrier
• V. Volpert

University of Maryland, Baltimore, MD, USA N.M. Ananyeva E.L. Saenko