3.0 - Doppler physics and fluid dynamics

Question 1

Stroke volume calculation

Answer 1

SV = CSA (cm2) x VTI (cm)

CSA = Pi x (diameter/2)^2

Question 2

What is the continuity equation and what are its assumptions?

Answer 2

Used to calculate valve area.

CSA A x VTI A = CSA B x VTI B
CSA AV = CSA LVOT x (VTI LVOT) / (VTI AV)

Law of conservation of mass:
The volume through a closed system is constant so the blood flow rate in one area is equal to the blood flow rate in another area.

This assumes that the blood is incompressible and the vessel is not elastic.

Question 3

What are the differences between laminar and turbulent blood flow?

Answer 3

Laminar = Blood flows in parallel channels which are uniform in velocity (normal blood flow).

Turbulent = Blood flows in different directions with different velocities (areas of stenosis).

Question 4

What is Reynolds’ equation?

Answer 4

Used to assesses blood flow patterns to assess if the blood flow is laminar or turbulent.

Re = (p x v x D) / u
p = density
v = velocity
D = length/diameter
u = viscosity

< 2000 = laminar flow
2000-4000 = transitional flow
> 4000 =turbulent flow

Question 5

What is the Bernoulli equation?

Answer 5

Pressure gradient across a valve.

∆P = 4 x (V2– V1)^2
P=4(v)^2.

If the proximal velocity (V1 - LVOT) is higher, the full Bernoulli equation is used and if the distal velocity (V2 - CWD through AV) is higher, the simplified Bernoulli equation is used.

Question 6

What is the relationship between blood speed, static pressure and potential energy?

Answer 6

P + 1/2pv2 + pgh = constant

P = static pressure (pa)
p = density (kg/m3)
v = velocity (m/s)
g = acceleration time due to gravity (9.81m/s2), h = height (m) which represents the potential energy per unit mass

The higher the speed, the lower the pressure and the lower the potential energy.

If the blood is moving from high to low, the potential energy decreases and the kinetic energy increases.

Question 7

What is the Coanda effect?

Answer 7

A jet of fluid follows the curvature of the surface, not a straight line.
Fluid jet creates a low-pressure area between the jet and the surface = difference in pressure = jet to adheres to surface.

Question 8

What occurs in the transition from laminar flow to turbulent flow?

Answer 8

The transition from laminar flow to turbulent flow is affected by the Reynolds number (fluid density, fluid velocity, fluid viscosity, vessel length), surface roughness and the flow path.

The transition involves the breakdown of uniform channels, the formation of eddies (swirling of fluid and reverse of flow), and increased mixing which result in chaotic flow patterns.

The higher the blood density and velocity, the lower the blood viscosity, and the wider or longer the vessel, the higher the risk of turbulent flow.

Question 9

What is the doppler effect?

Answer 9

Change in the wavelength / frequency of a sound wave between the source and the receiver.

US wave moving towards the receiver = wavelength decreases & frequency increases.

Used to measure velocity.

Question 10

In doppler physics, what is the effect of beam angle on velocity?

Answer 10

Increased angle (misalignment) = underestimated velocity due to a smaller cosine factor.

Particularly in angles >20°.
0° = parallel to flow = most accurate velocity measure.

Question 10

What is the doppler equation?

Answer 10

V = (c x fd) / (2 x ft x cosθ)

velocity = (speed of sound x doppler shift) / (2 x frequency x cos⁡(angle between blood and ultrasound))

Rearrange the equation to give you the doppler shift equation.

Question 11

What is the fast fourier transform?

Answer 11

• Spectral analysis
• Averages the frequencies
• Converts them into velocities
• Displays the spectrum of frequencies as doppler waveforms to allow spectral analysis

Question 12

Describe the spectral doppler display.

Answer 12

It plots frequency shift (velocity) on the y axis and time on the x axis.

Flow towards the transducer is plotted above the line and flow away from the transducer is plotted below the line.

The density of the display represents the amplitude of the signal at that velocity.

