Doppler ultrasound

Doppler ultrasound is a technique for making non-invasive velocity measurements of blood flow. Christian Doppler was the first to describe the frequency shift that occurs when sound or light is emitted from a moving source and the effect now bears his name. For the velocity measurement of blood, ultrasound is transmitted into a vessel and the sound that is reflected from the blood is detected. Because the blood is moving, the sound undergoes a frequency (Doppler) shift that is described by the Doppler equation:

F = Fo ?(c + v ?cos(q))/ (c - v ?cos(q))

where:

c is the acoustic velocity in blood, i.e., 1.54?0 ⁵ cm/s;
F o is the transmitted frequency;
q is the Doppler angle;
v is the velocity of the blood.

The equation is often expanded to yield the following approximation:

F ~ Fo + (2 ×F o ?v ?cos(q))/ c = Fo + f

where f is the Doppler shift frequency. The equation can be rearranged to give:

v = f ?c/ (2 ?F o ?cos(q))

The Doppler angle in these equations are measured from the B-mode image of the vessel as shown in Figure 1. The cos(q) in the denominator ofthe last equation requires that the Doppler angle be less than about 70? otherwise a small error in q will produce a large error in the measured velocity. The acoustic velocity in blood is often assumed to be 1.54 x 10 ⁵ cm/s. The Doppler shift of the moving blood is monitored continuously to form the Doppler signal. Because the transmit frequency is about 2 to 4 MHz, the Doppler shift of moving blood is in the audible range, e.g., ~2 kHz, and can thus be heard through a pair of stereo loudspeakers. The forward Doppler signal is made audible through one loudspeaker and the reverse Doppler signal is made audible through the other loud speaker. The resulting sound is distinct and provides feedback to the operator, allowing the appropriate placement of the Doppler sample volume.

There are three main techniques for making Doppler ultrasound velocity measurements of blood flow; continuous wave Doppler, pulsed Doppler, and color Doppler. Pulsed Doppler can be referred to as pulsed Doppler, spectral Doppler, or duplex Doppler.

Pulsed (gated) and spectral Doppler

Pulsed Doppler ultrasound is a technique for measuring the velocity of blood in a small sample volume (Figure 1). Shown in Figure 2 is the spectral Doppler measurement of blood flow in the common carotid artery. The location of the Doppler sample volume is illustrated by a cursor overlaid on the B-mode image shown as Figure 1. To provide a localised velocity measurement, the instrument transmits a pulse that is 6 wavelengths to 40 wavelengths long - depending on the desired length of the sample volume.

The received signal is gated so that the time elapsed between the transmission of the pulse and the opening of the gate determines the depth of the velocity measurement, i.e., the position of the sample volume. The Doppler signal is processed by a Fourier spectrum analyser, which performs a Fourier transform on the Doppler signal at intervals of approximately 10 ms. The amplitudes of the resulting spectra are encoded as brightnesses and these are plotted as a function of time (horizontal axis) and frequency shift (vertical axis) to provide a two-dimensional spectral display. With this technique, a range of blood velocities in the sample volume will produce a corresponding range of frequency shifts on the spectral display. The incorporation of pulsed Doppler and B-mode imaging into one instrument allows the position of the Doppler sample volume to be known and enables the measurement of the Doppler angle as is shown in Figure 1.

Quantitative Doppler techniques

Doppler ultrasound provides one component of the velocity vector of blood flow as given by the last equation. Spectral Doppler (Figure 2) and color Doppler images (Figure 3) can provide an overwhelming amount of information concerning the flow of blood, e.g., color Doppler can make over 20000 velocity measurements per second. Often, one would like to describe the Doppler velocity information using only a few diagnostic parameters. Thus, many techniques have been proposed for quantifying the Doppler velocity measurements and for deriving other parameters such as volume blood flow and waveform indices. These measurements would ideally correlate well with the severity of a disease and therefore be very useful for both diagnoses and follow up of the disease.

Velocity measurements

Spectral Doppler velocity measurements of blood flow within a vascular narrowing have been used to quantify stenoses. However, ratios of velocity measurements, such as those made within and distal to the stenosis, have been shown to be a better indicator of the degree of narrowing. Color Doppler is normally only used as a visual guide for locating the region of maximum stenosis. However, others have suggested that color Doppler be used for stenosis quantification. In some cases, such as assessing the portal vein before and after a liver transplant, one needs to know whether there is blood flow or the vessel is occluded.

Spectral Doppler waveform measurements

Doppler waveform analysis is often used as a diagnostic tool in the clinical assessment of disease. The complex shapes of Doppler waveforms can be described by relatively simple waveform indices, which have been used to evaluate foetal health and organ blood flow. The use of waveform indices to quantify a number of physiological quantities is frequently used. Common indices are the pulsatility index (PI), resistance index (RI), and systolic/ diastolic ratio (S/D, or A/B).

