Det medisinske fakultet











Basic Doppler ultrasound for clinicians











Christian Andreas Doppler
(1803 - 1853)
The Doppler effect
My cat Doppler
(2004 -    
The page is part of the website on Strain rate imaging
Contact address: asbjorn.stoylen@ntnu.no


This section updated:  April 2016

This section is the Doppler part of the former "Basic ultrasound, echocardiography and Doppler for clinicians". Due to the size and number of illustrations, the page tended to load very slowly. It has now been split into one section on Basic ultrasound, Doppler, and this one on Doppler, including tissue Doppler. In addition, the background paragraphs from the previous mathematics section on the derivation of the Doppler equation and  the phase analysis have been included here (but can be bypassed, of course, for those not interested).

Technical or mathematical background is not necessary, explanations are intended to be intuitive and graphic, rather than mathematical.
This section is important for the understanding of the basic principles described in detail in the section on measurements of strain rate by ultrasound. Especially in order to understand the fundamental principles that limits the methods. The principles will also be useful to gain a basic understanding of Doppler echocardiography in general, and may be read separately, even if deformation imaging is not interesting.

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The Doppler effect

The Doppler effect was discovered by Christian Andreas Doppler (1803 - 1853), and shows how the frequency of an emitted  wave changes with the velocity of the emitter or observer. The theory was presented in the royal Bohemian society of Science in 25th of May1842 (5 listeners at the occasion!), and published in 1843 (119). The premises for his theoretical work was faulty, as he built his theory on the work of James Bradley who erroneously attributed the apparent motion of stars against the background (parallax effect) to the velocity of the earth in its orbit (instead of the effect of Earth's position in orbit on the angle of observation). Further, Doppler attributed the differences in colour of different stars to be due to the Doppler effect, assuming all stars to be white.  Finally, he theoretised over the effect of the motion  of double stars that rotate around each other, assuming a  Doppler effect  from the motion.  The changes in wavelength from the Doppler effect, however, is too small to be observed.

However, Doppler did a theoretical derivation of the effect of the motion of the source or observer on the perceived wavelength from the premises of a constant propagation velocity of the waves in the medium, and this is entirely correct, valid both for sound waves and electromagnetic radiation of all kinds. The basis for the Doppler effect is that the propagation velocity of the waves in a medium is constant, so the waves propagates with the same velocity in all directions, and thus there is no addition of the velocity of the waves and the velocity of the source. Thus, as the source moves in the direction of the propagation of the waves, this does not increase the propagation velocity of the waves, but instead increases the frequency.The original derivation of the Doppler principle as well as the extension to reflected waves is explained in more detail here. As a work of theoretical physics, it is thus extremely important. In addition, it has become of practical importance, as  the basis for the astronomical measurement of the velocity of galaxies by the red shift of the spectral lines, in Doppler radar, Doppler laser and Doppler ultrasound.

The theory was experimentally validated by the Dutchman Christoph Hendrik Diderik Buys Ballot (120), with the Doppler effect on sound waves, who placed musicians along a railway line and on a flatbed truck, all blowing the same note, and observed by subjects with absolute pitch, who observed the tones being a half note higher when the train was approaching as compared to the stationary musicians, and a half note lower as the train receded.

(This can be observed in everyday phenomena such as the sound of f.i. an ambulance siren, the pitch (frequency) is higher when the ambulance is coming towards the observer, hanging as it passes,  and lower as it goes away.

This is illustrated below:

 

The Doppler effect. As the velocity of sound in air (or any other medium ) is constant, the sound wave will propagate outwards in all directions with the same velocity, with the center at the point where it was emitted. As the engine moves, the next sound wave is emitted from a point further forward, i.e. with the center a little further forward. Thus the distance between the wave crests is decreased in the direction of the motion, and increased in the opposite direction. As the distance between the wave crests is equal to the wavelength, wavelength decreases (i.e. sound frequency increases) in front of the engine, and increases (sound frequency decreases) behind it. This effect can be heard, as the pitch of the train whistle  is higher coming towards a listener than moving away, changing as it passes. The effect on the pitch of the train whistle was published directly, but later than Doppler and Buys Ballot.


If the sound source is stationary, the effect on  moving observer is similar. The train will meet the wave crest with shorter intervals, as the train moves into the incoming sound. In ultrasound, the wave is sent from a stationary transducer, the moving blood or muscle is  firstly moving towards the transducer and then following the reflected wave towards the transducer, thus the Doppler shift is approximately twice as great. In the case of reflected ultrasound, the Doppler shift is:


Derivation of the Doppler equation

The following is the original derivation of the equation by CA Doppler (119).

The Doppler effect is the effect of the velocity of the
observer (A) or the wave source (B) on the perceived wavelength,. The basic fact is that the velocity of a wave, c, is constant in a given medium, and equal to the number of oscillations per second, times the wavelength (length of one oscillation):
 
The time of one oscillation, i.e. the time it takes for the wave to move one wavelength is then:


A
B

The Doppler effect for a stationary wave source and a moving observer. For the time the wave has moved the distance , the observer has moved the distance closer to the source (determined by the velocity v of the observer), corresponding tho the difference between the real wavelength and the apparent wavelength . This results in an apparent shortening of wavelength (increase in frequency) as shown by Doppler (119) and reproduced below this image. .

The Doppler effect for a moving source and a stationary observer. In the time between waves (which is 1/f0), the source has moved the distance closer to the source, (determined by the velocity v of the source), corresponding tho the difference between the real wavelength and the apparent wavelength . This results in an apparent shortening of wavelength (increase in frequency) as shown by Doppler (119) and reproduced below this image.
Thanks to Hon Chen Eng of University of Toledo who pointed out an inconsistency in the original illustration and showed a better way of illustrating the Doppler effect in this image. 
An observer (blue) moving towards a stationary wavesource with the velocity:

will meet the wave as the wave have moved a distance , which is the perceived wavelength. The observer has moved the distance:

The motion of the wave and the motion of the observer happen during the same time interval:

The motion of the observer thus shortens the original wavelength  by , i.e:



Thus:



The change in frequency, the Doppler shift is:


If the source moves toward a stationary observer with the velocity:             

In the time the wave moves one wavelength, the source moves the distance:                                                                            

The motion of the wave and the motion of the source happen during the same time interval:


The distance from the next wave emitted from the new position of the source (small dotted red circle)
to the observer (blue) is shortened by 
in the direction of the motion, so the new wavelength representing the distance between the first and second waves is

Thus:




The change in frequency, the Doppler shift is:




If  v << c, then:


and:


For reflected ultrasound, the effect is twice as great. A reflector moving towards the source will shorten the incoming wavelength in the same way as an observer moving towards the source, and the reflected ultrasound wavelength will be further shortened in the same way as a moving source following the reflected ultrasound, Thus, the effect is:

(The approximation in case B is small, the velocity of ultrasound in tissue is 1540 m/s, while the velocity of blood is between 0,2 and 6 m/s, and tissue between 0.05 and 0.2 m/s, giving a v/c of maximum 0.004, i.e the approximation in B is maximum 0.4% and in reflected ultrasound 0.2%). In all cases, if the velocity vector has an angle with the direction of the observation, the effective velocity is as discussed below, in the case of reflected ultrasound, the angle is the angle between the emitted ultrasound beam and the  velocity vector. Thus the full Doppler equation for reflected ultrasound is:

In all cases it is evident that velocities at right angle to the ultrasound beam will result in no Doppler shift (Cos 90º = 0), and if the reflector moves away from the ultrasound source, there is a negative Doppler shift (cos 180º = -1).

