Physical Principles of Ultrasound and Generation of Images


Ultrasound imaging is ubiquitous in medical practice and is used to image all regions of the body, including soft tissues, blood vessels, and muscles. The machines used for ultrasound imaging range from small hand-held ultrasound devices no bigger than a smartphone to more elaborate and complex systems capable of advanced imaging techniques such as three-dimensional (3D) imaging. Although imaging of the heart and great vessels has traditionally been referred to as “echocardiography,” the fundamental physical principles of image generation are common to all ultrasound devices. These principles should be familiar to the end-user because they are essential to understanding the utility and limitations of ultrasound and to the interpretation of ultrasound images and can help optimize the use of ultrasound systems to obtain the highest-quality images.


Doppler echocardiography, echocardiography image generation, hemodynamics, image resolution, ultrasound transducers



Ultrasound imaging is ubiquitous in medical practice and is used to image all regions of the body, including soft tissues, blood vessels, and muscles. The machines used for ultrasound imaging range from small hand-held ultrasound devices no bigger than a smartphone to more elaborate and complex systems capable of advanced imaging techniques such as three-dimensional (3D) imaging. Although imaging of the heart and great vessels has traditionally been referred to as “echocardiography,” the fundamental physical principles of image generation are common to all ultrasound devices. These principles should be familiar to the end-user because they are essential to understanding the utility and limitations of ultrasound and to the interpretation of ultrasound images and can help optimize the use of ultrasound systems to obtain the highest-quality images.

Generation of Images by Ultrasound

The generation of images by ultrasound is based on the pulse-echo principle. It is initiated by an electric pulse that leads to the deformation of a piezoelectric crystal housed in a transducer. This deformation results in a high-frequency (>1,000,000 Hz) sound wave (ultrasound), which can propagate through a tissue when the transducer is applied, resulting in an acoustic compression wave that will propagate away from the crystal through the soft tissue at a speed of approximately 1530 m/s. As with all sound waves, each compression is succeeded by decompression: the rate of these events defines the frequency of the wave. In diagnostic ultrasound imaging, this applied frequency is generally between 2.5 and 10 MHz, which is far beyond the level audible by humans, and is thus termed ultrasound .

The principal determinants of the ultrasound wave are: (1) wavelength (λ), which represents the spatial distance between two compressions (and is the primary determinant of axial resolution, as defined later), (2) frequency (f), which is inversely related to wavelength, and (3) velocity of sound (c), which is a constant for any given medium ( Fig. 1.1A and B ).These three wave characteristics have a set relationship as c = λf. An increase in the frequency (i.e., shortening of the wavelength) implies less deep penetration due to greater viscous effects leading to more attenuation. As the acoustic wave travels through tissue, changes in tissue properties, such as tissue density, will induce disruption of the propagating wave, leading to partial reflection (specular reflections) and scatter (backscatter) of its energy ( Fig. 1.2 , Box 1.1 ). Typically, specular reflections originate from interfaces of different types of tissue (such as blood pool and myocardium or myocardium and pericardium), whereas backscatter originates from within a tissue, such as myocardial walls. In both cases, reflections propagate backwards to a piezoelectric crystal, again leading to its deformation, which generates an electric signal. The amplitude of this signal (termed the radiofrequency [RF] signal ) is proportional to the amount of deformation of the crystal (i.e., the amplitude of the reflected wave). This signal is then amplified electronically, which can be modified by the “gain” settings of the system that will amplify both signal and noise. In addition to defining the amplitude of the returning signal, the depth of the reflecting structure can be defined according to the time interval from emitting to receiving a pulse, which equals the time required for the ultrasound to travel from the transducer to the tissue and back. The data on amplitude and depth of reflection are used to form scan lines , and the overall image construction is based on repetitive operations of the previously mentioned procedures of image (scan line) acquisition and (post-) processing. During image acquisition, transducers emit ultrasound waves in pulses of a certain duration (pulse length), at a certain rate, termed the pulse repetition frequency (PRF), which is one of the determinants of the temporal resolution of an echo image (obviously limited by the duration of the pulse-echo measurement [i.e., its determinants]), as elucidated further (see Fig. 1.1C ).

FIG. 1.1

(A and B) Depiction of an (ultra)sound wave as a sine wave. The wave propagates through tissue at a given wavelength that is determined by frequency (to which it is inversely related) and at a given amplitude that quantifies the amount of energy (i.e., the pressure change) transported by the wave. For sound waves, frequency is observed as pitch, whereas amplitude is observed as loudness of the tone. (C) Pulse length (duration) is primarily determined by the transducer frequency, to which it is inversely related (e.g., higher-frequency transducers can emit pulses of shorter pulse length). These pulses are emitted at a certain rate, termed the pulse repetition frequency .

Courtesy of Bernard E. Bulwer, MD, FASE.

FIG. 1.2

The interaction of the transmitted wave with an acoustic interface (i.e., cardiac structures).

A segment of the transmitted wave is reflected at the interface, while another part is transmitted through the tissue. Such a wave can be refracted, while the transmitted wave may also reflect and return to the transducer (thus carrying information on signal amplitudes) as a specular reflection (mainly occurring at the interfaces of different types of tissue, such as myocardium and pericardium), or as backscatter reflection (mainly originating from within the myocardial walls). LV, Left ventricle; PM, papillary muscle; PSAX, parasternal short-axis view; RV, right ventricle.

