# Doppler Effect and Principles

Doppler Effect and Principles

Jan Kasal

1. Please select the parameters that best match Figure 7.1.

A. 1—pulse duration, 2—period, 3—pulse repetition period (PRP), 4—amplitude

B. 1—wavelength, 2—pulse duration, 3—pulse repetition frequency (PRF), 4—amplitude

C. 1—period, 2—pulse duration, 3—PRP, 4—amplitude

D. 1—frequency, 2—period, 3—spatial pulse length (SPL), 4—amplitude

1. Correct Answer: C. 1—period, 2—pulse duration, 3—PRP, 4—amplitude

Rationale: Several parameters can describe ultrasound waves, which can be viewed as a function of time or a function of distance.

When visualizing the pulsed-wave (PW) Doppler ultrasound waveform as a function of time (Figure 7.13), it can be described by the following parameters: (1) is the duration of one wave and is called the period (P) (expressed in units of time). Its inverse is called the frequency (f) (expressed in Hz). In other words, the frequency is the number of cycles in one second. (2) is the pulse duration (PD), which consists of a discrete pulse of ultrasound energy emitted by the ultrasound probe. Note that in the PW Doppler mode, the PD is limited (the probe sends a signal) and followed by a period of listening without any pulse sent. In CW Doppler, the pulses are sent continuously, without interruption while the probe simultaneously listens. (3) is the pulse repetition period (PRP) and describes the duration between the cycles (1 PRP in PW = emitting time + listening time). The inverse of PRP is called the pulse repetition frequency (PRF). PRF limits the maximum Doppler shift (and thus velocity) that the PW Doppler can measure without aliasing (the Nyquist limit = PRF/2). (4) is the amplitude (A) and describes the difference between the maximum and the mean value of the acoustic signal. The amplitude contributes to acoustic power and intensity. Higher power is associated with the risk of bioeffects.

When visualizing the ultrasound waveform as a function of distance (Figure 7.14), the wavelength (λ) is the spatial distance between individual sound waves, expressed as a unit of distance. The total length of the wave emitted during a PW Doppler pulse is called the spatial pulse length (SPL), and it determines the axial resolution (PW can distinguish between two points along the path of the wave only when the distance between them is more than half of the SPL). One clue for helping to eliminate incorrect answer choices is to pay attention to the units; options offering distance-based parameters (wavelength, SPL) will not be correct here because the x-axis in the diagram is time.

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 27.

2. The following Doppler tracing was recorded from an apical four-chamber view in a patient receiving mechanical ventilation, with a mean airway pressure of 28 cmH2O, and positive end-expiratory pressure (PEEP) of 16 cmH2O (Figure 7.2). Which of the following statements is most accurate?

A. Small deviations in cursor angle may cause a large underestimation in maximal velocity

B. Lowering the lateral resolution underestimates the maximal recorded velocity

C. Increasing the signal-to-noise ratio (SNR) will overestimate the maximal recorded velocity

D. Manipulation of the time gain compensation will improve the estimation of the correct velocity

2. Correct Answer: A. Small deviations in cursor angle may cause a large underestimation in maximal velocity

Rationale: Figure 7.2 shows the continuous-wave (CW) Doppler waveform of tricuspid valve regurgitation in a patient with acute cor pulmonale secondary to ARDS, who is on a significant amount of positive pressure. The objective is to correctly measure the velocity of the blood flow of the tricuspid regurgitation jet using CW Doppler and then apply the modified Bernoulli equation to calculate the pressure gradient. The correct measurement of velocity is essential for an accurate estimate of the gradient between the right atrium and the right ventricle (RV), which can be used to estimate the pulmonary artery systolic pressure.

It is important to understand which variables are susceptible to errors in the examination technique. These will lead to inaccurate velocity and pressure calculations, according to the Doppler equation (7.1): where v = velocity of interest, Δf = change in frequency between the emitted and received waves, f0 = frequency of the transmitted wave, cos θ = incident angle between the blood flow and ultrasound beam (angle of insonation), and c = speed of the ultrasound wave. Because the magnitude of the Doppler shift is proportional to the cosine of the angle of insonation, relatively small deviations in the angle of insonation can result in significant underestimation of flow velocity, so there should be a concerted effort to align the ultrasound beam parallel to the blood flow to obtain the most accurate velocity measurement (choice A is correct). An angle exceeding 20° generally results in an unacceptable underestimation of the velocity. No Doppler shift at all occurs at a completely perpendicular angle (90° or 270°).

