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BLOOD CIRCULATION
Department of Biomedical Sciences
Medical University of Lodz
CONSTRUCTION OF THE
CIRCULATORY SYSTEM
Circulatory System
VESSELS CONSTRUCTION
HEART
The primary function of
the heart is blood
pumping
Pumping is done by the
rhythmic contractions of
different batches of the
heart
Factors causing
contractions - are
periodically passing
through the heart muscle
cells membranes - waves
of depolarization and
repolarization of cells to
the resting phase
THE RHYTHM OF THE HEART
It is relatively constant. At rest, the number of heartbeats per 1
minute depends on age (in children is higher), gender (in women
is higher than man) and level of physical strenght
In an adult an average value is 60-80 beats/min.
Heart rhythm accelerates under the influence of emotional
factors, elevated ambient temperature and physical effort
During each contraction of the heart, the main artery is extruded
to a certain amount of blood called the ejection fraction (in the
systemic circuit). The average value for healthy adults in rest is
50-70 ml.
Thus, the total amount of blood extruded per minute through the
left ventricle into the circulatory system is defined as a minute
or cardiac output – it is the product of the rhythm and the level
of the systol
In adults and healthy people, with an average level of fitness, at
rest, 4-5 liters of blood is pumped by the heart per one minute
(the cardiac output)
ENERGETICS OF HEART ACTION
•
Volumetric = External Work (P dV) – performed against
the pressure in the aorta and pulmonary artery
•Kinetic = Internal Work (½ ρν2) – performed in order to
introduce kinetic energy to the blood (to move blood)
were:
W – work [J]
V – volume [m3]
P – pressure [Pa]
ρ − density [kg/m3]
ν – velocity [m/s]
WL = PL ∆V + ½ ρν2 ∆V
WR = PR ∆V + ½ ρν2 ∆V
Left
Right
Volumetric work 0.91 J/contraction
0.15 J/contraction
Kinetic work
0.006 J/contraction
0.006 J/contraction
At rest:
Volumetric work = 1.1 J/contraction
Kinetic work
= 0.01 J/contraction
HEART ACTION
The heart is a pump where energy
is used not to fill the atrium and
the ventricle with blood, but for
emptying it
It is not a lift-and-force pump, the
vacuum is not produced during its
filling
The pressure in the heart
chambers is always positive
The efficiency energy of the
heart is:
at rest - 15%
in stress conditions - 40%
BLOOD FUNCTIONS:
Transport - atmospheric oxygen from the lungs to the tissues
and CO2 from the tissues to the lungs; of nutrients from the
digestive tract and removal of metabolic products; of
hormones, enzymes and antibodies.
Maintaining a relatively constant H2O content in the tissues
through the exchange of fluids (with lymph or urine).
Control of body temperature - blood moves towards the
skin to cool us down, as excess heat can escape easier.
Protection - in the form of our immune system. Blood carries
white blood cells which help fight disease. Platelets also clot
the blood to stop us from bleeding.
BLOOD COMPOSITION
BLOOD OXYGEN CAPACITY
100 ml of blood contains 15 g of hemoglobin
1 g of hemoglobin binds ca. 1.34 ml of O2
Maximum oxygen capacity of blood is 20 ml
per 100 ml of blood (ratio 1:5)
PRESSURE GRADIENT IN LARGE AND
SMALL CIRCULATION
Aorta
Caval vein
100 hPa (70 mm Hg)
160 hPa (120 mm Hg)
0
Pulmonary artery 10 hPa (8 mm Hg)
30 hPa (15 mm Hg)
Pulmonary vein
9 hPa (7 mm Hg)
diastole
systole
diastole
systole
MOVEMENT OF BLOOD IS CAUSED BY PRESSURE DIFFERENCE
BETWEEN ARTERIAL AND VENOUS SYSTEMS
AND THAT IS SUSTAINED BY HEART WORK
INFLUENCE OF GRAVITY FIELD
Hydrostatic blood pressure P = ρ x g
For ρ ≈ 103 kg/m3
g ≈ 10 m/s2
x
h
P = (100h) in hPa
P = (75 h) in mm Hg
Pressure in the artery of the head:
(height (h) =0.5 m) = 130 – 50 = 80 hPa
Pressure in the large artery of the foot:
(h = 1 m) = 130 + 100 = 230 hPa
LAMINAR BLOOD FLOW
Laminar flow - the normal condition for blood flow throughout
most of the circulatory system
Concentric layers of blood are moving in parallel down the length
of a blood vessel
The highest velocity (Vmax) - the center of the vessel.
The lowest velocity (V=0) - along the vessel wall
The flow profile is parabolic once laminar flow is fully developed
Characteristic for the long, straight blood vessels, under steady
flow conditions
TURBULENT FLOW
Laminar flow – a fluid flows in parallel layers
Turbulent flow – only immediately after the semilunar
valves close (heart sounds)
Re η
νk =
rρ
Re – Reynolds’ number (approx.
