Ronald A. Kahn and Ivan S. Salgo

The Doppler Principle

When a wave is reflected from a moving object, the frequency of the wave will be different from the original emitted wave. This frequency change is known as the Doppler principle. The magnitude and direction of the frequency shift are related to the velocity and direction of the moving target. The velocity of the target may be calculated with the Doppler equation:

where

Rearranging the terms,

As is evident in the second equation, the greater the velocity of the object of interest, the greater the Doppler frequency shift ( Fig. 3-1). Additionally, the magnitude of the frequency shift is directly proportional to the initial emitted frequency. Lower emitted frequencies produce low Doppler frequency shifts, while higher emitted frequencies produce greater Doppler frequency shifts. This phenomenon becomes important with aliasing, as will be discussed later. Furthermore, the only ambiguity in the second equation is that the direction of the ultrasonic signal could refer to either the transmitted or the received beam. By convention, Doppler displays are made with reference to the received beam, however, so if the blood flow and the reflected beam travel in the same direction, the angle of incidence is zero degrees and the cosine is +1. As a result, the frequency of the reflected signal will be higher than the frequency of the emitted signal.

Most modern echo scanners combine Doppler capabilities with their two-dimensional (2D) imaging capabilities. Information on blood flow dynamics can be obtained by applying Doppler frequency shift analysis to echoes reflected by the moving red blood cells.1,2 Blood flow velocity, direction, and acceleration can be instantaneously determined. After the desired view of the heart has been obtained by 2D echocardiography, the Doppler beam, represented by a cursor, is superimposed on the 2D image. The operator positions the cursor as parallel as possible to the assumed direction of blood flow, and then empirically adjusts the direction of the beam to optimize the audio and visual representations of the reflected Doppler signal. At the present time, Doppler technology can be utilized in at least four different ways to measure blood velocities: pulsed, high repetition frequency, continuous wave, and color flow.

Equipment currently used in clinical practice displays most Doppler blood flow velocities as waveforms. The waveforms consist of a spectral analysis of velocities on the ordinate and time on the abscissa. By convention, blood flow toward the transducer is represented above the baseline, and blood flow away from the transducer below the baseline. When the blood flow is perpendicular to the ultrasonic beam, no blood flow will be detected. Since the cosine of the angle of incidence is a variable in the Doppler equation, blood flow velocity is measured most accurately when the ultrasound beam is parallel or antiparallel to the direction of blood flow. In clinical practice, a deviation from parallel of up to 20 degrees can be tolerated, because this only results in an error of 6% or less.

Pulsed Wave Doppler (PWD)

In pulsed wave Doppler (PWD), blood flow parameters can be determined at precise locations by emitting repetitive short bursts of ultrasound at a specific frequency (pulse repetition frequency, or PRF) and analyzing the frequency shift of the reflected echoes at an identical sampling frequency (f_s) ( Fig. 3-2). A time delay between emission of the ultrasound signal burst and sampling of the reflected signal determines the depth at which the velocities are sampled; the delay is proportional to the distance between the transducer and the location of the velocity measurements. To sample at a given depth (D), sufficient time must be allowed for the signal to travel a distance of 2 × D (from the transducer to the sample volume and back).

The operator varies the depth of sampling by varying the time delay between emission of the ultrasonic signal and sampling of the reflected wave. In practice, the sampling location or sample volume is represented by a small marker that can be positioned at any point along the Doppler beam by moving it up or down the Doppler cursor. On some devices, it is also possible to vary the width and height of the sample volume.

The inherent limitation to measurement of flows at precise locations is that ambiguous information is obtained when flow velocity is very high. Information theory suggests that an unknown periodic signal must be sampled at least twice per cycle to determine even rudimentary information such as the fundamental frequency; therefore, the rate of PRF of PWD must be at least twice the Doppler shift frequency produced by flow. ³ If not, the frequency shift is “undersampled.” In other words, this frequency shift is sampled so infrequently, the frequency reported by the instrument is erroneously low. ⁴

A simple reference to Western movies will clearly illustrate this point. When a stagecoach gets underway, its wheel spokes are observed as rotating in the correct direction. As the speed of the spokes approach the frequency of the camera frame rate, the spokes appear to rotate in the reverse direction. In PWD, the ambiguity exists because the measured Doppler frequency shift (f_d) and the sampling frequency (f_s) are in the same frequency range. Ambiguity will be avoided if the f_D is less than half the sampling frequency:

The expression f_s/2 is also known as the Nyquist limit. Doppler shifts above the Nyquist limit will create artifacts described as “aliasing” or “wraparound,” and blood flow velocities will appear in a direction opposite to the conventional one ( Fig. 3-3). Blood flowing with high velocity toward the transducer will result in a display of velocities above and below the baseline. The maximum velocity that can be detected without aliasing is dictated by:

where

Based on this equation, this “aliasing” artifact can be avoided by either minimizing R or f₀. Decreasing the depth of the sample volume in essence increases f_s. This higher sampling frequency allows for the more accurate determination of higher Doppler shift frequencies (i.e., higher velocities). Furthermore, since f₀ is directly related to f_d (see equation 2), a lower emitted ultrasound frequency will produce a lower Doppler frequency shift for a given velocity (see Fig. 3-1). This lower Doppler frequency shift will allow for a higher-velocity measurement before aliasing occurs.

