Doppler effect and Doppler echocardiography
The Doppler effect
When sound waves hit objects some of the sound waves are reflected back to the sound source. If the reflector (i.e the object reflecting the sound waves) is stationary, then the reflected sound waves will have the same frequency as the sound waves emitted by the sound source. If the reflector is in motion, however, then the frequency of the reflected sound waves will differ from the emitted sound waves. The change in frequency is referred to as the Doppler effect.
The Doppler effect was first described in 1843 by the Austrian astronomer Christian Doppler. It can be illustrated by studying how the frequency of reflected sound waves are modified by the direction of movement of the sound source. Figure 1 presents three trumpets; one placed on a table, and two are mounted on ambulances driving towards and away from the observer. When the sound source moves towards the observer, the sound waves are compressed, which leads to a shortening of the wavelength and thus increased frequency. When the sound source moves away from the observer, the sound waves are stretched out, which results in increased wavelength and decreased frequency.
The Doppler principle is primarily used to study blood flow and myocardial motion.
The sound source in echocardiography (i.e the transducer) is stationary. The moving objects are instead the blood cells (primarily erythrocytes) and tissues (primarily myocardium). The Doppler principle, however, remains unchanged: when the sound source and reflectors move towards each other, sound waves are compressed and vice versa.
Erythrocytes reflect ultrasound waves. Because erythrocytes are small, round and have an irregular surface, the reflected sound waves are scattered in all directions (Figure 2). Although only a fraction of the sound waves are reflected back to the transducer, the billions of erythrocytes in the blood will collectively generate enough reflections to be detected and analyzed by the ultrasound machine.
Flowing erythrocytes will alter the frequency of reflected sound waves. Erythrocytes flowing towards the transducer will reflect the sound waves with higher frequency. Erythrocytes flowing away from the transducer will reflect sound waves with reduced frequency (Figure 3).
Doppler effect occurs when reflectors (structures reflecting sound waves) move towards or away from the transducer. Objects moving towards the transducer will compress the sound waves and reflect them at a higher frequency. Objects moving away from the transducer will generate reflections with lower frequency.
The Doppler effect is utilized to calculate velocity and direction of moving objects. To calculate the velocity of blood flow, the frequency difference between emitted and reflected ultrasound waves is analyzed. This difference is called Doppler shift. The Doppler shift depends on the velocity of blood flow (v), the frequency of the emitted ultrasound (fu), the frequency of the reflected ultrasound (fr), the ultrasound velocity in the tissue (c) and the cosine of the angle between the direction of blood flow and the reflected ultrasound wave (cos θ). The Doppler equation follows:
v = [c·(fr-fu)] / [2·fu·cos ϴ]
Significance of the angle of insonation
Doppler calculations are highly dependent on the angle of insonation. It is crucial that the ultrasound waves are directed parallel to the direction of blood flow or tissue motion. Ideally, there should be no angle (0°) between the ultrasound beam and the direction of blood flow or tissue motion.
When the ultrasound waves and the direction of movement are parallel, the angle is 0° and cosine 0° is equal to 1. If the angle increases, then the cosine of the angle will be less than 1, which will lead to an underestimation of the velocity. Thus, all angel errors lead underestimation of velocities (Figure 4).
In clinical practice, it is frequently difficult to obtain an ideal angle. However, small angle errors are without significance. For example, cosine 10° is equal to 0.98, and cosine 20° is 0.94. This implies that small angel errors have a negligible impact on the calculations.
The 2D image is used to correctly align the ultrasound beam along the direction of movement. This is not, however, always straight forward. There may be a discrepancy between the 2D image and the optimal Doppler signal; the best 2D image may offer a poor angle of insonation for Doppler measurements and vice versa. In such situations, one should prioritize the quality of the Doppler signal (i.e the amplitude of the signal and the angle of insonation).
Spectral Doppler analysis
Laminar blood flow
Blood flow is laminar throughout the circulatory system. This implies that blood flows in concentric layers with varying velocities. The highest velocity (vmax) is found in the center of the vessel. The lowest velocity (vmin) is found along the vessel wall. This yields a parabolic flow profile, as illustrated in Figure 6. Laminar flow is most pronounced in long, straight blood vessels, under steady flow conditions.
The advantage of laminar flow is its preservation of kinetic energy. The concentric layers and the parabolic flow profile reduces the energy losses by minimizing viscous interactions between the adjacent layers and the wall of the vessel. Disruption of laminar flow leads to turbulence and increased energy losses.
Due to the laminar flow, erythrocytes passing any section of a vessel have different velocities. Moreover, blood flow is pulsatile, peaking during systole and reaching a minimum during diastole. Laminar flow and pulsatility result in reflected waves displaying large variations in Doppler shifts. This variation is called the Doppler spectrum.
On the echocardiogram, the Doppler signal is presented with a colored band or area (Figure 7). The colored area contains all the velocities recorded in a selected area during a specific phase of the cardiac cycle. The stronger the Doppler signal, the denser the spectral curve on the echocardiogram.
Presentation of the spectral curve
Figure 7 shows the presentation of Doppler signals on the ultrasound image. The type of Doppler shown in Figure 7 is called pulsed wave Doppler (discussed later). It is conventional that velocities (i.e blood flow or myocardial movements) in the direction towards the transducer yields a signal above the baseline and velocities away from the transducer are depicted with signals below the baseline. The x-axis displays time, and the y-axis displays velocity (m/s). As also shown in Figure 7, it is necessary to manually direct the Doppler line. This is done using the 2D image to align the Doppler cursor.
The Doppler shift is audible
Although ultrasound is not within the audible range for humans, it is possible to hear the Doppler shift. This is due to the fact that the Doppler shift, i.e the difference between the emitted and reflected sound waves, falls within the frequency range that humans can hear. The Doppler shift is the swishing sound from the speakers of the ultrasound machine.
The next chapter discusses different types of Doppler studies.