Doppler Principles

The doppler effect applies to all waves, both sound and electromagnetic radiation. It is used to measure the velocity of moving particles such as red blood cells. The frequency of the reflected wave decreases with blood moving away from the probe.

The Doppler effect – applies to both electromagnetic radiation and sound. It changes the frequency of reflected ultrasound waves (not velocity), shows a shift to a lower frequency if the source if moving away from the receiver and can indicate the velocity of the red blood cells.

The Doppler effect is defined as: The frequency change of a wave due to the relative motion between a source and an observer. When the source starts to move towards the observer, the wavelength of the waves is shortened — the sound therefore appears at a higher frequency to the observer. The frequency is increased when the source is moving towards the observer; the frequency is decreased when the source is moving away from the observer. This applies to ultrasound in the exact same way as it does to sound waves.

Describes the change in the transmitted frequency of a sound wave (ft) compared to the reflected (observed) frequency of the wave (fr) that occurs due to the relative motion between the observer and the source. If the source and the observer are stationary any waves reflected back will be of the same frequency (fr = ft). If the source is moving toward the observer it causes waves to be more closely packed together, so the observer witnesses a higher frequency wave (fr > ft). Conversely, if the source is moving away from the observer, it causes waves to be more loosely packed together, so the observer witnesses a lower frequency wave (fr < ft). It does not matter whether it is the source or the observer that is moving. An example in every day life is the change in pitch of a siren as a police car passes by.

Doppler echocardiography can be used to measure blood flow velocity, as well as tissue velocity. As a reflector (e.g. RBCs) moves towards or away from the transducer, it changes the reflected ultrasound (echo) frequency. The echo frequency (fr) is higher than the original transmitted frequency (fo) when the reflector is moving towards the transducer and is lower when moving away. The machine calculates the velocity from the Doppler shift, defined as the difference between the transmitted frequency and echo frequency (fo − fr).

What is the Doppler shift or Doppler frequency (fd)? Refers to the change in the observed frequency from that originally transmitted due to moving red blood cells or tissue. It is proportional to the relative velocity between the source and the observer. Can be described by the equation: f_D = f_e − f_t, where fD = Doppler frequency, ft = transmitted frequency, fe = echo frequency.

While the frequency of ultrasound is not affected by tissue density, it changes when there is a relative motion between the transducer and the reflector. Since the transducer is mostly stationary when acquiring an image, any change in frequency is assumed to be due to moving reflectors in the body. Common moving reflectors in echocardiography are blood cells, heart valves, and myocardium.

How is the Doppler equation modified to account for the angle between the ultrasound beam and blood flow? The detected Doppler shift frequency (fd) can be used to calculate the velocity (v) using the 'doppler equation': f_D = (2 · f_t · v · cosθ) / c, where v = flow velocity [m/s], c = average speed of sound in tissues [m/s] (taken as 1540 m/s), fD = Doppler frequency / shift [Hz], fT = transmitted frequency [Hz], θ = angle between the ultrasound beam and the blood flow.

To find the velocity of blood flow the equation can be rearranged as: v = (f_D · c) / (2 · f_t · cosθ).

In clinical imaging, Doppler frequency is inversely proportional to the speed of sound in tissues. It is directly proportional to the velocity of the red cells, the transmitted frequency, and the cosine of the angle of insonation. FD = FR − FT = (V · 2FT · cosθ)/C, where FD = Doppler frequency; FR = received frequency; FT = transmitted frequency; V = velocity of red cells in blood; cosθ = angle of insonation; C = speed of sound in blood.

How does the angle of isonation effect the Doppler equation? The Doppler equation is only valid when the ultrasound beam is parallel to blood flow (angle of isonation 0° or 180°). If the angle (θ) between the ultrasound beam and the blood flow is greater than zero, the measured velocity (vʹ) will be underestimated by a factor of cos θ. v′ = v · cosθ, where v' = measured velocity, v = flow velocity, θ = angle between the ultrasound beam and the blood flow. It is apparent that as θ increases, the error in measuring the velocity also increases. Ultrasound machines assume θ is zero, hence operators need to minimize θ as much as possible, so that v' approximates v. For practical purpose, θ should be kept less than 20° where the measurement error is less than 10%.

1.10.1 Doppler Angle Error. To obtain accurate velocity measurements, the ultrasound beam needs to be parallel to the flow, i.e. Doppler angle = 0°. The velocity will be underestimated when the Doppler angle deviates from 0°. The operator should minimise this angle to less than 20°, which corresponds to <10% underestimation of velocity.

