Pulsatile flow - Chapter 4 Flashcards
For continuous flow in a rigid tube, what are the 3 main influences on flow? (laws)
- Bernoulli’s Principle
- Pouseuille’s Law
- Reynolds Number
Explain Bernoulli’s principle in words?
An increase in speed of fluid occurs simultaneously with a decrease of static pressure or the fluid’s potential energy
What is Bernoulli’s principle derived from?
The conservation of energy and Newton’s second law of motion
What does Poiseuille’s law state?
That flow rate is proportional to the radius to the power of 4
What is the difference between velocity waveforms and flow waveforms?
They will have the same shapes, but units will be different
v = m/s
flow = ms-3
How many radians are in 360 degrees?
2 Pi radians
What are harmonic frequencies?
The simple component sine waves that make up complex waveforms
What are fundamental frequencies?
The lowest frequency of a series of harmonic frequencies that makes up a waveform.
- aka first harmonic
It has the same frequency as the repitition frequency of the complex waveform
What is the fundamental frequency of arterial waveforms?
Heart rate
What are the second and third harmonics?
Sine waves at 2 and 3 times the frequency of the fundamental frequency
What is Fourier Analysis?
Analysis of the amplitude and phase of each harmonic
In theory, how many harmonics can a waveform have?
Infinite
What happens to amplitude as harmonics get higher?
Amplitude decreases
What is the Moens-Korteweg equation?
it determines the speed at which pulse pressure wave travels down an artery
What is Poiseuillie’s law
Change in pressure = (8uLQ) / Pi R**4
What does a negative phase mean?
The waveform lags behind the reference waveform
How do you obtain the original waveform from the harmonics?
You add each harmonic with the correct amplitude and phase
What are continuous or zero-frequency components of waveforms?
The components that give mean amplitude of waveform
What is the Moens-Korteweg equation?
Speed of blood c = Sqrt( E h / 2 r p)
h = wall thickness
p = fluid density
E = rigidity of vessel wall
Why is the true speed of sound by a pulse pressure wave slightly higher than that of the Moens-Korteweg equation
Because compressibility of the wall must be taken into account - wall thickness decreases as it stretches
What are 5 key points of the Moens-Korteweg equation?
- Pulse speed will increase as vessel radius decreases
- Pulse speed will increase as elasticity of the vessel wall decreases
- Peripheral arteries are more elastic (and smaller radius) than large arteries, so pulse speed will be higher
- Atherosclerosis and ageing causes decrease in compliance of arteries = faster pulse
- Higher blood pressure will preload artery wall compliance - so wall will be more rigid, so pulse will be higher
What causes the small increase in pressure following exit from a stenosis?
The conversion of kinetic energy back to fluid pressure
What is pressure?
P = F / A
Force divided per unit area
Does Poiseuille’s law apply to pulsatile or continuous flow?
Continuous
How do you measure pressure difference in pulsatile flow?
Measure instantaneous pressure at different points within the tube
What causes the flow waveform?
The fluid velocity changes caused by the local pressure gradient
Why does peak flow velocity occur before peak pressure?
Flow responds to pressure gradient, rather than pressure itself
- think of surfer ahead of wave
What occurs first: peak flow velocity or peak pressure?
Peak flow velocity
Why does the change in flow lag behind pressure gradient (after first peak)?
Due to Inertia and momentum in the moving column of fluid within the vessel
What does a faster pressure gradient change cause?
A greater lag behind in flow
Is phase lag of flow compared to pressure greater in smaller or larger vessels
Larger vessels
- viscous frictional effects are particularly associated with the boundary layer near the vessel walls
- in wide vessels, walls are further from centre
- so when fluid starts to change direction, it takes longer for the viscous boundary layer to affect the bulk of the fluid
- The bulk of fluid is then initially only affected by inertial forces
What does the Wormsley parameter indicate?
It indicates how a fluid subject to pulsatile flow behaves in a vessel
- it is the equivalent of Reynolds number for unsteady flow
What does a larger Wormsley parameter indicate?
A greater phase lag between the pressure gradient and flow
What happens to amplitude as harmonic increases?
Amplitude decreases - why some can be ignored
What does flow result from in pulsatile waveforms?
Point-to-point pressure gradient
What is characteristic impedance of a waveform?
The ratio of the amplitude between the pressure wave and the flow wave
What does waveform characteristic impedance depend on?
NOT the shape of the waveform
- Properties of the vessel e.g. vessel wall thickness, blood density, XSA,
What does characteristic impedance of a vessel a measure of?