For motion measured in the same direction as the sound propagation.





Angle deviation in Doppler:

However, ultrasound, being high frequency, behaves more like beams, as explained in the beginning, there may be an angle between the direction of the motion and the ultrasound beam. This means that  the angle deviation will result in a change in the measured velocity, but in this care the angle deviation results in an underestimation of velocity by the cosine of the angle deviation.

Left: distance along the axis x, imagined along the ultrasound beam y where is the angle between the direction of the motion and the ultrasound beam (insonation angle).. The angle effect is:

This means that motion along an M-mode line will increase by the cosine of the angle deviation. This is explained above. The angle deviation gives an increase in wavelength, similar to the increase in distance:

Frequency of ultrasound is the inverse of wavelength, so:



thus:

and:




Thus, in the case of reflected ultrasound, the complete Doppler equation is:


where v is the blood or tissue velocity, c is the sound velocity in tissue, f0 is the transmitted frequency, fD is the Doppler shift of reflected ultrasound and is the insonation angle, between the ultrasound beam and the direction of motion (velocity vector).


Angle distortion in Doppler. The image on the left has applied angle correction, and then adjusted to scale. The angle correction is somewhat above 45 °, so the velocities are more than halved.
Thus:


But this also means that if motion is derived from integration of velocities, it will decrease with the angle, while tracking by B- or M- mode results in an increase with the angle as discussed in the basic ultrasound section.


Spectral analysis:

Fourier analysis of the returned Doppler signal resolves the Doppler shift into the different frequencies, as well as the amplitude for each spectrum. As shown above, the frequency is related to the different velocities.

In principle the Doppler signal can be sampled at the same sampling rate as M-mode. around 1000 samples per second, and the frequency shift could be determined between any two pulses as in colour Doppler. However, this would yield only one velocity value per pulse. For spectral analysis, resolving the dispersion of velocities, the velocities has to be sampled over a range of samples.

The Fourier analysis thus uses a time window. At the outset, the time window decides the effective display rate, thus a window of 100 ms at a sampling frequency of 1000 Hz, would give a display rate of 33. However, the time window used for analysis can use a sliding window, that means that windows overlap, which will increase the effective display rate. And the samples within the window can be weighted (f.i. by a Gaussian algorithm), so not the whole window has equal weight. Thus the effective display rate will be higher, but usually in the vicinity of 90 - 120, depending on depth, probe frequency, sample size etc.




Spectral analysis. The Doppler frequencies are distributed according to this frequency - amplitude diagram. The Tissue echoes has high amplitude of the reflected signal, but low velocities (resulting in low Doppler frequencies). Blood has higher velocities 8with a wider distribution), but lower amplitude. The signal is filtered. For Doppler flow, a high pass filter (low velocity reject) is applied to suppress the tissue echoes. The filter is variable, and thus can be applied to select for v very high velocities in insufficiency jets. A low pass filter (high velocity reject) can be applied to suppress noise above the velocity range. In tissue Doppler, the high pass filter can be removed, or at least partially, to allow the low velocities from the tissue (usually on the order of 1/10 of flow). It can partially be maintained to suppress absolutely stationary echoes, among other from the reverberations. The blood signal can be removed both by reducing the gain, and by applying a low pas filter. For detailed explanation see below.  Applied by me from Angelsen BA Ultrasound  imaging (117)

In the heart, the velocities are variable with time. Thus the velocity, or frequency shift is a function of time. At the same time, the amplitude is a function of the velocities, as the velocities will be  concentrated in a narrow band.  To display this, an approach similar to the M-mode can be applied. Amplitude is displayed as brightness, in a manners similar to B.mode, while Frequency / Velocity are displayed on the y - axis and time on the x - axis. This results in the typical Doppler flow velocity curves:



Typical spectral flow curves. Left: Flow in the Left ventricular outflow, right in the mitral annulus. Velocities toward the probe (positive Doppler shift) are shown as positive velocities, velocities away from the probe (negative Doppler shift) are shown as negative velocities. The velocities are sampled at a certain depth by pulsed Doppler (see below). Thus, the velocity distribution is limited to a fairly narrow band. Note the absence of velocities near zero, due to the high pass filter.


Width of the spectrum

As can be seen from the illustrations above, the velocity spectrum has a certain width. In the blood, this partly reflects the spread of velocities between the multiple scatterers in the blood, as shown below:



Spectrum width. Left mitral flow, showing a fairly narrow spectrum band, indicating a relatively homogeneous velocity distribution.
Right pulmonary venous flow, showing a wide distribution of velocities.


However, this is not the only explanation. As the bandwidth is a function of the pulse length as illustrated above, spectral analysis will yield a spectrum that minimum is as wide as the bandwidth. Ideally, the pulse length in Doppler should be long, in order to increase velocity resolution. However, this will reduce the spatial (axial) resolution.

Thus, if the dispersion of velocities is larger than the bandwidth, as in flow measurements, this is the most important. On the other hand, if there is little dispersion of velocities, as in tissue Doppler, the width of the spectrum reflects the bandwidth.

But the insonation angle also has an influence, not only in the velocity measurement according to the Doppler equation. but also in the bandwidth as shown below.


As can be seen, the direction of the motion  of the scatterer in relation to the direction of the pulse, may influence the number of oscillations that are actually used for measurement. Thus, a high  insonation angle is equivalent to a virtual shortening of the pulse length, and results in a wider bandwidth (spectrum).

Finally, stationary reverberations, creating artificially stationary echoes will result in widening of the spectrum in tissue Doppler. In flow, this will basically be removed by the high pass filter.

Pulsed and continuous wave Doppler:

Doppler pulses can either be used as a pulsed Doppler, where a pulse is sent out, and the frequency shift in the reflected pulse is measured after a certain time. This will correspond to a certain depth (range gating), i.e. velocity is measured at a specific depth, which can be adjusted. The width is the same as the beam width, and the length of the sample volume is equal to the length of the pulse. The same transducer is used both for transmitting and receiving.

A problem in pulsed Doppler is that the Doppler shift is very small compared to the ultrasound frequency. This makes it problematic to estimate the Doppler shift from a single pulse, without increasing the pulse length too far. A velocity of 100 cm/s with a ultrasound frequency of 3.5 MHz results in a maximum Doppler shift of  2.3 KHz. The solution to this problem is shooting multiple pulses in the same direction and produce a new signal with one sample from each pulse, the Doppler curve from this signal will be a new curve with the frequency equal to the Doppler shift. (This means that a full package of pulses is considered one pulse in the sampling frequency sense).

The pulsed modus results in a practical limit on the maximum velocity that can be measured. In order to measure velocity at a certain depth, the next pulse cannot be sent out before the signal is returned.  The Doppler shift is thus sampled once for every pulse that is transmitted, and the sampling frequency is thus equal to the pulse repetition frequency (PRF). Frequency aliasing occurs at a Doppler shift that is equal to half of the PRF.
fD = ½ * PRF
This is illustrated below with an analogy:

The Nykvist phenomenon.