Optimal angles for incident wave for flow velocity assessment are 0° and 180° because the cosine of both angles is 1. At 90°, no velocity is detected because cosine 90 = 0. Interrogation at 20° or less is considered acceptable as the underestimation error in the calculated velocity is less than 6% and can be ignored. For arterial ultrasound imaging, use of angle correction is acceptable up to 60°; however, the use of angle correction is discouraged in cardiac imaging because significant errors can be introduced.

Incident ultrasound waves are backscattered by red blood cells. Red blood cells are poor reflectors of ultrasound because of their shape and size: They have irregular surfaces and their diameters are less than the wavelengths of transmitted ultrasound. Accordingly, any incident ultrasound waves are scattered in all directions rather than being directly reflected back in relation to the angle of insonation. Consequently, only a small proportion of transmitted ultrasound returns to the transducer during Doppler interrogation. This has implications for the power requirements and gain adjustment for Doppler ultrasonography, compared to B-mode imaging. Doppler frequency shift is typically in kilohertz and are audible.

Scattering: When the size of a reflector is smaller than λ (e.g. RBC), the ultrasound pulse is scattered in all directions. As a result, only a very small portion of echoes return to the transducer. Scattering gives rise to the characteristic acoustic appearance of the tissue.

The change in frequency when ultrasound encounters a moving object is a small fraction of the transmitted frequency (typically about 0.1%). Accordingly, the Doppler frequency will fall well within the range which humans can hear (2–20 kHz). This is the underlying principle for simple bedside Doppler machines for monitoring peripheral pulses.

Spectral Doppler: Velocity information detected from a single location is displayed in the form of a frequency shift–time plot. The vertical distance from the baseline corresponds to Doppler shift. The greyscale indicates the amplitude of the detected ultrasound of a particular frequency.

The Doppler spectral display is a time velocity plot that helps discern red blood cell velocity and direction as well as the amplitude of the backscattered signals from the red blood cells. The Doppler spectral analysis is used to convert the frequencies of backscattered signals into flow velocities that are then plotted on a vertical axis against time on the horizontal axis. The loudness (amplitude) of each of these signals is depicted using a grey scale. The deeper the shade of grey, the greater the amplitude and/or the number of red cells creating those frequencies. By convention, flow toward the transducer is displayed above the zero baseline, and vice versa.

The echoes returning from the same location are received and stored for several cycles. Each echo pulse is resolved into individual frequencies by spectral analysis. These frequencies are converted to Doppler frequencies and finally to the corresponding velocities using the Doppler equation. Power spectrum is constructed using the velocities and the amplitude information. Combining power spectra obtained consecutively gives rise to the Doppler spectrum. (Spectral display: mean, modal and peak velocities.)

What are the formats of Doppler available? Continuous wave Doppler; Pulsed wave Doppler; Tissue pulsed wave Doppler; Colour Doppler. Modern machines provide four Doppler modalities: PW Doppler, CW Doppler, CFD, and PW tissue Doppler (PWTD). Each of these modalities has its unique properties and applications.

PW Doppler is ideal for measuring blood flow velocity less than 1.5 to 2 m/s; CW Doppler is used for high velocity measurements such as regurgitations and stenosis; CFD allows visualization of blood flow and is an invaluable aide for detecting regurgitation and stenosis; PWTD measures the myocardial velocities which is useful for assessing cardiac systolic and diastolic functions.

Practical Tips: Use PW Doppler to measure low-velocity (e.g. ≤1.7 m/s) signal and when you want to measure the velocity at a specific location. Use CW Doppler to measure high-velocity (e.g. ≥1.7 m/s) flow, e.g. regurgitant or stenotic flows.

What is continuous wave Doppler? Continuous-wave (CW) Doppler splits the piezoelectric crystals on the transducer into two sets for data acquisition: (1) one set (usually 50%) of the crystals are used for ultrasound transmission; and (2) the other set for receiving echoes. Ultrasound transmission and reception are simultaneous and continuous in CW Doppler.

Continuous Wave (CW) Doppler: The transducer transmits and receives ultrasound continuously. All echoes along the beam path will be received and interrogated. Hence, the operator cannot choose the location of measurement.

What is range ambiguity in CW Doppler and why does it occur? As CW Doppler receives echo signal continuously, one major problem is that all flow signals along the beam path will be received and interrogated giving rise to the issue of range ambiguity — the inability to resolve the specific location of flow signal when two or more flows are present. This gives rise to a masking effect, where a high velocity signal masks the low velocity signal. For example, if a low flow signal lies in the same beam path as a high flow signal, such as left ventricular outflow tract (LVOT) and stenotic aortic valve, the two signals overlap, thus masking the low velocity LVOT flow. Masking is usually not an issue if only the highest velocity is the focus of the study because signals are not additive. Does Aliasing occur in CW Doppler? Aliasing is not observed in CW Doppler because Doppler pulses are not used and therefore the issue of the Nyquist limit does not exist.

