DOPPLER2 (Раздаточные материалы), страница 5

If instead of a single point target, the system is used to interrogate the flow of blood, then the only difference will be that the amplitude of the returning echo (and thus the correlator output) will fluctuate in time as different ensembles of red corpuscles pass through the resolution cell of the flowmeter. Once again the Doppler-shift spectrum will be broadened by this transit-time effect. In fact Newhouse (1973) has shown that when interrogating blood flow, the correlator output from the random noise device has precisely the same spectral characteristics as a pulse-Doppler output so long as the transmitted power spectral densities are identical in both cases. Furthermore the expression for C(t) in Eqn (2.42) indicates that the correlator output rapidly approaches zero when t_s - t_d ~ 1/B. The range resolution Dz can therefore be approximated by

which is exactly the same as for any pulse-echo system. Thus in terms of both velocity and range resolution it appears that the random noise system is in no way superior to the more simple pulsed or FM devices. However, Jethwa et al. (1975) disagree with this and state that "the range and velocity resolution (of a random signal Doppler system) can be independently controlled". It can be seen that this claim must be incorrect simply because the random signal device like any other range sensitive system creates a sample volume from which the detected echoes must originate. The general analysis which was developed in Section 2.3a(viii) to describe the effects of transit time in range discriminating systems must therefore apply to the random noise device.

(v) Advantages of Random Noise Systems

The random signal device is superior to a pulsed-Doppler in two respects. Firstly, because both range and velocity resolution depend on the transmitted noise bandwidth rather than the length of the transmitted pulse, the power in the noise Doppler can be spread over a much longer time than in the pulse Doppler. The peak-to-average power ratio can be decreased and, if peak power is limited by patient safety, the sensitivity of the random noise device can be considerably greater than pulse systems. Secondly, and perhaps more importantly, the random signal Flowmeter is not restricted by the range-velocity limitation of Eqn (2.25). Remembering the previous suggestion that the continuous noise signal can be considered to be a series of random noise bursts, it can be seen that the range ambiguity has been removed because each interval or burst of signal is different from every other. This means that echoes originating from any one burst will not correlate with any other burst and so it is not necessary to wait for all echoes from one burst to return before transmitting the next. This also implies that there is no Nyquist limit on the maximum frequency which can be sampled and therefore no restriction on the maximum Doppler frequency which can be detected. (In fact a sampling limit is eventually reached where the Doppler shift approaches the frequency corresponding to the averaging time of the correlator. So long as full use is made of the transducer bandwidth this Doppler shift usually corresponds to velocities which are much higher than those encountered in the clinical situation.)

(vi) Practical Limitations of Noise Dopplers

lt. seems that in principle the noise Doppler has more to offer than pulsed or FM devices. However, in practice it has been found (Cooper and McGillem, 1972) that if noise is transmitted continuously then reverberations between strongly reflecting targets produce correlating echoes from outside the sample volume which tend to degrade the signal-to-noise performance of the system. If this cannot be tolerated and if the offending targets are sufficiently far apart, then Bendick and Newhouse (1974) suggest that this problem can be overcome by transmitting discrete bursts of noise which are short enough to intercept only one target at a time. However, this modification obviously increases peak-to-average power and re-introduces undesirable range-velocity limitations. An alternative solution suggested by Furgason et al. (1975) is to use separate transmitting and receiving elements arranged so that their diffraction patterns intercept only at the selected range of interest. Although reverberation artefact can be reduced using this configuration, there would most likely be alignment problems when using the system in vivo

In conclusion, it seems that, in principle, the random noise Doppler flowmeter is an elegant solution to problems encountered using more simple transmission codes. However, practical implementation of the technique is difficult and perhaps not always suitable for medical application.

2.4 DOPPLER DEMODULATION

In any practical situation Doppler signals do not return in isolation but are combined with echoes from surrounding stationary structures such as vessel walls and other tissue interfaces. Up until this point it has purposely been assumed that the Doppler shifted components could be separated and extracted from the complex of returning echoes to give the Doppler difference signal. In this section the various ways in which the returning echoes can be "demodulated" to reveal their Doppler content will be described. The analysis will begin with coherent non-directional demodulation and progress through non-coherent detection to the more involved fully directional demodulation. As weII as developing a mathematical vector-type analysis, every attempt will be made to describe the concepts of each demodulation process in practical terms.

2.4a Basic Requirements

Modulation is a process whereby information (that is, the signal) is impressed onto a carrying (or carrier) wave. Conversely, demodulation is the detection and extraction of the signal from the carrier wave. In the case of Doppler flowmeters, it is the moving target which modulates the transmitted ultrasound by changing its frequency content. The purpose of demodulation is to extract the Doppler information contained as frequency shifts in the returning echo.

