Rheology of blood circulation
. Basic physical laws of liquids
Law of Pascal
Liquid column causes a pressure (hydrostatic pressure) that is directly proportional to the height of the liquid column (h), density of the liquid (p) and gravitational acceleration (g).
h ^height p ^density g = gravitational acceleration
C^\33,322 Pa = 1 mm Hg^>
760 mmHg= 1 atm = 10.3 m H20
Effect of gravity on arterial and venous pressure
CO
Per each 10 cm
Law of Laplace
Relation between distending pressure (P [N/m2]) and tension in the wall of hollow object (T [N/m]) :
For vessel:
Considering thickness of vesse wall (h [m]): T=P-R/h [N/m2]
and R2 are the biggest and the smallest radii of curvature
For sphere:
R1 = R2
Characteristics of vessels
( P.R
	h ^ y-'		P.R/h
vessel	P [kPa]	radius	tension (N/m)	wall thickness	tension (N/m2)
aorta	133	13 mm nebo mene	170	2 mm	85000
| arteries	12	5 mm	60	1 mm	60000
arterioles	8	150-62 |Lim	1.2-0.5	20 |Lim	40000
1 capillaries	4	4 |iim	L6.10"2	1 (Lim	16000
venules	2.6	10 Kim	2,6.10"2	2 (Lim	13000
veins	2	200 |Lim a vice	0,4	0,5 mm	800
vena cava	1,33	16 mm	21	1,5 mm	14000
Continuity equation
The volume of fluid flowing through a tube (vessel) per unit of time (Q [\/s]) is constant
vessel
aorta arterioles capilaries venules vena cava
v - velocity      S - area Average blood velocity in vessels
■
5.6 l/min
diameter
- 2.6 cm 20-50 |wn
4-9 |um
- 20 [am
- 3 cm
number
1
~5x106 ~5x109 32x106
total area
-5.3 cm2 ~ 60 cm2
2000 cm2 -100 cm2 ~ 14 cm2
1.5 cm/s
~ 0.04 cm/s
~ 1 cm/s
7 cm/s
Relation between total cross-sectional area of vessels and
mean flow velocity
aorta
arteries
arterioles
capilares
venules
veins
v. cava
Individual vessel diameter (cm) 2.6
+ 0.8
9
0.3-0.06   0.002 0.0009
Number 1            Increasing 0.16-109	5-109 0.5-109	Decreasing 2
Joint cross-sectional area (cm2)	3500	
	^^^ 2700	
500/		
_    5.3          20 20		^^100       30 10
Mean flow velocity Va (cm * s 1)
6
Implication at aortic aneurysm
S^Vj = S2v2 a je-li Sf^S,, musi pl&tit: Vj>v,
2* R2
1 2 2		
		
For
P2>Pi
Poiseuille - Hagen equation
co
0 1	r
<-	-►
The flow of liquid \n the cylindrical tube (Q) is directly proportional to the pressure difference between two ends of the tube (AP=PA-PB), to the fourth power of the tube radius (r) and inversely proportional to tube length (I) and to the viscosity of liquid (r|).
Limitation:
» For stationary flow in Newtonian fluids where viscosity is constant and independent on flow velocity.
Vascular resistance (Rv):a consequence of the friction vessel wall.
een fluid and
Parallel arrangement of vessels
Series arrangement of vessels
Relation between vessel radius and peripheral resistance
Total peripheral resistance (TPR) of vascular system
90 ml/s
,mean
3 mm Hg
a,mean
AP      Pa-Pv Pa ~   Q ~    Q     ~   Q ~ 90
93__mmHg s
ml
For constant Q: tTPR =^> t Pa =^> hypertension,....
2. Rheological features of blood
and vessels
Blood viscosity
Effect of hematocrit
Effect of diameter in small vessels
8
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	6
	
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4—>	
	
	
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>,	
-t—»	
"co	
C	
	2
>	
	1
	0
Fahraes-Lindqvist efekt
Blood
I I
Plasma Water
cap. arterioles
J-L
J_L
5 10 50 100 500 1000 Vessel inside diameter (u:m)
Other factors causing increase of viscosity:
• decrease of blood flow velocity
• elevation of plasma proteins
• In small arteries the velocity profile of the flowing blood has a parabolic shape. In the bigger arteries it has a piston shape.
• The layer close to vessel wall is poor of erythrocytes.
Pathological states causing turbulent flow: aneurisma, stenosis, arteriosclerosis, decreased blood viscosity, .
Elasticity of vessels
Pulse wave velocity (PWV)
I- /v
h
*•  PWV P
Einc) - modulus of stiffness
Moens-Korteweg (1878)
In aorta PWV = 4 - 6 m/s
Mechanisms of venous return
od circulati
plic .kap iláry lie. artérie
Low-pressure system (reservoir function)
pulmonary 100% circulation
systemic circulation
15%
25%
skin and other organs ■ /
plic. vény 4 velké plieni
vény
Cardiac output in rest 5 - 6 l/min
After load up to 20 l/min
15% (3%)
120/80 mm Hg
(50%) aort
artérie
arterioly (4%) kapiláry
20% (3%)
High-pressure system ^jJ (3^b)        (supply function)
Blood pressure
Dependence of blood pressure on cardiac output and vascular parameters
Model of blood pressure changes in aorta