Arterial System & Hemodynamics
Arterial system
Pressures in the circulation
Arterial pressure during diastole
Pulse pressure and work of the heart
Hemodynamics is the study of the physical principles
that govern blood flow in the cardiovascular system.
Factors affecting resistance to flow
Laminar & turbulent flow
Tension, pressure and radius
Arterial system
The arterial system consists of:
Elastic arteries: major distribution vessels with a large component of elastic
tissue and low resistance: aorta, brachiocephalic, common carotid, subclavian
and pulmonary arteries.
Muscular arteries: distributing branches with more muscular tissue and less
elastic tissue: radial, femoral, coronary and cerebral arteries.
Arterioles: terminal branches that supply the capillaries.
Mean & pulse pressures in the circulation
80
Systolic pressure
60
40
Diastolic
pressure
20
Shaded area = systolic pressure - diastolic = pulse pressure
L ventricle
L atrium
Veins
Capillaries
Arteries
Rt ventricle
Rt atrium
Veins
Venules
Pulmonary
Capillaries
Arteries
Systemic
Arterioles
100
Pulse pressure
Pressure, mm Hg
120
L ventricle
= MAP
Pulse pressure depends on stroke volume and aortic compliance
Peak systolic pressure & pulse pressure are determined by
stroke volume & aortic compliance.
Compliance depends on the elastic tissue of the aorta.
Aortic valve closure
Stroke volume
Pulse pressure
Mean arterial pressure
Aortic
compliance
Pulse pressure = peak systolic minus diastolic pressure.
A decrease in aortic compliance will result in a higher peak systolic
pressure & pulse pressure (assuming stroke volume is unchanged).
Arterial pressure is maintained during diastole by recoil of the aorta
The stroke volume is ejected during the rapid ejection period & is
accommodated by expansion of the aorta.
Aortic pressure is maintained during diastole by recoil of the aorta as blood
flows to the periphery.
Because of the elasticity of the aorta and large arteries, the pulsatile pressure signal
is gradually dampened so that flow is steady (not pulsatile) in the venules.
pressure
Aorta
systole
Left Ventricle
diastole
During diastole the aortic valve is closed and recoil
of the elastic aorta drives blood to the periphery
Central and peripheral aortic pressures
Simultaneously recorded pressures from the aortic root (Ao) and femoral artery (FA)
demonstrate delayed transmission and a higher systolic pressure in the femoral
artery.
Although peak pressure is higher in the femoral artery than the aorta, average
driving pressure (MAP) is higher in the aorta than the femoral artery.
There is smoothing of the pressure waveform and loss of the dicrotic notch between
the aorta and femoral artery.
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The work of the heart consists of pumping volume against pressure
Work = force (f) operating over distance (dl): W = (f)( dl)
For work done by a piston with area A moving against pressure P,
f
A
f  P A 
P
A
W  P A dl 
A dl  volume
W  P V 
(V) so
dl
For the left ventricle:
P = afterload = arterial pressure when the aortic valve is open &
V = stroke volume, so
cardiac work = stroke volume x afterload
P
Systolic and pulse pressures increase with age
Arterial pressure
Determinants of pulse pressure:
Stroke volume
Aortic compliance
Aging & atherosclerosis
 aortic compliance
 systolic pressure & pulse pressure
 cardiac work due to  systolic pressure
150
systolic
100
mean
diastolic
50
20
40
60
80
Age
A decrease in aortic compliance or an
increase in afterload increase cardiac work
% increase in volume
Cardiac work = stroke volume x afterload.
Cardiac work  stroke volume x systolic BP.
Increasing systolic pressure increases cardiac work.
Compliance of the aorta minimizes peak systolic pressure & cardiac work.
Cardiac work increases with age, & in hypertension, aortic stenosis or coarctation.
C = DV/DP
250
Difference in aortic compliance in
young versus old subjects
200
150
75 years old
100
50
60
100
140
Pressure, mm Hg
180
Arterial, arteriolar & capillary resistance
The resistance of an individual vessel is inversely proportional to radius so
R artery < R arteriole < R capillary
The total resistance of a category of vessels is determined by the total cross
sectional area of all the vessels and the radius of the individual vessels.
Comparing arteries & arterioles supplying an organ, the total resistance of the
arterioles is greater than the resistance of the arteries.
Comparing arterioles & capillaries, the total cross sectional area of the capillaries
is so much greater than the area of the arterioles that the total resistance of the
capillaries is less than the resistance of the arterioles.
The greatest pressure drop in the circulation is across the arterioles.
Series & parallel resistances
Series and parallel resistance
Resistances in series are additive; total resistance equals
the sum of individual resistances.
Resistances in parallel add as the inverse sum, like
parallel electrical circuits:
1
R total

1
1
1


...
R1 R 2 R 3
Most vessels of a given category are arranged in parallel.
Conductance is the inverse of resistance.
Conduc tan ce 
1
F

