Doppler ultrasound methods

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Doppler ultrasound methods

The Doppler effect

The Doppler effect is observed regularly in our daily lives. For example, it can be heard as the changing pitch of an ambulance siren as it passes by. The Doppler effect is the change in the observed frequency of the sound wave compared to the emitted frequency which occurs due to the relative motion between the observer and the source. If a stationary source transmits sound wave of frequency f and an observer is moving towards the source, the observed frequency f´ will be given by

´

,

where c is the speed of sound and vO is the velocity of the observer. The bserved frequency is higher than the emitted frequency. If the observer is moving away from the stationary source, the observed frequency will be lower than the emitted frequency and will be given by

´

.

Similarly, if a source of sound (frequency f) is moving with velocity vS towards a stationary observer, the observed frequency f´ will increase and will be given by

´

.

If a source of sound (frequency f) is moving with velocity vS away from a stationary observer, the observed frequency f´ will decrease and will be given by

´

.

It does not matter if the source or the observer is moving. If either one is moving away from the other, the observer will witness a lower frequency than that emitted. Conversely, if either the source or observer moves towards the other, the observer will witness a higher frequency than that emitted.

The Doppler effect in ultrasound diagnostics The Doppler effect enables ultrasound to be used to detect the motion of blood and to measure the velocity of blood flow. Ultrasound transducer or probe transmits into the tissue ultrasound wave of frequency f0. If the ultrasound wave passes through a vessel filled with blood, the ultrasound wave will interact with blood cells and a part of ultrasound energy will be scattered back towards the transducer, where it will be detected. The concentration of red blood cells is much higher than the concentration of other blood particles, therefore we can consider that red blood cells are responsible for the interaction with ultrasound. The speed of sound in blood is 1570 m/s. Therefore the wavelength of ultrasound wave of frequency 2 MHz is 0.79 mm. As the size of red blood cells (7.5 µm) is much smaller than the wavelength of the ultrasound wave, Rayleigh scattering occurs. The intensity of ultrasound wave, which is scattered back towards the probe, is much lower than in the case of reflection of ultrasound wave (type of interaction between tissue and ultrasound wave responsible for creation of ultrasound images). If the ultrasound wave interacted with stationary red blood cells, the frequency of backscattered ultrasound wave would be the same as that emitted. If the red blood cells move towards or away from the ultrasound probe with velocity v, the probe will detect due to the Doppler effect ultrasound wave of higher or lower frequency than that emitted.

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Let us consider red blood cells that are moving with velocity v towards the ultrasound probe.

The ultrasound probe transmits ultrasound wave of frequency f0. Red blood cell can be considered as a detector of ultrasound that will due to its movement witness the frequency f´, given by

´

.

As the red blood cell scatters the ultrasound wave, it now acts as a source of ultrasound of frequency f´, which is moving at velocity v towards a stationary detector (ultrasound probe).

Frequency f´´ detected by the probe is thus given by

.

As the velocity of red blood cells in human body v is much lower than the speed of sound in blood c, we can rearrange the previous equation as follows

,

where can v2/c2 be considered as negligibly small and therefore can be ignored. The detected frequency is then given by

´´

.

We can see that for v much lower than c, the change of frequency is the same as in the case of stationary source and moving detector. We can substitute in this equation for f´ and we have

´´

,

v2/c2 can be again ignored. The Doppler shift or Doppler frequency fD is the difference between transmitted and received frequency. It can be thus calculated as follows

.

If the red blood cells move with velocity v away from the ultrasound probe, the Doppler frequency can be analogically calculated using equation

.

These equations can be used only in the case that the direction of blood movement is parallel to the direction of ultrasound wave propagation. If the direction of blood

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movement is other, the Doppler shift will be given by the velocity component parallel to the ultrasound path v‖, which is given by

, where angle α is known as the angle of insonation or Doppler angle.

The general relationship between the Doppler frequency and red blood cells velocity (known as Doppler equation) is therefore

.

If the Doppler angle is known, it is possible to use the measured Doppler frequency to estimate the velocity of red blood cells (the velocity of blood flow) using Doppler equation

.

There are two main display modes used in modern Doppler systems – spectral Doppler measurements and 2D colour flow imaging.