Question 13

What is the modal velocity?

Answer 13

The most common velocity and is the brightest part of the display.
Used to assess the dominant flow pattern.
Use doppler

Question 14

What is the mean velocity?

Answer 14

• Use doppler
• An average of all of the velocities.
• Obtain from tracing around the doppler waveform (get this at the same time as you get VTI).

Question 15

What is the maximum/peak velocity?

Answer 15

Highest velocity.
Used to assess valvular stenosis or regurgitation severity.

Question 16

What is velocity variance?

Answer 16

Measures the variability in velocity.
A high velocity variance indicates turbulent blood flow.

Useful where mean velocity is assessed but mean velocity fails to assess turbulent flow and differentiate complex flow patterns.

Question 17

What is aliasing?

Answer 17

When the RBC velocity (velocity returned to the transducer) is greater than the Niquist limit so the PWD is unable to accurately measure the RBC velocity.

The spectral doppler display will show the top of the waveform to be missing and to be transposed to the opposite side of the baseline.

Aliasing may be present in PWD and CFD.

Question 18

What is the Nyquist theorem?

Answer 18

To measure the wavelength, the waveform needs to be sampled a minimum of twice per cycle.

Question 19

What is the Nyquist limit?

Answer 19

The highest doppler shift which is able to be measured by PWD.

Nyquist limit = PRF/2

Question 20

What 5 things can be done to minimised aliasing?

Answer 20

• Decrease the transmitted frequency
• Decrease the distance between the sample volume and the transducer
• Increase the angle of incidence
• Adjusting the doppler baseline
• Adjusting the doppler velocity scale

Question 21

What is high PRF PWD (extended range PWD)?

Answer 21

A high PRF is used = sampling at 2+ sites on the ultrasound beam, one at the point of interest and one or more in an area of low velocity.

Therefore, higher RBC velocities can be measured without aliasing but high PRF PWD causes range ambiguity (the inability to identify the location of the ultrasound).

Question 22

What are the advantages and disadvantages of CWD, PWD and high PRF PWD?

Answer 22

CWD:
- 2 crystals - one transmits and the other receives.
- Obtain the highest velocities
- Unable to assess velocities at specific points = (range ambiguity/lack of depth resolution)

PWD:
- Assess velocities at specific points with a high resolution
- Unable to assess high velocities due to aliasing.

H-PRF PWD:
- Increase the range of velocities measured (compared to PWD), to partially oppose aliasing
- But uses multiple sample volumes and causes range ambiguity

Question 23

In doppler physics, which methods are used to estimate the velocity?

Answer 23

Moving target indication:
- Used to estimate the velocity of moving targets and differentiate between fast moving targets (e.g. blood) and slow moving or static targets (e.g. endocardium).
- Uses doppler shift to assess moving targets with high frequency shifts by filtering out signals from static targets with no/low frequency shifts.

Autocorrelation:
- CFD, used to estimate the velocity of moving targets across different areas of interest across the image.
- The returning signal is analysed over time for every pixel.
- Autocorrelation compares the signal over time to estimate the frequency shift.
- Frequency shift is correlated with the velocity.
- Autocorrelation estimates the velocities and creates a colour map representing the velocity and direction of blood flow (BART).

Question 24

What are the advantages and disadvantages of using mean velocity?

Answer 24

• It is quantifiable.
• Fails to assess turbulent flow and differentiate complex flow patterns.

Question 25

What is PW TDI?

Answer 25

Uses PWD to quantitatively assess myocardial velocity in one area.

S’ - velocity towards the apex/transducer during systole
E’ - the movement away from the apex/transducer during early diastole
A’ - the further movement away from the apex/transducer during atrial systole.

Question 26

What filters are required by PW TDI?

Answer 26

Low pass low gain filters to remove high velocity/frequency low amplitude signals from RBCs because myocardial velocity is low and myocardial amplitude is high.

Question 27

What are the principles of CFD?