The Nykvist phenomenon (121) is an effect of the relation between the sampling frequency and the observed velocity. If you sample at a certain frequency, the direction of the motion becomes ambiguous, more frequent sampling will give the correct direction, less frequent  sampling results in an apparent motion in the opposite direction. This can be observed with a stroboscopic light, for instance illuminating the flow of water, or with old fashioned wagon wheels in old moves which often seem to revolve slowly backwards when the wagon moves forwards.


This is illustrated below.

Constant rotation velocity, decreasing sampling frequency:

The easiest is to show how reducing the sampling frequency affects the apparent motion. All circles rotate with the same rotation velocity clockwise. The sampling frequency is reduced from left to right. It can be seen that the red dots is at the same positions when they are seen to move.





a:      8:1
8 samples per rotation, the red point is seen in eight positions during the rotation.

b:     4:1
4 samples per rotation, the red point is seen to rotate just as fast, but is only seen in four positions
c:    2:1
2 samples per rotation, i.e. the sampling frequency is exactly half the rotation frequency. Here, the red dot is only seen in two positions, (but it is evident that it is in the same positions at the same time as in a and b). However,  it is impossible to decide which way it is rotating. This is the Nykvist limit; sampling rate = 1/2 rotation rate.
d:    1.5:1
1.5 samples per rotation,or  one sample per three quarter rotation, making it seem that the red dot is rotating counter clockwise. Again, the dot is in the same position at the same time as in a and b.



Constant sampling frequency, increasing rotation velocity

The same principle applies when there is a fixed sampling frequency, but increasing rotational velocity. In the images below, the frames are seen to shift simultaneously, but the positions of the red dots are different due to the different rotational velocity.





a:    1:8
One rotation per 8 samples. The sampling catches the red dot in 8 positions during one rotation.
b:    1:4
Rotation velocity twice that i a; one rotation per four samples, the sampling catches the red dot only in four positions
during one rotation.
c:   1:2
Rotation velocity four times a; one rotation per two samples, this catches the red dot in only two positions, giving directional ambiguity as above.
d:   1:1,5
Rotation velocity six times a; one rotation per 1,5 samples, or 3/4 rotation per sample, giving an apparent counter clockwise rotation.

Sampling from increasing depth will  increase the time for the pulse returning, thus increasing the sampling interval and decrease the sampling  frequency.  The Nykvist limit thus decreases with depth. This means that pulsed Doppler has depth resolution, but this leads to a limit to the velocities that can be measured.

The Nyquist limit is dependent on the depth (D) of the sampling volume. The larger distance from the probe, the  longer time for the pulse to pass to the desired depth and back, and the  lower the Nyquist limit. The time for the return of the pulse is:

T = 2D/c and the maximum PRF as PRF = c/2D

Thus, the maximum Doppler shift that can be measured is:
fD = c/4D (from: fD = ½ * PRF) and from the Doppler equation ( v = fD * c / 2f0) the maximum velocity (Nyquist velocity vN):
vN = c2/8Df0


Aliasing is no problem in pulsed tissue Doppler, as tissue velocities are far below the Nykvist limit. However, in colour tissue Doppler, harmonic imaging is halving the effective frequency, and leads to aliasing as shown below.

Continuous Doppler,

on the other hand, will measure all velocities along the ultrasound beam: The beam is transmitted continuously, and the received echoes are sampled continuously with no range gating. Thus, there is no information about the time interval from the signal to the reflection, and, hence, no information about the depth of the received signal; the signal may come from any depth. The continuous Doppler has no Nykvist limit, and can measure maximal velocities. It is used for measuring high velocities.

This means that both methods has limitations: pulsed Doppler has velocity ambiguity at high velocities, and continuous wave Doppler has depth or range ambiguity. Thus, for continuous Doppler the pulse length can be long, as there is no depth resolution, while in pulsed Doppler it has to be shorter in order to achieve a sufficient depth resolution.



Examples of continuous wave versus pulsed wave, and the Nykvist effect. Left: Aortic insufficiency shown by cw Doppler. It van be seen that there are a fair distribution of velocities in the whole spectrum. However, There are far more velocities blow 2 m/s. In this case, the low pass filter is only set to suppress tissue velocities. If the point is to get a clear visualisation of the maximal velocities in the jet, at 4 - 6 m/s, the filter should be set higher. Left, the same patient by pulsed Doppler of the LVOT. The outflow can be seen as a narrow band, within the velocity range, while the regurgitant jet has velocities outside the Nykvist range, and there is total velocity ambiguity.

High Pulse Repetition Frequency (HPRF)

A way around the problem, is to use high pulse repetition frequency pulsed Doppler. This means that one or more new pulses are sent out before the echo from the desired depth of the first is received. This will increase the pulse repetition frequency, and thus increase the Nykvist limit as the fN = ½ * PRF. On the other hand it will be impossible to determine which pulse is the origin of the echo, and thus it will result in a partial depth ambiguity.


The principle of HPRF.  Pulses are transmitted with three times the frequency that is necessary to allow the echo from the furthest depth to return. Thus, the echo of pulse 1 will return from level 3 at the same time as the echo of pulse 2 from level 2 and and of pulse 3 from level 1, and there is no way to determine whether a signal is from level 1, 2 or 3. HPRF pulsed Doppler recording (right). with one sample volume in mid ventricle and one in the mitral ostium. The recording shows a systolic dynamic gradient (due to inotropic stimulation with dobutamine), as well as an ordinary mitral inflow curve.  There is no way in the pulsed recording to determine which velocities that originate from which sample volume (except from á priori knowledge, of course, a dynamic gradient like this is usually mid ventricular, and the mitral inflow in the annulus is easily recognised). 


Colour Doppler mode (CFM)

The colour Doppler mode is based on analysing the phase shift of the reflected pulse, which is equivalent to the Doppler shift. Shooting at least two (or more) pulses in rapid sequence, (NOT to be confused by sampling one pulse at two timepoints as illustrated above) results in the possibility to analyse the Doppler shift in terms of the phase shift between the pulses. The phase shift analysis is based on the principle that when pulse 2 hits a moving scatterer, the scatterer will have moved a little away from, or towards the probe, and the return pulse 2 will then be in  a different phase from pulse 1. The distance the scatterer has moved, is of course a function of the velocity of the scatterer and the time between pulses given by the pulse repetition frequency, thus:
d = v * t = v * 1/PRF.

In order to avoid aliasing, the distance the scatterer moves should be less than half a wavelength, i.e. the Nykvist limit. This is thus given by the pulse repetition frequency, exactly as in pulsed Doppler. In this case, the PRF is 1/t, the time delay between the two pulses in one package. In order to obtain an acceptable Nykvist limit, the PRF need to be at least 1 KHz which will result in a Nykvist limit of 19.8 at a depth of 15 cm





Two pulses sent toward a scatterer with a time delay  t2 - t1 = 1/PRF. Given that the scatterer has a velocity, it will have moved a distance, d, that is a function of the velocity and the time (d = v x t).  Thus, pulse 2 travels a longer (or shorter) distance equal to d with the speed of sound, c, before it is reflected.  During the time pulse2 has travelled the distance d to the new position of the scatterer and back to the point of the reflection of pulse 1, i.e. a distance 2d,  pulse 1 has travelled the same distance away from the reflection point. (The scatterer will have travelled further, but this is not relevant).  Thus the displacement of the waveform of pulse 2 relative to pulse 1, is 2d. This corresponds to a phase shift from pulse 1 to pulse 2 of  , and  = 4  f0 / v PRF (see below). By sampling the two pulses simultaneously at two timepoints, as shown in the previous illustration, the phase of each pulse can be determined as shown below. The phase analysis  of the relative positions of all four points is done by autocorrelation, a quick (and dirty?) method that allows online computation.