Spectral Doppler measurements of blood flow

This display mode is used to detect the blood velocity information from a single location within the blood vessel (the sensitive region is known as the sample volume). The velocity information is displayed in the form of Doppler spectrum.

Doppler spectrum displays time along the horizontal axis and the measured Doppler frequency shift or calculated velocity along the vertical axis. Conventionally, positive Doppler frequencies and velocities (blood flowing towards the probe) are plotted above the baseline and negative Doppler frequencies and velocities (blood flowing away from the probe or reverse flow) are plotted below the baseline. The brightness of the display indicates the amplitude of each of the Doppler frequency components present, i.e. the relative proportion of the blood travelling with a particular velocity. We can see that the Doppler ultrasound signal from a blood vessel contains a range of Doppler frequencies at any particular point in time. This means that all red blood cells within the sample volume are not travelling with the same velocity. Typically, the velocity is highest in the centre of the vessel and lowest near the vessel wall. This variation of blood velocity across the vessel is called the velocity profile.

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Parabolic flow profile is observed in a smooth, rigid tube with slow continuous laminar flow. Liquid in the centre of the tube moves with maximal velocity, but the velocity decreases towards the tube wall due to the viscous drug exerted by the walls. The fluid at the wall remains stationary. The flow velocity v in the distance r from the tube centre is given by

,

where R is the tube radius and vMAX is the velocity in the centre of the tube. The Doppler spectrum contains all the velocities between 0 and vMAX. The average velocity is equal to the half of the maximum velocity. In contrast, in the case of the plug flow profile, nearly all the fluid across the lumen moves within a narrow range of high velocities. The velocity at the wall is still zero, but velocity increases more rapidly away from the wall. The Doppler spectrum then contains only a narrow range of nonzero signal and so called spectral window (zero signal for lower velocities).

The flow in arteries is in fact pulsatile and therefore the velocity profile across an artery varies over time. Typically, the measured Doppler frequencies are in the order of hundreds and thousands of Hz. Therefore, the Doppler signal can be converted to acoustic signal and acoustic output is second way of presenting the velocity information. Doppler systems for spectral Doppler measurements can be divided into two groups – continuous wave systems and pulsed wave systems. Continuous wave systems – CW Doppler – transmit and receive continuously ultrasound waves. Therefore, the probe must contain two elements – one for transmission and one for reception of ultrasound. The region from which Doppler signals are obtained (the sample volume) is determined by the overlap of the transmit and receive ultrasound beams. The position and the size of the sample volume cannot be changed – this is the main disadvantage of these systems. Pulsed wave systems – PW Doppler – transmit short pulses of ultrasound and Doppler signals can be acquired from a known depth. In order to detect the signal from a specific depth in the tissue, a “range gate” is used. This enables the system to only receive the returning signal at a given time after the pulse has been transmitted, and then for a limited period of time. In the probe only one element is needed, serving both the transmit and receive functions.

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Today, pulsed Doppler systems for spectral Doppler measurements are usually used in conjunction with ultrasound B-mode imaging - this combination is known as duplex ultrasound. Duplex ultrasound enables precise location of the Doppler sample volume. It is also possible to estimate the angle of insonation using the angle correction cursor, enabling the velocity of the blood to be calculated using the Doppler equation. Modern duplex scanners use arrays of elements to produce both the B-mode image the Doppler spectrum.

Spectral Doppler controls Transmit power Transmit power determines the amplitude of the ultrasound transmitted into the tissue. Increasing the output power will increase the amplitude of returning Doppler shifted signal, but it will also increase the patient’s exposure to ultrasound. Therefore, the transmit power should only be increased after other controls, such as gain, have been optimised to obtain the best possible Doppler spectrum. Gain As the received backscattered signal from blood is small it will need to be amplified before it can be analysed. Increasing the spectral gain increases the brightness of the spectrum on the screen. However, the gain control increases the amplitude of not only the Doppler signal but also the background noise. Transmit frequency As high-frequency ultrasound is attenuated more than low-frequency ultrasound, the appropriate Doppler transmit frequency needs to be selected to ensure adequate penetration of ultrasound. Most modern ultrasound systems use broadband transducer technology, which means it is possible to operate the transducer over a range of different frequencies without too much loss in efficiency. Pulse repetition frequency - scale (PW Doppler) When using PW Doppler, the Doppler frequency is derived from samples of signal obtained over several transmitted pulses. The transmitted pulses are sent at a rate called the pulse repetition frequency. It is known that there must be at least two samples within one cycle of the Doppler signal to unambiguously determine the Doppler frequency. That is, at least two samples are required to know that the amplitude has oscillated above and below zero within the time of one period. This is known as the Nyquist limit. The maximum frequency that may be unambiguously is equal to the half of the pulse repetition frequency. Therefore, increasing of pulse repetition frequency increases the range of measurable Doppler frequencies (velocities). In contrast, there is not any upper limit of measurable Doppler frequency in CW Doppler systems.

