• Conduits – To conduct blood to the organs and periphery • Impedance matching – Minimise cardiac work – Minimise pulse pressure – Control flow according to demand What are arteries for?
Dec 24, 2015
• Conduits– To conduct blood to the organs and periphery
• Impedance matching– Minimise cardiac work– Minimise pulse pressure– Control flow according to demand
What are arteries for?
• What are arteries made of?
• Why do large arteries become stiffer with age (and disease)?
• Why are some people affected more than others?
QuestionsConduit arteries: large arteries near the heart and their main branches
• Why are conduit arteries distensible?
Arteries are distensible because:
80
100
120
1 sec
• The wheel has yet to evolve in the animal kingdom (bacteria have propellers)
• Therefore(?) the heart is a pulsatile pump.
• Its output consists of a pulse wave superimposed on a steady component.
Systolic pressure
Diastolic pressure
Average pressure
Pulse pressure = systolic pressure - diastolic pressure
80
100
120
1 second
Pre
ssur
e [m
mH
g]Aortic pulse wave
• Average pressure determined by resistance of peripheral arteries
• Pulse pressure determined by elasticity of large arteries
Pulse pressure = systolic pressure - diastolic pressure
Systolic pressure
Diastolic pressure
Average pressure
80
100
120
1 second
Pre
ssur
e [m
mH
g]
The pulse is a wave of dilatation
With thanks to Chris Martyn
Similar to a surface wave
A heavenly wave
Speed of the wave is related to the stiffness of the artery it is
traveling in
The stiffer the artery;
the higher the wave speed
Wave speed is proportional to the square root of arterial stiffness
Blood vessel elasticity
• Inelastic Pseudo elasticity
• Non linear• Large strains Strain energy function/incremental approach
• Anisotropic Uni-axial expts./circumferential direction
• Viscoelastic Quasi static experiments
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Stress, strain and elastic modulus
A reminder.
• Stress (, sigma)– Force per unit area = (F/A)
• Strain (, epsilon)– Change in length per unit length = (L/L0)
• Elastic (Young’s) modulus (E)– stress/strain =
F L0
A L=
• Poisson’s ratio (, nu)– transverse strain /longitudinal strain = -x/y – for incompressible materials
2001000
Pressure (mmHg)
Rela
tive R
ad
ius
1.0
1.5
2.0
P
P
R R
P
P
R R
€
inc =ΔR
R Incremental strain
€
inc =ΔPR
hIncremental stress
€
E inc =σ inc
ε inc
= 0.75ΔPR 2
ΔRhIncremental elastic modulus
(structural stiffness)
2001000
Pressure (mmHg)
RR
1.0
1.5
2.0
P
R R
P
2001000
Pressure (mmHg)
Rela
tive R
ad
ius
1.0
1.5
2.0
P
P
R R
P
P
R R
Mean circumferential stress (s) ≈PR
h
(1)
Circumferential strain (e) = C
C
=
R
R
(2)
Circumferenti alelasti cmodulus (E) ≈
1 − υ
2
( )
σ
ε
(3)
≈
0 . 75
PR
2
Δ Rh
(4)
2.62.42.22.01.81.61.41.21.0
R/Ro
0
5
10
15
Einc [Nm-2 x 105]
Variation of Einc with stretch
Structural & functional stiffness
€
E p =ΔPR
ΔR
€
E inc = 0.75ΔPR 2
ΔRh
€
=0.75ΔPR
ΔR x
R
h
€
E p =1.5E inc
h
R
Geometry
Structure
Functionalstiffness
€
E inc = 0.75E p
R
hStructuralstiffness
Some haemodynamics
P Q
Steady flow resistance
= k2
pE
R2
= k
µl
R4
µ: viscosityl: lengthR: inner radiusk1: constant
Zc ˆ P ˆ Q
Characteristic impedance(pulsatile flow “resistance”)
Just a touch more
Zc
c
R2 c: pulse wave velocity: tissue & blood density
c kEpMeasure pulse wave velocity non invasively to estimate functional stiffness
= k2
Ep
R2
SummaryThe relationship between vessel dimensions,
elasticity and blood flow
€
€
E inc =1.5ΔPR 2
ΔR h
E p =ΔPR
ΔR
Zc =ˆ P ˆ Q
Structural stiffness
Functional stiffness
Characteristic impedance(a measure of all the factors which combine to limit pulsatile flow due to a pulsatile pressure gradient)
€
=1.5E inc
h
R
€
=kE p
R2
Structure &geometry
Functional stiffness &diameter
Electrical analogue
R1 : resistance of large vesselsL1 : inertia of bloodC1 : compliance of large vesselsR2 : peripheral resistanceR3 : source resistance of heart
R1 L1
R3 R2C1
ReflectionsIn the arterial system reflections of pressure and flow waves occur wherever there is a change in the local fluid impedance
• Decrease in diameter or increase in stiffness ->positive reflection of pressurenegative reflection of flow
• If no reflections: pressure and flow waves are the same shape
• Arterial disease usually associated with increased reflections (except aneurysms)
• Energy is lost so cardiac output must increase to maintain a given flow
Wave reflection
€
=P
Q mean pressure/mean flow
€
Zc =ˆ P ˆ Q
pulsatile pressure/pulsatile flow
resistance
characteristic impedance
∆t
Pressure
Flow
Time
Fourier analysis36027018090-2-1012 36027018090-2-1012 H1 + H2
H3
36027018090
-2
-1
0
1
2 H1 + H2 + H3H4
36027018090-2-1012
Mean
H1H2
Measured
H1+H2+H3+H4
Q(t) = q0
+ q1Cos(t - 1)+ q2Cos(t - 2)+ q3Cos(t - 3)+ ...
P(t) = p0
+ p1Cos(t - 1)+ p2Cos(t - 2)+ p3Cos(t - 3)+ ...
|Z| = |pn|/|qn|Pressure/Flow
F = n - n Pressure - Flow