Modified from Bulwer BE, Shernan SK, Thomas J. Physics of echocardiography. In: Savage RM, Aronson S, Shernan SK, eds. Comprehensive textbook of perioperative transesophageal echocardiography. Philadelphia: Lippincott, Williams & Wilkins; 2009:15.

BOX 1.1

The attenuation of soft tissue is typically expressed in decibel per cm per MHz (i.e., dB/cm per megahertz), given that the attenuation is dependent on both frequency and propagation distance of the wave. A typical value for attenuation in soft tissues is 0.5 dB/cm per megahertz, implying that for 20-cm propagation (e.g., from the probe to the mitral annulus and back for an apical transducer position) of a wave generated by a common adult cardiac ultrasound transducer (i.e., 2.5 MHz) the amplitude of the acoustic wave has decreased by 25 dB, meaning that the wave received back at the probe surface will—at best (i.e., assuming perfect reflection and optimal focusing)—have only 5% of the amplitude of the transmitted wave. When doubling the frequency to 5 MHz (i.e., pediatric probe) the total attenuation doubles to 50 dB, implying that only approximately 0.3% of the transmitted amplitude returns from 20 cm deep, which can become difficult to detect. Hence the proper choice of transducer is required based on the depth at which structures need to be visualized.

Reflection and refraction of sound waves occur at structures of differing acoustic impedance (i.e., mass density and/or compressibility) that are large compared with the wavelength (i.e., significantly > 0.5 mm for a 2.5 MHz wave). In this case the behavior of acoustic waves is very similar to optic (i.e., light) waves: part of the energy is transmitted into the second medium under a slightly different angle (i.e., the refracted wave) while part of the energy is reflected (i.e., the reflected wave). As a simple example, you can think of what you see when holding your hand under water: your arm appears to make an angle at the water surface. The reason is light wave refraction at the water surface, and the exact same phenomenon exists for ultrasound waves. One may thus think that the posterior wall would appear distorted (cf. your arm under water) due to the wave being refracted at the septal wall interfaces. Although this is true, in practice these refraction effects are—luckily—most often negligible.

Attenuation, Reflection, and Refraction of Ultrasound Waves

The data obtained from scan lines can be visually represented as A- or B-mode images ( Fig. 1.3 ). The most fundamental modality of imaging RF signals is A-mode, where A = amplitude, in which such signals are imaged as amplitude spikes at a certain distance from the transducer; however, because visualization of the A-mode signals is relatively unattractive, A-mode is not used as an image display option; further processing is used to create a B-mode (B = brightness) image in which the amplitudes are displayed by a gray scale (see Fig. 1.3 ). To achieve such gray scale encoding, multiple points of the signal (i.e., pixels) are, based on the local amplitude of the signal, designated with a number that further represents a color on the gray scale. The B-mode dataset can then be displayed as an M-mode (M = motion) image, which displays the imaged structures in one dimension over time (distance of the imaged structures from the transducer is shown on the y-axis, and time is recorded on the x-axis; optimal for assessments requiring high temporal resolution and for linear measurements) or as a 2D image. By convention, strong, high-amplitude reflections are given a bright color and weak, low-amplitude reflections are dark ( Box 1.2 ).

FIG. 1.3

Generation of images by ultrasound.

After an ultrasound pulse is emitted by the piezoelectric crystals located in the transducer (upper left) , it travels through tissue, reflects from structures, and propagates backwards to the transducer. The received signals undergo processing and are displayed according to their amplitudes and depth of reflection (upper right) . The fundamental A-mode display images the signals as amplitude spikes (upper right) . On B-mode, these amplitude spikes are translated to a gray scale, such that the least reflective tissues (e.g., blood pool) are visualized as black (upper right) . B-mode images can further be displayed as a two-dimensional cross-sectional image (bottom left) or in M-mode, which visualizes the imaged structures in one dimension over time (bottom right) . Note that reflections with the highest amplitudes originate from tissue interfaces such as the myocardium and pericardium or blood pool and myocardium (upper and lower panels). IVS, Interventricular septum; LV, left ventricle; PW, posterior wall.

Courtesy of Bernard E. Bulwer, MD, FASE; Modified from Solomon SD, Wu J, Gillam L, Bulwer B. Echocardiography. In: Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s heart disease: a textbook of cardiovascular medicine. 10th ed. Philadelphia: Elsevier; 2015:180.

BOX 1.2

The pixel values range from 0 to 255 (i.e., 2 8 ) for an 8-bit system, where 0 typically represents black, 255 represents white, and the intermediate numbers correspond to hues of gray, which can be extended to a spectrum of, for example, 65,536 (2 16 ) nuances of gray for the current systems with 16-bit resolution images. Furthermore, contemporary ultrasound systems also offer a choice of color maps, in which case these values correspond to hues of, for example, bronze or purple. Although gray-scale color maps are most often used, there is no scientific rationale for this and some people prefer to use other color schemes; this thus remains a matter of personal preference.

Color Maps

Another point in processing the RF signal overcomes a potential technical limitation of echocardiography; namely, reflections from tissues more distant from the transducer are inherently smaller in amplitude, due to attenuation (see Box 1.1 ). In practice, this implies that the segments of the ultrasound image depicting, for example, the atria in the apical views would be less bright than the myocardium. However, attenuation correction can compensate for this effect, automatically amplifying the signals from deeper segments, defined as automatic time-gain compensation (TGC) ( Fig. 1.4 ). In addition to the automatic TGC, most systems are equipped with TGC sliders that enable modification of the automated TGC by the operator during image acquisition. Because the attenuation effect can be variable among patients, the acquisition of echocardiographic images should commence with a neutral setting of the sliders, which are then individually modified according to the patient and the current echocardiographic view. Of note, attenuation cannot be corrected for after image acquisition. The final step in image optimization, which can be performed during post-processing, is log-compression —most often applied in diagnostic imaging as the “dynamic range.” This method enables the increase of image contrast by modifying the number of gray values, thus leading to nearly black-and-white images (low dynamic range) or more gray images (high dynamic range).

