Haemodynamics - Chapter 3 Flashcards
Which cardiac phase is usually displayed in spectral waveforms?
Both although in healthy large arteries, there is nearly no diastolic flow in diastole
- diastolic is usually phases 2+3 of triphasic
What are the 2 fundamental properties of a fluid that are important when determining fluid motion?
Density and Viscosity
Why is density of a fluid (p) assumed as constant?
Fluid is generally assumed incompressible
What is viscosity?
‘Stickiness’ caused by the internal friction and shear (sliding of layers over each other)
What is a Newtonian fluid?
A fluid with constant viscosity for all velocity changes or shear rates
What is shear rate?
The velocity gradient caused by fluid layers sliding over each other
What does viscosity of fluid depend upon?
Temperature and haematocrit
Why is volume flow innacurate?
Vessel wall diameter changes at different points in the cardiac cycle
How does flow change in a tube with no branches?
Volume flow is constant throughout its length
How does flow change post-bifurcation?
The sum of the flow in the 2 vessels must equal the flow in the parent vessel
What is the continuity equation?
A2 = A1 v1/v2
A = area
v = velocity
What are the two energy components of blood flow?
Kinetic Energy and Potential Energy
Why do we use energy density rather than total energy for blood flow?
Blood is liquid and will change shape
What is potential energy equal to?
The pressure of the fluid on an object placed within it - blood pressure or fluid pressure
How does fluid incompressibility impact pressure changes?
A change in pressure at one point will be transmitted to all other points
What is pressure?
Force / area (N / m^2, Pascals)
How does mmHg compare to N?
1mmHg = 133.3 Pa
What are the 3 components to fluid pressure?
- Static filling pressure
- Hydrostatic pressure
- Dynamic pressure
What is static filling pressure?
The residual pressure that exists in a supine person in the absence of any blood flow - e.g. dead person
- results from fact circulation is closed system e.g. pressure in a bike tyre
- is typically 5 - 10 mmhg
What is hydrostatic pressure?
The fluid pressure due to the force of gravity acting between 2 points
Why does hydrostatic pressure have a negative sign?
An increase in height causes a decrease in hydrostatic pressure
What is the equation for hydrostatic pressure?
Hydrostatic pressure = pgh
Why is hydrostatic pressure not available to do work on blood flow?
Circulation is a closed system - increases in pressure at one point will cause decrease in pressure elsewhere
What is dynamic pressure?
The increase in pressure as a result of contraction of the ventricles
- it is the only component of the total fluid pressure that is available to do work on the blood
What is kinetic energy?
The energy associated with a moving mass
What is the equation for kinetic energy?
KE = 1/2 mv**2
What is p(rho)?
Density
How does KE relate to density?
KE = 1/2 pv**2
How much energy us stored as pressure?
120mmHg * 133.3 = 15,996Jm-3
How big is kinetic energy in normal arteries?
p = 1.06x10-3 kgm-3
v = 0.6m/s
KE = 190Jm-3
How does KE compare to the energy due to fluid pressure?
It is much smaller
Why does blood flow around the circulation?
Due to differences in total fluid energy - in particular blood flows down a pressure gradient
What is the Bernoulli Principle?
Just as mass of fluid does not change, the total energy of blood remains constant
- assuming no energy is lost to friction and there is steady flow
How does the Bernoulli principle relate to vessel diameter decreases?
Area decreases so velocity will increase, so for energy to be conserved, fluid pressure must decrease
Why does fluid pressure drop as blood moves around the circulation?
Energy losses due to acceleration and deceleration (inertial losses) and viscous losses (friction)
What is the main source of energy loss as fluid moves steadily along a smooth tube?
Frictional losses due to viscosity of the fluid
What equation relates viscosity and energy loss?
Poiseuille’s Law
What can Poiseuille’s Law be used to calculate?
The work that must be done to move fluid along the length of a tube
What is Poiseuille’s Law dependent on?
- Strongly dependent on radius (r**2)
- Linearly dependent on length of the tube
- Linearly dependent on the velocity of fluid
What is approx. resistance of large arteries?
Low < 5 mmHg
What is total resistance of vessels 1 & 2 in series?
RT = R1 + R2
What is total resistance of vessels 1 & 2 in parallel?
1 / Rt = 1/R1 + 1/R2
What is EDV very dependent on?
Peripheral Resistance
Why does distal artery disease cause increases in EDV/
Distal disease can restrict the outflow - this causes the pressure gradient to remain positive throughout the whole cardiac cycle
What are inertial forces?
The forces causing fluid to resist changes in direction or velocity
- The fluid tends to resist in proportion to its mass
What is Newton’s second law?
F = ma
What are inertial losses?
The energy losses when there is a change in direction or velocity of blood
How does inertial energy loss compare with viscous energy loss?
Inertial energy loss is proportional to v**2 and viscous energy loss is just proportional to v
- hence inertial losses often exceed viscous
What are streamlines?
Lines indicating the direction of flow of individual particles - tangents of flow
When does plug flow occur?
In large arteries e.g. aorta
What are the units for Reynolds number?
No units - they cancel
What is Reynolds number dependent on?
Vessel diameter, density, velocity and viscosity
What is the Reynolds equation?
Re = (Dpv) / u
At what Reynolds numbers does the transition from laminar to turbulent flow occur?
