DOPPLER2 (1040787), страница 2
Текст из файла (страница 2)
lt. will be shown in the next section which deals with range-resolving flowmeters how this spectral broadening limits the velocity resolution of the Doppler device. At this stage, however, it should be noticed that the precision with which the target velocity can be estimated is determined by the width of the Doppler spectrum which, remember, is inversely proportional to the beamwidth. Furthermore, the spatial resolution, that is, the precision with which the target position can be estimated, is directly proportional to the beamwidth. It therefore appears that there might be a type of "uncertainty" relationship linking velocity resolution with spatial resolution in such a way that the product of the two remains constant. For instance, improving spatial resolution by narrowing the beam will reduce the transit time thereby broadening the Doppler spectrum and thus tending to degrade the velocity resolution. A more exact mathematical formulation of this relationship is reserved for the next section dealing with range resolving Doppler systems.
2.2c Blood Target
It is rather restricting to assume that the target is a single point scatterer but much more useful to investigate the behaviour of the velocimeter with blood as the moving target. It has already been shown in Chapter 1 how a random distribution of red corpuscles produces a granular diffraction pattern with fluctuations on the scale of a pulse-length or a beamwidth. Thus if blood moves sideways through the beam of a CW velocimeter, the scattering power will change on a scale determined by the beamwidth. For a constant blood velocity, the amplitude modulation of the Doppler signal will occur at a rate which is inversely proportional to the beamwidth (see Eqn (1.27b)). Thus, similar to a point target, the spatial resolution characteristics of a CW flowmeter once again define the precision with which the blood velocity can be determined.
2.3 RANGE DiSCRiMiNATiNG FLOWMETERS
A major disadvantage of the simple continuous-wave flowmeter is its inability to discriminate in range. The continuous-wave transmission creates an ultrasonic beam which occupies the complete diffraction pattern of the transducer. Any target moving within this beam will contribute to the final Doppler output. During clinical use of CW devices this sometimes makes it impossible to isolate flow in adjoining blood vessels. For example, in the B-scan tomograms of the abdomen shown in Fig. 2.6, a continuous-wave flowmeter transducer situated at P and interrogating flow in the portal vein (PV) would also receive interfering signals from the more distant inferior vena cava (IVC). Range selectivity can sometimes be a vital requirement in Doppler investigations and so this section describes the various methods of coding the transmitted burst and processing the received echo so that the range of the moving targets can be determined. During the description the effects on the basic Doppler equation of imposing restraints on the axial selectivity of the flowmeter will be investigated.
2.3a Amplitude Modulation (the Pulse-Doppler)
The most straightforward method of coding the ultrasonic wave is to amplitude modulate the CW transmission. In a device known as the pulse-Doppler flowmeter, short bursts of ultrasound are transmitted at regular intervals towards the moving target and the echoes examined for Doppler frequency shifts. This method was adapted from a technique developed in radar (see for example, Skolnik, 1970) and was first described in terms of its potential clinical use by Wells (1969) and Baker (1970).
(i) Basic Principles
Pulse-Doppler combines the range discriminating capabilities of a pulse-echo system with the velocity detection properties of a Doppler device. As in any pulse-echo system the principle of operation (illustrated in Fig. 2.7) is to transmit a short burst of waves towards the target and then wait for the echoes to return. Because the sound waves travel at an essentially constant velocity through human tissue, the time delay between transmission of the pulse at (a) and reception of the echoes at (c) depends upon the range of the target. When the echoes are sampled for Doppler shifts at a fixed time after transmission, the resulting Doppler signal can originate only from those targets moving within the "sample-volume" corresponding to the selected delay time.
(ii) The Sample Volume
At any instant in time after pulse transmission, the sample volume can be visualized as being that region in front of the transducer from which all returning echoes must have originated. The dimensions of the sample volume are defined axially by the pulse 'length (as seen by the receiver) and laterally by the beamwidth of the combined transmitter-receiver system. If ultrasound travels at a constant velocity c then, following transmission,
the sample volume moves away from the transducer face at a velocity c/2 since the pulse has had to travel both to and from the target. Thus the pulse-Doppler is sensitive to the movement of only those targets which are momentarily in the sample volume as this region scans outwards from the transducer face following each transmission. By choosing to sample only those Doppler components which return after a preset constant delay from transmission, it is possible to define the position of a fixed sample volume and thus interrogate only those targets moving at a particular range from the transducer.