FIG. 1.4

Attenuation correction settings.

Optimal settings of time-gain compensation (TGC) can provide a uniform display of signal intensity for echoes from similarly reflecting structures, across various depths of the scan sector.

From Bulwer BE, Shernan SK. Optimizing two-dimensional echocardiographic imaging. In: Savage RM, Aronson S, Shernan SK, eds. Comprehensive textbook of perioperative transesophageal echocardiography. Philadelphia: Lippincott, Williams & Wilkins; 2009:59.

Typically, the duration of the pulse-echo event is approximately 200 μs, taking into consideration the usual wave propagation distance during a cardiac examination (∼30-cm distance from the chest wall to the roofs of the atria and back) and the speed of ultrasound propagation through soft tissue. This implies that approximately 5000 pulse-echo measurements can be undertaken every second, while approximately 180 of these measurements are performed in the construction of a typical 2D image of the heart, by emitting pulses in 180 different directions within a 90-degree scanning plane, reconstructing one scan line for each transmitted pulse. In summary, a construction of one echocardiographic image requires approximately 36 ms (180 measurements × 200 μs), which translates to approximately 28 frames created per second. However, the number of frames (i.e., the frame rate ) can be multiplied by various techniques, some of which are implemented in most current systems, such as the multiline acquisition that constructs two or four lines in parallel, leading to a fourfold increase in the 2D image frame rate. For more information on high frame rate imaging, see Box 1.3 .

BOX 1.3

Multiple approaches have been proposed to increase frame rate (i.e., time resolution) of the echocardiographic recordings. Most high-end commercially available systems reconstruct 2 to 4 image lines from each transmitted pulse, but 3D imaging systems reconstructing up to 64 lines for each transmit are commercially available. Although this “parallel beam forming” results in better time resolution of the images, it typically comes at the cost of reduced spatial resolution and/or signal-to-noise ratio of the images. Finding the optimal compromise between these parameters is a major challenge for all vendors of ultrasound equipment. Alternative imaging techniques to speed up the acquisition process but with potentially less effects on spatial resolution and signal-to-noise ratio (e.g., multiline transmit and diverging wave imaging) are being developed. Two popular approaches that are currently being explored are “multiline transmit” imaging and “diverging wave” imaging. For the former a number of pulse-echo measurements are done in multiple directions in parallel, a challenge being to avoid crosstalk between the simultaneously transmitted pulses. In the latter technique the whole field of view (or a large part of it) is insonified by a very wide (i.e., defocused) ultrasound beam, allowing to reconstruct the whole image with a very small number of transmits (i.e., 1 to 5). In this way, frame rate is increased tremendously (up to 1 to 5 kHz), the challenge being to preserve spatial resolution and contrast of the images (i.e., image quality). Despite these remaining challenges, fast imaging approaches will undoubtedly enter clinical diagnostics in the years to come.

High Frame Rate Imaging

Resolution of Echocardiographic Images

Resolution is defined as the shortest distance between two objects required to discern them as separate. However, resolution in echocardiography, being a dynamic technique, consists of two major components: spatial and temporal resolution. Furthermore, spatial resolution mainly comprises axial and lateral resolution, depending on the position of the objects relative to the image line, and various determinants will influence each component of image resolution ( Figs. 1.5 to 1.7 ). Temporal resolution (i.e., frame rate) represents the time between two subsequent measurements (i.e., the ability of the system to discern temporal events as separate).

FIG. 1.5

Components of spatial resolution.

Lateral resolution refers to the spatial resolution perpendicular to the beam, axial resolution refers to resolution along the image line, and elevation resolution is also perpendicular to the image line; however, its determinant is the dimension of the beam in the elevation direction.

Modified from Bulwer BE, Shernan SK. Optimizing two-dimensional echocardiographic imaging. In: Savage RM, Aronson S, Shernan SK, eds. Comprehensive textbook of perioperative transesophageal echocardiography. Philadelphia: Lippincott, Williams & Wilkins; 2009:54.

FIG. 1.6

Features of axial resolution are based on pulse duration (spatial pulse, length), which is predominantly defined by the characteristics of the transducer (i.e., its frequency).

(A) The two reflectors (echo 1 and echo 2) are located apart enough to be resolved by the separately returning echo pulses. (B) The two reflectors (echo 1 and echo 2) are located too close, and the returning echo pulses will merge. (C) An increase in the transducer frequency from 3 to 7 MHz will shorten the spatial pulse length (and pulse duration), thus permitting the returning echoes from these reflectors to be resolved.

Courtesy of Bernard E. Bulwer, MD, FASE.

FIG. 1.7

Lateral resolution is predominantly determined by beam width, such that a narrower beam will allow for greater lateral resolution.