The echo returning to the receiving transducer of a Doppler flowmeter will most likely consist of a combination of components. As well as containing Doppler shifted returns from moving targets the received signal will also contain clutter, that is, unwanted signals from stationary (or slow moving) targets located within the sample volume. The returning ultrasound can therefore be regarded as being a carrier wave modulated by both clutter and Doppler signal alike, However, since the echoes from blood are small relative to returns from larger structures such as vessel walls and other tissue interfaces (see Chapter 1 ), the clutter component is usually of much greater amplitude than the DoppIer shifted signal. In addition, because the factor v/c is very small (usually less than 1/100 for physiologically-encountered blood flows), successful Doppler demodulation demands the detection and extraction of small amplitude Doppler shifted signals which are less than one per cent away from the transmitted frequency and which are buried in much larger amplitude clutter returns.

2.4b Coherent Demodulation

Because the Doppler deviations are very small relative to the ultrasonic frequency, it is usually impractical to detect the Doppler shift directly at the carrier (but see Section 2.4e(i)). lt. is, however, much easier to compare the frequency of the returning echo with that transmitted so that the Doppler shifted components produce "beats" at the Doppler difference frequency. The clutter which is at the same frequency as the transmission then maintains a fixed phase relationship to the reference, and therefore contributes a constant d.c. level to the output.

In practice the transmitted signal is stored as a continuously running local oscillation known as a reference signal and combined with the incoming received signal in a phase sensitive detector. (This process is known as coherent demodulation because the local oscillation maintains a phase and frequency reference against which all received waveforms are compared.) The basic principles of phase sensitive detection are illustrated in Fig. 2.20. Two sinusoidal waveforms A and B at frequencies ¦₀ and (¦₀ + ¦_d), representing the reference oscillation and Doppler shifted component respectively, are multiplied together to give the product waveform C. When low-pass filtered to remove frequencies around 2¦₀ the result is D, the Doppler difference signal. Because the system is linear and since the echoes from stationary targets remain fixed in phase relative to the reference, any clutter signal at the input will only superimpose a d.c. Level at the output.

(i) Mathematical Interpretation

The mathematical analysis is best formulated in terms of the input and output voltages to and from the ultrasonic transducer and electric demodulator, as follows. Suppose the signal T(t) transmitted from a CW flowmeter can be described by

T(t)=cos w_ot (2.45)

where w₀ ( = 2p¦₀) is the ultrasonic angular frequency. Ignoring diffraction effects, the Doppler shifted echo R_d(t) received from a target moving at velocity v will have the general form

R_d(t) = B cos(w₀t + w_dt + Æ_d) (2.46)

while clutter echoes from stationary targets can be expressed as

R_c(t) = A cos(w₀t+Æ_c) (2.47)

where A, B describe the echo amplitudes and Æ_c, Æ_d their phase relative to the transmitted wave at t = 0. The Doppler shift frequency w_d, is given by the Doppler relation

The clutter and Doppler echoes combine linearly to give the total received signal R(t)

R(t) = A cos(w₀t + Æ_c) + B cos(w₀t + w₀t + Æ_d) (2.49)

The Doppler components can be extracted from Eqn (2.49) by coherent demodulation which involves first multiplying the received signal by the transmitted signal to get D(t), giving

D(t) = [A cos(w₀t + Æ_c) + B cos(w₀t + w₀t + Æ_d)] cosw₀t (2.50)

or, expanding

The high frequency components in the region of 2w₀ are then removed by filtering leaving

Coherent demodulation has eliminated the carrier and shifted the signal information into the base-band of the frequency spectrum. Notice however that both the upper and lower sidebands (that is, positive and negative Doppler difference frequencies produced by movement towards and away from the transducer respectively) demodulate into the same region of the base-band. This rather straightforward demodulation process has destroyed the directional information contained in the returning signal. The Doppler frequency is the difference, independent of sign, between the transmitted and received signals. More useful processes which retain the directional information will be described later in Section 2.4e. First however an alternate method of extracting Doppler components will be investigated.

2.4c Non-coherent Demodulation

lt. is apparent from Eqn (2.47) that the clutter signal reflected from stationary targets can be regarded as being an attenuated and phase-shifted version of the transmitted waveform. Because it is at essentially the same frequency as the transmitted signal, this clutter component can be used as the basis for a reference with which to compare Doppler shifted returns. Such a process is known as non-coherent demodulation because the echo provides its own source of phase and frequency reference.