As explained in Chapter 1, two-dimensional imaging is based on the intensity and time delay of reflected ultrasound. To determine the velocity of blood flow, Doppler systems examine the change in frequency of the ultrasound reflected from red blood cells. Our ability to use the movement of red blood cells to gauge blood flow velocity dates back to the experiments of the Austrian physicist Christian Doppler. Trumpeters on a high-speed locomotive played a tone at a specific pitch so that the effects of motion on sound frequency could be examined. A second group of musicians stationed on a loading dock played the same tone as the train passed by. As Doppler had predicted, the two tones were audibly different. The change in pitch, known as the Doppler effect, occurs because the motion of an object causes the sound wave to be compressed in the direction of the motion and expanded in the direction opposite to the motion.

Red blood cells reflect ultrasound as they travel through the blood stream. By directing an ultrasound signal at flowing blood and listening for the change in frequency produced by the red cell reflections, Doppler echocardiography can assess the direction and speed of blood flow.

Figure 5.1 illustrates the principle of the Doppler effect for cardiac applications. When ultrasound is transmitted to blood, it is scattered by the multitude of red blood cells, and a small portion of this scattering is reflected back toward the transducer. The strength of the echoes returning to the transducer is related to the number of particles reflecting the ultrasound. If the hematocrit is increased, more interfaces are available for reflection and the ultrasound signal is stronger. However, this effect is self-limited because at a hematocrit exceeding 30%, the reflected signal strength is weakened by destructive interference. Modern echocardiography systems are designed to detect Doppler signals over a wide range of hematocrit values.

If the red cells are stationary, the signal is reflected at the same frequency as the transmitted signal. Since no Doppler frequency shift occurs, the situation is similar to that of two-dimensional echocardiography.
When blood flows toward the ultrasound transducer, the reflected signal is compressed by the motion of the red cells, and its frequency is higher than that of the transmitted signal. Conversely, when blood flows away from the ultrasound transducer, the frequency of the reflected signal received by the transducer is lower than that of the transmitted signal. The technical term for the alterations in the frequency of the ultrasound signals caused by the Doppler effect is modulation. Through analysis of the modulated signal, both the direction and speed of the red blood cells can be determined.

The Doppler equation describes the relationship between the alteration in ultrasound frequency and blood flow velocity (Fig. 5.2):

Δf = v × cos θ × 2 f_t/c

where Δf is the difference between transmitted frequency (f_t) and received frequency, v is blood velocity, c is the speed of sound in blood (1,540 m/s), and θ is the angle of incidence between the ultrasound beam and blood flow.

Conceptually, the equation can be simplified based on the observation that the change in ultrasound frequency is directly related to just two variables: blood velocity and cos θ. The remaining factors in the equation, the speed of sound in blood (c) and the transmitted frequency (f_t), are constants. The Doppler signal is shifted only by the component of the blood velocity that is in the direction of the beam path (i.e., v cos θ). For example, when the direction of the ultrasound beam is parallel to the blood flow, the observed Δf fully reflects total blood velocity (cos θ = 1). With nonparallel orientation of the ultrasound beam to blood flow, Δf is reduced by the factor cos θ. As illustrated in Figure 5.3, when the beam angle divergence is small, the effects on Δf are limited. However, with angles greater than 30°, the value of cos θ decreases rapidly. When the direction of the beam is perpendicular to the blood flow (90°, cos 90 = 0), the movement of blood is no longer appreciated by the Doppler system (Δf = 0).