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Baseline The baseline represents the zero Doppler frequency shift. The position of the baseline can be changed by the operator to allow optimum use of all the spectral display, depending on the relative size of the forward and reverse flow velocities present. Inversion of the spectrum This control enables to display positive velocities below the baseline and negative velocities above the baseline. Conventionally, arterial flow is plotted above the baseline and venous flow below the baseline. Wall filter The wall filter is used to remove high-amplitude low-frequency Doppler shifts caused by reflection from the slowly moving vessel wall. The wall filter acts as the high-pass filter, which removes frequencies lower than the set threshold value. As some of the true spectral information on flow is removed by the filter, there will be some error in the average velocity calculation. The wall filter should be always set to a minimum frequency compatible with its purpose of eliminating unwanted wall echoes. Sample volume size and position (PW Doppler) The size and position of the sample volume or the range gate can by selected by the operator when using PW Doppler. The precise location of sample volume is possible when using duplex systems. The sample volume length may affect the appearance of the Doppler spectrum and therefore may affect the results of spectral Doppler measurements – if the operator locates a short sample volume near the centre of the vessel, low velocities that occur near the vessel wall will not be detected. Doppler angle cursor In order to calculate the velocity of blood from the measured Doppler shift frequencies, the angle of insonation between the Doppler beam and the direction of flow must be known. Duplex scanners have the facility to allow the operator to line up an angle cursor with the vessel wall as seen in the B-mode image. The scanner can then convert the Doppler frequencies to velocities and velocity scale will be seen alongside the spectral display. Errors in the alignment of the angle correction cursor can lead to significant errors in velocity measurements. Focal depth In many systems the Doppler beam is focused. This may be fixed or adjustable, depending on the ultrasound system. In some systems the Doppler beam focal depth automatically follows the sample volume, when the operator moves it.

Spectral Doppler measurements Measurements of blood velocities are often used to quantify diseases of the cardiovascular system. If the Doppler angle α is known the Doppler equation can be used to estimate the velocity of the blood from the measured Doppler frequency fD

.

There is usually a spread of velocities within the sample volume. The maximum velocity at peak systole is often used to quantify the carotid artery disease. The ultrasound system can calculate the average or mean Doppler frequency (velocity) by finding the average of all the frequencies in the spectrum at a given instant in time. Many ultrasound systems are also capable of providing velocity measurements averaged over time. One such measurement is the mean velocity averaged over a number of complete cardiac cycles, usually known as time average velocity TAV. This can be used to estimate volume flow. Volume flow is measured using duplex ultrasound. Flow can be calculated by multiplying the TAV by the cross-sectional area A of the vessel. One method of

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estimating the cross-sectional area is to measure the diameter of the vessel d. The volume flow can be then calculated using equation

.

Several indices for quantitative evaluation of Doppler waveform shape were introduced. These indices can be calculated even if Doppler angle is unknown. The value of these indices is calculated using peak systolic velocity S (peak systolic Doppler frequency), end-diastolic velocity D (end-diastolic Doppler frequency) and mean value of maximum velocity over complete cardiac cycle M (mean value of maximum Doppler frequency over complete cardiac cycle).

The pulsality index is defined as

.

The resistance index, which describes the peripheral resistance to flow seen by the artery at the site of measurement, is defined as

.

This index is low for arteries with low-resistance flow (cerebral and renal arteries, limb arteries during exercise) and high for arteries with high-resistance flow (limb arteries in rest). Last example of quantitative indices is systolic-diastolic ratio defined as

.

Artefacts To be able to correctly interpret Doppler spectra and Doppler waveforms, it is necessary to know the common artefacts which can occur during spectral Doppler measurements. Aliasing can occur due to the undersampling of the Doppler signal when using PW Doppler systems. If the pulse repetition frequency is set to low the Doppler signal with frequency higher than Nyquist limit will be incorrectly displayed in the reverse channel.

