Biomedical Engineering Reference
In-Depth Information
The coagulation cascade is initiated by a chemical substance
84
with concentration
Ǜ, called stimulation intensity.
85
It is possible to show that there exists a threshold
value Ǜ
THR
for this stimulation intensity. For sub-threshold stimulation there only
exists a single steady solution in which all concentrations vanish, with the exception
of ŒVIIa, while for higher stimulation an extra nonzero (i.e., positive) steady
state solution exists. The threshold value Ǜ
THR
is fully determined by the model
coefficients:
D K
a
K
1
K
2
K
3
K
4
k
1
k
2
k
3
k
4
Ǜ
THR
(7.77)
Many other models of this type have been developed in the past and are still
used nowadays. After the success of the above simple nonlinear model, a more
complicated one was published in [
253
] with six equations combining linear first
order kinetics with second order and Michaelis-Menten kinetics reaction terms.
This model was capable to simulate the whole coagulation pathway starting from
extrinsic part up to fibrin production. The paper also provided valuable comparison
with experimental data. The same part of coagulation cascade was simulated later in
[
122
] using already 20 coupled ODEs. Even a more complicated model for Tissue
Factor activated coagulation was presented in [
142
] including already 36 equations
to simulate the serine protease inhibition. To study the contact activation (intrinsic
initiation) of blood coagulation, a model with nine equations was proposed and
theoretically studied in [
196
]. A special mathematical model with 35 equations was
proposed in [
133
] for the analysis of Activated Partial Thromboplastin Time (APTT)
commonly used as a laboratory test for diagnosis of blood coagulation disorders. To
include also the role of platelets a simple model with 6 equations was developed
in [
260
] assuming that the concentration of platelets is a function of thrombin
concentration. One of the most commonly used models was published in [
105
]
for the study of stoichiometric regulation of blood coagulation in extrinsic (and
common) pathway cascade. It describes the evolution of 34 species and contains 42
rate constants. This model was used, e.g., in [
43
] to evaluate the significance of the
circulating Factor IXa, in [
40
] for Factor Xa generation by computational modeling,
or in [
41
] to model thrombin generation and risk of disease.
The above list of models is incomplete and still open. Many other models are
used in their spatially nonhomogeneous version or as a part of more complex multi-
scale or multi-phenomena models. Some of those models are mentioned in other
parts of this overview.
84
released from an injured vessel wall (Tissue Factor TF)
85
From the biochemical point of view the first term on the right-hand side of (
7.73
) has a dubious
interpretation. Actually VIIa is present in small quantities but its production has to come from VII
and is mediated by VIIa itself (positive loop), in addition to the Xa coming out at the initiation
stage. All this is replaced by a constant stimulus Ǜ. Thus it should be kept in mind that this model
is a shortcut. Actually, it bypasses the action of the tenase complex, which in turn involves VIIIa
and IXa.
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