Principles of Echocardiographic Image Acquisition and Doppler Analysis

An understanding of the basic principles of ultrasound imaging and Doppler echocardiography is essential both during data acquisition and for correct interpretation of the ultrasound information. Although, at times, current instruments provide instantaneous images so clear and detailed that it seems as if we can “see” the heart and blood flow directly, in actuality, we always are looking at images and flow data generated by complex analyses of ultrasound waves reflected and backscattered from the patient’s body. Knowledge of the strengths, and more importantly, the limitations, of this technique is critical for correct clinical diagnosis and patient management. On the one hand, echocardiography can be used for decision making with a high degree of accuracy in a variety of clinical settings. On the other hand, if an ultrasound artifact is mistaken for an anatomic abnormality, a patient might undergo needless, expensive, and potentially risky other diagnostic tests or therapeutic interventions.

In this chapter, a brief (and necessarily simplified) overview of the basic principles of cardiac ultrasound imaging and flow analysis is presented. The reader is referred to the Suggested Reading at the end of the chapter for more information on these subjects. Because the details of image processing, artifact formation, and Doppler physics become more meaningful with experience, some readers may choose to return to this chapter after reading other sections of this book and after participating in some echocardiographic examinations.

Ultrasound Waves

Sound waves are mechanical vibrations that induce alternate refraction and compression of any physical medium through which they pass (Fig. 1-1). Like other waves, sound waves are described in terms of (Table 1-1):

TABLE 1-1

Ultrasound Waves

Figure 1–1 Schematic diagram of an ultrasound wave.

Frequency: cycles per second, or hertz (Hz)

Velocity of propagation

Wavelength: millimeters (mm)

Amplitude: decibels (dB)

Frequency (f) is the number of ultrasound waves in a 1-second interval. The units of measurement are hertz, abbreviated Hz, which simply means cycles per second. A frequency of 1000 cycles/s is 1 kilohertz (KHz), and 1 million cycles/s is 1 megahertz (MHz). Humans can hear sound waves with frequencies between 20 Hz and 20 kHz; frequencies higher than this range are termed ultrasound. Diagnostic medical ultrasound typically uses transducers with a frequency between 1 and 20 MHz.

The speed that a sound wave moves through the body, called the velocity of propagation (c), is different for each type of tissue. For example, the velocity of propagation in bone is much faster (about 3000 m/s) than in lung tissue (about 700 m/s). However, the velocity of propagation in soft tissues, including myocardium, valves, blood vessels, and blood is relatively uniform, averaging about 1540 m/s.

Wavelength is the distance from peak to peak of an ultrasound wave. Wavelength can be calculated by dividing the frequency (f in Hz) by the propagation velocity (c in m/s).

(1-1)

Since the propagation velocity in the heart is constant at 1540 m/s, the wavelength for any transducer frequency can be calculated (Fig. 1-2) as:

Figure 1–2 Transducer frequency versus wavelength and penetration of the ultrasound signal in soft tissue.
Wavelength has been plotted inversely to show that resolution increases with increasing transducer frequency while penetration decreases. The specific wavelengths for transducer frequencies of 1, 2.5, 3.5, 5, and 7.5 MHz are shown.

or as:

For example, the wavelength emitted by a 5 MHz transducer can be calculated as:

Wavelength is important in diagnostic applications for at least two reasons:

Image resolution is no greater than 1 to 2 wavelengths (typically about 1 mm).

The depth of penetration of the ultrasound wave into the body is directly related to wavelength; shorter wavelengths penetrate a shorter distance than longer wavelengths.

Thus, there is an obvious tradeoff between image resolution (shorter wavelength or higher frequency preferable) and depth penetration (longer wavelength or lower frequency preferable).

The acoustic pressure, or amplitude, of an ultrasound wave indicates the energy of the ultrasound signal. Power is the amount of energy per unit time. Intensity (I) is the amount of power per unit area:

(1-2)

This relationship shows that if ultrasound power is doubled, intensity is quadruped. Instead of using direct measures of pressure energy, ultrasound amplitude is described relative to a reference value using the decibel scale. Decibels (dB) are familiar to all of us as the standard description of the loudness of a sound. Decibels are logarithmic units based on a ratio of the measured amplitude (A₂) to a reference amplitude (A₁) such that:

(1-3)

Thus, a ratio of 1000 to 1 is:

a ratio of 100 to 1 is:

and a ratio of 2 to 1 is:

