Modelling blood coagulation
Part I: the biological background
Prague, August 2011
Antonio Fasano Dipartimento di Matematica U. Dini, Univ. Firenze
Istituto di Analisi dei Sistemi ed Informatica “A. Ruberti” - CNR Viale Manzoni 30, Roma, 00185, Italy
Survey paper:
A. Fasano, A. Sequeira, R. Santos.
Blood coagulation: a puzzle for biologists, a maze for mathematicians.
MODELLING PHYSIOLOGICAL FLOWS D. Ambrosi, A. Quarteroni, G. Rozza (Editors), Springer Italia. Chapt. 3, (2011) 44-77
When a lesion is produced on a blood vessel an impressively complex machine is set in motion
leading to coagulation. The result is the
formation of a clot (or thrombus) sealing the wound.
Blood coagulation goes in parallel with the
antagonist process (fibrinolysis) whose goal is the dissolution of the clot.
A two-step process
• primary hemostasis: platelets bind to von Willebrand Factor and collagen at the wound site, forming the so-called “white thrombus”
• secondary hemostasis: goes through a chemical cascade in which many “Factors” intervene
clot remains confined
The hemostatic system is in a state of permanent background activity
but also normally inhibited
an engine permanently on a brake constantly applied
Maria Spelterini crossing Niagara Falls (July 7, 1876)
Difference: blood coagulation has to
be fast .
Similarity: no mistakes are allowed
Correct path for blood coagulation is narrow
thrombosis
What a pulmonary embolism can produce
(courtesy of Dr. Jeremi Mizerski)
Bleeding disorders
Thrombocytopenic purpura (due to low platelets count)
FIBRIN
PLATELETS (linked among themselves and to fibrin)
RBC
WBC
Clots are many components systems
Some history
The Yellow Emperor (Huang Di)
Before 2600 B.C.
Symptoms attributable to arterial thrombosis
Hippocrates ( 460 370 B.C.)
With the term leucophlegmatia describes limbs swelling
Hippocrates’ humoral theory: blood, phlegm, black bile, yellow bile
Aristotle (384-322 B.C.)
Blood coagulation needs some “fibrous material” and is due to heat loss
A fibrous component of clots was isolated by Marcello Malpighi (1628-1694)
Galen of Pergamon
Aelius (Claudius) Galenus (129-200?)
Coined the word thrombosis
(from the Greek thrombos = clot)
He sketched an erroneous scheme of blood circulation.
William Harvey (1578-1657)
Exercitatio anatomica de motu cordis et sanguinis in animalibus (1628)
Firts systematic description of blood circulation
Robert Hooke (1635 –1703)
Discovered what he called cells in thin slices of cork (1665)
Anthony Leeuwenhoek (1632-1723)
Greatly improved the microscope.
He investigated on RBC’s (1674)
(previously identified in frogs by Jan Swammerdam (1658 ))
Jean-Louis Petit (1674–1750)
French surgeon
Connected the formation of clots to the process of
hemostasis
The three elements
Hypercoagulability Hemodynamic changes (stasis, turbulence) Endothelial injury/dysfunction
are today known as the “Virchow triad”
Rudolf Virchow (1821-1902)
described pulmonary embolism in 1846
Giulio Bizzozero (1846 – 1901)
Max Johann Sigismund Schultze (1825-1874)
The discovery of platelets (1865)
Platelets have a number of receptors on their membrane which intervene in many processes:
• aggregation,
• binding to specific molecules,
• reacting to stress,
• etc.
Platelets perform a number of operations
They possess two families of granules: -granules and dense ()-granules, able to release various substances when platelets are “activated”, able to activate more platelets (*)
They can synthesize factors important in the coagulation process
They can modify their cytoskeleton to assume different shapes
(*) ASPIRIN exterts its anticoagulant action at this stage
activated platelets
Red Blood Cells (RBC): diam. 8 m, concentration 56/mm3, lifespan 120 days (approximate data), no nucleus
Platelets: diameter of 24 m, life span 5-9 days, discoid shape (at rest), concentration 1.54105 /mm3, no nucleus
star shaped platelets (rolling)
adventitia Tunica media
intima
Erik Adolf von Willebrand (1870-1949), Finland
Identified (1924) the bleeding disorder later called von Willebrand disease (vWD)
Today we know that vWD is due to deficiency or dysfunction of the so-called von Willebrand Factor (vWF): it is released by Weibel-Palade bodies
vWF is one of the many “Factors” entering the coagulation process
Some of the Factors have been labelled by Roman numbers
in the order of their discovery: FI – FXIII
Usually they come in pairs: inactivated (usually a zymogen = enzyme precursor) and activated (usually an enzyme)
FI = fibrinogen FIa = fibrin : the polymer making the clot skeleton
FII = prothrombin FIIa = thrombin (has a key role)
There are many more !!
