4. Arterial Wave Speed

What is pulse wave velocity

The speed at which pressure or velocity changes travel through blood in the arteries

What is arterial wave speed directly related to

arterial stiffness

Why is PWV clinically useful

It provides a quantitative surrogate measure of arterial stiffness and risk of cardiac/cerebral events

What are major cardiovascular risk factors that promote arterial stiffness

High cholesterol, high blood pressure, diabetes, smoking, and ageing

What serious consequences can increased arterial stiffness cause

Heart failure and stroke

What are the cardiovascular risk factors that promote arterial stiffness

high cholesterol, high blood pressure, diabetes, smoking and ageing

What are the three separate processes that increase stiffness in the arterial system

Structural Breakdown of Elastin Fibers, Damage to Endothelial Function, Increase in Mean Arterial Pressure

Structural Breakdown of Elastin Fibers

Occurs primarily in the aorta and Age driven

Damage to Endothelial Function

• Occurs primarily in the smooth muscle conduit arteries

• Disease driven (e.g. T2DM, hypercholesterolemia, atherosclerosis)

Increase in Mean Arterial Pressure

• Occurs systematically throughout the arterial system

Wave Speed Definition

The speed by which the changes in the pressure or velocity travel in a certain medium, and in the context of arterial system, the medium is the blood.

Wave speed is a physical property of the arterial wall and can be either…

regional (along an arterial segment) and local (at the measurement site)

What has PWV been widely used in clinical practices as a surrogate marker for

• cardiac and cerebral events

• Arterial tree stiffness

How can wave speed be measured

Wave speed can be measured regionally or locally

What is foot-to-foot (called time-of-flight)

A method for the measurement of regional wave speed and has been used extensively clinically. It relies on measuring either the pressure or flow waveform at two locations that are at a known distance apart

Wave speed equation

c= 𝐿 /∆t

What is the most commonly used distance for the measurement PWV

carotid-femoral

Sphygmocor

instrument for the measurement of the foot-to-foot wave speed.

How is the ‘foot’ determined

The minimum pressure of each respective wave

How is the time difference determined

The femoral pressure is reversed backward in time until its foot superimposes the foot of the aorta pressure

How is the distance determined

estimate of the distance between the two measurement locations

Reimann Equation

c=sqrt(1/pDs)

Arterial Segment Distensibility Equation

Ds=Cs/A

Ds (Arterial segment distensibility)

the fractional change of the cross sectional dA/A in response of a change in pressure dP

Moens-Kortweg Equation

c=sqrt(Eh/pD)

Assumptions in Moens-Kortweg Equation

• h is very small with respect to D; h«D

• The tube is perfectly elastic

• The fluid is incompressible

Jokowsky Equation

∆𝑃 =𝜌𝑐∆𝑈

Otto Frank Equation

c=sqrt(k/p) ; K=A(dP/dA)

Bramwell-Hill equation

c=1/sqrt(pDs) ; Ds=1/A(dA/dP)

Richard Skalak equation

d𝑃±=𝜌𝑐 𝑑𝑈±

Nico Westerhof Equation

Z0=𝑃̅ / 𝑈̅

Pressure-velocity loop (PU-loop) equation

A PU-loop which provided a graphical as well as quantitative value of the wave speed. The method relied on the water hammer equation in the forward direction

d𝑃+ = 𝜌𝑐 𝑑𝑈+

d𝑃+ and 𝑑𝑈+ are the changes of the measured P and U in the forward direction

Integrating this equation gives

d𝑃+ = 𝜌𝑐 𝑑𝑈+ + P0

P+ are the pressure in the forward direction

𝑈+ are the velocity in the forward direction

P0 is an integration factor (reference pressure)

p is the blood density

c is the wave speed

This is an equation of a straight line, indicating during that during early part of systole when the relationship between P and U is linear, due to the absence of reflected waves

Wave Speed equation

c=+- 1/p (dP+/dU+)

Why can obtaining simultaneous measurement of pressure and velocity be a challenge

Due to the difference in the frequency response of the equipment used for obtaining the measurements.

Diameter-velocity loop (InDU-loop)

c=±1/2 *(𝑑𝑈± /d𝑙𝑛𝐷 ±)

tube law

relating arterial pressure with the luminal cross-sectional area is called the tube law

P = 𝛽 𝐴0 (√𝐴 −√𝐴0 ) + Γ (𝜕𝐴 /𝜕t)

Where 𝛽 = 4 3 ⁄ √𝜋 ℎ𝐸 and Γ = 𝛾 2 ⁄ √𝜋𝐴0

𝛽 and Γ are assumed to be constant and related to the elastic and visco-elastic properties of the arterial wall. A0 is the lumen cross sectional area at P=0

diameter-pressure loop (D2P-loop) equation

c=D0*sqrt(dP/p(dD²))

Theoretical determination of wave speed

c=sqrt ((B/2p) (A^1/4/Ao))

B constant

B=4/3*sqrt(pi) hE

wave speed in terms of cross-sectional area and wall properties

c=sqrt(B/2p * A^1/4/A0)