The phase analysis is done by treating the waveform as a sine curve, where the phase of a point is represented as an angle.

Phase analysis

In colour Doppler, the analysis is done in terms of the phase shift: A wave can be described as a sine wave, and thus, any point on the wave can be described by which phase of the wave the point is, as illustrated below:




Phase analysis.  If the waveform is treated as a sine curve,  every point on the curve corresponds to an angle, and the phase of the point in the curve can be described by this angle; the phase angle  From the diagram, it's also evident that a full wavelength, , is equivalent to 2, and for every point the corresponding fraction of a wavelength is equivalent to an angle which is the fraction of 2. However, from the diagram at the top, it is evident that by sampling the waveform only once, the phase is ambiguous, it is not possible to separate the phase of point a from point b.  The two points are separated by a quarter of a wavelength, or 90° (). In order to determine the phase of the points unambiguously, the pulse has to be sampled at to points separated by less than a quarter wavelength. Then it can be seen that point a is in increasing phase from a1 to a2,  corresponding to a phase angle of  0 - /2 while b is in a decreasing phase corresponding to an angle of /2 - .



Shooting at least two (or more) pulses in rapid sequence, (NOT to be confused by sampling one pulse at two timepoints as illustrated above) results in the possibility to analyse the Doppler shift in terms of the phase shift between the pulses. The phase shift analysis is based on the principle that when pulse 2 hits a moving scatterer, the scatterer will have moved a little away from, or towards the probe, and the return pulse 2 will then be in  a different phase from pulse 1. The distance the scatterer has moved, is of course a function of the velocity of the scatterer and the time between pulses given by the pulse repetition frequency, thus:
d = v * t = v * 1/PRF.







As descibed above, a pulse has a certein bandwidth, describing the frequency content of the pulse. In spectral analysis, this will give a spectrum of a certain width, corresponding to the velocity distribution of flow velocities. In phase analysis, this will correspont to a certain distribution of phase angles as illustrated. Autocorrelation, however, will only result in the average phase angle.
In the case of stationary noise (clutter) as f.i. reverberations, the autocorrelation will result in an average phase angle that is in between the signal and the noise. The clutter noise will have to be removed by a low velocity filter in order to avoid severe underestimation of flow velocities.




In order to avoid aliasing, the distance the scatterer moves should be less than half a wavelength, i.e. the Nykvist limit. This is thus given by the pulse repetition frequency, exactly as in pulsed Doppler. In this case, the PRF is 1/t, the time delay between the two pulses in one package. In order to obtain an acceptable Nykvist limit, the PRF need to be at least 1 KHz which will result in a Nykvist limit of 19.8 at a depth of 15 cm


Thus, as a wavelength equals 2, the displacement (2d) of pulse 2 in relation to pulse 1 relative to equals the phase shift relative to 2:    2d/= /2. As d = v*t, t = 1/PRF and = c/f, it follows that:

= 4  *f0 / v*PRF

Thus, the phase analysis is based on the phase shoft from one pulse to next, instead of the apparent shortening of the wavelength by the motion of the source or observer (or reflector, which amounts to the combination of both. However, the phase shift from one pulse to the next is completely equivalent to the change in wavelength in one pulse, so the two are equivalent for all practical purposes.

The motion of the scatterer, d, is the same as the motion in the derivation of the Doppler equation, and the  displacement between the pulses, 2d is the same as the combined Doppler equation for reflected ultrasound: the displacement of sorce/observer as a fraction of the wavelength.
 





The two pulses represent a pulse package. The time between the two pulses represent 1/PRF; determining the Nykvist limit. The time between two packages is 1/FR. The time between packages can be used for sampling B-mode data for a B-mode image in a composite image.

The method will give the velocity at a certain depth, depending on the range gating as in pulsed Doppler. By gating multiple sampling times from the same pulse package in post processing, the Doppler shift can be measured at multiple depths along the line. As opposed to HPRF, only one pulse package can be sent out along one line in order to await the return signal down to maximum depth (range), in order to avoid range ambiguity. This means that the method is more similar to B-mode than HPRF, and the velocity ambiguity is similar to pulsed Doppler. In fact, colour Doppler can be seen as a B-mode, where the phase (or frequency) shift is analysed instead of the amplitude, stored as numerical values in each pixel (as amplitude is in B-mode), but displayed as colour instead of brightness.

This again means that in order to build a sector, the next package has to be sent along next line, and a new package can only be sent out along the first line when a complete set of scan lines has been built up. Thus the time between packages in one line, and hence, the temporal resolution, is dependent on the frame rate, just as in B-mode as described above. The temporal resolution can be increased by reducing sector depth, sector width and line density. In addition, sampling at longer gating intervals, due to one package being two pulses, reduces radial (depth) resolution. However, as the region of flow is only the cavity, and the region of interest usually being only part of this, reducing sector size in order to obtain an acceptable frame rate is a feasible solution as shown below.





Principle of package acquisition. Time depth diagram of the position of a moving scatterer. Each dot represent one pulse. Packages of two pulses are sent to the scatterer with intervals. The time between the pulses in one package is given by 1/PRF, and decides the Nykvist limit. The time between packages is the time it takes to build a full sector of lines in colour flow mode (CFM) and is given by the frame rate (FR), the time interval being 1/FR. This decides the temporal resolution of the CFM.
CFM sector superposed on a B-mode sector. By reducing sector size, line density and sampling frequency, the CFM image can achieve an acceptable frame rate.  This is feasible because the region of interest for the flow is usually only a part of the ROI for The B-mode, ,flow being intracavitary as shown below.

In principle, two pulses are sufficient for phase analysis with perfect signals. However, more than two pulses can be used in order to make the analysis more robust, in the autocorrelation method. This results in better accuracy (reliability) of the velocity estimate. This, however increases the duration of each package (as the time between two pulses is 1/PRF, a package of N pulses will have a duration of N-1/PRF), and thus it will affect frame rate.

A theoretical frame rate of 1 KHz will make the use of packets unnecessary (as then PRF = FR, and phase analysis can be done from one puls to the next, with the same Nykvist frequency). This is technically feasible (272), and has been implemented in a novel application; Ultra high frame rate tissue Doppler (UFR-TDI) (
215 ,268).



Also, the possibility to display the full velocity information in each pixel is limited. In order to display multiple velocities in real time over a sector, the numerical values are usually displayed only semi quantitatively as color. Power Doppler shows the amplitude of the Doppler shifted signal, i.e. the blood flow.