A simple rule to remember is that a 6-dB change represents a doubling or halving of the signal amplitude or that a 40-dB change represents a 100 times difference in amplitude (Fig. 1-3). If acoustic intensity is used instead of amplitude, the constant 10 replaces 20 in the equation so that a 3 dB changes represents doubling, and a 20 dB change indicates a 100-fold difference in amplitude. Either of these decibel scales may be used to refer to transmitted or received ultrasound waves or to describe attenuation effects. The advantages of the decibel scale are that a very large range can be compressed into a smaller number of values, and that low-amplitude (weak) signals can be displayed alongside very high-amplitude (strong) signals. In an echocardiographic image, amplitudes typically range from 1 to 120 dB. The decibel scale is the standard format both for echocardiographic image display and for the Doppler spectral display, although other amplitude scales may be an option.

Figure 1–3 Graph of the decibel scale.
The logarithmic relationship between the decibel scale (horizontal axis) and the amplitude ratio (vertical axis) is seen. A doubling or halving of the amplitude ratio corresponds to a 6-dB change, and a 100-fold difference in amplitude corresponds to a 20-dB change.

Ultrasound Tissue Interaction

Propagation of ultrasound waves in the body to generate ultrasound images and Doppler data depends on a tissue property called acoustic impedance (Table 1-2). Acoustic impedance (Z) depends on tissue density (ρ) and on the propagation velocity in that tissue (c):

TABLE 1-2

Ultrasound Tissue Interaction

(1-4)

Although the velocity of propagation differs between tissues, tissue density is the primary determinant of acoustic impedance for diagnostic ultrasound. Lung tissue has a very low density compared to bone, which has a very high density. Soft tissues, such as blood and myocardium, have much smaller differences in tissue density and acoustic impedance. Acoustic impedance determines the transmission of ultrasound waves through a tissue; differences in acoustic impedance result in reflection of ultrasound waves at tissue boundaries.

The interaction of ultrasound waves with the organs and tissues of the body can be described in terms of (Fig. 1-4):

Figure 1–4 Diagram of the interaction between ultrasound and body tissues.
Doppler analysis is based on the scattering of ultrasound in all directions from moving blood cells with a resulting change in frequency of the ultrasound received at the transducer. 2D imaging is based on reflection of ultrasound from tissue interfaces (specular reflectors). Attenuation limits the depth of ultrasound penetration. Refraction, a change in direction of the ultrasound wave, results in imaging artifacts.

Ultrasound transducers use a piezoelectric crystal both to generate and to receive ultrasound waves (Fig. 1-5). A piezoelectric crystal is a material (such as quartz or a titanate ceramic) with the property that an applied electric current results in alignment of polarized particles perpendicular to the face of the crystal with consequent expansion of crystal size. When an alternating electric current is applied, the crystal alternately compresses and expands, generating an ultrasound wave. The frequency that a transducer emits depends on the nature and thickness of the piezoelectric material.

Figure 1–5 Schematic diagram of an ultrasound transducer.
The piezoelectric crystal both produces and receives ultrasound signals, with the electric input-output transmitted to the instrument via the cable. Damping material allows a short pulse length (improved resolution). The shape of the piezoelectric crystal, an acoustic lens, or electronic focusing (with a phased-array transducer) are used to modify beam geometry. The material of the transducer surface provides impedance matching with the skin. The ultrasound pulse length for 2D imaging is short (1-6ms), typically consisting of two wavelengths (λ). “Ring down”—the decrease in frequency and amplitude in the pulse—depends on damping and determines bandwidth (the range of frequencies in the signal).

Conversely, when an ultrasound wave strikes the piezoelectric crystal, an electric current is generated. Thus, the crystal can serve both as a “receiver” and as a “transmitter.” Basically, the ultrasound transducer transmits a brief burst of ultrasound and then switches to the “receive mode” to await the reflected ultrasound signals from the intracardiac acoustic interfaces. This cycle is repeated temporally and spatially to generate ultrasound images. Image formation is based on the time delay between ultrasound transmission and return of the reflected signal. Deeper structures have a longer time of flight than shallower structures, with the exact depth calculated based on the speed of sound in blood and the time interval between the transmitted burst of ultrasound and return of the reflected signal.

