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Home , Sound, Ultrasound

1

Physics of

J. Anthony Seibert

Imaging systems using ultrasound have attained a large contraction of the crystal surface by an external power presence as point-of-care (PoC) devices across many source introduces into the medium as a series of clinical domains over the past 10 years. The success compressions and rarefactions, traveling as a front of ultrasound for this purpose is attributed to several in the direction of travel, known as a , characteristics, including the low cost and portability as shown in Fig. 1.1. of ultrasound devices, the nonionizing nature of ultra- , and the ability to produce real-time , , Speed images of the acoustic properties of the tissues and tis- The wavelength (λ) is the distance between any two sue structures in the body to deliver timely patient care, repeating points on the wave (a cycle), typically mea- among many positive attributes. An understanding of sured in millimeters (mm). Thefrequency (f) is the num- the basic of ultrasound, in addition to hands-on ber of times the wave repeats per second (s), also defined training, practice, and development of experience are of in (Hz), where 1 Hz = 1 cycle/s. Frequency identi- great importance in its effective and safe use. This chap- fies the category of sound: less than 15 Hz is , ter describes the characteristics, properties, and produc- 15 Hz to 20,000 Hz (20 kHz) is audible sound, and tion of ultrasound; interaction with tissues, acquisition, above 20 kHz is ultrasound. typi- processing, and display of the ultrasound image; the cally uses in the million cycles/s megahertz instrumentation; achievable measurements, including (MHz) range, from 1 to 15 MHz, with some specialized blood ; and safety issues. ultrasound applications beyond 50 MHz. The period is the time duration of one wave cycle and is equal to 1/f. CHARACTERISTICS OF SOUND The , c, is the distance traveled per unit time through a medium and is equal to the wavelength Sound is mechanical energy that propagates through a (distance) divided by the period (time). As frequency is continuous, elastic medium by the compression (high inversely equal to the period, the product of wavelength ) and rarefaction (low pressure) of particles and frequency is equal to the speed of sound, c = λf. The that comprise it. Compression is caused by a mechani- speed of sound varies substantially for different mate- cal inward by an external force, such as an rials, based on compressibility, stiffness, and density expanding and contracting transducer crystal composed characteristics of the medium. For instance, air is highly of multiple elements in contact with the medium. During compressible and of low density, with a relatively low transducer surface expansion, an increase in the local speed of sound; is stiff and dense, with a relatively pressure at contact occurs. Contraction of the crystal very high speed of sound; and soft tissues have com- follows, causing a decrease in pressure. The mechanical pressibility and density characteristics with intermedi- energy imparted at the surface is transferred to adjacent ate speeds, as listed in Table 1.1. Of importance are the particles of the medium, which travels at the speed of average speeds for “soft tissue” (1540 m/s), fatty tissue sound through the medium. Continuous expansion and (1450 m/s), and air (330 m/s). To relate time with depth

2 CHAPTER 1 Physics of Ultrasound 3

Contraction Expansion Compression Wavelength, λ (mm)

1 cycle Pressure Transducer Rarefaction Fig. 1.1 Mechanical energy is generated from an expanding and contracting crystal in contact with a medium, introducing high-pressure (compression) and low-pressure (rarefaction) variations of the constituent particles that transfer the energy to adjacent particles as a longitudinal wave.

TABLE 1.1 Density, Speed of Sound, In a homogeneous medium, ultrasound frequency and for Tissues and and speed of sound are constant. When higher ultra- Materials Relevant to Medical Ultrasound sound frequency is selected, the wavelength becomes shorter, giving better detail and spatial resolution along Material Density (kg/m3) c (m/s) Z (rayls)* the direction of propagation. For instance, in soft tis- 2 Air 1.2 330 3.96 × 10 sue with a speed of 1540 m/s, a 5-MHz frequency has a 3 Lung 300 600 1.80 × 10 wavelength in tissue of λ = c / f ; 1540 m/s ÷ 5,000,000/s = Fat 924 1450 1.34 × 106 0.00031 m = 0.31 mm. A 10-MHz frequency has a wave- Water 1000 1480 1.48 × 106 length = 0.15 mm (Fig. 1.2). Although higher frequen- “Soft tissue” 1050 1540 1.62 × 106 cies provide better resolution, they are also more readily Kidney 1041 1565 1.63 × 106 attenuated, and depth penetration can be inadequate for Blood 1058 1560 1.65 × 106 certain examinations, such as for the and abdomen. 1061 1555 1.65 × 106 Muscle 1068 1600 1.71 × 106 The amount of ultrasound energy imparted to the 6 bone 1912 4080 7.8 × 10 medium is dependent on the pressure amplitude vari- 7 PZT 7500 4000 3.0 × 10 ations generated by the degree of transducer expan- *Acoustic impedance is the product of density and speed of sion and contraction, controlled by the transmit gain sound. The rayl is the named unit, with base units of kg/m2/s. applied to a transducer. Power is the amount of energy Acoustic impedance directly relates to the propagation charac- per unit time introduced into the medium, measured in teristics of ultrasound in a given medium and between media. milliwatts (mW). Intensity is the concentration of the power per unit area in the ultrasound beam, typically expressed in mW/cm2. used for creating images interactions in the patient, medical ultrasound devices are derived from ultrasound interactions in the tissues assume a speed of sound of 1540 m/s, despite slight dif- and the returning intensity of the produced echoes. ferences in actual speed for the various tissues encoun- Absolute intensity depends on the method of ultrasound tered. Changes in the speed of sound can affect how production and can result in heating or mechanical dis- ultrasound travels through the tissues and may result ruption of tissues, as discussed later in this chapter. in unexpected artifacts (see Chapter 2 on speed artifact and artifact). The product of the density and INTERACTIONS OF ULTRASOUND WITH speed of sound is known as the acoustic impedance. This TISSUES characteristic of the tissues is intrinsic in the generation of ultrasound echoes, which return to the transducer to Interactions of ultrasound are chiefly based on the acous- create the ultrasound image. More detail is in the next tic impedance of tissues and result in , refrac- section on ultrasound interactions. tion, , and of the ultrasound energy. 4 SECTION 1 Principle of Ultrasound