Power Doppler image of the renal circulation. The amplitude is a function of the number of scatterers, i.e. the number of blood cells with a Doppler shift. This is shown as the brightness (hue) of the signal. In addition, direction of flow can be imaged by different colours (red - positive flow - towards probe, blue - negative colours - away from probe), and still the brightness may show the amplitude.
Colour flow showing a large mitral regurgitation. Velocities away from the probe is shown in blue (converting to red where there is aliasing), towards the probe is red. In this image, the green colour is used to show the spread (variance) of velocities. This will also reflect areas of high velocities (high variance due to aliasing). The sector with colour flow is seen to be far smaller than the B-mode sector. The image displays the direction, extent and timing of the jet.





2D colour flow gives mainly information on the direction of velocities, as well as colour M-mode giving the direction - timing information. However, the information is numerical, and can be extracted as is done in colour tissue Doppler, but this gives far less accurate values than pulsed and cw Doppler, as well as a reduced frame rate.








Recording from a patient with apical hypertrophic cardiomyopathy. Ejection can be seen in blue, and there is a delayed, separate ejection from the apex due to delayed relaxation. There is an ordinary mitral inflow (red), but no filling of the apex in the early phase (E-wave), while the late phase (A-wave) can be seen to fill the apex.  Left,  a combined image in HPRF and  colour M-mode.  The PRF is adjusted to place two samples at thr mitral annulus and in the mid ventricle just at the outlet of the apex. The mitral filling  is shown by the green arrows,  and the late filling of the apex is marked by the blue arrow.  In addition, theere is a dynamic mid ventricular gradient shown by the red arrow, with aliasing in the ejection signal in colur Doppler. The delayed ejection from the apex is marked by the yellow arrow (the case is described in (87).  The utility of the different methods is evident: HPRF (or cw Doppler) for timing and velocity measurement, but with depth ambiguity, colour M-mode for timing and location of the different jets, direction being displayed by the colour. 
 

The phase analysis is often done by the process known as autocorrelation. This will result in a values that does not reflect the spectrum, but only mean values in the spectrum. But if there is clutter in the region (stationary echoes), this will be incorporated in the mean, resulting ion lower values. In Doppler flow, this can be filered by the high pass filter, and thus will represent a small problem. In tissue Doppler, this may be a more significant problem, as the velocities are only about 1/10 of the flow values, and thus clutter may be more difficult to separate from true velocities. Thus, a substantial amunt of clutter may reduce autocorrelation values for tissue Doppler more than pulsed Doppler as discussed below. In addition, it is customary to analyse the tissue Doppler values in native, rather than harmonic imaging, due to the Nykvist limitation. Thus, there is a greater amount of clutter than if harmonic imaging had been used, as shown in B-mode images.

For optimal colour flow, it is important to realise that there may, in some scanners, be an inverse relation between the gain of colour Doppler and B-mode. (In some scanners it is possible to adjust the priority, or to adjust the gain settings separately). This, however, is an acquisition finction, and not image adjustment, and thus cannot be compensated afterwards. This is illustrated below:


Effect on B-mode gain on colour Doppler imaging. Left pulmonary venous flow by pwDoppler, showing a systolic flow component, although low velocities. Middle, colour M-mode of the same patient. Only the diastolic flow component can be seen. Right, reducing B-mode gain increases the gain of colour flow, and the systolic pulmonary venous flow can be seen.




Tissue Doppler.

The Doppler principle can be used both for blood flow and Tissue velocities. Tissue Doppler was first decribed in 1989 (53). It is simply a question of different filtering of the Doppler signals. The main principle is that blood has high velocity (Typically above 50 cm/s, although also all velocities down to zero), but low density, resulting in low intensity (amplitude) reflected signals. Tissue has high density, resulting in high intensity signals, but low velocity (typically below 20 cm/s). The difference in the applications used for the two sets of signals is mainly differences in filtering, applying a high pass filter in Doppler flow, and low pass filter in tissue Doppler (Although the latter is not absolutely necessary).

Spectral tissue Doppler

It is again important to realise that pulsed tissue Doppler has a high sampling rate (up to 1000), but a low temporal resolusion (effective frame rate usually below 100 FPS) due to the Fourier analysis over a long window as explained above.




The diagram to the left shows the placement of flow and tissue signals on this intensity (amplitude) / velocity diagram. Velocity given as the height ogf the bars, intensdity showb both by the placement on the x axis, as well as the darkness of the bars, black being the highest intensity. The flow signals are low intensity but mostly high velocity, while the tissue is exclusively low velocity, high intensity. The heart valves, however, are solid structures which moves with the velocity of the passing blood, resulting in high intensity signals giving a saturation of the Doppler spectrum. A typical flow curve from the right ventricular outflow tract is shown to the left, with the valve click.


Application of a high pass filter (low velocity reject) shown schematically to the left and in practice applied to a mitral flow curve to the right. Velocities lower than the limits of the green bar (showing the range of the filter) are removed seen in the dark zone in the middle of the spectrum. The setting rejects velocities at blood intensities below 15 - 20 cm/s, which is too high for normal flow velocities as in this instance, although may often be useful  in continuous wave Doppler recordings of high velocities in jets.

The filter is adjustable and is here reduced to 10 cm/s


Further reduction in the filter below 10 cm/s results in high intensity signals becoming visible, especially in early diastole. This is tissue signals from the mitral ring.


Fully removing the filter results in a dense band of high intensity tissue signals around the baseline. The signal is difficult to analyse, as it has so high amplitude that the display is saturated.


Decreasing the scale and gain (shown as all signals being illustrated in lighter colour, but with the same relative placement on the x axis), and placing the sample volume near the mitral ring, discloses the tissue velocity curve of the ring, still taken with an ordinary Doppler. The flow signal, having a much lower amplitude, is removed simply by reducing the gain.


All modern ultrasound machines today has separate applications for tissue Doppler which optimises the signal for this purpose, among other things by applying a low pass filter that removes most of the flow velocities. This results in a cleaner signal.

Colour Tissue Doppler

The basic principles of colour tissue Doppler are the same as for colour flow mode (222). The difference is the same as in spectral Doppler flow versus colour Doppler flow, except for the differences in filtering as shown above. colour However, the region of interest is the same as in B-mode, being the myocardium. Thus the solution of a small sector within the B-mode sector is unfeasible. However, as velocities are measured only along the ultrasound beams, and cavity signals are filtered by low gain / low pass filter, the line density need not be high. In addition, as the data are for numerical analysis, not imaging, artifacts from MLA are unimportant. Thus, high frame rate in a full B-mode sector is achieved with a very low line density, and a higher MLA (typically 4). Thus the B-mode and colour Doppler images are displayed superposed, but the acquisition is interleaved, recording a multiple of colour Doppler images between each B-mode frame. (For instance 16 lines acquired by 4 MLA in colour Doppler interleaved with one B-mode image acquired with 64 lines at 2MLA for every fourth Doppler image will result in a Doppler frame rate of 160 for a B-mode frame rate of 40).

Both velocity and strain rate information can be displayed on the B-mode image, just as in colour flow. However, as seen below, in this case it does not display location of jets, as most motion and deformation is fairly more uniform. In addition, shifts are too quick to visualise entirely.

Thus, in colour tissue Doppler, the main function is to get data for post processing. The advantage over pulsed Doppler, is the near simultaneity of the data over the sector, being important in comparing regional motion from different segments of the wall. In colour flow, simultaneity is less important, and so quantitative information is rather acquired by pulsed or cw Doppler, giving higher temporal resolution.