Aliasing Aliasing can be removed by increasing the pulse repetition frequency or by the change of baseline position. Inverted image of Doppler spectrum (the same Doppler spectrum

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above and below the baseline) can occur if the gain is set to high or if the Doppler angle is near 90°.

Inverted image of Doppler spectrum

Similar Doppler spectrum can be observed also in the case of turbulent flow when the blood really moves with positive as well as negative velocity. It is necessary to distinguish these two situations. Mirror artefact can be removed by decreasing the gain or by changing the Doppler angle, but in the case of turbulent flow, positive as well as negative velocities remain in the Doppler spectrum after the change of these parameters. The Doppler shift frequencies detected are dependent on the Doppler angle (Doppler frequencies decrease with increasing Doppler angle). The Doppler angle should be kept as small as possible and should never exceed 60°. Accurate estimation of Doppler angle is necessary for accurate velocity measurements. Complete and uniform insonaion of the vessel lumen is necessary for accurate measurements of the mean or average velocity. When the Doppler signal is detected only from the central part of the vessel, low velocities that occur near the vessel wall will not be detected, which leads to overestimation of the true average velocity. Similar consequences can be observed if the wall filter is set to high.

Colour flow imaging

In the case of colour flow imaging, the blood velocity information is colour coded and superimposed on the B-mode image. Production of a 2D colour flow image includes elements of B-mode image formation and pulsed Doppler techniques. As in B-mode image formation, the image consists of individual lines. The image lines are created by transmitting ultrasonic pulses and processing the sequence of returned echoes. However, unlike B-mode image formation in which echo amplitude information is processed to form the image, the echoes are used to measure the Doppler frequency shifts. In the pulsed wave spectral Doppler systems, the Doppler information was obtained from only a single sample volume. In colour flow systems, each line of the image is made up of multiple adjacent sample volumes. The Doppler shift information for each line is obtained from several transmission pulses, the B-mode image can be obtained from only one transmission pulse. Therefore the frame rate of colour image is lower than the frame rate of B-mode image (for comparable number of scan lines). However, the colour coded flow information is usually displayed only in a limited region of interest called the colour box within the displayed B-mode image. The lower number of image lines leads to the increase of the frame rate. The width and depth of the colour box are under operator control. Unlike the spectral Doppler display mode, it is not possible to display the complete blood velocity information in the colour image. Colour Doppler mode displays the mean or average velocity of the flow in each pixel of the colour box. Conventionally, the flow towards the probe is coded with red colour and flow away from the probe is coded with blue colour. The brightness of the colour determines the flow velocity.

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Color Doppler Power Doppler mode displays the power of the Doppler signal backscattered from blood in each pixel of the colour box. This mode thus does not provide blood velocity information, but rather information about the total number of moving red blood cells. This mode is usually used to display the flow in small vessels.

Power Doppler Although colour flow imaging does not provide complete blood velocity information, it is very useful. It allows rapid visualisation of the flow pattern in vessels, allowing high-velocity jets in arteries and in cardiac chambers to be seen. In addition, it facilitates the placement of the Doppler sample volume in spectral Doppler investigation, hence reducing scanning time. Modern ultrasound systems can operate in so-called triplex mode, which combines Colour flow imaging (B-mode image + colour box) and spectral Doppler measurements.

Colour flow imaging controls Most controls – transmit power, gain, transmit frequency, pulse repetition frequency, baseline and wall filter – have the same function as in the case of spectral Doppler measurements of blood flow. In colour flow imaging it is not possible to set the value of the Doppler angle and therefore it is not possible to measure accurate values of velocity. Persistence (frame averaging) Persistence refers to the averaging of Doppler shift estimates from current and previous frames. Increasing of the persistence will lead to decreasing of the noise in the colour image, but rapidly changing flow patterns will not be properly visualised.

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Flow sensitivity This parameter determines the number of pulses used to generate each colour line. Increasing the number of pulses per image line increases the sensitivity to slow flows, but decreases the frame rate. Colour versus echo priority The colour coded flow information is usually superimposed only over dark B-mode pixels (the blood is generally anechogenic which means that in B-mode image will be displayed as black). Colour versus echo priority enables to set the threshold pixel value which determines if the colour information will be displayed or not. If the priority is set to low the colour coded information will not be superimposed over the vessel wall, however the information about the flow in small vessels can be lost (the lumen of very small vessels is not black in the B-mode image).

