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Blood as a new type of active medium
Spatial dynamic of clot formation and coagulation disorders

F.I. Ataullakhanov, M.A. Panteleev

National Research Center for Hematology, Moscow, Russia


The coagulation cascade: a simplified scheme


Real-time in vivo thrombus formation: confocal microscopy
platelets tissue factor fibrin platelets + tissue factor tissue factor + fibrin platelets + fibrin platelets + fibrin + tissue factor

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


The problem of complexity

?


The problems of complexity in coagulation: specification
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...

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

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.

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


Mathematical model
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 (37єC, pH 7.2­7.4, 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


A typical model equation
(for a one-dimensional reaction-diffusion system)

[VIIIa]
t

2

= DVIIIa

VIII [VIIIa] kcat , + 2 K x

IIa

[VIII ]
+

VIII , IIa M

[IIa ] [IIa ]
F F

h

VIIIa

[VIIIa]

Diffusion

Production

Inhibition

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


Task 1: Activation threshold


Final clot density VS activation: model reduction
Factor V is activated
7 6 7 6

No factor V activation

Fibrin

4 3 2 1 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12

Fibrin

5

5 4 3 2 1 0 0.00 0.02 0.04 0.06 0.08 0.10 0.12

Activation

Activation

y= Ae

(

Bx

1

)

y = Ax


Final clot density VS activation: the experiment
Fibrin clot density (a.u.)
1.0 0.8 0.6 0.4 0.2 0.0 0.00 0.02 0.04 0.06 0.08

Activation (pM of TF)


Activation threshold

Activation


Task 2: Spatial propagation

IN VITRO

TIME

IN VIVO


Hemophilia A

Normal

The end


Contribution of two pathways to factor X activation: the model

Panteleev et al. Biophys J. 2006


Factor X activation in the reaction-diffusion system
Factor Xa (nM)
0.6

0.6

Factor Xa (nM)

0.6

Extrinsic

0.5 0.4 0.3 0.2 0.1 0.0 40

Intrinsic

0.5 0.4 0.3 0.2 0.1 0. 400 30 20

Summary

0.5 0.4 0.3 0.2 0.1 0. 400

(min)

(min)

30 20

20 0.0 0.5 1.0 1.5 2.0 2.5 3.0 0

Time

0.0

0.5

1.0

Distance (mm)

1.5

2.0

2.5

3.0

0

0.0

0.5

1.0

Distance (mm)

1.5

2.0

2.5

3.0

0

Time

10

Distance (mm)

2.0

Theory

Factor VIII 0% 1% 1.5 5% 10% 1.0 20% 40% 100%
0.5

2.0

Experiment

Clot size (mm)

0.0

0

10

20

30

Clot size (mm)

1.5

1.0

0.5

0.0

0

10

20

30

Time (min)

Time (min)

Panteleev et al. Biophys J. 2006

Time

10

10

(min)

30

Factor Xa (nM)


Spatial propagation
Propagation


Task 3: Termination of propagation


Clot localization by thrombumodulin
Model
Final clot size (mm)
2.0

Model+Experiment
2.0 1.5 1.0 0.5 0.0

Clot size (mm)

Control
1.5

10 nM thrombomodulin
1.0

0.5

100 nM thrombomodulin

0.0

0

20

40

60

0

20

40

60

80

100

Time (min)

Thrombomodulin (nM)

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


Coagulation inhibition by blood flow: the model
Normal plasma Factor VII activation by Xa is accelerated 10-fold Factor VII activation by Xa is slowed down 10-fold

Lag time (min)

60

40

20

0

0

100

200

300

400

500

Shear rate (min-1)


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 University of Lyon-1, Lyon, France J.V. Krasotkina J.-C. Bordet M.V. Ovanesov C. Negrier M.A. Panteleev V. Volpert A.V. Pokhilko V.I. Sarbash A.M. Shibeko University of Maryland, Baltimore, MD, USA E.I. Sinauridze N.M. Ananyeva A.A. Tokarev E.L. Saenko V.I. Zarnitsina Moscow State University, Moscow, Russia A.N. Balandina A.A. Butylin E.N. Lipets E.S. Lobanova