Axial resolution refers to resolution along the image line (i.e., two objects located one behind another, relative to the image line) (see Fig. 1.6 ). Its principal determinant is pulse length (which is, similarly to wavelength, inversely related to frequency), such that a shorter ultrasound pulse will allow for better axial resolution (typically 1.5 to 2 times the wavelength). Pulse length is predominantly defined by the characteristics of the transducer: a higher-frequency transducer provides shorter pulses, yielding better axial resolution. In practical terms, a typical scanning frequency of 2.5 MHz implies a wavelength of approximately 0.6 mm, at which an axial resolution of approximately 1 mm is obtained. However, higher frequencies have reduced penetration due to more attenuation by soft tissue, implying that a compromise between axial resolution and image depth needs to be made. Therefore high-resolution imaging is predominantly limited to pediatric echocardiography, where transducers up to 10 to 12 MHz can be used for infants, as opposed to 2.5- to 3-MHz transducers typically used in adult echocardiography.

Lateral resolution refers to the spatial resolution perpendicular to the beam (i.e., two objects located next to each other, relative to the image line) (see Fig. 1.7 ). It is predominantly determined by beam width, which depends on depth and the size of the transducer footprint ( Box 1.4 ). Lateral resolution will thus be increased with a narrower beam (i.e., larger transducer footprint and/or shallower scanning depths).

BOX 1.4

As a first approximation the beam width can be calculated as: 1.22.λ. d/D with “λ” the wavelength, “d” the focal depth, and “D” the dimension of the transducer footprint. The ratio of d/D is called the f-number of the transducer. From the previous equation, it is clear that transducer size directly impacts the spatial resolution for a given depth. Unfortunately, for cardiac applications, transducer footprint needs to remain limited (and hence the spatial resolution) due to the limited size of the acoustic window towards the heart (i.e., the intercostal space). Although, for example, fetal cardiac imaging is possible with a cardiac ultrasound probe, image resolution will intrinsically be much better when using a large, curved array as used in obstetrics.

Beam Width

Elevation resolution —resolution perpendicular to the image line—is somewhat similar to lateral resolution. In this case the determinant is the dimension of the beam in the elevation direction (i.e., orthogonal to the 2D scan plane). Elevation resolution is more similar to lateral in newer systems with 2D array transducer technology (compared with 1D transducers).

Temporal resolution , as mentioned previously, is predominantly determined by PRF, which is limited by the determinants of the duration of the pulse-echo event—the wave propagation distance (the distance from the chest wall to the end of the scanning plane) and the speed of ultrasound propagation through soft tissue (which is considered constant). Frame rate can be increased either by reducing the field of view (a smaller sector requires the formation of fewer image lines, allowing for a faster acquisition of a single frame) or by reducing the number of lines per frame (line density), controlled by a “frame rate” knob on the system. Reduced line density jeopardizes spatial resolution because it sets the image lines further apart. There is an intrinsic trade-off between the image field of view, spatial resolution, and temporal resolution and should be kept in mind as a potential shortcoming of the technique ( Box 1.5 ). For advice on image optimization, see Box 1.6 .

BOX 1.5

The trade-off between spatial resolution, temporal resolution, signal-to-noise ratio and field of view of the echocardiographic data is intrinsic and application dependent. Indeed, when measuring, for example, the dimensions of a given cardiac structure, time resolution may be less critical and system settings could be adjusted to get the best possible spatial resolution and signal-to-noise ratio at the cost of time resolution. On the other hand, when making a functional analysis of the heart (e.g., when applying speckle tracking), improved time resolution may be important and justify reducing the overall image quality. It is thus important to realize that optimal acquisition settings are application dependent.

The Trade-off Between Temporal and Spatial Resolution

BOX 1.6

  • For optimal spatial resolution, use highest possible transducer frequency

  • For optimal temporal resolution, use narrowest possible sector and highest frame rate setting (i.e., lowest line density)

  • Optimize depth and focus according to imaged structure; use minimal depth settings

  • Optimize gain and dynamic range settings to obtain optimal image contrast: start with a black blood pool, increasing gain to a minimal amount that allows for definition of the heart structures

  • Time gain compensation should be used to homogenize the image at various depths; start at a neutral position of the sliders

Image Optimization General Points

Phased Array and Matrix Array Transducers

As opposed to mechanically rotating transducers used in earlier echocardiography systems, contemporary 2D imaging is based on electronic beam steering. This is achieved by an array of piezoelectric crystals (typically up to 128 elements), while the time delay between their excitation enables emission of the ultrasound wave in various directions across the scan plane and the generation of multiple scan lines ( Fig. 1.8 ). The sum of signals received by individual elements translates to the RF signal for a certain transmission, a process referred to as beam forming ( Box 1.7 ), which is crucial for acquiring high-quality images. Three-dimensional imaging relies on matrix array transducers, which are based on a 2D matrix of elements, thus enabling the steering of the ultrasound beam in three dimensions. This allows for both simultaneous multiplanar 2D imaging, as well as for volumetric 3D imaging.

FIG. 1.8

The phased array transducer technology.

Current echocardiography transducers steer the ultrasound beam (also termed sweep ) across the scan plane, thus creating a fairly wide scan sector (center) . During ultrasound transmission the time delays in activating the piezoelectric crystals induce the sweep of the scan line over the scan plane (left) . During reception, the reflected echo signals are out of phase when received by each crystal and need to be shifted in time (i.e., phased) prior to summation and further processing (right) .

Courtesy of Bernard E. Bulwer, MD, FASE; Modified from Solomon SD, Wu J, Gillam L, Bulwer B. Echocardiography. In: Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s heart disease: a textbook of cardiovascular medicine. 10th ed. Philadelphia: Elsevier; 2015:180.