The response in flow to an applied pressure
What properties cause an artery to have a large characteristic impedance?
Stiff walls, small radius
Why may diabetic patients still have pulsatile waveforms at the ankle?
Stiff vessels - calcification
Small diameter
= High characteristic impedance
Generally, how does characteristic impedance of daughter vessels compare to those before bifurcation?
Daughter vessels often have smaller radius and are generally more rigid
= Higher acoustic impedance
What does a change in characteristic impedance cause?
Reflections
What do reflections at the abdominal aorta bifurcation cause?
An increase in abdominal aorta pressure - thought to contribute to aneurysms
Which harmonic of the abdominal aorta is a resonant frequency?
The 4th Harmonic
Why are pressure and flow waves different in practice?
Flow wave is reflected in anti-phase and subtracts from the forward flow phase.
Whereas pressure waves reflect in-phase and add to forward pressure
What describes the forces that need to be overcome by a pulse travelling along a vessel?
Visco-elastic losses
What do visco-elastic losses depend on?
The frequency of oscillation
What causes attenuation of a pulse travelling along a vessel?
Visco-elastic losses
What percentage of attenuation does blood viscosity provide?
Only ~25 - 30%
- the rest is due to visco-elastic losses
What impact does frequency have on attenuation of a wave?
Attenuation increases with frequency, hence higher harmonics are attenuated more than low frequencies
What are harmonic frequencies?
Multiples of the fundamental frequency
What causes the more rounded and damped waveforms further down the arterial tree?
The greater attenuation of the higher frequencies
- hence lower frequencies predominate
What opposes the increased attenuation further down the arterial tree?
The stiffer vessels and smaller diameters
What is radial taper?
The decrease of artery radius further down the arterial tree
What is elastic taper?
The decrease in elasticity of arteries further down the arterial tree
How do elastic taper and radial taper influence characteristic impedance?
They gradually increase characteristic impedance along an unbranched vessel
How is pulse pressure impacted by characteristic impedance?
If characteristic impedance increases, the pulse pressure amplitude also increases
How do non-linear effects impact waveform shape?
They increase the pulsatility of the waveform by moving energy from low frequency harmonics into higher ones
- this increases systolic rise time
What are the two causes of non-linear effects?
- Stress-strain curve for arterial walls is non-linear
- as pressure increases during systole, walls become more rigid - Presence of reflected waves
How does fluid pressure change along the arterial tree?
It decreases, otherwise we would not get net flow
What causes waveform recovery?
The amplification of the pulse pressure wave by radial and elastic taper, and by reflection and non-linear phenomena
Note: velocities will be low and the flow will be poor
What can second peaks or ‘knees’ indicate?
Reflections from distal disease
Why do reflections from multiple branches of the arterial tree overlap each other?
Due to the high velocity of the pulse
ASSUME 1 functionally discrete reflection site
What is the greatest contributor to reflected components of pulse waves?
The higher characteristic impedance of distal branches
What happens to the carotid waveforms when a patient is running?
Iliac and peripheral arteries dilate = less reflection
- So there is a sharper downstroke with no shoulder before the notch
What factors cause waveform damping?
- Small arteries
- increased attenuation of higher frequency harmonics as the Wormersley parameter increases - Distal to a tight stenosis - act as low-pass filter
- In vessels with high flow and turbulence throughout most of the cardiac cycle
- the presence of turbulence indicates that the Reynolds number is high
- flow is unlikely to increase with any physiological change, other than change in HR
- vessel is considered to be carrying maximal flow
- e.g. vertebral flow when ICA is occluded
What is a typical normal SRT?
Systolic Rise Time < 100ms
What is viscous diffusion?
How viscous forces move towards the wall to the centre line
What happens to the boundary layer when fluid flows in one direction for longer?
It gets thicker
What two factors influence how much the boundary layer affects the velocity profile?
- The diameter of the vessel
- The frequency of oscillations
What is the impact of a flattened velocity profile on spectral waveform?
It creates a window
What is a waveform?
The overall change in velocity (or frequency shift) with time for a sample volume
Are accelerating, continuous or decelerating flows more stable?
Accelerating
What are typical speeds of the pulse?
5 - 8 m/s
- note blood speeds are typically much lower < 1m/s
How long does a typical pulse take to reach the extremities?
< 250m/s
Why is pulsatile flow seen in the vena cava?
There is back pressure from the right atrium of the heart
What is phasic flow?
Periods of increased then decreased or absent flow occurring over time
- unrelated to heart rate