Thus, tissue velocities can be extracted to numerical traceses, to enable measurements of
However, both the primary velocity data, as well as the calculated date can be displayed as parametric (colour) images images, of which the curved M-mode is the most useful so far. Mainly for assessment of timing.


Curved anatomical M-mode

This method, developed by Lars Åke Brodin and Bjørn Olstad shows the whole time sequence in one wall at a time. (18). By this method, a line is drawn in the wall, and tissue velocity data are sampled for the whole time interval (e.g. one heart cycle) and displayed in colour along a line in a time plot, as shown below. This has the advantage of displaying the whole sequence in a still picture, giving a temporal resolution like the frame rate of the 2D tissue Doppler.



Velocity and strain rate imaging of the same (normal) left ventricle.  The colour sector can bee seen to be equal to the B-mode sector.Velocity is red in systole when all parts of the heart muscle moves toward the probe (apex) and blue in diastole. The changes are too quick to observe entirely, to make full use of the information the image has to be stopped and scrolled. Curved anatomical M-mode (CAMM). A line is drawn from apex to base, and velocity data over time are sampled along the line and displayed in colour along a straight line. The numbers on the curve and the M-mode are included for reference and corresponds to the numbers on the B-mode image.  This example shows the septum from the apex to base along one axis, and one heart cycle along the other, in a two - dimensional space - time plot. S: systole, E: early relaxation, A: atrail contraction.

Velocity traces

The information coded in the colour images, is fundamentally numerical for all varieties of colour Doppler. Thus, the velocity time traces can be extracted fom any point in the image as shown below.

Extracted velocity curves from three points in the septum. As in colour flow, the M-mode gives the depth - time - direction information, while the curves give the quantitative information.

Thus: 2D images show the whole sector image at one point in time, velocity or strain (rate) traces shows the whole time sequence (f.i. a heart cycle) at one point in space, while CAMM shows the time sequence as well as the length of the line, but only semi quantitative motion / deformation information.

Velocity gradient


As the apex is stationary, while the base moves, the displacement and velocity has to increase from the apex to base as shown below.




As the apex is stationary, while the base moves toward the apex in systole, away from the apex in diastole, the ventricle has to show differential motion, between zero at the apex and  maximum at the base. As motion decreases from apex to base, velocities has to as well. This is seen very well in this plot of pwTissue Doppler recordings showing decreasing velocities toward apex. Thus, there is a velocity gradient from apex to base


The simultaneous measurement of velocities by colour Doppler in the whole sector, enables the measurement of instantaneous velocity differences.


The velocity gradient is the velocity difference between two material points, divided by the instantaneous difference between them:
 

Longitudinal velocity gradient, where v1 and v2 are two different velocities measured at points 1 and 2, and L the length of the segment between those points. Spatial distribution of systolic velocities as extracted by autocorrelation. This kind of plot is caled a V-plot (247). It shows velocities as near straight lines, and thus, a constant velocity gradient, which is the slope of the curve from base to apex. .





The distance L changes with time, if v1 and v2 are different. The unit of the velocity gradient is cm/s/cm, which is equal to s-1.

Longitudinal strain rate, on the other hand, was originally measured as the instantaneous velocity difderence between two fixed points in space, divided by the distance between them.


This is a different algorithm from the velocity gradient, but it can be proved that the two formulas result in the same ratio. The distance  is called the offset distance or strain length.






The strain rate can be described by the instantaneous velocity gradient, in this case between two material points, but divided by the instantaneous distance between them. In this description, it is the relation to the instantaneous length, that is the clue to the Eulerian reference.
train rate is calculated as the velocity gradient between two spatial points. As there is deformation, new material points will move into the two spatial points at each point in time. Thus, the strain that results from integrating the velocity gradient, is the Eulerian strain. In this view, the relation to the spatial, rather than material reference is very evident.


The two methods shown above are not identical, But it can be shown that they are equivalent.
In the material velocity gradient the L changes in the spatial it is constant. Thus, they are not equal, except at the point in time when x equals L, then v(x) = v2 and v(x+x) = v1. However, Usually, however, L will differ from x, for most frames and objects, and the velocities will hence differ too. Under the assumption that the strain is equally distributed over the length of the object (spatially constant), SR will still be equal to the velocity gradient, i e the values of the two ratios will be the same. Strain being spatially constant means that the velocity increases linearly along the length as shown in the diagram:



For any L that is different from x, v2 – v1 will be greater or smaller than v(x) – v(x + x) by the same ratio. In the figure, this is evident, as the slope of the curve is the same wherever it is measured. As v1 and v2 are the velocities of the end points of L, the ratios SR and VG will be the same, and thus the expressions are equivalent: SR = VG and the strain rate by tissue Doppler (SR) equals Eulerian strain rate. Thus:        



Velocity gradient by linear regression

Instead of measuring just the velocities at the ends of the offset distance;  or  respectively, the velocity gradient / strain rate can be calculated as the slope of the regression line of all velocities along the offset distance as described originally (14). With perfect data, the values will be identical, both formulas defining the slope. With imperfect data, this method will tend to make the method less sensitive to errors in velocity measurements, as the value is an average of more measurements.



Strain rate calculated over an offset  (strain length) of  12 mm (L). "True" strain rate at the end points are v1 = 0 and v2 = 1.2 cm s-1 giving a strain rate of -1.0 s-1 (blue squares), the strain rate is actually the slope of the line between the points, being equal to (v2 - v1)/L. Due to random variability of the measurements, the measured values deviate from the slope. Here velocities are sampled for each 0.5 mm along the strain length (red points), and are seen to be dispersed around the true strain rate line. The regression line through the points (red line) is fairly close to the true strain line, and results in a strain rate measurement of -1.14 s-1. This makes the measurement far less vulnerable to measurement variability than simply measuring the two velocities at the end of the strain length (points in the green open squares), and compute SR = (v2 - v1)/L shown by the green line, yielding a strain rate of -1.63 s-1.



Measurement of peak values in relation to the Doppler spectrum

The width of the spectrum in Doppler flow is mainly determined by the dispersion of velocities. However, the main use of pulsed wave tissue Doppler is for measuring annulus velocities, and the annulus is stiff, with little probability of dispersion of velocities. Also, in pulsed tissue Doppler, the insonation angle is small. Despite this, the spectrum has a certain width, indicating a spectrum of velocities:


Spectrum width in tissue Doppler.  Image courtesy of H Dalen.


Thus, the main determinant of the width of the spectrum is determined by the bandwidth. The bandwith is determined by the pulse length and pulse frequency, and represents the frequency spectrum in the received signal. As this frequency is due to the frequency distribution in the transmitted signal, as well as the uncertainty in frequency measurement, the frequency distribution is statistical, and more or less normally distributed around the mean frequency (or velocity).


Left: spectral tissue Doppler, illustrating the width of the spectrum. The modal (or mean) velocity curve is indicated in black.  Right, colour tissue
Doppler from the same location in the same patient, obtained by autocorrelation, giving average values directly. Peak values correspond fairly.



Ideally, the most representative value of the spectrum is the modal velocity (the velocity in the middle of the spectrum), not the maximal value (at the top of the spectrum). This will also be the values that are most similar to the tissue Doppler values obtained by autocorrelation (colour tissue Doppler) as shown below.


