Physical Principles of Ultrasound and Generation of Images

Introduction

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 ).

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 ).

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).

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 .

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).

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

Beam Width

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.

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 Temporal and Spatial Resolution

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.

BOX 1.6

Image Optimization General Points

• 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

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.

BOX 1.7

Beam Forming

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.