Biomedical Engineering Reference
In-Depth Information
of keeping up with the developments of the medical theory and of the therapeutical
practice of this multifaceted subject.
3.1 Introduction
Blood coagulation is a well familiar process following a wound and leading to bleed-
ing termination (
hemostasis
). Such a goal is achieved by sealing the lesion with a
clot (or
thrombus
). It is in fact much more important than that, since it intervenes
in repairing small internal injuries that occur spontaneously in blood vessels. It is a
physiological process which keeps alive any being provided with blood, but it can
also be very harmful if it derails from its carefully planned path. Arteries or veins
occlusion
1
(
thrombosis
) can be the consequence of excessive coagulation, while
e.g. spontaneous bleeding is related to defective parts of the coagulation machin-
ery. The aim of this paper is to present a concise review of the literature concerning
mathematical modelling of blood coagulation. Before we come to the mathematical
models, it will be necessary to synthesize the present view of this incredibly com-
plex biological process (Sect. 2), as well as the bleeding disorders that arise as a
consequence of deficiency or dysfunctions of some of the many elements playing
a role in it (Sect. 3.3.1). Previous physiological models will be shortly mentioned
(Sect. 3.3.2, 3.3.4).
First of all, it can be useful to go through some history. Of course bleeding and
blood coagulation have been observed since ancient times. A good review article
on written historical documents is [4]. We quote also the topic [60]. To Huang Ti
(or Di), the legendary Yellow Emperor who reigned sometime between 2698 BC
and 2599 BC, and credited to have founded the Traditional Chinese Medicine
2
,it
is attributed the description of symptoms that clearly suggest arterial thrombosis.
Hippocrates (ca. 460 BC - 370 BC) used the term
leucophlegmatia
for classes of
symptoms including limb swelling, which might well include thrombotic episodes.
Aristotle (384 BC - 322 BC) attributed blood coagulation to the presence in blood
of a fibrous material (we know that Fibrin is a basic constituent of clots), whose re-
moval would prevent the phenomenon. Only at the beginning of the XVIII century,
F. Ruysch in Amsterdam did report experiments of that kind [77]. Aristotle, how-
ever, said that clotting was due to the loss of the heat generated in blood (kind of
congealing), an idea which influenced later scientists (as other wrong statements by
him), due to his enormous reputation. The term thrombosis (from the Greek throm-
bos = clot) is due to Galen (ca. 130 AD - 200 AD), who proposed in particular a
scheme (though far from reality) of the circulatory system. However he still worked
1
Artery thrombosis is painful, while venous thrombosis is not, since veins are not equipped with
nerves. Venous thrombosis presents the risk of pulmonary embolism, which occurs when a throm-
bus fragment gets into the bloodstream reaching a lung.
2
Many discoveries and inventions (the compass, the Chinese calendar) have been attributed to the
Yellow Emperor in a legendary form, but his actual existence is a matter of debate.
