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? Questions Conduit arteries: large arteries near the heart and their main branches Why are conduit arteries distensible?

Arteries are distensible because: 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 second Pressure [mmHg] 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 second Pressure [mmHg]

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/L 0 ) Elastic (Young’s) modulus (E) –stress/strain=  F L0F L0 A LA L = Poisson’s ratio (, nu) –transverse strain /longitudinal strain= -  x /  y –for incompressible materials 

Pressure (mmHg) Relative Radius PP P RR R PP P RR R

Incremental strain Incremental stress Incremental elastic modulus (structural stiffness) Pressure (mmHg) RR PP RR R P Pressure (mmHg) Relative Radius PP P RR R PP P RR R 

R/Ro E inc [Nm -2 x 10 5 ] Variation of E inc with stretch

Structural & functional stiffness Geometry Structure Functional stiffness Structural stiffness

Some haemodynamics  P Q Steady flow resistance = k  p E R 2 = k  µl R 4 µ:viscosity l: length R: inner radius k 1 :constant Z c  ˆ P ˆ Q Characteristic impedance (pulsatile flow “resistance”)

Just a touch more Z c  cc R2R2 c:pulse wave velocity  :tissue & blood density c  k  E p Measure pulse wave velocity non invasively to estimate functional stiffness = k  E p R 2

Summary The relationship between vessel dimensions, elasticity and blood flow Structural stiffness Functional stiffness Characteristic impedance (a measure of all the factors which combine to limit pulsatile flow due to a pulsatile pressure gradient) Structure & geometry Functional stiffness & diameter

Electrical analogue R 1 : resistance of large vessels L 1 : inertia of blood C 1 : compliance of large vessels R 2 : peripheral resistance R 3 : source resistance of heart R1R1 L1L1 R3R3 R2R2 C1C1

Reflections In 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 pressure negative 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 mean pressure/mean flow pulsatile pressure/pulsatile flow resistance characteristic impedance ∆t Pressure Flow Time

Fourier analysis H1 + H2 H H1 + H2 + H3 H4 Mean H1 H2 Measured H1+H2+H3+H4

Q(t) = q 0 + q 1 Cos(  t -  1 ) + q 2 Cos(  t -  2 ) + q 3 Cos(  t -  3 ) +... P(t) = p 0 + p 1 Cos(  t -  1 ) + p 2 Cos(  t -  2 ) + p 3 Cos(  t -  3 ) +... |Z| = |p n |/|q n |Pressure/Flow F =  n -  n Pressure - Flow