Biomedical Engineering Reference
In-Depth Information
actions occur in a thin boundary layer above the injured surface where all species
are well mixed and are described by a large system of nonlinear ODEs (more than
fifty!), involving kinetic constants taken from the literature. The authors observe
that even these may be not sufficient to describe the specific processes in which they
are interested. The non dimensionalized system is solved by appropriate methods
for stiff ODEs. Numerical simulations have shown that the increase or decrease of
Thrombin concentration depends on the flow shear rate. They also have shown that
an increase in TF binding sites, expected in case of a vascular injury, is respon-
sible for a significant change in the production of Thrombin. Therefore, the avail-
ability of particular surface binding can be a useful threshold. As for the complex
FVIIa-TF activity, it was suggested that platelets adhering to and covering the en-
dothelium might play a dominant role, instead of being chemical inhibitors. From
here one could say that the role of the Tenase pathway, for activating FX is to con-
tinue its production, after the covering of FVIIa-TF by platelets. Finally, regarding
bleeding disorders, the model was able to give a kinetic explanation of the reduced
Thrombin production in the cases of Hemophilia A and B (see also Sect. 3.3.1 and
Sect. 3.4.2).
Extensions of this model to incorporate the chemistry of the Activated Protein C
(APC) pathway on endothelial cells adjacent to the injury, the transport of Throm-
bin and APC between the injury and these endothelial cells, as well as to explore
the effectiveness of coagulation inhibitors like TFPI and APC at a site of injury-
induced thrombosis, have been considered in [25]. See also [41] that presented an
early large scale model for thrombin generation via the extrinsic pathway, involv-
ing 18 ODEs; this model has been extended in [35] to include the role of inhibitors,
namely
stoichiometric anticoagulants
; it consists of 34 ODEs with 42 rate constants,
and in particular shows that for concentrations above the TF threshold the amount
of Thrombin produced is quantitatively equivalent.
Another dynamic model including the role of activated platelets in the coagula-
tion cascade and based on biochemical experiments, was introduced by Xu, Zeng
and Gregersen in [96]. It relies on the concept of the biological cell-based models
and provides a generalization of Khamin and Semenov's model [44]. It consists of a
system of nonlinear ODEs which relates the rate of change in the concentrations of
FXa, FIXa, FVa, FVIIIa and Thrombin at any time, with its rate of formation, inhi-
bition or breakdown. Thrombin is formed in the initiation stage, in small amounts,
thereby activating platelets. It is assumed that the fraction
c
of activated platelets at
a given time depend on its initial value
c
0
and on the Thrombin concentration, as
follows:
f
([
FII
a
])
=
+
c
c
0
FII
a
])
where
f
is at least twice differentiable. The system of ODEs is given by
1
+
f
([