The effect of the beam angle on Doppler measurements has important clinical implications. In clinical practice, the ultrasound system measures the frequency shift to calculate velocity. By rearranging the Doppler equation, the calculated blood velocity is derived as follows:

v = Δf/cos θ × c/2f_t

The angle of incidence between the beam and the blood flow is not easily determined. Although a twodimensional image of the blood vessel allows the echocardiographer to estimate the angle in the x– and
y-planes, the orientation in the z-plane remains indeterminate. Assessment of the interrogation angle is further complicated by eccentrically directed blood flow, as in mitral regurgitation. Most Doppler systems default to a value of cos θ of 1, with the assumption that the echocardiographer has directed the ultrasound beam to be nearly parallel with the blood flow of interest. This approach has the advantages of stronger Doppler signals and a lower rate of errors as a consequence of the plateau shape of the cosine curve at angles of low incidence. Therefore, in clinical practice, the transducer should be positioned such that the beam and blood flow are nearly parallel for accurate velocity calculations. Figure 5.3 illustrates the basis for the clinical practice of requiring the beam angle to be within 30° of the direction of blood flow, so that the rate of anglerelated errors remains less than 15%. The assumption that the orientation of the ultrasound beam is parallel to the blood flow leads to a common error in Doppler velocity calculations. Because of the shape of the cosine curve, when the incident angle between the beam and the blood flow is greater than 30°, the blood flow is markedly underestimated (Fig. 5.4). However, even the 30° standard may not be acceptable in certain conditions. For example, when very high velocities are interrogated, as in aortic stenosis, even a 15% underestimation will correspond to a large difference in velocity and may result in an underestimation of the severity of aortic stenosis.

For the Doppler system to determine the frequency shift caused by red blood cells, it must first distinguish red cell-modulated echoes from all the other nonfrequency-shifted echoes created by reflections from tissue (Fig. 5.6). This demodulation process is often accomplished by comparing the returning echoes with internal reference signals that are in phase and 90° out of phase with the transmitted signal, a process known as quadrature demodulation. Once the Doppler signal has been isolated, its frequency content can then be determined by means of the fast Fourier transform technique. This approach transforms the demodulated Doppler signal into its individual frequency components. The process is analogous to identifying the individual harmonics that comprise a musical chord. At each time point, the analysis provides the range of frequencies (i.e., velocities) detected and their magnitude (i.e., the number of red cells moving at this speed).

Blood flow in the heart and great vessels creates a Doppler frequency shift in the kilohertz (kHz) range, with a high-velocity aortic stenotic jet generating a Doppler frequency shift in the order of 20 kHz. Since these frequencies are within the audible range, most echocardiography machines provide a sound system that amplifies and broadcasts the signal to the operator. By listening to the loudness and pitch of the broadcast Doppler frequencies, the echocardiographer can precisely position the Doppler beam to interrogate the desired flow signal. Typically, the ideal location is identified when the signal reaches its highest frequency and greatest loudness. Soft, low-decibel signals indicate that the Doppler beam is misdirected and is only glancing a small part of the blood flow. In addition, the texture and pitch of the Doppler signal are useful in diagnosis. For example, when transvalvular flow across the aortic valve is examined, a coarse, high-pitched signal is diagnostic of a high-velocity, turbulent jet caused by aortic stenosis and contrasts markedly with the smoothsounding, low-pitched signals generated by the laminar flow in a normal aortic valve. The ability to use the
audible Doppler signal to guide beam positioning is a favored technique of experienced echocardiographers, and development of this skill remains a goal for all trainees.

Presenting Doppler data as a time-velocity plot is known as a spectral display (Fig. 5.7). At each point in time, the spectrum of velocities detected by the Fourier transformation is displayed. For blood flow measurements, the low-velocity signals emanating from myocardial motion are filtered and not displayed (the use of these “tissue Doppler” signals is presented in Chapters 3 and 7). Frequencies with greater amplitude (loudness) are marked with brighter pixels. The excellent temporal resolution of the spectral display allows beat-to-beat assessment of blood flow and is the basis for the quantitative calculations of cardiovascular hemodynamics.
Measurement of peak velocity, acceleration (Δv/Δt), and the velocity-time integral (represented by the area under the velocity-time plot from a single cardiac cycle) are examples of the many important measurements that are easily obtained from the spectral display (see Chapter 6 for a detailed examination of the use of these measurements in clinical echocardiography).