Lowering the lateral resolution and time gain compensation is related to properties of a two-dimensional (2D) image, not spectral Doppler velocities (choices B and D are incorrect). With an increased SNR, the correct velocity (the signal) will be more easily differentiated from noise (an incorrect, usually falsely high velocity). The result would be a reduced, not increased, velocity measurement (choice C is incorrect).

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 27.

3. If the frequency of the probe is 2 MHz and the returned signal frequency coming back toward the probe is 2.05 MHz, the Doppler shift (Δf) is:

A. -50 kHz

B. 50 kHz

C. -50 Hz

D. 50 Hz

3. Correct Answer: B. 50 kHz

Rationale: The Doppler shift describes the difference between the frequency transmitted and received after reflection from a moving reflector (Δf = freceivedftransmitted). In this case, 2.05 – 2 = 0.05 MHz, or 50 kHz. It is important to pay attention to the correct units (MHz = 1000 kHz = 1,000,000 Hz). The positive shift means the object is moving toward the probe (returned frequency increased), while a negative shift implies the object is moving away from the probe (returned frequency decreased).

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 27.

4. While examining the left ventricular outflow tract (LVOT) velocity, there is no pulsed-wave (PW) Doppler signal obtained. Which of the following is the most likely reason for the inadequate signal?

A. The difference in direction between the ultrasound beam and blood flow

B. High volumetric blood flow

C. Wall filters set too low

D. Dynamic LVOT obstruction

4. Correct Answer: A. The difference in direction between the ultrasound beam and blood flow

Rationale: Recall the effect of the angle of insonation (θ) in the Doppler equation: Δf = (2 f0 × v × cos θ)/c. An angle of insonation less than 20° (in other words, as parallel as possible) from blood flow direction will result in cosine close to 1 and therefore will not significantly underestimate the measured Doppler shift, and will not reduce Doppler signal substantially. As the angle of insonation approaches 90° (perpendicular), cosine approaches 0 and significantly reduces or eliminates the Doppler shift (choice A is correct).

High volumetric blood flow will result in an increased, not reduced, Doppler signal (choice B is incorrect). Wall filters allow higher frequency signals (blood flow) to pass through while eliminating the low-frequency signals (tissue). Wall filters set too high could eliminate all signals, both low and high frequency, while wall filters set too low could allow lower frequency signals to pass through and increase, not decrease or eliminate, Doppler signal (choice C is incorrect). Dynamic LV tract obstruction increases the velocity of flow and alters the Doppler envelope causing a distinct shape of the Doppler waveform (“dagger shaped”), but does not eliminate the Doppler signal (choice D is incorrect).

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 4.

5. A 75-year-old man is admitted with septic shock. After a 30 mL/kg lactated Ringer’s bolus, he remains hypotensive. In an attempt to assess for preload responsiveness by measuring breath-to-breath variability in stroke volume, a Doppler waveform is obtained through the LVOT (Figure 7.3). Which of the following would be most effective to improve this evaluation?

A. Increase the Doppler velocity scale

B. Measure the LVOT cross-sectional area

C. Increase the sweep speed

D. Move the sample volume to a different location

5. Correct Answer: D. Move the sample volume to a different location

Rationale: The velocity scale is not optimal. The Doppler signal in Figure 7.3 appears too small due to an excessively large scale. Because of the small Doppler envelope, it would be difficult to trace the VTI contour correctly. Decreasing, not increasing, the Doppler velocity scale would increase the size of VTI contour and would allow more accurate tracing of the VTI (Figure 7.15) (choice A is incorrect).

It is not necessary to measure the LVOT area to compare stroke volume changes in this case, because it will not change with the respiratory cycle. The stroke volume is directly proportional to the VTI (VTILVOT × AreaLVOT) (choice B is incorrect).

Changing the sweep speed will change the number of Doppler tracings on the screen. The number of Doppler tracings (two in this case) is not sufficient to make conclusions about the breath-to-breath variability of stroke volume. Decreasing, not increasing, the sweep speed from 100 mm/s (Figure 7.15) to 35 mm/s (Figure 7.16) allows for more waveforms with the LVOT VTI spectral Doppler signal (Figure 7.16) (choice C is incorrect).