1000)
νk – critical velocity [m/s]
η – viscosity coefficient [Ns/m2]
r – vessel radius [m]
ρ – blood density [kg/m3]
CHANGE IN VESSEL LUMEN
LAWS REGULATING BLOOD FLOW
1) FLOW CONTINUITY PRINCIPLE
∆t
∆V
∆t
∆V
ν1
J=
Flow rate
S1
ν
x
1 = S2 x
S – area [m2]
ν- velocity [m/s]
t – time [s]
V – volume [m3]
ν2
ν2
∆V [m3]
∆t
[s]
J1 = J2
Accounting for vessel ramification
J = ∑ Jn
S = ∑ Sn
S
capillary
Saorta
= 750
Not accounted for:
• vessel pulsation
• exchange of blood with
the surroundings
2) BERNOULLI’S LAW
p + hρ
ρg + ½ ρv2 = const
where:
p – static pressure [Pa]
h – hight [m]
ρ – density [kg/m3]
v –velocity [m/s]
g – acceleration of gravity [m/s2]
For horizontal vessel:
p + ½ ρv2 = const
THE TOTAL SUM OF STATIC PRESSURE (p), HYDROSTATIC
PRESSURE (hrg) AND HYDRODYNAMIC PRESSURE (½ ρv2) IS
CONSTANT
DURING THE FLOW FOR ANY CROSS-SECTION OF THE TUBE
3) POISEUILLE’S LAW
For non-turbulent, non-pulsatile fluid flow through a uniform straight pipe,
the volume flow rate (J) is:
1) directly proportional to the pressure difference (∆P) between the ends of
the tube,
2) inversely proportional to the length (l) of the tube,
3) inversely proportional to the viscosity (η) of the fluid,
4) proportional to the fourth power of the radius (r4) of the tube.
π 1 r4
∆V
J=
=
8ηl
∆t
1
J=
∆P
R
8
R=
η l4
r
π
∆P
[m3/s]
R – resistance of the vessel blood inflow [Pa s/m3]
2-FOLD INCREASE IN RADIUS DECREASES RESISTANCE BY 16-FOLD!
I.E. RESISTANCE VERY SENSITIVE TO RADIUS
VASCULAR WALL RESILIENCE
left ventricle
pump
arteries
veins
air chamber
heart (right part)
container
resistance
Arterial walls – characterized by large resilience
module, are always outstretched, fulfill the role of
potential energy container
Venous walls – easily change their volume, fulfill the
role of voluminal container, the venous part contains
70% of the blood
VASCULAR RESISTANCE
VOLUME
veins
RESISTANCE
venules
arteries
arterioles
arteries
Capillaries
Capillaries
veins
venules
arterioles
Volume
Resistance
vessels
vessels
GEOMETRIC FACTOR OF VASCULAR
RESISTANCE TO BLOOD FLOW
L
r4
= geometric factor
F
L
= spring tension
The effect of spring tension
is spring pressure of the wall in accordance
with the law of Laplace :
T
P=
r
where: P – wall spring pressure on blood [Pa]
T – spring tension in the wall [N/m]
r – vessel radius [m]
Small deformations (elastin fibers)
Large deformations (collagen fibers)
PULSE
Every 0,8 s 70 cm3 of blood is
ejected (ejection volume at
rest)
Loop resistance causes bulge
in aorta, i.e. blood kinetic
energy is changed into
potential energy of the aorta
wall resilience
Pulse wave occurs – a wave of
spring deformations in the
wall of artery vessels
C=F
√
Εd
2 ρr
C – pulse wave velocity [m/s]
F – empirical coefficient
ρ – density [kg/m3]
E – Young module [Pa = N/m2]
d – artery wall thickness [m]
r – vessel radius [m]
BLOOD VISCOSITY
F=
ηA
∆ν
∆H [N]
F
A
- shear stress [N/m2]
ν
H
- shear rate [1/s]
shear stress
η =
shear rate
Viscosity coefficient
[Ns/m2] is the ratio of
the shearing stress to
the shear rate in a fluid.
where:
A – area [m2]
H – hight [m]
v –velocity [m/s]
η – viscosity coefficienty [Ns/m2]
FACTORS AFFECTING BLOOD
VISCOSITY
diameter of blood vessels - below 0.3mm viscosity is lower
(Magnus Effect)
temperature – in 0°C viscosity is 2.5-times higher
concentration of plasma proteins
flow rate – diameter 0.1-0.2mm: velocity increases but
viscosity decreases
presence of cellular components of blood, particularly
hematocrit (% of content of erythrocytes in the blood volume)
size (7µm) and deformability of erythrocytes
AXIAL
ACCUMULATION OF
BLOOD CELLS
(MAGNUS EFFECT)
VISCOELASTICITY
Vessels smaller tham
3 µm – viscosity increases,
but elasticity occurs