Artefacts Aliasing will be displayed in the colour image as a transition from maximum brightness of one colour to maximum brightness of second colour which corresponds to the flow in the opposite direction. Similarly as in the PW Doppler, aliasing can be removed by increasing the pulse repetition frequency or by the change of baseline position.

Aliasing If the Doppler angle is near 90° the ambiguity of the flow direction can be observed – in one part of the vessel the blood flows towards the probe, in other part of the vessel the blood flows away from the probe and where the Doppler angle is equal to 90° no flow is detected.

Ambiguity of the flow direction In the presence of a strongly reflecting surface, multiple reflections may occur, leading to the appearance that Doppler signals are detected outside the vessel. This will affect both the spectral Doppler and the colour flow image. This is known as a mirror image.

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Instruction for practical tutorial

Task

1) Using the colour flow imaging display the flow in tubes of inner diameter 8 and 4 mm.

2) Using spectral Doppler flow measurements measure the maximum and average velocity in tubes of inner diameter 8 and 4 mm. Calculate the volume flow in these tubes.

3) Compare the character of velocity spectrum and maximum and average velocities in prestenotic and poststenotic region.

Diagnostic ultrasound system TITAN

Diagnostic ultrasound system TITAN is equipped with convex probe C15.

Be extremely careful when using the ultrasound system and especially the probe! Basic control of the ultrasound system is described below.

1 Power turn on/off

2 Gain

A gain applied to the near field of the image

B gain applied to the far field of the image

C

overall gain applied to the whole image

gain applied to the active mode (Color,

Doppler)

3 Depth adjusts the imaging depth in 2D

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4 Caliper activates measurements using cursor

5 Calcs activates calculations

6 Freeze „freezing“ of the image

7 Touchpad moving and selection of objects on the screen

8 Select confirmation of the selection

9 Save saves the image to the memory

10 control of parameters displayed on the

bottom bar of the screen (see below)

11 Patient access to patient information

12 Update toggles between display modes

13 Doppler activates spectral Doppler measurements

14 Color activates colour flow imaging

15 2D activates B-mode imaging

Adjustable controls of colour flow imaging (bottom bar of the screen)

Flow sensitivity

Scale (pulse repetition frequency)

Wall Filter

Invert (inversion of colour map)

Adjustable controls of spectral Doppler measurements (bottom bar of the screen)

Doppler angle cursor

Sample volume size (gate range)

Scale (pulse repetition frequency)

Line (change of the baseline position)

Invert (inversion of the Doppler spectrum)

Volume (audio output)

Wall Filter

Sweep speed

Trace (calculation and display of average velocity)

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Blood vessel phantom

The blood vessel phantom is composed of a plastic box filled with agar-based material whose acoustic parameters are similar to acoustic parameters of human soft tissues. One tube of inner diameter 4 mm and two tubes of inner diameter 8 mm are embedded in the agar-based material. These tubes replace the function of blood vessels and are filled with a fluid whose acoustic parameters are the same as the acoustic parameters of human blood. Using a three-way valve, it is possible to select which tube will the fluid flow through. The fluid is driven by an electrical pump. The pump can you turn on/off using the red switch. The pump should be turned on only during the measurement. Turn

off the pump when you finish the measurement. Be extremely careful when using the blood vessel phantom (especially during the placing of the probe on the surface of the phantom)! In case you are not sure, contact your professor assistant.

Instructions

1) Familiarize yourself with handling of the diagnostic ultrasound system TITAN and with handling of the pump.

2) Turn the ultrasound system on and press the „Patient“ key. Select „New“ from the bottom bar of the screen and fill in your first name and surname. Select „Abdomen (Abd)“ as the exam type and confirm the selection by pressing „Done“ on the bottom bar of the screen.

3) Set the three-way valve in such a way that the fluid flows through the tube No. 1 (inner diameter of 8 mm). The red lever of the three-way valve indicates the tube, whose inlet will be stopped. The valve should be always rotated counterclockwise.