What is pulsed wave Doppler? Used for estimating velocity of flow at a defined location. Uses the same piezoelectric crystals to send and analyse sound waves: sends short pulses of ultrasound; analyses reflected sound waves between the pulses. Therefore emitted sound waves can be associated with reflected sound waves making it possible to determine the distance of the reflector. However, signal reception is gated so that only signals from the preset sample volume position are processed, permitting velocity estimation at that position. This is why the spectral envelope is empty as velocities from all other locations are ignored.

Pulsed-Wave (PW) Doppler: As in 2D echo, PW Doppler utilises ultrasound pulses. Using the sample volume (gate), the operator can choose the location of measurement.

Which factors can be used to describe the doppler signal generated by pulsed wave doppler? Pulse repetition period (PRP), typically between 80 and 250 µsec; Pulse Duration (PD), in the range of 1 to 2 µsec; Pulse repetition frequency (PRF = 1/PRP), typically 4000 to 12 000 Hz; Duty Factor (DF = pulse duration / pulse repetition period × 100), usually 0.1–1%. PRP is determined by the depth of the sample gate. The size of the sample gate is typically set between 2 and 5 mm but can be adjusted by the operator. A small sample gate size improves range specificity (location certainty). Spatial pulse length is not the same as pulse duration: pulse duration is a time measurement, while spatial pulse length is the physical length a pulse occupies in space (number of cycles × wavelength). Pulse duration is solely determined by the source of the ultrasound and is independent of depth of imaging.

What is aliasing in pulse wave Doppler? Signal aliasing occurs when the direction of flow cannot be determined because the Doppler frequency exceed the Nyquist limit. In that event, the signal is truncated at the edge of the display and the excised portion appears on the opposite edge. This 'wraparound' continues until the difference in the Doppler frequency and the Nyquist limit is exhausted. Aliasing is not seen with continuous wave Doppler.

Why does aliasing occur in pulse wave Doppler? A minimum of two pulses per beat are required to correctly define the fD, hence flow velocity. This is achieved by using a high sampling rate (i.e. PRF). In other words, the maximal fD, hence maximal blood flow velocity (vmax), can be detected is: Maximal fD = PRF/2. The aforementioned relationship is known as the Nyquist limit, which states that the fD should not exceed half the sampling frequency (i.e. PRF) or the PRF should be more than twice the fD. When the sampling rate is less than two pulses per beat (long PRP), the Doppler frequency fD will be underestimated resulting in a lower velocity. Underestimation of fD is usually accompanied by a phase shift. The ultrasound machine interprets this phase shift and displays the aliasing flow in the opposite flow direction resulting in a 'wrap-around' phenomenon.

1.11 Aliasing (Echocardiography in ICU). Aliasing only occurs in PW Doppler where ultrasound is transmitted in pulses. The rapidity of the pulses transmitted (or pulse repetition frequency (PRF)) determines the maximal blood flow velocity (vmax) the PW Doppler can measure. The higher the PRF is, the higher is the vmax. In most ultrasound machines, the vmax is usually between 1.5 and 1.7 m/s. When the blood flow velocity is higher than the vmax, such as a regurgitant or stenotic jet, aliasing occurs. Aliasing is characterised by the inability of the screen to show the high-velocity region (above vmax), and that region is 'cut' and 'paste' above the baseline if blood is flowing away from the transducer (or below the baseline if blood is flowing towards the transducer). This is known as the 'wrap-around' phenomenon.

What affects the Nyquist limit? Nyquist limit is equal to half the pulse repetition frequency. The Nyquist limit is the maximum detectable velocity. It is dependent on the frequency of sampling, not the frequency of the transmitted wave. Aliasing occurs when the velocity exceeds the Nyquist limit. The Nyquist limit is determined by the PRF and PRF = 77 000/depth in cm. Hence decreasing the sample volume depth will increase the PRF, which in turn will increase the Nyquist limit.

What methods can be used to correct for aliasing in pulsed wave doppler? Practical Tips: Correction of Aliasing. Aliasing can be corrected by one or more of the following manoeuvres: 1. Increasing the velocity scale 2. Shifting the baseline 3. Increasing PRF (use high PRF mode) 4. Reducing transducer frequency.