The burst, or pulse, of ultrasound generated by the piezoelectric crystal is very brief, typically 1 to 6 µs, because a short pulse length results in improved axial (along the length of the beam) resolution. Damping material is used to control the ring-down time of the crystal and, hence, the pulse length. Pulse length also is determined by frequency because a shorter time is needed for the same number of cycles at higher frequencies. The number of ultrasound pulses per second is called the pulse repetition frequency, or PRF. The total time interval from pulse to pulse is called the cycle length, with the percent of the cycle length used for ultrasound transmission called the duty factor. Ultrasound imaging has a duty factor of about 1% compared to 5% for pulsed Doppler and 100% for continuous-wave (CW) Doppler. The duty factor is a key element in the patient’s total ultrasound exposure as discussed in Bioeffects and Safety, p. 27.

The range of frequencies contained in the pulse is described as its frequency bandwidth. A wider bandwidth allows better axial resolution because of the ability of the system to produce a narrow pulse. Transducer bandwidth also affects the range of frequencies that can be detected by the system with a wider bandwidth, which allows better resolution of structures distant from the transducer. The stated frequency of a transducer represents the center frequency of the pulse.

Types of Transducers

The simplest type of ultrasound transducer is based on a single piezoelectric crystal (Table 1-3). Alternate pulsed transmission and reception periods allow repeated sampling along a single line, with the sampling rate limited only by the time delay needed for return of the reflected ultrasound wave from the depth of interest. An example of using the transducer for simple transmission-reception along a single line is an A-mode (amplitude versus depth) or M-mode (depth versus time) cardiac recording when a high sampling rate is desirable.

TABLE 1-3

Ultrasound Transducers

Formation of more complex images uses an array of ultrasound crystals arranged to provide a 2D tomographic or 3D volumetric data set of signals. Each element in the transducer array can be controlled electronically both to direct the ultrasound beam across the region of interest and to focus the transmitted and received signals. Echocardiographic imaging uses a sector scanning format with the ultrasound signal originating from a single location (the narrow end of the sector), resulting in a fanlike shape of the image. Sector scanning is optimal for cardiac applications because it allows a fast frame rate to show cardiac motion and a small transducer size (aperture or “footprint”) to fit into the narrow acoustic windows used for echocardiography. Three-dimensional imaging transducers are discussed in Chapter 4.

Most transducers can provide simultaneous imaging and Doppler analysis, for example, 2D-imaging and a superimposed color Doppler display. Quantitative Doppler velocity data are recorded with the image “frozen” or with only intermittent image updates, with the ultrasound crystals used to optimize the Doppler signal. Although CW Doppler signals can be obtained using two elements of combined transducer, use of a dedicated nonimaging transducer with two separate crystals (with one crystal continuously transmitting and the other continuously receiving the ultrasound waves) is recommended when accurate high-velocity recordings are needed. The final configuration of a transducer depends on transducer frequency (higher-frequency transducers are smaller) and beam focusing, as well as the intended clinical use, for example, transthoracic versus TEE imaging.

Beam Shape and Focusing

An unfocused ultrasound beam is shaped like the light from a flashlight, with a tubular beam for a short distance that then diverges into a broad cone of light (Fig. 1-6). Even with current focused transducers, ultrasound beams have a 3D shape that affects measurement accuracy and contributes to imaging artifacts. Beam shape and size depend on several factors, including:

Figure 1–6 Schematic diagram of beam geometry for an unfocused (left) and focused (right) transducer.
The length of the near zone and the divergence angle in the far field depend on transducer frequency and aperture. The focal zone of a focused transducer can be adjusted, but beam width still depends on depth. Side lobes (and grating lobes with phased-array transducers) occur with both focused and unfocused transducers and, like the central beam, are 3D.

Transducer frequency

Distance from the transducer

Aperture size and shape

Beam focusing

Aperture size and shape and beam focusing can be manipulated in the design of the transducer, but the effects of frequency and depth are inherent to ultrasound physics. For an unfocused beam, the initial segment of the beam is columnar in shape (near field F_n) with a length dependent on the diameter D of the transducer face and wavelength (λ):

(1-6)

For a 3.5-MHz transducer with a 5-mm diameter aperture, this corresponds to a columnar length of 1.4 cm. Beyond this region, the ultrasound beam diverges (far field), with the angle of divergence θ determined as:

(1-7)

This equation indicates a divergence angle of 6° beyond the near field, resulting in an ultrasound beam width of about 4.4 cm at a depth of 20 cm for this 3.5-MHz transducer. With a 10-mm diameter aperture, F_n would be 5.7 cm and beam width at 20 cm would be about 2.5 cm (Fig. 1-7).