Answer 27

Assess blood flow at multiple points in one area, not within one sample volume (Multi-sampled pulsed wave - system takes multiple Doppler measurements at different locations along the vessel or heart chamber creating creates a more complete and accurate representation of the flow over a larger area).

CFD box is superimposed on the 2D image. The CFD display colour codes the blood flow based on its direction and mean velocity within the area. Blood flow towards the transducer is red and blood flow away from the transducer is blue

BART – blue away red towards
Turbulent blood flow, areas with a high velocity variance, are green.

Question 28

What is packet size in CFD?

Answer 28

The number of ultrasound pulses along every scan line used to generate CFD information. The bigger the packet size, the higher the number of pulses, the higher the spatial resolution. The smaller the packet size, the lower the number of pulses, so the higher the temporal resolution (FR). The bigger the packet size, the lower the risk of aliasing.

Question 29

What is the effect of colour scale on frame rate and aliasing?

Answer 29

The higher the velocity scale, the higher PFR, so the higher frame rate (because there is less processing). The higher the velocity scale, the higher the PRF, so the higher the Nyquist limit, so the lower the risk of aliasing.

Question 30

What are the spectral doppler controls (power and gain)?

Answer 30

Transmit power is the level of energy delivered to the patient.

Gain is the amplification of the signal. Gain increases the brightness of the trace. High gain settings increase low level signals but also increase noise.

Baseline shift adjusts the zero line of the display.

Question 31

How does CWD work?

Answer 31

Continuously transmits and receives ultrasound. There are two crystals in the transducer, one transmits ultrasound and the other receives ultrasound. CWD measures signals for the whole length of the beam. Therefore, the spectral doppler display reflects the direction and velocity of the RBCs at every point on the line, not at one point on the line like PWD.

Question 32

How does PWD work?

Answer 32

Intermittently transmits and receives ultrasound. The transducer transmits the pulse, waits for the pulse to return, then transmits another pulse. The transducer samples the received pulse at the sample volume by calculating the time the pulse will take to travel between the transducer and sample volume and back and detecting the signal at that point and ignoring the signals from other points. PWD measures RBC velocity at a set point using the sample volume at the point of interest. CFD uses the principles of PWD.

Question 33

What is volumetric flow and how is it calculated?

Answer 33

• Volume of blood that passes through a specific area of the heart or a vessel over a given period

VolumetricFlow(Q)=CSA×VTI
cm^3

CSA=π×(diameter/2)^2
cm^2

VTI (velocity time integral)= distance a column of blood travels in one cardiac cycle.
cm

Question 34

Cardiac output equation

Answer 34

CardiacOutput=StrokeVolume × HeartRate

SV = CSA X VTI

Question 35

What is the audible range of doppler shift frequencies?

Answer 35

20Hz - 20,000 Hz (20KHz)

Question 36

How does transducer frequency, sample depth and beam angle influence aliasing?

Answer 36

Transducer frequency:
- Higher frequency = higher Doppler shift frequencies. If the Doppler shift exceeds the Nyquist limit, aliasing will occur.
- Lower frequency = reduce the Doppler shift = decrease the likelihood of aliasing.

Sample depth:
- Distance from the transducer to the region of interest.
- Sample depth increases, the PRF decreases = Nyquist limit decreases = increases aliasing likelihood.
- A greater velocity × depth product can cause aliasing more easily, as the system may not be able to sample fast enough to avoid wrapping the frequency back into the detectable range.

Beam angle:
- Good alignment will result in a larger doppler shift = increased chance it will exceed Nyquist limit.

Question 37

List 3 methods to reduce aliasing:

Answer 37

• Use a lower transducer frequency
• Reduce sample depth
• Use higher PRF settings

Question 38

What is scan frequency and what is its effect on the Nyquist limit?

Answer 38

Scan frequency - the frequency of the ultrasound pulses that are emitted by the transducer in a given period.

Higher scan frequencies = higher PRF = raises the Nyquist limit = can measure higher Doppler shifts (therefore higher velocities) before aliasing occurs.