The Doppler VTI signal through the LVOT in Figure 7.3 is not optimal. An optimal LVOT VTI signal should be narrow, with a central “clearing,” reflecting laminar flow. The signal in Figure 7.3 shows spectral broadening. This is consistent with measuring multiple different velocities, raising the suspicion of measuring turbulent, nonlaminar, flow. Additional positioning of the sample volume (ideally 5 mm proximal to the aortic valve in the center of the LVOT) might optimize the Doppler signal (choice D is correct).

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Slama M, Masson H, Teboul JL, et al. Respiratory variations of aortic VTI: a new index of hypovolemia and fluid responsiveness. Am J Physiol Heart Circ Physiol. 2002;283(4):H1729-H1733.

6. The following image is obtained from an apical long-axis (three-chamber) view, with a Doppler tracing through the LVOT (Figure 7.4). There are two Doppler flow patterns present, LVOT velocity-time integral (VTI), and a second signal. Which of the following would most effectively optimize the second Doppler flow signal?

A. Decrease PRF

B. Increase depth

C. Decrease baseline

D. Change to continuous-wave (CW) mode

6. Correct Answer: D. Change to CW mode

Rationale: The image in Figure 7.4 shows a well-defined PW Doppler waveform during systole, directed away from the probe (below the baseline). The second waveform is a diastolic signal both above and below the baseline, caused by aortic regurgitation (AR), which should be directed toward the probe (above the baseline). Aliasing creates this “confusion” of the direction of flow if the velocity measured exceeds the capability of PW Doppler to measure it correctly, resulting in the signal “wrapping around” the baseline (appearing both above and below the line). The maximum measurable velocity is limited by the Nyquist limit (fmax), which is the frequency equal to one-half of the PRF (fmax = PRF/2). Once the detected Doppler shift exceeds half of the PRF, aliasing will occur.

Decreasing PRF would decrease the maximum velocity that PW can measure, and it would increase the likelihood of aliasing (choice A is incorrect).

Increasing the depth means there would be more time needed between transmitting the pulses. The time between transmits is called the PRP. Since PRP = 1/PRF, higher PRP = lower PRF = increased aliasing (fmax = PRF/2) (choice B is incorrect).

Changing the baseline on the screen to a higher or lower position while still in PW Doppler will move the aliasing flow up or down on the screen, but it would not change the degree of the aliasing (choice C is incorrect).

The best solution would be to use CW Doppler. CW Doppler is not subject to aliasing and will allow the correct examination of high-velocity flows, such as those through stenotic or regurgitant lesions. The limitation of CW is range ambiguity (inability to localize where along the line of interrogation the measurement is occurring), which is not a concern here, since AR would be the highest diastolic flow velocity along the entire tract of ultrasound beam (choice D is correct).

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 27.

7. What would be the maximum detectable Doppler shift, using PW Doppler, if the PRP is 0.125 ms?

A. 0.125 kHz

B. 2 kHz

C. 4 kHz

D. 8 kHz

7. Correct Answer: C. 4 kHz

Rationale: According to the Nyquist limit, the maximum detectable shift in PW mode equals one-half of the PRF (fmax = PRF/2). PRF is the inverse of PRP (PRF = 1/PRP). If PRP = 0.125 ms, then PRF = 1/0.125 ms = 8 kHz. The maximum detectable shift (Nyquist limit) will be half the PRF = 8 kHz/2 = 4 kHz.

Selected Reference

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

8. Which of the following modes does not have a Nyquist limit?

A. Color Doppler

B. Tissue Doppler

C. CW Doppler

D. PW Doppler

8. Correct Answer: C. CW Doppler

Rationale: PW Doppler (whether measuring blood flow or tissue velocity) is subject to aliasing and therefore has a Nyquist limit. Color Doppler is based on PW Doppler and is also subject to aliasing. CW Doppler is not subject to aliasing and therefore does not have a Nyquist limit.

Selected References

1. Miele FR. Essentials of Ultrasound Physics. Pegasus Lectures; 2008:chapter 4.

2. Oh JK, Kane GC, Seward JB, Tajik AJ. The Echo Manual. 4th ed. Wolters Kluwer; 2019:chapter 4.

9. The following Doppler pattern was obtained during a transthoracic echo examination of an intensive care unit (ICU) patient with heart failure (Figure 7.5A and B). Which flow does this waveform most likely represent?

A. Right ventricular outflow tract (RVOT)

B. Pulmonary veins

C. Hepatic vein (HV)

D. Descending aorta