• 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

}

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