Reflections of the pulse wave

Occur whenever there is a change in vessel cross section or stiffness.

Local hydraulic impedance

+

-

+

-

Less stiffStiff

StiffLess stiff

BigSmall

BigSmall

Less stiffStiff

Less stiff

Stiff

Positive and negative wave reflections

Pressure increasesFlow decreases

Pressure decreasesFlow increases

Pressure increasesFlow decreases

Pressure decreasesFlow increases

Reflection coefficient

€

Rp =ZD − ZUZD + ZU

€

=1−cucd⋅adau

1+cucd⋅adau

=1− (velocity ratio/area ratio)

1+ (velocity ratio/area ratio)

Zc = c/a

How to separate forward and backward traveling

waves• Multiple measurements of pressure/flow

diameter and numerical processing of data

• Total occlusion methods

• Impulse methods

Total occlusion method

• Measure pressure in region of interest

€

Pm = Pf + Pb

€

Pmocc = 2Pf

∴ Pf =Pmocc

2

€

Pb = Pm − Pf

= Pm −Pmocc

2

• Apply a total occlusion distal to the region and re-measure pressure

• Substitute for P

How to separate forward and backward traveling

waves• Multiple measurements of pressure/flow

diameter and numerical processing of data

• Total occlusion methods

• Impulse methods

Impulse method

• Generate a sharp spike of pressure/flow and track its movement at different points.

• If sharp enough its reflection can be observed in isolation from the incident wave

Measurement of pulse transmission in vivo

Measurement of pulse transmission in vitro

In-vivo or in-vitro

Propagation and reflection in a uniform tube

50 ms

20 k

Pa

0

150

300

0

100

200

Distance

Distance

Wave propagation in arterial models

Normal artery

Stenosed artery

Reflections at the aorto iliac trifurcation

Reflections in vivo

Vasoconstriction

Pm

Newman DL & Greenwald SE Cardiovascular Research 113: 595-600. (1979)Bertram, CD et al. (1997). Medical Engineering and Physics 19: 212-222.

Pf

Pb

Vasodilation

Pm

Pf

Pb

Do negative reflections occur in the “healthy”

vascular system?

Effect of age on aorto-iliac reflection coefficient

• Post mortem measurements of velocity and area ratios• 46 subjects aged between 3 months and 88 years• Velocity of pressure wave from catheter• Dimensions of junction from radiography

Catheter tip manometer

Abdominal aorta

Greenwald, S.E. et al. (1990) Circulation 82, 114-23.

Effect of age on area & velocity ratio

y = 0.0175x + 0.56R = 0.92

0.5

1.0

1.5

2.0

2.5

0 20 40 60 80 100

Age [y]

AR

y = -0.0023x + 0.95R = 0.92

or

VR

Effect of age on aorto-iliac reflection coefficient

y = -0.0059x + 0.28r = 0.65

-0.50

-0.25

0.00

0.25

0.50

0 20 40 60 80 100

Age [y]

Rp

Young Old/Hypertensive

Pb

Pm

Pb

Pf

Aortic pressure wave

Late reflection augmentsdiastolic pressure

Early reflection augmentssystolic pressure

Pf

Pm

Time scale