BOX 1.7

Phased array transducers enable steering and focusing of the ultrasound beam simply by adjusting the electrical excitations of the individual transducer elements (see Fig. 1.7 , left panel ). Similarly, during reception, the received signals coming from individual transducer elements will be delayed in time to correct for the differing time of flight of a given echo to the individual transducer elements as a result of the differences in path length to each of these elements (see Fig. 1.7 , right panel ). The former is referred to as “transmit focusing,” whereas the latter is “receive focusing.” Interestingly, during receive focusing, one can dynamically adjust the focus point as one knows a priori from which depth echo signals are arriving at a given time point after transmission given the sound velocity is known. As such, the time delays applied to the signals coming from the different elements is adjusted dynamically in time to optimally focus the ultrasound beam at all depths. Similarly, given that focusing works better close the probe (see Box 1.4 ), some elements near the edge of the probe can be switched off when (receive) focusing close to the probe to reduce the effective transducer size, thereby making its ability to focus worse. The advantage of this approach is that the beam width becomes more uniform as a function of depth and thus so does the lateral image resolution. These beam-forming modalities are referred to as “dynamic receive focusing” and “dynamic apodization,” respectively, and are implemented on all cardiac ultrasound systems.

Beam Forming

Second Harmonic Imaging

Current ultrasound systems are based on fundamental and harmonic imaging. In fundamental imaging the transducer listens for the ultrasound of equal frequency to the emitted wave. However, at higher amplitudes of the transmitted wave, wave distortion may occur during propagation, causing harmonic frequencies (multiples of the transmitted frequency), which can be received by the transducer when properly implemented ( Fig. 1.9 ). Such second harmonic images have significantly improved signal-to-noise ratio and in particular improved endocardial border definition. However, this comes at the cost of poorer axial resolution (due to longer transmitted pulses), which may cause some structures, such as heart valves, to appear thicker on harmonic imaging. The transition between fundamental and harmonic imaging is achieved by the selection of transmit frequency: lower frequencies automatically enable harmonic imaging, which is discernible by both the transmit and receive frequency displayed on the screen (e.g., 1.7/3.4 MHz), whereas a single displayed frequency implies fundamental imaging.

FIG. 1.9

Tissue harmonic imaging.

Tissue harmonic imaging allows for improved image quality by using second-order harmonics in which specific frequencies of ultrasound induce tissue vibrations at twice the frequency. Listening for such higher frequencies of returning ultrasound allows for dramatic improvement of the signal-to-noise ratio. Second-harmonic imaging provides images with clearly ameliorated tissue definition and less affected by acoustic noise and artifacts (right) .

Courtesy of Bernard E. Bulwer, MD, FASE; From Solomon SD, Wu J, Gillam L, Bulwer B. Echocardiography. In: Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s heart disease: a textbook of cardiovascular medicine. 10th ed. Philadelphia: Elsevier; 2015:181.

Principles of Doppler Imaging

Although imaging of the morphology of cardiac structures is increasingly complemented by other modalities such as magnetic resonance imaging (MRI) or computed tomography (CT) imaging, the diagnostic role of echocardiographic imaging in the evaluation of valvular function and noninvasive assessment of hemodynamics remains fairly unique. Such assessments are based on the Doppler principle, which allows for the calculations of blood velocities within the heart or in blood vessels. The Doppler effect states that the frequencies of transmitted and received waves differ when the acoustic source moves towards or away from the observer (due to wave compression or expansion, depending on the direction of motion) ( Fig. 1.10 ). For example, this is noticed as a higher-pitched sound of the siren as the ambulance approaches the observer, compared with it moving away. The Doppler effect can be applied to measuring blood (and tissue) velocities, by measuring the difference between the frequency of emitted and received ultrasound, which will be reflected off moving red blood cells. Should the blood cells be moving in the direction of the transducer, the reflected waves will be compressed and the frequency of the received ultrasound will be higher compared with the emitted ultrasound. Conversely, the frequency of the received ultrasound will be lower with blood cells moving away from the transducer. This difference between the emitted and received frequency is termed the Doppler shift or Doppler frequency , which is directly proportional to the velocity of the reflecting structures (red blood cells, i.e., blood flow):

<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='fd=2ftv(cosθ)/c’>fd=2ftv(cosθ)/cfd=2ftv(cosθ)/c
f d = 2 f t v ( cos θ ) / c
where f d is the Doppler frequency, f t is the original transmitted ultrasound frequency, v is the magnitude of the velocity of blood flow, θ stands for the angle between the ultrasound beam and the blood flow (i.e., the angle of incidence/the angle of insonation), and c is the velocity of ultrasound through soft tissue (1530 m/s). The main limitation of the Doppler equation is the angle of incidence, such that its increase decreases the calculated velocity: cos 0 degrees = 1, which implies that data acquisition with the ultrasound beam parallel to the direction of blood flow would be ideal; conversely, cos 90 degrees = 0, implying that motion orthogonal to the ultrasound beam cannot be detected regardless of the velocity magnitude. Practically, an angle lower than 20 degrees is considered adequate for acceptable measurements (of note, there is no possibility of velocity overestimation due to this phenomenon). To optimize alignment, Doppler imaging can be used in conjunction with 2D imaging, which allows for optimal placement of the Doppler cursor prior to Doppler data acquisition. Furthermore, should the angle of incidence be known, it can be corrected for in the Doppler equation of the velocity estimate by means of a feature available on many ultrasound systems, usually termed angle correction. However, this is acceptable for laminar flow conditions (typically in vascular ultrasound, in particular of nonstenosed vessels), whereas the exact direction of flow within the heart is, in fact, unknown. For this reason, it is not recommended to use angle correction in cardiac ultrasound (or if applied, use with caution and awareness of the issue).