There are four general methods to correct for aliasing: (1) Provided that the PRF is not at its maximum, the PRF can be increased by increasing the velocity scale. (2) Adjust the baseline to devote the entire range of velocity range to the correct flow direction. This can double the Vmax without aliasing. (3) From v max = PRF × c / 4 f0, reducing the transducer frequency (fo) increases vmax. (4) PRF is inversely proportional to the depth (d) of the sample volume: PRF = c/2d. Reducing the depth can therefore increase the PRF. Reducing depth in the same acoustic window is often not possible as the PW Doppler measurements are location specific; however, using other acoustic windows may help in reducing the depth (e.g. parasternal rather than apical windows). Otherwise, continuous-wave Doppler should be deployed.

What is the effect of adjusting the velocity scale to mitigate aliasing? Adjusting the velocity scale to its maximum for that depth is effectively maximizing the pulse repetition frequency. Maximizing the velocity scale will reduce sensitivity to lower velocities. Also note that the deeper the site of interest, the lower the pulse repetition frequency; as such, Nyquist limit will decrease as depth of interest increases.

What is colour flow Doppler? Used to provide a real-time visualization of blood flow on the display. When CFD function is activated, the ultrasound machine places a 'CFD window' (or CFD box) with multiple PW Doppler gates over the 2D images. The echoes from these gates are interrogated using PW Doppler and the mean velocities of blood flow from each of these gates are displayed on the screen using a colour that matches the colour-flow map. Colour flow Doppler is a multi-gated form of pulse wave Doppler and is subject to all the limitations and features of pulse wave Doppler (PWD). Because of the large amount of Doppler data generated, CFD uses autocorrelation to resolve and calculate mean velocity.

Color Doppler (Echocardiography in ICU), also known as color flow mapping, is used to visualise blood flow in echocardiography and vascular ultrasound. Using different colours and saturation, the direction and velocity of blood flow can be appreciated on the screen. Color Doppler uses multiple PW Doppler sample volumes to gather flow (velocity) information over an area, as defined by the color box.

Direction of blood flow: The transducer is used as a reference point. Although any two colors can be chosen, the widely accepted convention is BART — Blue is flowing Away from the transducer and Red is Towards the transducer. As the mean velocities are determined by the Doppler principle, the detection of the velocities will be subjected to the same Doppler angle limitation; flows perpendicular (90°) to the transducer do not register any hue and appear black.

Area of colour: The area of a particular colour represents the number of sample gates with the same mean velocity. Hence, a larger area of the same colour implies a larger amount of blood flowing at that same mean velocity. Of note, the area does not reflect flow velocity; only the colour correlates with velocity.

Velocity of blood flow: In CFD, the intensity of the colour denotes blood flow velocity. Dark or deep shades usually represent low velocities whereas light shades represent high velocities. As motion of the myocardium can also be detected by CFD, a wall filter is also applied to eliminate the low range myocardial velocities. In parabolic or plug flow, the range of mean velocities is relatively narrow and the maximal mean velocity is usually within the Nyquist limit. However, in situations where turbulence is present or flow velocity is high, as in regurgitations and stenosis, the range of mean velocities is large and exceeds the Nyquist limit. As in PW Doppler, velocities that exceed the Nyquist limit appear as aliasing and 'wrap-around' the colour-flow map; the aliasing velocities will be depicted as the opposite flow colour, or as different colours such as green or yellow if a variance Doppler map is used.

The boundary between two hues represents blood flowing at the aliasing velocity (vmax) — the isovelocity contour in colour-flow 2D images. In the three-dimensional perspective, the boundary forms an isovelocity shell and is used for calculation of effective regurgitant or stenotic orifice (PISA). Shifting the baseline has the effect of increasing or decreasing the aliasing velocity, thereby moving the isovelocity shell towards or away from the transducer. Increasing the scale of the colour-flow map increases the PRF, hence vmax. (Echocardiography in ICU: where a variance colour flow map is used, aliasing is presented as a different color e.g. green; when flow is turbulent, a mosaic color is shown.)

What is pulsed Wave Tissue Doppler (PWTD) or Tissue Doppler imaging (TDI)? An adaptation of Doppler imaging used to assess cardiac function by measuring cardiac wall motion velocity: an extension of PW Doppler and uses the same principles. Instead of measuring the velocity of blood flow, estimates the peak myocardial velocity (normally about 10 cm/s). Similar to blood flow Doppler, positive and negative waves denote myocardial motion towards and away from the transducer, respectively.

Two main characteristics distinguish myocardial velocity to that of blood flow velocity: myocardial velocity is a low velocity signal typically less than 20 cm/s, whereas blood flow velocity is at least four to five times higher; and myocardial velocity is a high amplitude (intensity or gain) signal. Accordingly, TDI uses filters to extract velocities less than 20 cm/s. To obtain myocardial velocity of a particular segment, place the sample gate of PW Doppler at the region of interest, reduce the velocity scale, and reduce the gain so that the low-intensity, high-velocity blood flow signal is filtered out. The standard location to perform PWTD is at the level of tricuspid or mitral annulus in the apical views.

