Marjorie Nicolas, Jean-François Abgrall, Vincent Rodin,
Pascal Ballet and Jacques Tisseau.
Multiagent simulation of blood coagulation.
ISTH'01, Congress of the International Society on Thrombosis and Haemostasis,
Supplement to the Journal Thrombosis and Haemostasis, page 2139,
Paris (France), 6-12 July 2001.
Abstract:
We propose a new computerized approach to model and simulate blood coagulation.
Our model is based on multi-agents system, individual-centered, where
autonomous entities - the agents - perceive their environment with adapted
sensors, decide what to do according to their internal state, and finally react
with other agents. This kind of computerized agent are very similar to
biological cells and molecules. The design of cells follows three main stages.
First, we choose a 3D geometrical shape as the cell membrane. Second, we put
sensors - the cell receptors - on this virtual membrane. Third, we define
the behavior of the virtual cells. Behaviors can be either algorithms
- mathematical functions, differential equations, production rules -
or another multi-agent to model the cell functions. The choice between
algorithm and multi-agent system depend on the type of cell. A library of
predefined behaviors is available in our system: expression of receptors,
internalization of receptors, mitosis, apoptosis, signal transduction, and
new behaviors can be implemented according to specific need. We design a
multi-agent model of coagulation: the vessel wall area is 200x200
µm2 wide, covered with endothelial cells topped by a volume
of 200x200xx50 µm3 of plasma.
An injury of 50x30 µm2 is created in the center of the
endothelium, under which appear tissue factor on fibroblasts and von Willebrand
factor. Platelets, coagulation factors - II, V, VII, VIII, IX, X, XI -,
inhibitors - antithrombin AT, protein C, protein S, thrombomodulin,
protein C-inhibitor, protein Z and ZPI, TFPI, alpha-2M- are all randomly
distributed with their known concentration within the plasma. Inhibition by AT
and the protein C-protein S complex take also place on the endothelium surface.
The main steps of coagulation are simulated: 41 reactions occur concerning 32
types of proteins and three types of cells, into the blood as well as onto
the surface of platelets. In this model, interactions between agents - cells,
enzymes, cofactors - are local: two agents can interact only if they are in the
immediate surrounding, taking into account their relative distance and affinity.
The instantaneous state of each agent may be observed at any time, viewed on
different curves, and even modified by the user.
The thrombin generation curve obtained in our model is very similar to the one
observed in vitro: initialy a small amount of thrombin is generated
corresponding to extrinsic pathway, quickly inhibited by the TFPI complex, and
is followed by an explosive generation of thrombin. Then a slow decrease of the
curve takes place due to the inhibition systems. The coagulation process can be
inspected during simulation using a 3D viewer. To validate our system, we
simulate hemophilia A and B, their treatment by means of factor VIIa;
thrombophilia - factor V Leiden, antithrombin deficiency, protein C
deficiency -, and treatment by heparin. So our model can be used as a tool to
experiment new biological models, to discover new thrombophilic abnormalities,
to test interactions between different thrombophilic disorder, to prepare in
vitro experiments on coagulation, and to find new anticoagulants. It is the
individual-centered approach that enables the modelling of complex biological
systems.
[link]
[Nicolas01a.pdf]