FIG. 1.10

The Doppler principle and Doppler frequency shift.

Ultrasound emitted from the transducer reflects off moving red blood cells and returns to the transducer: if reflected from red blood cells moving in the direction of the transducer, the echo returns at a higher frequency (shorter wavelength) than the emitted ultrasound pulse (upper left) ; conversely, if blood cells are moving away from the transducer, a lower-frequency echo will be reflected back to the transducer (lower left) . The difference between the transmitted and the returning frequency equals the Doppler shift, which is used by Doppler echocardiography systems to calculate velocities of blood flow. These velocities are graphically displayed by spectral Doppler as a time velocity spectrum (spectrogram), where a positive Doppler shift (implying flow toward the transducer) is depicted above the baseline, and a negative Doppler shift (flow away from the transducer) is drawn below the baseline (right) . In color flow Doppler the direction of flow can be detected according to the color-coded velocities.

Courtesy of Bernard E. Bulwer, MD, FASE; Modified from Solomon SD, Wu J, Gillam L, Bulwer B: Echocardiography. In Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s Heart Disease: A Textbook of Cardiovascular Medicine. 10th ed. Philadelphia: Elsevier; 2015:182.

Continuous Wave Doppler

The Doppler modalities used in echocardiography are pulsed wave (PW) and continuous wave (CW) Doppler ( Fig. 1.11 ), as well as color flow mapping (color flow Doppler). In CW, separate piezoelectric crystals continuously emit and receive ultrasound waves, and the difference between the frequencies of these waves (the Doppler shift) is calculated continuously. In PW Doppler, ultrasound is emitted in pulses, as is the case with standard image acquisition. According to the Doppler equation, the Doppler shift is translated to velocity, which is then displayed over a certain time frame (determined by the sweep speed of the image), and is termed the spectrogram . As red blood cells travel at different velocities within the ultrasound beam, various receive frequencies will be detected, implying that a spectrum of Doppler shifts will be calculated and displayed on the spectrogram—thus termed spectral Doppler ( Fig. 1.12 ). In CW the spectrum is rather broad due to the large sample volume, which accounts for a wide range of detected velocities, as opposed to PW. Although ultrasound is well beyond the limits of human hearing, the frequencies of the Doppler shift for typical blood velocities are actually within the audible range and can be heard during an examination: a higher-pitched sound corresponds to higher velocities (larger Doppler shift), whereas lower velocities generate a lower-pitched sound (smaller Doppler shift). Furthermore, because the ultrasound waves are emitted (and received) continuously in CW (i.e., the ultrasound system is not “waiting” for the reflection and return of the emitted pulse), the location of the reflected sound cannot be determined and therefore no spatial information is available by CW. However, all frequency shifts (i.e., velocities) along the beam are measured, which allows for high-velocity measurements by CW, typically used in the assessment of high velocities (turbulence) across the aortic valve in patients with aortic stenosis or in the approximation of pulmonary artery pressure from the velocity of the tricuspid regurgitation jet. As is the case in 2D imaging the attenuation effect also takes place in CW, as a consequence of which velocities from deeper tissue contribute less to the displayed signal ( Fig. 1.13 ). For advice on CW Doppler optimization, see Box 1.8 .

FIG. 1.11

Comparison of continuous wave (CW) Doppler and pulsed wave (PW) Doppler.

Courtesy of Bernard E. Bulwer, MD, FASE; Modified from Solomon SD, Wu J, Gillam L, Bulwer B. Echocardiography. In: Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s heart disease: a textbook of cardiovascular medicine. 10th ed. Philadelphia: Elsevier; 2015:182.

FIG. 1.12

The properties of spectral Doppler.

The velocity of blood flow is graphically displayed on the y-axis, and time is on the x-axis. Flow direction can also be determined, depending on the relation of the spectrogram to the baseline: flow toward the transducer is imaged above and flow away from the transducer is imaged below the baseline. The signal intensity reflects the quantity of red blood cells that are moving at a specific velocity range. In continuous wave the spectrum is rather broad due to the wide range of velocities detected by the beam, as opposed to pulsed wave (which is imaged here). A4C, Apical four-chamber.

FIG. 1.13

The depth attenuation effect seen on continuous wave (CW) Doppler in aortic stenosis.

With minimal gain settings, it can be appreciated that the velocities from deeper tissues contribute less to the spectrogram: the Doppler signal from the aortic root is attenuated and much weaker than that from the left ventricular outflow tract (LVOT). With higher Doppler gain (second heart cycle), the effect is less obvious. A5C, Apical five-chamber.