R DP
For Parallel circuits conductances are additive
Ctotal = C1 + C2 + C3
Parallel resistances in the systemic circulation
Arterial beds are arranged in parallel
Venous pressure is small compared to arterial
pressure.
Blood pressure is nearly the same in all large
arteries, so DP is the same in all vascular beds:
DP = MAP – VP  MAP and
MAP = CO X TPR
The resistance of each arterial bed is set by its
own arteriolar tone
Coronary arteries
Arteries to CNS
Arteries to limbs
& trunk
Aorta
TPR is less than the resistance of any single
arterial bed.
For example:
Arteries to stomach,
spleen, pancreas, gut
TPR = MAP/CO
Renal resistance = MAP/renal flow
Hepatic artery
And renal flow < CO so
Renal resistance > TPR
There are multiple parallel paths for blood
flow so total peripheral resistance is less
than resistance in any one bed.
Renal arteries
Laminar & turbulent flow
Normal flow in the circulation is laminar.
Laminar (or streamlined) flow exhibits maximal
velocity at the center of the vessel, and
concentric thin layers of plasma with gradually
decreasing velocity toward the walls of the
vessel. Laminar flow is silent.
Plasma flowing closest to the vessel wall
exerts a drag on the wall (shear stress) that
influences endothelial function.
Turbulent flow exhibits irregular radial mixing of
blood as overall flow occurs in the longitudinal
direction.
Turbulent flow usually causes vibrations that
are audible with the stethoscope as murmurs
or bruits.
The pressure gradient required to drive
turbulent flow is greater than that required to
drive laminar flow so turbulence increases
cardiac work.
Laminar
Turbulent
Causes of turbulent flow
Flow in the vascular system is normally laminar.
Turbulence occurs if Reynold’s number (NR) exceeds 3000:
NR 
rDv
h
Factors predisposing to development of turbulence in flowing fluid include:
Greater density (r)
larger vessel diameter (D)
High velocity (v)
Low viscosity (h)
In addition, turbulence is likely in the presence of abrupt changes in vessel diameter
or irregularities in vessel walls as may occur with atherosclerosis or other pathology.
Examples of turbulent flow:
Flow across an obstruction (aortic stenosis, coarctation)
Abnormally high flow velocity (high CO & reduced viscosity in severe anemia)
Regurgitant flow across an incompetent heart valve
Abnormal shunt from a high to low pressure chamber (ventricular septal defect)
Presence of turbulent flow increases the likelihood of development of blood clots
Viscosity and hematocrit
Viscosity of a fluid is its resistance to flow resulting from molecular cohesion.
Blood is a complex mixture of fluid and cells; blood viscosity increases with
hematocrit.
Resistance to blood flow is
proportional to viscosity (h):
R
8Lη
πr 4
viscosity
Viscosity of whole blood (solid line) relative to
plasma (dashed line) as a function of hematocrit
Normal
hematocrit
polycythemia
anemia
10
30
50
Hematocrit
70
Vessel diameter and viscosity of blood
Blood viscosity decreases in vessels with diameter < 0.3 mm (300 mm)
Mechanism is complicated but the effect reduces resistance to blood flow.
Most of the resistance in the systemic circulation is from arterioles with small
diameters. Lower resistance reduces the work of the heart.
Viscosity increases at low temperature, & may reduce blood flow in the
Relative viscosity
extremities & contribute to frost bite.
0.1
0.3
0.2
0.4
Vessel diameter, mm
0.5
Law of Laplace
The law of Laplace states that tension (T) in the wall of a blood vessel
equals the product of transmural pressure (P) and radius (r):
T  Pr
P
T
Tension is a force acting tangential to the surface of a cylinder.
P is transmural pressure (internal pressure minus external)
Transmural pressure equals blood pressure minus tissue pressure.
Extravascular tissue pressure is small & can be ignored so
T  (int ralu min al P)(r )
Law of Laplace and tension in blood vessel walls
Elastic arteries
Distributing arteries
Arterioles
Capillaries
Venules
Veins
Vena cava
Intravascular Pressure
mm Hg dynes/cm2
I00
130,000
90
120,000
60
80,000
30
40,000
20
26,000
15
20,000
10
13,000
Radius
1.3 cm
0.5 cm
0.15 mm - 62 mm
4 mm
10mm
200 mm
1.6 cm
Tension
dynes/cm.
270,000
60,000
1,200 - 500
16
26
400
21,000
Amount of
Elastic tissue
++++
+++
elastic intima
None
None
+
++
T = Pr
The amount of elastic tissue in the vessel wall correlates with the wall tension.
Elastic tissue maintains wall integrity against the outward force of the pressure.
The table shows that a very small tension in the wall of the capillaries suffices to withstand
the intraluminal pressure. For comparison, the breaking strength of a strip of Kleenex one
cm wide is about 50,000 dynes per cm, over 3000 times as great as the tension required to
maintain a capillary wall.
Compliance of the aorta as an
example of an elastic artery
Relative volume, %
Slope = Compliance = DV/DP
400
300
200
Compliance decreases
slightly at higher pressures
100
50
100
150
200
Pressure, mm Hg
In this figure smooth muscle is relaxed pharmacologically so the vessel’s compliance
is due primarily to the compliance of the elastic tissue. Compliance of elastic arteries
is nearly constant over the physiological range of pressure.
Compliance in the vena cava as an
example of a large vein
Relative volume, %
Slope = Compliance = DV/DP
400
300
200
Compliance
decreases as cross
section becomes
circular
100
50
Maximal physiological
pressure
100
150
Pressure, mm Hg
In this figure smooth muscle is relaxed; the compliance is due primarily to
the changes vessel geometry.
Contribution of collagen & elastic fibers to passive tension development
Collagen fibers only
Tension, dynes/cm x 103
T= Pr
160
Intact artery
120
Collagen fibers are least
compliant, develop greatest
tension for a given radius.
80
elastic fibers only
40
100
120
140
160
180
Relative radius, %
Passive tension development (smooth muscle relaxed) with increasing radius in
an intact artery or an artery with only collagen fibers (elastic fibers digested) or
only elastic fibers (collagen fibers digested).
Arterial segment studied in vitro by injecting fluid & measuring radius & tension.
Wall tension and pathological changes
T = Pr
Arteries: If weakening of the wall causes dilatation (aneurism) , as the radius
increases the tension required to maintain wall integrity increases. If the wall is
too weak to maintain the tension, it will rupture.
The heart: Pathological dilation of the heart as occurs in heart failure increases
the radius of the ventricles. As a result, more tension must be generated to
create a given pressure, increasing the work of the heart & causing
progression of heart failure.