Biomedical Engineering Reference
In-Depth Information
in a framework (the Hippocratic
humoral theory
3
) quite far from the modern scien-
tific approach and that was going to influence the studies of medicine for long time.
We must bear in mind that the discovery of cells dates back to 1655 (Robert Hooke)
and that Red Blood Cells (RBCs) were first described in a frog by the Dutch bio-
logist Jan Swammerdam in 1658 and later (1674) by the initiator of microbiology,
Antoni Ph. van Leeuwenhoek (1632-1723) (a Dutch too). Therefore, before those
dates, only a qualitative approach to the blood coagulation problem can be found.
Many physicians described pathological conditions in women during pregnancy and
post partum that were actually related to thrombosis, but without identifying the real
cause, though the idea that oedema of a limb can be caused by the obstruction of
a blood vessel was occasionally put forward. The celebrated Italian physician Mar-
cello Malpighi (1628-1694) isolated a fibrous component in the clot. The French
Jean-Louis Petit (1674-1750) related the formation of clots with the phenomenon of
hemostasis in a time in which medicine was already gradually adopting a rigorous
scientific attitude
4
. Nevertheless, a real progress in the study of blood coagulation
was still quite far.
Thrombi formation and pulmonary embolism were described in 1846 by Rudolf
Virchow [93], still today remembered for the “Virchow triad”, schematically ex-
pressing that vessel wall, altered flow conditions and coagulation are mutually in-
teracting entities [49] (his contributions to medicine were far more important than
the formulation of such a triad). However, a substantial approach to understand-
ing coagulation had to wait until the discovery of
platelets
(see [11, 29, 70]), due
to Max Schultze (in 1865) and to Giulio Bizzozero (1846-1901), who understood
their role in blood coagulation (1881) as Fibrin producers and coined the Italian
name
piastrine
and the German
Blutpl achtten
. Fibrin and its precursor
Fibrinogen
were discovered by Alexander Schmidt (1831-1894), who also conjectured the ex-
istence of an enzyme responsible for the corresponding transition, to which he gave
the name presently used (
Thrombin
) and of its precursor (
Prothrombin
) [81]. The
way was opened to a real scientific investigation of blood clotting. We will return
to the early attempts of modelling the blood coagulation process in Sect. 3.3.4. Here
we stress that all branches of medicine dealing with blood are intimately related to
molecular biology ([67]), and blood clotting can only be explained through a cas-
cade of chemical reactions. In conclusion, we are dealing with a substantially young
and still evolving discipline. Moreover, another frightening step is awaiting the dar-
ing mathematicians: blood rheology. Indeed, from the analysis which follows it will
be clear that no model for blood clotting can be formulated without specific refer-
ence to the fluid dynamical regime in which it takes place. Thus, while the biological
puzzle has gradually taken shape (through laborious assembling and disassembling),
mathematicians (in the authors' opinion) are still wandering in a maze. . .
3
According to Hippocrates four
humours
(blood, phlegm, black bile and yellow bile) had to be in
a proper balance in healthy individuals.
4
A cornerstone in this process was the publication of the topic The
Philosophical Principles of
Medicine
(1725) by Thomas Morgan, philosophically inspired to Newton's
Principia
(1687).
