2012.09.18.
Biophysics
of blood
circulation
Circulatory system
Talián Csaba Gábor
University of Pécs
Department of Biophysics
2012.18.09.
MRI record
Why does blood flow?
Pressure gradient created by the heart
= ∆
= ~ = Blood pressure: pressure exerted by the flowing blood on the vessel
walls, and on the neighbouring amount of blood
It rhythmically fluctuates because of the
intermittent functioning of the heart
The pressure wave running through the blood
puts the vessel wall in motion: expansion and recoil
palpable (pulse) and measurable
Highest value: systolic pressure
Lowest value: diastolic pressure
p
p
p
Part of the blood’s kinetic energy
is transformed into the potential
(elastic energy of the vessel wall
1
= + ("#" − )
3
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2012.09.18.
Blood pressure
In every 10 cm
∆ = ∆ℎ ∙ ()*++ ∙ = 0,1 ∙ 1.065
= 1.0457 = 8, 9:;<<
1
∙ 9,81 5
2
Systolic (mmHg)
Diastolic (mmHg)
Left ventricle
120
0
Aorta
120
75
Venae cavae
~0
~0
Right atrium
4,5
-4,5
Right ventricle
35
0
Pulmonary artery
35
7-9
Pulmonary vein
7
7
Left atrium
4,5
-4,5
Head arteries (~ +50cm)
~ 80
Foot arteries (~ -100cm)
~ 200
Peripheral circulation
∆ = ( ∙ ∙ ∆ℎ
Peripheral resistance
Function of peripheral circulation: maintain a steady, unidirectional and
laminary (relatively slow) flow
= (Q =)
2. Law of Hagen-Poiseuille
Laws of hydrodynamics can be applied
pressure gradient
∆U = V ∙ W
R ∙ S ∆
∙
8∙T resistance
stroke volume
1. Continuity equation
= = 5 >= ∙ ?= = >5 ∙ ?5
A
= @ B=
A
> = @ >
B=
> ∙ ? = Σ> ∙ ?̅ = constant
It can be influenced by:
Elasticity of the vessels
Intermittent work of the heart
Changes in blood volume (lymph formation)
Σ>KL**M#
O 750
>+MN
Resistance is different in the various kinds of vessels and depends on
pressure fall
viscosity of blood
cross-section of the vessels
Distributive vessels
Resistance vessels
Diffusive vessels
Capacitance vessels
high pressure
high resistance
low velocity, filtration
low pressure
aorta, arteries
arterioles
capillaries
veins, lymph vessels
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2012.09.18.
Pressure fall/gradient
Laws of Kirchoff:
serial coupling
MX" = = + 5 + ⋯ + A
parallel coupling
1
1
1
1
= +
+ ⋯+
MX"
= 5
A
Many small parallel sub-circuits
Lower resultant resistance
Local, independent regulation of the flow
Better oxygen supply
Capillaries in serial coupling only at specific places (e.g. 2 blood circuits!)
Aneurism
Viscosity
Viscosity transforms kinetic energy into heat and lowers blood pressure
positive feedback
Average viscosity of blood ~4,5 mPa·s
A1
v1
incr.
A2
p1
decr.
v2
continuity
equation
It depends on
1.
haematocrit (e.g. leukemia)
2.
concentration of plasma proteins (e.g. globulinemia)
3.
deformability of the cellular components (rbc)
incr.
p2
law of
Bernoulli
suspension of similar sized solid particles is
hard as brick, viscosity of 95% rbc-suspension
is only ~20 mPa·s
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2012.09.18.
Cross-section of the vessels
4.
Aggregation property of rbc (raises viscosity)
5.
flow velocity
= (Q =)
R ∙ S ∆
∙
8∙T = = Z5
= = [\5
rouleaux
Most important way to regulate intensity of current and blood pressure:
Neural and hormonal (chatecolamines)
Segré-Silberberg effect
6.
Vessels’ cross-section (Fåhræus-Lindqvist effect)
In vessels with substantial smooth muscle content:
cell-free
zone
muscular arteries and arterioles
„plasma skimming”
Heart cycle
Generation of impulse
Isovolumetric contraction
Ejection (rapid and reduced)
Ventricular diastole 0,5s
Flow is normally under critical velocity, laminary
At some spaces (valves, stenosis) can speed up causing turbulence
It can be heard as various sounds (heart sounds and murmurs, Korotkov sound)
Ventricular systole 0,3s
Isovolumetric relaxation
Rapid filling
Diastasis
Atrial systole
Atrial systole 0,1s
Atrial diastole 0,7s
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Heart cycle
Pump function
Cardiac output = stroke volume x heart rate
Heart rate = end-diastolic volume – end-systolic volume
120 − 50 = 8_<`
70
ℎ
x75
= 5.250
ℎ
Daily
~ 108.000 heartbeats (75x60x24)
~ 7.560 L blood ejected (5,25x60x24)
Yearly
~ 40 million heartbeats
~ 2,76 million L (2.760m3) blood ejected
http://library.med.utah.edu/kw/pharm/hyper_heart1.html
Components of stroke volume
Ejection fraction (EF)
Ratio of stroke volume and end-diastolic volume
70
O 60%
120
Preload
ab =
End-diastolic pressure or volume in the ventricle
Load/stretch of the heart muscle (cell) before contraction
Effect of the blood returning to heart („filling pressure”)
Increases sarcomer length
Determined by the venous pressure and venous return
Afterload
Tension in the ventricle wall needed to eject blood
Pressure in the ventricle needed to open the semilunar valve
Determined by the systemic resistance/aortic pressure and pulmonary
pressure
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2012.09.18.
Heart muscle
Components of stroke volume
Contractility
Force exerted by the myocytes during contraction
Frank-Starling law of the heart:
stroke volume is directly proportional to end-systolic ventricular volume
higher preload causes a greater stretch of the myocytes (increased sarcomer
length) enhancing contractility
1,6µm
1,0µm
Work of the heart
Volume-pressure loop
A.
B.
C.
D.
Closure of mitral valves
Opening of aortic valve
Closure of aortic valve
Opening of mitral valves
pe O 100Hgmm O 13,5kPa
pe O 3Hgmm O 0,5kPa
staticcomponent = m ∙ ∆n
[
kineticcomponent = o ∙ pe Z
Z
q = 13 ∙ 102 7 ∙ 70 ∙ 10rs q + 0,5 ∙ 0,071 ∙ (0,5 )5
= 910mJ + 9mJ O uZ_ov
Additional effect: stretch of the muscle fibre enhances troponin-C
sensitivity for Ca that increases the number of actin-myosin cross-bridges
rightatrium O 160mJtotal O [, [v
power: P =
1,1J
O [, }~
0,8s
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2012.09.18.
Summary
Gross anatomy of the cardiovascular system
Blood pressure
Peripheral resistance
THANK YOU FOR YOUR ATTENTION!
Pressure fall
Viscosity
Cross-section of the vessels
Phases of the heart cycle
Cardiac output
Work of the heart
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2012.09.18.
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