Biomedical Engineering Reference
In-Depth Information
ficult is to explain the adhesion process, since platelets receptors are specifically
designed to bind e. g. to vWF or to Fibrin. A reasonable explanation is that Fibrin
itself, once produced, can adhere to the surface, providing a suitable substrate to
platelets. In this scenario, the shear stress induced by mechanical devices activates
platelets (even a modest hemolysis (distruction of RBCs), releasing ADP, can help
activating platelets). Let us add that recently in [79] it has been proposed that FXII
can contribute to Thrombin formation, by
autoactivation
to FXIIa in the presence of
an injury or of
artificial surfaces
, somehow reviving its role in intrinsic coagulation.
Indeed it was already observed by O. Rotter (the discoverer of Hageman Factor) that
FXII can become activated in contact with glass [68]. Still in [79] it is suggested that
FXII may have a more important function in angiogenesis.
3.3.4 Some historical remarks on coagulation models
In the Introduction we have reported some historical notes about observations of
blood coagulation. Modelling attempts came much later. Whereas Thrombin forma-
tion and embolism were already known by 1860 ([93]), a first scheme of coagula-
tion was proposed in 1905 by Paul Morawitz ([54]). It was based on just four factors,
namely the last four in the larger modern scheme, FII, FIIa, FI, FIa, and assumed that
thromboplastin (TF) and calcium were responsible for the conversion of Prothrom-
bin into Thrombin. As we said, the theory of the 3-pathway Cascade, that came in
1964, dominated for about forty years. The reader may wonder why in the course of
the exposition of the blood coagulation process we have mentioned Factors from I
to XIII, but we omitted FIV and FVI (we also pointed out that FIII, i.e TF, has an
abnormal position in the list, since it actually comes only in the active form). FIV
and FVI are out of the current terminology. FIV is nothing but the ion Ca2+, and
FVI used to designate an intermediate molecule between FV and FVa, but it was
later identified with FVa. The existence of FVI was suggested by the discoverer of
FV (see P. Owren [62]).
3.4 Mathematical models and numerical simulations
Comprehensive mathematical models of the blood coagulation and fibrinolysis pro-
cesses, describing either the classical concept of
coagulation cascade
or the recently
adopted
cell-based model
, and taking into account physiologic and mechanical fac-
tors, have the potential to identify regions of the arterial tree susceptible to the for-
mation of blood clots and could contribute to a better understanding of these com-
plex phenomena. Kinetic models generally consist of a nonlinear system of partial
differential equations of advection-diffusion-reaction type or a set of ordinary dif-
ferential equations (ODEs), along with appropriate initial and boundary conditions.
Each equation in the system describes the evolution of the concentration of each
species entering the process that leads to clot formation and dissolution. Boundary
conditions simulate the beginning of the whole process following a vessel wall in-
jury. Due to the size of the system and to its nonlinearity, a solution in a closed