Recordings from basal septal mitral ring in a subject without substantial clutter. Spectral Doppler shows the dispersion of velocities, although this is probably an effect of bandwidth. The colour Doppler recording is superposed and aligned with both vertical and horizontal scale. In this instance can be seen to give values close to the middle of the spectrum (modal velocity).

However, historically the peak value (at the top of the spectrum), has been used in pulsed Doppler. Thus, most of the differences reported between pw Tissue Doppler (145, 165) and colour tissue Doppler are due to the width of the spectrum. But if so, this would give a good correlation between methods, and a more or less constant offset (165, 267).

Id addition the width of the spectrum is sensitive to gain settings. As the frequencies are normally distributed around the mean, this means that the intensity in the periphery of the band is lowest, and will disappear earlier when gain is reduced. Increased gain setting increases the peak values (145) as illustrated below:


In this case, differences in gain leads to a difference of 3 cm/s in systolic peak values, and 3.5 cm/s in early diastolic peak values.





Same tissue Doppler recording with two different gain settings. We see that peak systolic velocity differs by 2 cm/s, and the lowest gain setting
is closest to the modal velocity. However, the modal velocity itself, remains unchanged by the gain setting.






Spectral Doppler reconstructed from IQ data. Candidates for measuring peak systolic velocity by the PW tissue Doppler spectrum. RED circle: peak of the spectrum at normal gain, GREEN circle: upper edge of
the strongest part (the part visualised at minimal gain), BLUE circle: middle of the strongest part. MAGENTA circle and line: autocorrelation. As seen, imn this example the autocorrelation corresponds to the middle of the spectrum. (Figure
courtesy of Svein Arne Aase, modified from (266))


We tested this in a preliminary study (266), using spectral Doppler reconstructed from IQ data.

For a reference method, Peak slope of systolic M-mode in the same time point was chosen:


Reference method. A: pw Doppler from the mitral ring (reconstructed from RF data). Peak velocity of the ring displacement can be identified. B: This corresponds to the maximal slope of the M-mode line at the same time point. C: The M-mode in the same time window from the RF data. This gives a far better resolution in space and slope.  D: In the RF M-mode the steepest sloe was identified automatically. This will be a reference for the maximal velocity. (Figure courtesy of Svein Arne Aase, modified from (266))

In this study of 9 healthy volunteers, we found that the middle of the spectrum was the cloasest value (although statstically significant under estimation, but that peak value of the strongest part would be close enough (266), with just a slightly higher over estimation.



As this figure shows, the peak spectrum results in a substatial over estimation. reducing the gain improves the over estimation, while the modal velocity is closest to the reference. Autocorrelation on the other hand results in significant under estimation, due to the presence of clutter. Only four subjects showed almost totall correspondence between autocorrelation and modasl velocity from spectral doppler. (Figure courtesy of Svein Arne Aase, modified from (266))



In perfect image quality, modal velocity should be equal to autocorrelation, but in the case there is clutter, autocorrelation would not give similar values, as clutter would be incorporated into the mean. In the study above, this was the case with most subjectys, resulting in a significant difference between modal velocity from spectral Doppler and autocorrelation. This is further discussed below.


It is evident that the modal velocity is closest to the "true" velocity, and thus if peak values are used, they should be obtained and analysed by the lowest readable gain setting.
On the other hand, filtering of the colour tissue Doppler reduces peak values, and will also increase the  difference between the methods (145). Autocorrelation with high filtering or low frame rate will thus underestimate the true mean value.



Reverberations (clutter) in tissue Doppler



However: Modal velocity may be influenced by reverberations. The mechanism for the formation of reverberations are explained in the basic ultrasound section.




Image from another subject in the study shown above (266). In this subjech there is some clutter from reverberations, as seen by the band in systole close to the zero line. In this case the peak velocity by autocorrelation is lower than the modal velocity of the main spectral band, which still was the one closest to the RF M-mode reference. (Figure courtesy of Svein Arne Aase, modified from (266)) Clutter filtering may reduce the problem, as seen here. There is aa band of clutter close to zero velocities, but as seen here, the spectral modality makes it very easy to separate the true and clutter velocities. However, the clutter affects the autocorrelation velocity (red line), giving lower velocities, but with clutter filter this effect is removed (red line) , and the peak value is substantially higher. Image modified from (268).




In some cases, the mean velocitymay be very far from the "true" modal velocuty:

In this case, the spectral Doppler is "smeared out, all the way down to the baseline. The mean of all frequencies is shown on the spectrum in black. It is far from the peak values. To the right is the values from autocorrelation, which are similar to the mean values.


Reverberations may not be entirely stationary. It the reflecting surface that gives rise to the reverberation moves, the reverberation bands will move also, as seen in the simulations above, as well as the real acquisition below

.
Normal tissue Doppler curve from the mitral ring. Peak systolic velocity around 8 cm/s. However, a band with approximately the same shape, but systolic amplitudes of around 2 m/s van be seen as well, probaby a reverberation from the apical part. 





Reverberations are often nearly stationary echoes, meaning that the echoes will incorporate zero velocities (clutter). Most of the reverberation echoes are in the fundamental imaging frequency. However, harmonic imaging halves the frequency, and thus the Nykvist limit. This means that there will be aliasing at half the velocity in harmonic imaging, compared to fundamental. And this is within the range of tissue velocities. Thus harmonic imaging is unfeasible in tissue Doppler, and the harmonic acquisition makes the method more vulnerable to reverberations than B-mode, as explained below.


Shadowy reverberations covering the anterior wall in this 2-chamber image. It is differentiated from drop out, as we can se a "fog" of structures covering the anterior wall. The structures are stationary. On the other hand, this is not distinct reverberations shadows, but incoherent clutter. Recordings from the basal anterior ring in a subject with substantial clutter. The tyrue signal is clearly visible as a normal curve, and can be seen separately from the clutter band, which is the horizontal spectral band along the baseline. The colour Doppler recording is superposed and aligned with both vertical and horizontal scale. The colour Doppler, using the autocorrelation algorithm, results in mean velocities that incorporate both signal and clutter, giving a severe underestimation of velocities.



This example might be supposed to be mostly drop out, but pw tissue Doppler curves from the same examination show normal peak velocities in the anterior wall as shown below. Once again spectral Doppler is able to overcome the clutter problem, showing true peak mitral ring systolic velocities of 8.5 cm/s, compared to the peak values of 2 cm/s seen by colour Doppler above.




Basal spectral tissue Doppler curve in the anterior wall. Peak systolic velocity ca 8.5 cm/s.
Midwall spectral tissue Doppler curve in the anterior wall. Peak systolic velocity ca 6.5 cm/s.
Apcal spectral tissue Doppler curve in the anterior wall. Peak systolic velocity ca 5 cm/s.

From this, it would seem that clutter is solely non-random noise, but in fact they also increases (relative) random noise.


Basically clutter is stationary echoes resulting in zero velocities as described more in detail in the basic ultrasound section. Thus, cutter is basically systematic noise, not random. However, in colour tissue Doppler clutter will also lead to increase in random noise. This is again due to the autocorrelation algorithm. The velocity estimate in each pixel will be an average of the amount of clutter and of moving echoes. The final velocity estimate will vary according to the relative amplitude of the clutter and the moving echo (weighted) (284), and this varies according to the speckle pattern as described here. Thus, in areas with much clutter, the velocity variations are larger than in high quality recordings:




IColour M-mode from the image shown above. The curved M-mode shows a fairly homogenous and normal signal in the inferior wall (top), but more or less random noise in the anterior wall (bottom), where the noise is seen as vertical stripes of alternating colours.
Velocity curves from the anterior wall, showing noise, and not much more, but at low level (within ± 0.3 cm/s).