2000 - 2500
What is critical velocity?
The velocity above which turbulence is likely to occur
How does critical velocity change with vessel diameter?
Smaller vessel diameter = bigger critical velocity
- unlikely to get turbulence in healthy, straight small vessel
When can turbulence be seen in normal vessel?
When the vessel is acting as a collateral for other vessels e.g. the vertebral for an occluded ICA
- turbulence is due to high flow
How does pulsatile flow impact turbulence?
Turbulence is more likely to occur with continuous flow when compared to pulsatile
What is the boundary layer?
The layer of fluid adjacent to the vessel wall, and is influenced by the solid drag of this surface
What is boundary layer separation?
When the boundary layer becomes detached
- can occur at low or high Reynolds numbers
- the boundary layer velocity may reverse
- can occur when flow decelerates when entering a wider vessel
What is post-stenotic dilatation?
Turbulence causing vibrations on the vessel wall may increase its diameter
How does flow through mild stenoses compare to severe?
Flow is still likely to be laminar in mild stenoses
However in severe stenoses, flow will become turbulent and losses will be almost entirely inertial
Why is energy lost according to Bernoulli equation in stenoses?
Heat in turbulent flow
What are entrance and exit losses?
Inertial losses due to the acceleration and deceleration of blood before and after stenoses
What provides most of the energy in blood flow?
Fluid pressure
What are the energy losses through a stenosis?
Entrance loss - inertial loss due to increase in speed
Viscous loss due to friction through the stenosis
Exit loss - inertial loss due to decrease in speed post-stenosis
- note exit loss is usually very large
What accounts for most of the pressure drop through a stenosis?
Entrance and exit losses
- hence two localised stenoses are likely to cause greater energy drop than one long stenosis
What percentage stenosis is needed to cause a significant pressure drop?
50% diameter reduction
What is viscous diffusion?
The process of the boundary layer gradually growing away from the vessel wall
What is the inlet length?
The distance along a narrowed tube that it takes for flow to become fully parabolic
- is also called entrance length
What does inlet length depend on?
Vessel Diameter and Reynold’s number
Why should you place Doppler sample volume at least 4 cm distal to any bifurcations?
This will avoid most distortions of the waveform caused by entrance effects
What is a fluid jet?
The fast jet that occurs when blood goes from stenosis to a larger vessel
- the jet will show turbulence even at low Reynolds numbers (e.g. Re > 10)
Why do eddies form?
Following stenosis, there is a free boundary layer between the fluid in the jet and the surrounding static fluid.
The shear flow along the boundary layer quickly becomes unstable and eddies form
What is a boundary layer?
The layer of fluid adjacent to a vessel wall, where the vessel wall is asserting viscous forces on blood flow
Why does the jet spread out in a cone shape post stenosis?
Small eddies along the boundary layer will transfer their energy to adjacent stationary fluid by viscous frictional forces
What is entrainment?
The process of the jet spreading out like a cone shape post-stenosis
What forces carry the energy in a jet forwards?
Inertial forces acting on the larger eddies
What are the differences between small and large eddies?
Large eddies carry most of the energy of the jet, mainly through inertial forces
Small eddies form around the large eddies and mainly dissipate energy through viscous forces
What forces need to be considered in a curved tube?
Centrifugal force which will push blood to the outside of the bend
- centrifugal forces are strongest on blood at highest velocity - is at the centre of the tube, centrifugal forces dominate pressure forces here
At the near side of the curve, viscous forces slow the fluid and pressure forces dominate.
This induces a circumferential motion along the edge of tube
What happens to flow post-bifurcation?
Velocity increases - fast streamlines will be immediately adjacent to the vessel wall
- this causes formation of another boundary layer
What is boundary layer separation?
Reverse flow close to the vessel wall that can cause eddies and vortices
- Occurs when the boundary layer has travelled far enough in an adverse pressure gradient
In which branch of a bifurcation is flow separation most likely to occur in?
The smaller of the two branches
What is a likely reason for why atheroma often builds up near to bifurcations?
Boundary layer and flow separation causes flow to be less mobile - causing regions of higher shear stress
- this can cause endothelial erosion
Hence, why plaque often builds up on the outer wall of the carotid bulb
What is extramural pressure?
The pressure outside the vessel wall
What is transmural pressure?
The difference between blood pressure and extramural pressure
What does the absolute tension in vessel walls depend on?
Elasticity and any muscle tone within the wall
What is Laplace’s law?
It states the relationship between vessel wall tension, transmural pressure and muscle tone
What is the usual extramural pressure at rest?
Close to atmospheric pressure, so can be considered as zero
What happens to extramural pressure as muscles contract?
This can increase extramural pressure and cause compression of the vessel wallsq
How can respiration influence extramural pressure?
During inhalation it can decrease extramural pressure
What 2 factors can cause the radius of a vessel to change?
- Change in transmural pressure
- If the stress in the vessel wall changes, through active contraction of smooth muscle or structural changes in elastic components of the wall
Is a small or large vessel easier to increase radius?
Larger - think of blowing up balloon
- demonstrated by Laplace’s law
What is strain?
The change in radius size divided by the original radius
What is the effect of increasing smooth muscle tone in a vessel wall?
The wall becomes stiffer, so the stress for a given radius is increased
What is circumferential stress?
The circumferential force per unit area exerted on the vessel wall