They act through a chemical cascade
Rome (1958). Committee to number coagulation Factors
A first scheme for blood coagulation, proposed in 1905 by Paul Morawitz, was based on just four factors:
• prothrombin FII
• thrombin FIIa
• fibrinogen FI
• fibrin FIa
They do intervene in the last steps of the cascade
The 3-pathway Cascade Model was proposed in 1964 independently by
and by
It has remained unquestioned till very recently
The revolution of the last decade
etc…
Blood coagulation has two stages:
• primary hemostasis
• secondary hemostasis (cell-based model)
Primary Hemostasis
Platelets rolling on the blood vessel wall adhere at the lesion site to von Willebrand Factor and to Collagen
This is a very complicated 2-step process Two kinds of receptors intervene
(fast-reversible/slow-irreversible)
we omit the details
vWF can be released by activated EC’s even when damage is limited (Z. Xu et al. Soft Matter 5 (2009) 769-779)
Secondary hemostasis
(the cell-based model)
The triggering event is the exposure to
blood of the Tissue Factor (TF) contained
in the endothelium, which combines in a
complex with FVIIa circulating in very small quantities.
Initiation
End.Cell +TF
FVIIa FVII
End.Cell +TF
FVIIa FIX
FIXa
FX
FXa
FV
FVa
diffuses to platelets
End.Cell +TF
FXa+FVa: prothrombinase
FII FIIa Thrombin (small amount)
excess FXa inactivated
Lesion site
FVIIa available in small amounts in circulating blood
Activates complex TF-FVII
TF-FVII
Amplification
Small amount of thrombin and of FIXa available
FIIa breaks vWF
FVIII
vWF
FVIII
Platelet FV
FVa
+ stress
Cross links among platelets
FXI
FXIa
FIIa
FVIIIa
produces more FIXa
Platelets are activated and release the contents
of granules
Three actions of thrombin
1
2
3 and
activated platelet
FVIIIa + FIXa tenase
Propagation
FX
FVa + FXa prothrombinase
FII
FIIa more FVa is produced ETC.
To fibrin production …
FIIa
FI
FIa
FXIII
FXIIIa
Fibrin network
cross links
Fibrin production
Consolidation
thrombin
Endothelium TM
termination
TAFI (protects fibrin)
PC APC PS Va
VIIIa
AT III
TFPI
FIXa, FXa, FXIa, FXIIa, (FIIA)
FXa, TF+FVIIa
Thrombin Activatable Fibrinolysis Inhibitor
Tissue Factor Pathway Inhibitor
Heparin enhanced
fibrinolysis
Plasminogen (accumulated during the thrombus growth)
TAFI (Thrombin Activatable Fibrinolysis Inhibitor)
tPA urokinase
Plasmin
Grown fibrin network
fibrinolysis
(some fragments may recombine)
(retarded by plasmin inhibitors)
slowly released by endothelium
(positive feedback: produces tPA)
(tissue Plasminogen Activator)
WARNING
The preceding description has been simplified
• there are many more platelets activators (ADP, TxA2, etc.)
• vitamin K has an important role in catalyzing most of
the “activations”
• platelets may produce FXI and even TF !!!
WARNING
The preceding description has been simplified
• there are many more platelets activators (ADP, TxA2, etc.)
• vitamin K has an important role in catalyzing most of
the “activations”
• platelets may produce FXI and even TF !!!
A further revolution??
Papers reporting evidence of platelet-derived TF
G. Davì, C Patrono. Platelet activation and atherothrombosis. N.Engl. J. Med. 357 (2007) 2482-2494. O. Panes, V. Matus, C.G. Sàez, T. Quiroga, J. Pereira, D. Mezzano. Human platelets synthesize and express functional tissue factor. Blood 109 (2007) 5242-5250.
fibrin fibres are formed through a multi-step process
For details about fibrin and fibrin fibres formation see A.L. Fogelson, J.P.Keener. Toward an understanding of fibrin branching structure. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 81 (2010) 1-24
A way of understanding how each element works is to study the
bleeding disorder associated with its
deficiency or dysfunction
The list of bleeding disorders is impressively long
For instance
Hemophilia A, B, C are caused by deficiency of
Factors VIII, IX, XI respectively
The inadequacy of the 3-pathway cascade model
High Molecular Weight Kininogen
(slow activator of FXII, produced by
platelets)
Kallikrein: fast activator of FXII
From now on the process is similar to the cell-based
model
FVIII bypassed by the extrinsic pathway
In the cascade model
• the intrinsic and extrinsic pathway can independently produce coagulation
• the extrinsic pathway bypasses FVIII
Experimental facts:
• FXII deficiency mild (or no) bleeding disorder
• FVIII deficiency is the cause of Hemophilia A
We conclude that
• the extrinsic pathway cannot be correct
• the intrinsic pathway either is not present or at most it gives a small contribution
FXII can autoactivate in the presence of
artificial surfaces
(coagulation on implanted artificial bodies is a matter of great concern)
Modelling bleeding disorders is important in order to model therapies
What is the effect of Aspirin
Coumadin etc. ?
How to prevent coagulation after the implantation of stents?
Clotting is essentially related with the blood flow conditions
• thrombi in arteries are different from those in veins • altered flow conditions can cause thrombosis: remarkable examples are
atrial fibrillation Deep Vein Thrombosis (DVT)
Hence, whatever model is taken for the biochemical process has to be coupled with blood flow
Blood rheology is another very complicated field …