The principle of the effect of clutter. V-plot with clutter showing how the mean velocities are reduced, compared to the mormal expected values (red line). But in additions the variation of the velocity estimates from pixel to pixel is much higher, resulting in increased noise, but with reduced mean values. Combined pulsed Doppler (yellow bands) and colour Doppler green Aligned horizontally and vertically. The noise level can be seen to be b´very low, compared to the peak velocities shown in the pulsed Doppler recording. The clutter is the horizontal band around the baseline, and the width of the spectrum in this case is the noise.



Further examples are shown below:



Reverberations in the septum of a normal ventricle. The colour bands are  stationary
In pulsed wave tissue Doppler, the clutter will show up as a high amplitude band of zero velocities, but the true velocity curves can be seen as entirely separate from the clutter line, and thus peak velocities can still be measured.


Colour Doppler, calculating average velocities, will average in the clutter. Looking at the same example as above, we see the difference in peak values:


Velocity curves from the reverberations shown in the video above. Left colour Doppler from three sites showing peak systolic values of about 3, 2 and 1 cm/s, respectively. The pulsed Doppler recordings from the same sites separates the clutter from the velocity signal, and thus we find peak systolic velocities of about 12, 11 and 8 cm/s, respectively. Normally the systematic difference between the two methods is only about 1.5 - 2 cm/s as shown in the HUNT study.



Thus, maximum values are more robust in relation to artifacts than both taking the middle of the spectrum and than colour tissue Doppler, but the spectrum width will lead to som overestimation of peak values:
 

For the present, the best compromise seems to be: pw Tissue Doppler should be measured as maximal values, but with the lowest possible gain setting.


Ultra high frame rate tissue Doppler (UFR-TDI)

Ultra high frame rate tissue Doppler is done by combining more principles:

  • Using very little focussing (planar beams). This is feasible as tissue Doppler doesn't use harmonic imaging
  • Planar beams allows a high MLA factor. Again, this is feasible as tissue Doppler is about acquiring numerical values, not pretty images.
  • Broad beams and high MLA factor allows the whole of one wall to be covered by one transmit beam.
  • Designing the software so there is only sent one transmit beam along each wall per frame, i.e. only two pulses per frame. This is the extreme example of exchanging spatial for temporal resolution.

By this method, using two broad, unfocussed (planar) beams, each covering one wall, as well as 16 MLA and sparse interleaved B-mode imaging, it has proved possible to increase the TDI frame rate substatially (172, 268). it has been possible to increase frame rate to 1200 FPS in 2D imaging. 


Few beams give high frame rate. Image courtesy of Svein Arne Aase, modified from (172).


Already this has shown new information about both the pre ejection and post ejection dynamics.

3-dimensional tissue Doppler

Tissue Doppler is still limited to one velocity direction only. This means that the term "3-dimensional" refers to a three dimensional distribution of tissue velocities only, not velocity  vectors in a three dimensional coordinate system. However, data from the whole ventricle can be put together on a surface model of the left ventricle.




3D tissue Doppler is basically a grid of numerical values on a ventrricular surface.
Triplane tissue Doppler, showing three standard planes, with the assumption that the angle between them is 60°, the rest of the data between the planes are than interpolated. This gives a circumferential resolution of 60°.


As tissue data as about acquiring (and displaying, f.i. by colour) numerical data, the method do not have the same limitation as 3D B-mode. One method is to combine information from three standard planes, and then interpolating the data between the planes by for instance spline. The method has been explained elsewhere. This has been done both by combining sequentially acquired standard planes. It could also be done as a simultaneous triplane acquisition, but at the cost of a substantially reduced frame rate. Thus, freehand scanning has been preferred.


Systolic (left) and early diastolic (right) frame showing the 3D surface of the left ventricle, where longitudinal tissue Doppler values are displayed with colour. Red shows velocities toward the apex, blue velocities away from the apex.  (mark the colour gradient from base to apex, reflecting the velocity gradient).

This version of three dimensional tissue Doppler may be used for display, but also for area measurement, as the data are distributed over a representation of the (approximate) real ventricular area.

With the Ultra high frame rate tissue Doppler method, it is also possible to acquire three dimensional tissue Doppler in real time.

Using a 3D matrix probe, sending an array of 3x3 broad unfocussed or planar beams, and using a 4x4 matrix of receive beams for each transmit beam, giving a 16 (or 4x4) MLA, we have been able to achieve a volume rate of about 500 VPS (280), i.e. Ultra high frame rate 3D tissue Doppler.




Principle of beam formation, showing a matrix of 3x3 wide transmit beams (brown circles) and for each beam an array of 4x4 receive beams, i.e. a 16 MLA. (After 280).
Distribution of the transmit beams in relation to a cross section of the ventricle, endocardial and epicardial surfaces marked with black lines and arrows. the energu distribution of the beams is shown by the colour hue. The transverse plane shown to the right is marked by the thick line. (After 280).
Distribution of the transmit beams in an apical plane, the level of the cross section to the left is marked by the thick line. As evident from the illustration, the transmit beams do not cover the whole sector, but will cover most of the walls. (After 280).

By this method, t is possible to achieve a high circumferential resolution through the MLA technique at the same time as a high temporal resolution. The result can be displaued as a 3D figure, as with reconstructed 3D, and both curved M-modes and tivelocity curves can be extracted from this matrix:




3D surface with tissue velocity display. The ring represents a line for extraction of the curved M-mode shown top, left. (After 280). Data display from the 3D velocity figure to the right. Top: curved M-mode, showing the time variation of apically directed velocities in a ring around the mid ventricle.  Bottom, velocity curves from the basolateral part, red from UFR 3D TVI, extracted from the 3D data to the left, blue velocity from the same point in the same subject, but acquired bt conventional colur TDI (i.e. a different heartbeat).



Harmonic tissue Doppler

Harmonic imaging in tissue Doppler leads to aliasing, as seen by this colour M-mode. However, Strain rate imaging, using the velocity differences, will neutralise this, as usually both velocities in the equation (V1 - V2)/L are aliased, and thus the difference remains the same. So in strain rate imaging, aliasing is effectively unwrapped, as shown previously (167).



Colour M-mode (CAMM) of tissue velocities in fundamental (above) and harmonic (below) imaging. Slight aliasing can be seen in native
imaging in the e' wave at the base. In harmonic imaging, there is aliasing both in the S' wave, and the e' wave (double).

Colour tissue Doppler curved M-mode in harmonic imaging, velocity plot (above), strain rate (below). As can be seen there is heavy aliasing in the
velocity plot, but no aliasing in strain rate imaging.


However, this would imply that separate recordings had to be taken for strain rate and velocity analysis, instead of post processing strain rate from TDI recordings, but might improve the reverberation sensitivity of strain rate imaging by tissue Doppler.



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Editor: Asbjorn Støylen, Contact address: asbjorn.stoylen@ntnu.no