BOX 1.8

  • Optimize beam alignment with the direction of measured velocity (direction of flow)

  • Optimize gain to create a uniform Doppler profile free of “blooming”: to prevent loss of data due to insufficient gain, start with an overemphasized image, decreasing the gain to a minimal required amount

  • Optimize the “compress” control (assigns a certain shade of color to varying amplitudes): extreme values can affect the quality of the spectral analysis

  • The “low velocities reject” button discards the signals of lower amplitude, providing a cleaner image and more precise measurements

  • The “filter” reduces noise occurring from reflectors originating from the myocardium and other heart structures

Continuous Wave Doppler Optimization Points

Pulsed Wave Doppler

As opposed to CW, in PW Doppler ultrasound is emitted and received in a similar manner to 2D imaging: individual pulses are emitted as brief, intermittent bursts. After emitting such a pulse, the transducer “listens” to returning signals only during a short, defined time interval following pulse emission. This time interval corresponds to the time required for the pulse to reach a certain depth and travel back to the transducer. The depth is defined by the sample volume —in practical terms, a cursor that the operator places at a certain depth along the transmitted beam, on the superimposed 2D image; technically, this implies adjusting the timing between signal emission and reception. Furthermore, the previously mentioned pulse-echo measurement is repeated along a specific line, at a specific repetition rate, termed the PRF (i.e., the number of pulses transmitted from transducer per second). Such pulses require time to reflect and travel back to the transducer; thus the interval at which they are transmitted has to be long enough for the ultrasound system to be able to discern whether the reflected signal originates from the given pulse or a later one. Based on this concept the velocity of blood can be measured at a specific location in the heart by PW, thereby providing spatial information on flows. Therefore PRF represents the sampling rate of the ultrasound machine: higher blood velocities imply higher Doppler shift frequencies, requiring a higher sampling rate to detect the shift ( Box 1.9 ). Notably, PRF should not be mistaken for the frequency of the ultrasound wave: in analogy to music, the PRF denotes the rate at which a certain note is repeated, whereas the ultrasound wave frequency corresponds to the pitch of a certain note. The PRF is a principal determinant of the maximal Doppler shift (i.e., the maximal velocity within the sample volume that the ultrasound system can accurately quantify). This maximal velocity is also referred to as the Nyquist frequency (or the Nyquist limit) and is the maximal velocity that can be accurately interrogated within a certain sample volume. It is directly related to PRF, which is inversely related to the distance between the transducer and sample volume. The Nyquist limit equals one-half of the PRF. When imaging flows with velocities higher than double the PRF value, sampling of the waveform is inaccurate, disabling the accurate assessment of velocities, which can be detected by the appearance of aliasing in the generated image. Aliasing occurs due to the inability of the system to accurately determine the velocity or direction of flow at velocities exceeding the Nyquist limit ( Fig. 1.14 ). To avoid aliasing, a higher PRF should be used, although a lower PRF will enable a better estimation of the blood flow velocity—thus the lowest PRF possible without introducing aliasing should be used. Depending on the machine, the PRF adjustment is referred to as “scale,” “velocity range,” or “Nyquist velocity.” In addition, the baseline of the spectrogram should be shifted upwards in case of flow away from the transducer and downwards in case of flow towards the transducer, allowing for higher velocities to be measured. Finally, a lower or higher PRF needs to be applied depending on the depth of the measured flow: to “reach” flows at greater depths (further from the transducer) and carry the information back to the receiver, a lower PRF needs to be used, compared with flows closer to the transducer. In practice, this is particularly obvious when measuring pulmonary vein flow in the apical views: a dedicated “low PRF” button on the ultrasound system can be helpful to obtain an instantaneous shift in PRF and improve signal quality. In analogy, higher velocities can be sampled without aliasing at sample volume positions closer to the transducer. For advice on PW Doppler optimization, see Box 1.10 and Fig. 1.15 .

BOX 1.9

High PRF PW Doppler is also optional on some systems and can be recognized by the occurrence of several sample volumes along the Doppler beam. The measurement concept is based on the fact that the PW Doppler system knows exactly when to sample the echo signal (i.e., at the sample volume). As such, a new pulse can already be transmitted (to a more proximal/distal sample volume) before the echoes of the original transmit have been received without inducing artifacts. Thus the PRF (and Nyquist limit) can be increased by emitting one (or more) new pulses prior to receiving the signal of the first pulse from the expected depth. However, such construction of the spectrogram implies that the exact location of the origin of the signal along the Doppler beam cannot be known.

High Pulse Repetition Frequency Pulsed Wave Doppler

FIG. 1.14

The explanation of aliasing based the “wagon wheel” example, stemming from the wagon wheel illusion seen in old western motion pictures (an example from sampling theory): envision a rotating clock hand—in the top panel, it rotates at one revolution per minute. If one would “sample” the clock 4 times per minute (every 15 seconds) by shooting a picture, one could easily “capture” the motion of the clock, could comprehend that the direction of rotation is clockwise, and could perceive the rate of rotation. However, if the rotational speed were to be increased to two revolutions per minute, maintaining the sampling rate, one would “capture” only the hand at 12 o’clock and 6 o’clock, still being able to discern the rate of rotation, but not the direction (middle panel) . Ultimately, if the revolution velocity increased to three revolutions per minute (in the same direction), retaining the same sampling rate, the perceived rate of rotation would be one revolution per minute while the perceived direction would be counterclockwise (bottom panel) . In analogy to pulsed wave Doppler, at a certain sampling rate of the system, increasing velocities of blood flow cannot be assessed adequately, neither for their velocity, nor direction of blood flow.

From Solomon SD. Echocardiographic instrumentation and principles of Doppler echocardiography. In: Solomon SD, ed. Essential echocardiography—a practical handbook with DVD. Totowa, NJ, Humana Press; 2007:12.