(iii) Doppler Aspects
It is perhaps not immediately obvious that the short echo bursts reflected from the moving target in Fig. 2.7 actually contain Doppler-shifted components. The Doppler aspects of the device can perhaps more easily be appreciated by considering the transmission pulses to be bursts of a continuous "reference" sine-wave as illustrated in Fig. 2.8. These short pulses of ultrasound are transmitted at regular intervals Tp towards the plane target which is shown moving away from the transducer on the left of the diagram, As the target recedes the time-of-flight T¦ of the pulse increases slightly with each successive transmission, causing the return echo gradually to shift in phase past the reference oscillation. It is this gradual change in phase with time which indicates that the frequency content of the returning pulse is different from that transmitted. The Doppler components can be revealed by coherent demodulation (see Section 2.4b) of these short returning echoes using the continuous-wave oscillation as a reference. The result, shown on the right of Fig. 2.8, is a series of pulses varying in amplitude at the Doppler shift frequency. Thus the output of a pulse-Doppler device is identical to the output of a continuous-wave device but sampled at the pulse repetition rate. This seems sensible because unlike the CW device which monitors the target continuously, the pulse-Doppler interrogates the target only once every pulse repetition period and this defines the rate at which data is collected and thus the maximum frequency at which the Doppler waveform can be updated.
(iv) Pulse-Doppler Layout
Figure 2.9 shows the basic elements of a pulse-Doppler system. The master oscillator generates a sinusoidal waveform at the resonant frequency of the transducer. Once every pulse repetition period a few cycles of the master oscillation are passed via the transmission gate and amplifier to excite the transducer. The delay gate generates a time delay which allows the transmitted ultrasonic burst to travel to and from the selected range of interest. Returning echoes are then sampled by opening the range gate and fed to the coherent demodulator which is driven by the master oscillator. Each gated return echo produces a short output pulse from the demodulator which forms part of the sampled Doppler output from the device (see Fig. 2.8). If required, these samples can be stored (for example, on a capacitor plate) before being updated by the return following the next transmission pulse. This so-called "sample-and-hold" technique tends to produce a smoother output waveform which can then be low-pass filtered to remove any remaining components at the PRF and also high-pass filtered to remove low frequency clutter (see Section 2.4).
(v) Analysis of the Pulse-Doppler Principle
A mathematical description of the pulse-Doppler operation illustrated in Fig. 2.8 proceeds as follows. The phase difference Æ (measured in cycles of the reference oscillation at frequency /o) between the transmitted pulse and the received echo is related to the time of flight Td by the expression
Differentiating both sides with respect to time gives
Furthermore, the return time of Flight is equal to the total distance the pulse travels divided by the ultrasonic velocity c, or
where z is the instantaneous range of the target. The rate at which Td changes with time is
and since dz/dt = v, the target velocity, combining Eqns (2.19) and (2.17) gives
Finally, the frequency of any signal is defined as its rate of change of phase with time. Thus the frequency difference between the received echo and the transmitted pulse, that is the Doppler shift ¦d is, from Eqn (2.20),
which is the familiar Doppler relation.
(vi) Velocity Limitations
It is noticeable in Fig. 2.8 that if (as is shown) the target velocity is much smaller than the velocity of ultrasound, then phase variations due to the Doppler shifted components cannot be observed within a single pulse because the Doppler frequency deviation is much smaller (by a factor v/c) than the ultrasonic frequency. (More precisely, the bandwidth of the pulse is much larger than ¦d -but see later.) During the short interval that the ultrasound pulse is actually impinging on the target, the target moves only a very small indiscernible fraction of an ultrasonic wavelength and so the frequency shift cannot be observed during the pulse. However, the period between pulses is much longer and so the target can move much further creating a noticeable change in the phase of successive echo returns relative to the reference signal. In theory there is no lower limit to the minimum Doppler shift which can be coherently detected, and in a rather diverse application which measures changes in thickness of the Antarctic ice-sheet (Nye et al., 1972) a radar system which is effectively a radar pulse-Doppler velocimeter detects frequency shifts down to a few cycles per year!
The upper limit to the frequency shift however is limited by the Nyquist criterion. Because the Doppler waveform has to be reconstructed from a series of samples taken at regular intervals, the maximum Doppler frequency which can unambiguously be detected is one half the pulse repetition frequency. If higher frequency signals are present then the sampled waveform cannot be reconstructed correctly and a phenomenon known as "aliasing" (see Section 3.2b(ii)) occurs. This effect can also be interpreted in terms of the distance moved by the target between pulses. Figure 2. 10a shows how the phase of the echo from a moving plane target changes relative to the reference for six successive pulses. If the target moves less than one quarter of an ultrasonic wavelength between pulses then the reconstructed Doppler waveform shown on the right is an accurate representation of the changing phase of the returned echo. However, if as in Fig. 2.10b the target is moving at such a high velocity that it can travel more than l/4 during the interpulse interval, then successive returns will vary in phase by more than 180° and the output of the coherent demodulator will not correspond unambiguously to the phase of the returning echo.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