Figure 1–7 Transducer frequency versus near zone length and divergence angle.
Transducer frequency is shown on the horizontal axis with the length of the near zone shown in yellow and divergence angle in blue for unfocused 5- (squares) and 10-mm (triangles) diameter aperture transducers. Equations (1-6) and (1-7) were used to generate these curves.

The shape and focal depth (narrowest point) of the primary beam can be altered by making the surface of the piezoelectric crystal concave or by the addition of an acoustic lens. This allows generation of a beam with optimal characteristics at the depth of most cardiac structures, but again, divergence of the beam beyond the focal zone occurs. Some transducers allow manipulation of the focal zone during the examination. Even with focusing, the ultrasound beam generated by each transducer has a lateral and an elevational dimension that depends on the transducer aperture, frequency, and focusing. Beam geometry for phased-array transducers also depends on the size, spacing, and arrangement of the piezoelectric crystals in the array.

In addition to the main ultrasound beam, dispersion of ultrasound energy laterally from a single-crystal transducer results in formation of side lobes at an angle θ from the central beam where sin θ = m λ/D, and m is an integer describing sequential side lobes (i.e., 1, 2, 3, and so on) (Fig. 1-8). Reflected or backscattered signals from these side lobes may be received by the transducer, resulting in image or flow artifacts. With phased-array transducers, additional accessory beams at an even greater angle from the primary beam, termed grating lobes, also occur as a result of constructive interference of ultrasound wave fronts. Both the side lobes and the grating lobes affect the lateral and elevational resolution of the transducer.

Figure 1–8 Transducer beam side lobes.
Top: This diagram shows that side lobes occur at the points where the distances traversed by the ultrasound pulse from each edge of the crystal face differ by exactly one wavelength. The distance from the left edge of the crystal (P₁) to the position of side lobe 1 is exactly one wavelength (λ) longer than the distance from the extreme right edge of the crystal (P₂) to the position of side lobe 1. Bottom: The beam intensity plot formed by sweeping along an arc at focal length F. (From Geiser EA: Echocardiography: physics and instrumentation. In Skorton DJ, Schelbert AR, Wolf GL, Brundage BH [eds]: Marcus Cardiac Imaging, 2nd ed. Philadelphia: WB Saunders, 1996, p 280. Used with permission.)

Resolution

Image resolution occurs for each of three dimensions (Fig. 1-9):

Figure 1–9 Axial, lateral, and elevational slice thickness in three dimensions for a phased-array transducer ultrasound beam.
A, Axial resolution along the direction of the beam is independent of depth; lateral resolution and elevational resolution are strongly depth dependent. Lateral resolution is determined by transmit and receive focus electronics; elevational resolution is determined by the height of the transducer elements. At the focal distance, axial is better than lateral and is better than elevational resolution. B, Elevational resolution profile with an acoustic lens across the transducer array produces a focal zone in the slice thickness direction. (From Bushberg JT, et al: The Essential Physics of Medical Imaging. Philadelphia: Lippincott Williams & Wilkins, 2002, Fig. 16-21).

Axial resolution along the length of the ultrasound beam

Lateral resolution side to side across the 2D image

Elevational resolution or thickness of the tomographic slice

Of these three, axial resolution is most precise, so quantitative measurements are made most reliably using data derived from a perpendicular alignment between the ultrasound beam and structure of interest. Axial resolution depends on the transducer frequency, bandwidth, and pulse length but is independent of depth (Table 1-4). Determination of the smallest resolvable distance between two specular reflectors with ultrasound is complex but is typically about twice the transmitted wavelength; higher-frequency (shorter-wavelength) transducers have greater axial resolution. For example, with a 3.5 MHz transducer, axial resolution is about 1 mm, versus 0.5 mm with a 7.5 MHz transducer. A wider bandwidth also improves resolution by allowing a shorter pulse, thus avoiding overlap between the reflected ultrasound signals from two adjacent reflectors.

Table 1-4

Determinants of Resolution in Ultrasound Imaging

Axial Resolution

Transducer frequency

Transducer bandwidth

Pulse length

Lateral Resolution

Transducer frequency

Beam width (focusing) at each depth ^∗

Aperture (width) of transducer

Bandwidth

Side and grating lobe levels