BOX 1.10

  • Optimize beam alignment and gain, use the compress, reject and filter settings as for CW Doppler

  • Position the sample volume with particular caution: even slight changes can affect the measurements significantly ( Fig. 1.15 )

  • Shift the baseline upwards or downwards to use the entire display for either forward or backward flow (useful in unidirectional flows)

  • Optimize the PRF: use as high as possible to detect high velocities, avoiding aliasing

  • Use low PRF for flows distant from the transducer

  • Use high PRF with caution if the origin of flow is relevant

CW, Continuous wave, PRF, pulse repetition frequency.

Pulsed Wave Doppler Optimization Points

FIG. 1.15

The effect of sample volume position on the mitral inflow pattern.

For the assessment of left ventricular diastolic function, the pulsed wave Doppler sample volume should be positioned at the tips of the mitral valve leaflets, which would correspond to the mitral inflow pattern shown under the letter “E.” As can be observed, even small deviations from this position can dramatically impact the pattern as well as the obtained measurements, thus rendering an inaccurate assessment of diastolic function. LA, Left atrium; LV, left ventricle; MV, mitral valve; RA, right atrium; RV, right ventricle.

Modified from Appleton CP, Jensen JL, Hatle LK, Oh JK. Doppler evaluation of left and right ventricular diastolic function: a technical guide for obtaining optimal flow velocity recordings. J Am Soc Echocardiogr. 1997;10(3):271-292, with permission.

Color Flow Doppler

Color Doppler processing is based on PW Doppler imaging technology; however, in color flow Doppler the time shift between subsequent measurements is determined at multiple sample volumes along multiple scan lines. The calculated velocities are linked to a preset color scheme by means of a specific color map (displayed on the ultrasound image, Fig. 1.16 ), according to which the direction of flow and its velocity amplitudes can be determined. By convention, flow away from the transducer is colored in blue, whereas flow towards the transducer is coded in red. The color flow Doppler data are displayed superimposed on a 2D or M-mode image, allowing for visualization of flow patterns with additional information on the spatial location of the flow, nature of the flow (turbulence, direction of flow), geometry of potential connections between the heart chambers or great vessels, etc. Due to the same basic principles of PW Doppler, color flow Doppler is also subject to aliasing, whereas a high variance of velocity in a particular pixel is mostly displayed as shades of green, which is indicative of turbulent flow. Similar to PW Doppler, the appearance of aliasing can be reduced by increasing the PRF (however, PRF is coupled to velocity resolution) or by reducing the transmission frequency (rarely performed). The generation of a color flow Doppler image requires more “computing” time, and, to retain an acceptable temporal resolution, it is suggested that the region of color flow imaging (i.e., the color box) is kept to the minimal size required. For advice on color flow Doppler optimization, see Box 1.11 .

FIG. 1.16

Color flow Doppler imaging.

Color flow Doppler is superimposed on the two-dimensional image. By convention, blood flow with mean velocities traveling toward the transducer is encoded in red, and mean velocities moving away from the transducer are color-coded in blue. Similar to other forms of PW Doppler, high velocities and turbulent flow are subject to aliasing, which is in color flow Doppler depicted as a multicolored mosaic pattern (typically green and yellow). The color-velocity scale illustrates incremental velocities in both directions from the baseline, such that higher velocities appear in increasingly lighter hues. A4C, Apical four-chamber; BA RT, blue away – red toward; LA, left atrium; LV, left ventricle; RA, right atrium; RV, right ventricle.

Courtesy of Bernard E. Bulwer, MD, FASE; Modified from Solomon SD, Wu J, Gillam L, Bulwer B. Echocardiography. In: Mann DL, Zipes DP, Libby P, Bonow RO, Braunwald E, eds. Braunwald’s heart disease: a textbook of cardiovascular medicine. 10th ed. Philadelphia: Elsevier; 2015:183.

BOX 1.11

  • Optimize the size of the color box to the smallest necessary size

  • Optimize gain settings: start with overemphasized gain such that background noise is detectable, reduce until disappearance of background noise

  • Optimize the Nyquist scale according to the measured velocities: with high velocities, chose a high Nyquist limit (e.g., mitral regurgitation), and a low Nyquist limit when measuring low velocities (e.g., pulmonary vein flow)

Color Flow Doppler Optimization Points

Doppler Echocardiography in the Assessment of Hemodynamics

Doppler echocardiography is predominantly used for the assessment of velocities of blood flow within the heart and great vessels, which are determined by the driving pressure gradients between these structures (i.e., across heart valves). Analogously, the measured velocities of blood flow across a certain valve can be used in the assessment of pressure gradients between the relevant chambers: based on conservation of energy, the Bernoulli equation defines the relation between pressures and velocities for fluids in chambers separated by an orifice:

<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='P1−P2=12ρ(V22−V12)+ρ∫12dvdtds→+R(v→)ConnectiveAccelerationFlowAccelerationViscousFriction’>P1P2=12ρ(V22V21)+ρ12dvdtds+R(v)ConnectiveAccelerationFlowAccelerationViscousFrictionP1−P2=12ρ(V22−V12)+ρ∫12dvdtds→+R(v→)ConnectiveAccelerationFlowAccelerationViscousFriction
P 1 − P 2 = 1 2 ρ ( V 2 2 − V 1 2 ) + ρ ∫ 1 2 d v d t d s → + R ( v → ) Connective Acceleration Flow Acceleration Viscous Friction

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Sep 15, 2018 | Posted by in CARDIOLOGY | Comments Off on Physical Principles of Ultrasound and Generation of Images

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