3 Doppler Physics & Fluid Dynamics

Question 1

How is stroke volume calculated?

Answer 1

Blood flow velocity is pulsatile, not constant.

The CSA is the area and the VTI is the stroke distance.

CSA = 0.785 x (diameter)2

Volume (ml/beat) = CSA (cm2) x VTI (cm)

Question 2

What is the continuity equation and what are its assumptions?

Answer 2

The continuity equation is used to calculate valve area.

The law of conservation of mass states that 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.

CSA A x VTI A = CSA B x VTI B

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

Question 3

What are the differences between laminar and turbulent blood flow?

Answer 3

Normal blood flow is laminar in which the blood flows in parallel channels which are uniform in velocity.

Turbulent blood flow, in which blood flows in different directions with different velocities, is present at areas of stenosis.

Question 4

What is Reynolds’ equation?

Answer 4

Reynolds Equation is 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

A Re of < 2000 indicates laminar flow, a Re of 2000-4000 indicates transitional flow and a Re of > 4000 indicates turbulent flow.

Question 5

What is the Bernoulli equation?

Answer 5

The Bernoulli equation is used to calculate the pressure gradient across a valve.

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

∆P = 4 x (V2/2 – V2/1)
∆P = 4 x V2

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 phenomenon in which a jet of fluid follows the curvature of the surface, not a straight line. This is because the jet of fluid creates a low-pressure area between the jet and the surface, creating a difference in pressure, causing the jet to adhere to the 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

The doppler effect is the relative change the in wavelength or frequency of a sound wave between the source and the receiver. If the ultrasound wave is moving towards the receiver, the wavelength decreases and the frequency increases.

Question 10

What is the doppler equation?

Answer 10

V = (c x fd) / (2 x ft x cosθ)

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

Question 11

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

Answer 11

The greater the angle (misalignment), the more the velocity is underestimated, particularly in angles >20°.

Question 12

What is the fast fourier transform?

Answer 12

The fast fourier transform averages the frequencies, converts the frequencies to velocities, and displays the spectrum of frequencies as doppler waveforms to allow spectral analysis.

Question 13

Describe the spectral doppler display.

Answer 13

The spectral doppler display 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 14

What are the mean, modal and maximum velocities and what is velocity variance?

Answer 14

The mean velocity is an average of all of the velocities.

The modal velocity is the most common velocity and is the brightest part of the display. It is used to assess the dominant flow pattern.

The peak velocity is the highest velocity. It is used to assess valvular stenosis or regurgitation severity.

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

Question 15

What is aliasing?

Answer 15

Aliasing is present when the RBC velocity is greater than the Niquist limit and the PWD is unable to accurately measure the RBC velocity.

If the RBC velocity is greater than the Niquist limit, 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 16

What is the Nyquist theorem and the Nyquist limit?

Answer 16

The Nyquist theorem states that to measure the wavelength, the waveform needs to be sampled a minimum of twice per cycle.

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

Niquist limit = PRF/2

Question 17

How is aliasing minimised?

Answer 17

Decreasing the transmitted frequency, decreasing the distance between the sample volume and the transducer, increasing the angle of incidence, adjusting the doppler baseline and adjusting the doppler velocity scale.

Question 18

What is high PRF PWD?

Answer 18

High PRF PWD uses a high PRF so there is sampling at two or more 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 19

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

Answer 19

CWD is able to assess high velocities but is unable to assess velocities at specific points so causes range ambiguity.

PWD is able to assess velocities at specific points with a high resolution but is unable to assess high velocities due to aliasing.

H-PRF PWD is able increase the range of velocities measured (compared to PWD), to partially oppose aliasing, but uses multiple sample volumes and causes range ambiguity.

Question 20

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

Answer 20

Moving target indication is a method, in doppler, 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). Moving target indication uses doppler shift to assess moving targets with high frequency shifts by filtering out signals from static targets with no/low frequency shifts.

Autocorrelation in a method, in CFD, used to estimate the velocity of moving targets across different areas of interest across the image. In CFD, the returning signal is analysed over time for every pixel. Autocorrelation compares the signal over time to estimate the frequency shift. The 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 21

What are the advantages and disadvantages of using mean velocity and velocity variance?

Answer 21

The advantage of mean velocity is that it is quantifiable.

The disadvantage of using mean velocity is its its failure to assess turbulent flow and differentiate complex flow patterns.

Question 22

What are the principles of PW TDI?

Answer 22

PW TDI uses the principles of PWD to quantitatively assess myocardial velocity in one area.

The TDI trace shows the velocity towards the apex/transducer during systole (S’), the movement away from the apex/transducer during early diastole (E’), and the further movement away from the apex/transducer during atrial systole (A’).

Question 23

What filters are required by PW TDI?

Answer 23

Myocardial velocity is low and myocardial amplitude is high. Therefore, PW TDI uses low pass low gain filters to remove high velocity/frequency low amplitude signals from RBCs.

Question 24

What are the principles of CFD?

Answer 24

CFD uses the principles of PWD but CFD assesses blood flow at multiple points in one area, not within one sample volume. The 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 25

What is packet size in CFD?

Answer 25

Packet size is 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 26

What is the effect of colour scale on FR and aliasing?

Answer 26

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 27

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

Answer 27

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.

Velocity range adjusts the vertical velocity scale.

Question 28

How do CWD and PWD work?

Answer 28

CWD 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.

PWD 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.