PI = f max - f min/ f

RI = 1- (f min/ f max)

S/ D or A/ B= f max/ f min = 1/ 1- RI

where: fmax is the maximum systolic frequency,
fmin is the minimum diastolic frequency, and
f is the time-average peak frequency.

An advantage of these waveform indices is that they consist of ratios of Doppler shift frequencies and thus are independent of transmit frequency and Doppler angle. In addition, indices such as the RI and A/B only require a few measurements from the waveform and thus can be made manually. Reports on verifying the usefulness of these indices include clinical validation experiments, in vivo animal studies, and in vitro experiments. Several authors have made comparisons of different indices and have found that the commonly used ones produce similar diagnostic results. The effects of parameters such as sampling site, different instrumentation, and cardiac rate on various indices have been investigated. Computer modelling has also been performed with the aim of linking theoretically the waveform indices to physiological quantities such as vascular resistance.

In the umbilical artery for example, there is relatively high forward velocities during diastole, consistent with blood flow into a low-impedance vascular bed, the placenta. With advancing gestation, there is an increase in end-diastolic flow velocity relative to peak systolic velocity. This is attributed to decreased resistance in the placental circulation with advancing gestation. This change in the pulse velocity waveform can be quantified by the systolic-to-diastolic ratio (A/B ratio). In pregnancies in which the A/B ratio is elevated, there is an increase in intrauterine growth compromise due to a placental circulation that has diminished in volume owing to placental vascular occlusion.

The A/B ratio in a growth-retarded 24 weeks fetus (A/ B = 4.6

Volume blood flow measurements The volume of blood flowing through a vessel is often of clinical importance. By making assumptions about the sample volume size relative to the vessel size, spectral Doppler instrumentation can be used to measure volume blood flow. For example, volume flow measurements made with a uniform insonation technique assume that the sample volume is large compared to the vessel, while the assumed-profile technique assumes a small sample volume. Multi-gate techniques measure the Doppler shifts along a vessel diameter and make assumptions about the velocity profile to calculate volume flow. A technique described by Picot et al. (1995) uses transverse color Doppler images to calculate volume blood flow and thus eliminates any assumptions about the velocity profile. However, this method assumes that the color Doppler sample volumes are small relative to the vessel diameter. Unfortunately, the accuracy of volume flow measurements made with ultrasound has traditionally been very disappointing. It has not been shown whether improvements in Doppler instrumentation will increase the accuracy of volume flow measurements.

Color Doppler

Color Doppler ultrasound (also referred to as color flow ultrasound) is a technique for visualising the velocity of blood within an image plane. A color Doppler instrument measures the Doppler shifts in a few thousand sample volumes located in an image plane. For each sample volume, the average Doppler shift is encoded as a color and displayed on top of the B-mode image, such as shown in Figure 3. The way in which the frequency shifts are encoded is defined by the color bar located to the left of the image. Positive Doppler shifts, caused by blood moving towards the transducer, are encoded as red and negative shifts are encoded as blue. Color Doppler images are updated several times per second, thus allowing the flowing blood to be easily visualised. However, Color Doppler is very demanding of the electronics and computational power of the Doppler instrument and is therefore relatively expensive.

What is needed to produce a 'flow image' of blood vessels is that the amplitude, phase and frequency contents of the returned echoes from a single linear array probe are captured and very rapidly analysed. Japanese researchers first introduced a phase detector based on an autocorrelation technique in which the changing phase of the received signal gave information about changing velocity along the ultrasonic beam. This provided a rapid means of frequency estimation to be performed in real-time. This approach to color flow mapping is still in use today.

The basis of the autocorrelation detector is that the echo wavetrains from stationary targets have corresponding changes with time, whereas sequential echo wavetrains from moving targets have corresponding changes in the relative phase. The autocorrelaton detector produces an output signal that depends on the relative phases of consecutive pairs of received echo wavetrains. Thus, the echo wavetrains themselves are their own references for phas comparison. The autocirrelation detector functions by multiplying two echo wavetrains, one currently being received by the transducer and the other, having been received from the immediately preceding pulse transmission and delayed for a time exactly equal to the interval between pulse transmissions. The output from the autocorrelator has constant amplitude except where consecutive wavetrains have phase differences. In color doppler processors, a parrellel and separate process of velocity and velocity variance are made. The value of the velocity variance can be considered to be a measure of the width of the doppler frequency spectrum, which increases with the degree of flow disturbance. The final processor in the circuitiory, the color processor, assigns luminance, hue and saturation to the display, following one of the designated color-coding schemes.

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