High Pulse Repetition Frequency Doppler (HPRF)

On some instruments, PWD can be modified to high pulse repetition frequency (HPRF) mode. Whereas in conventional PWD only a single burst of ultrasound is considered to be in the body at any given time, in HPRF Doppler, two to five sample volumes are simultaneously presented. Information coming back to the transducer may be coming back from depths of either two, three, or four times the initial sample volume depth. The returning signals can be a mix of signals that have been emitted previously and have traveled to distant gates and other signals that were just sent and returned from the first range gate.

The HPRF mode allows an increase in the sampling frequency because the scanner does not wait for return of information from distant gates; nonetheless, it receives information back within the specified time gate period. Since higher sampling frequencies are used, higher velocities can be measured with this method than with PWD, but because the exact gate the ultrasound signals are reflected from is unknown, there is range ambiguity with HPRF.

Color Flow Doppler (CFD)

Advances in technology have allowed the display of real-time blood flow within the heart as colors, while also showing 2D images in black and white. In addition to showing the location, direction, and velocity of cardiac blood flow, images produced by these devices allow estimation of flow acceleration and differentiation of laminar and turbulent blood flow. CFD echocardiography is based on the principle of multigated PWD, in which blood flow velocities are sampled at many locations along many lines covering the entire imaging sector. ⁵ At the same time, the sector also is scanned to generate a 2D image.

Flow toward the transducer (top of image sector) is commonly assigned the color red and flow away from the transducer is assigned the color blue ( Fig. 3-4). This color assignment is arbitrary and determined by the equipment’s manufacturer and the user’s color mapping. In the most common color flow coding scheme, the faster the blood flow velocity (up to a limit), the more intense the color displayed. Flow velocities that change by more than a preset value within a brief time interval (flow variance or acceleration) may have an additional hue added. Both rapidly accelerating laminar flow (change in flow speed) and turbulent flow (change in flow direction) satisfy the criteria for rapid changes in velocity.

Continuous Wave Doppler (CWD)

The continuous wave Doppler (CWD) technique uses continuous rather than discrete pulses of ultrasound waves ( Fig. 3-5). During CW ultrasound, waves are continuously being both transmitted and received by separate transducers. As a result, the region in which flow dynamics are measured cannot be localized precisely. Because of the large range of depths being simultaneously insonated, a large range of frequencies is returned to the transducer. This large frequency range corresponds to a large range of blood flow velocities known as spectral broadening. Spectral broadening during CWD interrogation contrasts the homogenous envelope obtained with PWD ( Fig. 3-6). Since the sampling frequency is very high, blood flow velocity is measured with great accuracy even at high flows. CWD is particularly useful for evaluating patients with stenotic valvular lesions or congenital heart disease, in whom high-pressure/high-velocity signals are anticipated. It also is the preferred technique when attempting to derive hemodynamic information from Doppler signals.

Determination of Tissue Movement: Tissue Doppler and Speckle Analysis

Spectral Doppler is commonly used to determine blood flow velocities. Because these velocities are relatively high and the amplitude of the Doppler signal is low, high-amplitude/low-velocity ultrasound signals usually are ignored. In contrast, during tissue Doppler examination, the primary interest is in the high-amplitude/low-velocity ultrasound signals created by the myocardium; low-amplitude/high-velocity signals are ignored. Doppler tissue imaging (DTI) of the mitral valve annulus may be used to judge diastolic function. ⁶ Most modern ultrasound machines have presets optimized for tissue Doppler analysis to include the high-amplitude/low-velocity signals that normally are excluded.

The major limitation of tissue Doppler analysis is the need to align tissue movement with the ultrasound beam. If tissue movements occur at right angles to the projected beam, determination of DTI is impossible. An alternative for measuring tissue movements that are independent of the ultrasound beam direction is utilizing speckle analysis. Interactions of ultrasound with myocardium result in reflection and scattering, which generate a finely gray-shaded, speckled pattern. This speckled pattern is unique for each myocardial region and relatively stable throughout the cardiac cycle. The speckles function as markers; they are equally distributed within the myocardium and change their position from frame to frame in accordance with the surrounding tissue motion. In speckle track imaging, the speckles within a predefined region of interest are followed automatically frame by frame, and the change in their geometric position (which corresponds to local tissue movement) is used to extract information about its movement. Because these acoustic markers can be followed in any direction, speckle tracking is a non-Doppler, angle-independent technique for calculating cardiac deformation along two dimensions.

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