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