Tissue Doppler Velocity (Echocardiography in ICU): Cardiac function can be estimated by measuring the velocity of the myocardium. Myocardial velocity can be measured using PW Doppler by placing the sample gate at the AV valve annulus. For RV function, the sample volume is placed at the tricuspid annulus, and for LV function, the sample volume is placed at the mitral annulus, commonly at the medial (septal) and lateral aspect. Limitations of TDI: angle dependence; misplacement of sample gate location (velocity underestimated if the sample volume is placed below the AV valves); yields global regional information only and inability to give specific segmental wall information; motion artefact; arrhythmias; range ambiguity.

There are three main 'waves' in a typical longitudinal PW tissue Doppler recording: S is the ventricular systolic wave; E' is the early ventricular diastolic wave due to ventricular relaxation; A' is the late diastolic wave resulting from atrial contraction. IC and IR represent isovolumic contraction and isovolumic relaxation phases, respectively.

Components evident: 1. isovolumic contraction (IC) wave; 2. S-wave which represents ventricular systolic velocity — a stunned, hibernating, and scarred myocardial segment results in reduced S-wave; 3. isovolumic relaxation (IR) wave; 4. E'-wave which is the early ventricular diastolic velocity — reduced E'-wave is associated with ventricular diastolic impairment; and 5. A'-wave that is due to atrial contraction — absent in atrial fibrillation. (Echocardiography in ICU: Systolic and diastolic dysfunction is associated with a reduction in S and E' wave, respectively.)

Note that myocardial velocities at the apical-, mid-, and basal-segments are different, with the highest velocity observed at the basal-segment. At the apex, the myocardial velocity is close to zero as the motion and change in length is negligible. As one goes towards the base (mitral annulus), the myocardial velocity increases due to a summation effect; maximal velocity is seen at the base of the heart.

1.10 Limitations of Doppler Measurements. In order to have accurate and reliable Doppler measurements, operators need to be aware of two main limitations: (1) Doppler angle error in velocity measurement and (2) the assumptions of the modified Bernoulli equation (MBE) in pressure gradient measurements.

Assumptions of SBE: The SBE assumes that: 1. Blood flow is laminar. 2. Blood flow is non-pulsatile. 3. There is no resistance to blood flow. 4. The density of blood is constant. Violation of any of the above assumptions leads to inaccurate estimation (underestimation) of the pressure gradient. Bernoulli's assumptions are mostly valid when blood is flowing across a small orifice, such as stenosis and regurgitation, and is centrally directed into the distal chamber.

Notes — Echo Doppler pitfalls: Shadowing / enhancement; Doppler shift — aliasing artefact; Spectral Doppler — mirror image artefact; Direction ambiguity — occurs when near 90°; a 2 mm error induces a CO error of 20%.

1.9 Useful Doppler Measurements. 1.9.1 Peak Velocity: The peak velocity (v) is used to calculate the transvalvular pressure gradient (ΔP) using the simplified Bernoulli equation (SBE): ΔP = 4(v² − v0²) = 4v². SBE assumes that proximal velocity (v0) is zero, and v is the velocity at vena contracta. Peak velocity is used in estimating pulmonary artery pressures or ΔP in dynamic outflow obstruction.

1.9.2 Velocity Time Integral: Velocity time integral (VTI), the area under the velocity curve (Doppler spectrum), is obtained by tracing the spectrum for a single beat. Calculation of Volumetric Flow: Volumetric flow, such as stroke volume, can be obtained by multiplying the VTI with the cross-sectional area (CSA). Hence, if the left ventricular outflow tract's (LVOT) diameter (d) and velocity (VLVOT) is measured, then the stroke volume = CSA × VLVOT = π(d/2)² × VLVOT. Calculation of Mean Pressure Gradient: Mean ΔP is sometimes used to quantify the severity of valvular disease, such as aortic stenosis. It is obtained by tracing the Doppler spectrum, and the machine will automatically calculate the mean ΔP by averaging 4v² over the trace.

What is the doppler effect used for clinically? Oesophageal doppler cardiac output monitoring; Transcranial doppler monitoring of cerebral blood flow; Echocardiography: assessment of cardiac output, assessment of valvular dysfunction, assessment of diastolic dysfunction, assessment of pulmonary artery pressures; Vessel patency and flow: detection of arterial or venous thromboses, assessment of portal venous flow, assessment of renal blood flow.