4) Apply a layer of the gel on the surface of the probe. Place the probe on the surface of the vessel phantom – at the distance of 1/3 from the right edge of the phantom in the point where the tube No. 1 passes through the agar-based material.

5) Move the probe along the phantom surface (be careful!) until you find the tube in the B-mode image. Using the „Gain“ knob, set the gain to the lowest level (the lumen of

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the tube has to be dark). Using the „Depth“ keys, select an appropriate imaging depth – select lowest depth which allows you to view the tube.

6) Start to pump the fluid – turn on the pump using the red switch. 7) Press the „Color“ key. A colour box will be displayed on the screen. Using the

touchpad or the arrow keys on the keyboard, you can change the position of the colour box. When you press the „Select“ key, you can change the size of the colour box using the touchpad or the arrow keys on the keyboard. The new size of the box can be saved by pressing the „Select“ key. The position and size of the colour box should be set in such a way that the tube passes through its centre.

8) Using the control displayed on the bottom bar of the screen, set the flow sensitivity to „Low“ and set the wall filter to „Low“.

9) Using the „Gain“ knob, set an appropriate gain level - if the gain is set to high, the colour information is displayed outside the tube; if the gain is set to low, the colour information disappears from the tube lumen.

10) Using the control on the bottom bar of the screen, set an appropriate pulse repetition frequency – the measured signal should cover the widest possible range of colours without the presence of aliasing. Fill in the optimum value of the pulse repetition frequency into the protocol.

11) Check, that the aliasing appears in the colour image if the pulse repetition frequency is set to low. Fill in into the protocol in which part of the tube the aliasing appears.

12) Press the „2D“ key. The B-mode image is displayed. 13) Press the „Doppler“ key. A Doppler line with the sample volume will be displayed on

the screen. The position of the sample volume can be changed using touchpad – place the sample volume into the centre of the tube.

14) Using the control displayed on the bottom bar of the screen, select approximate value of Doppler angle; set the sample volume size to maximum value (5 mm).

15) Press the „Select“ key and set the true value of Doppler angle using the touchpad or the arrow keys on the keyboard. The Doppler angle cursor should be parallel to the tube wall. Confirm the new position of Doppler Angle cursor by pressing the „Select“ key.

16) Press the „Update“ key. The Doppler spectrum will be displayed in the lower part of the screen.

17) Using the „Gain“ knob, set an appropriate gain level – the appropriate gain level maximizes the signal amplitude without the presence of noise.

18) Using the control on the bottom bar of the screen, set an appropriate pulse repetition frequency – the measured signal should cover the widest possible range of spectrum without the presence of aliasing. Set the wall filter to „Low“.

19) Check, that the aliasing appears in the Doppler spectrum if the pulse repetition frequency is set to low. Check, that the mirror image appears in the spectrum if the gain level is set to high.

20) Select „Page 2…“ from the bottom bar of the screen and then select „Trace“. A yellow line will be displayed in the spectrum. The yellow line corresponds to the average flow velocity.

21) Optimize the parameters of the ultrasound system to obtain the best possible Doppler spectrum. Press the „Freeze“ key and measure the value of the maximum and average velocity. Press the „Caliper“ key. A cursor will be displayed in the Doppler spectrum. The value of velocity corresponding to actual position of the cursor is displayed below the spectrum. Measure the value of maximum and average velocity in three different points in time. Measured values fill in into the protocol.

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22) Using the same procedure measure the value of maximum and average velocity in the tube No. 3 (inner diameter of 4mm).

23) Calculate the volume flow in the tubes No. 1 and 3 (use the value of average velocity and inner diameter of the tube). Compare the measured values of velocity and calculated values of volume flow in the tubes No. 1 and 3.

24) Set the three-way valve in such a way that the fluid flows through the tube No. 2 (inner diameter of 8 mm, stenosis in the middle of the tube).

25) Using the spectral Doppler measurements, determine the differences between the flow in prestenotic and poststenotic region. The velocity in the prestenotic region should be measured at the distance of 1/3 from the left edge of the phantom; the velocity in the poststenotic region should be measured at the distance of 1/3 from the right edge of the phantom. Compare the measured values of maximum and average velocities in prestenotic and poststenotic region.

26) When you finish your work, turn off the pump. Remove the remainders of the gel form the probe and from the surface of the phantom. Cover the phantom by the plastic lid to prevent its drying.