between two tissues that have a difference in acoustic impedance (Fig. 1.3A). The fraction of incident inten- sity Ii reflected back to the transducer(I r) is the intensity 2 MHz λ = 0.77 mm reflection coefficient,I R , calculated as 2 Ir Z2 ‐ Z1 RI = = Ii ( Z2 + Z1 ) The subscripts 1 and 2 represent tissues that are prox- λ = 0.31 mm 5 MHz imal and distal to the boundary. The intensity trans- mission coefficient, T , is defined as the fraction of the λ = 0.29 mm Fat I incident intensity that is transmitted across an inter- face, equal to TI = 1 – RI. For a fat–muscle interface, the intensity reflection and transmission coefficients are cal- = 0.15 mm culated as 10 MHz λ 2 Ir 1.71 − 1.34 RI, Fat → Muscle = = = 0.015 ; Ii 1.71 + 1.34 0 0.2 0.4 0.6 0.8 1.0 TI, Fat → Muscle = 1 − RI, Fat → Muscle = 0.985 Distance (mm) Fig. 1.2 Wavelength and frequency are inversely proportional, A high fraction of ultrasound intensity is transmit- determined by the speed of sound in the medium. For soft tissue, with an average speed of 1540 m/s, the wavelength is directly ted at tissue boundaries for tissues that have similar calculated as the speed of sound divided by the frequency in acoustic impedance. For tissues with large differences cycles/s. As frequency remains constant in different media, wave- of acoustic impedance, such as air-to-tissue or tissue- length must change. Shown is the wavelength for a 5-MHz fre- to-bone boundaries, most of the intensity is reflected, quency in fat (red line), with a speed of sound of 1450 m/s. with no further propagation of the ultrasound pulse. At a muscle–air interface, nearly 100% of incident intensity Acoustic Impedance is reflected, making anatomy unobservable beyond an Acoustic impedance, Z, is a measure of tissue stiffness air-filled cavity. Acoustic coupling gel placed between and flexibility, equal to the product of the density and the transducer and the patient’s skin is a critical part of speed of sound: Z = ρc, where ρ is the density in kg/m3 the standard ultrasound imaging procedure to ensure and c is the speed of sound in m/s, with the combined good transducer coupling and to eliminate air pockets units given the name rayl, where 1 rayl is equal to 1 kg/ that would reflect the ultrasound. For imaging beyond (m2s). Air, soft tissues, and bone represent the typical lung structures, avoidance of the ribs and presence of low, medium, and high ranges of acoustic impedance a “tissue conduit” are necessary to achieve propagation values encountered in the patient, as listed in Table 1.1. of the pulse. When an ultrasound pulse is incident on a The efficiency of transfer from one tissue tissue boundary at an angle other than 90 degrees (nor- to another is largely based on the differences in acoustic mal incidence), the reflected ultrasound is directed impedance—if impedances are similar, a large fraction away from the transducer and does not generate a . of the incident intensity at the boundary interface will be transmitted, and if the impedances are largely dif- Refraction ferent, most will be reflected. In most soft tissues, these Refraction is a change in direction of the transmitted ultra- differences are typically small, allowing for ultrasound sound pulse when the incident pulse is not perpendicular travel to large depths in the patient. to the tissue boundary and the speeds of sound in the two tissues are different. The frequency does not change, but Reflection the ultrasound wavelength changes at the boundary due to Reflection occurs when a beam is traveling perpendicu- the speed change, resulting in a redirection of the transmit- lar (at normal incidence or 90 degrees) to the boundary ted pulse, as shown in Fig. 1.3B. The angle of redirection CHAPTER 1 Physics of Ultrasound 5

A Normal incidence B Nonnormal incidence

θi=θr

θ θ Reflection Reflection i r (echo return to (echo away from transducer) transducer) z1 = p1c1 Boundary z2 = p2c2 Direction Refraction c >c unchanged 2 1 Transmission θt c2

is dependent on the change in wavelength; no refraction Boundary interactions occurs when the speed of sound is the same in the two tis- sues or with perpendicular incidence. Because a straight- line propagation of the ultrasound pulse is assumed, misplacement of anatomy can result when refraction occurs. See Chapter 2 on ultrasound artifacts for further discussion and manifestation of this type of artifact.

Scattering Specular (smooth) Nonspecular Scattering arises from objects and interfaces within a tis- reflection (diffuse) reflection sue that are about the size of the ultrasound wavelength Fig. 1.4 Specular and nonspecular reflection boundaries are or smaller. At low frequencies (1–5 MHz), chiefly dependent on wavelength of the ultrasound beam are relatively large, and tissue boundaries appear smooth and therefore frequency. Higher-frequency operation gener- ates shorter wavelengths that are about the same size as the or specular (mirror-like). A specular reflector is a smooth boundary variations, leading to nonspecular interactions and boundary between two media. At higher frequencies diffuse reflection patterns. (5–15 MHz), wavelengths are smaller, and boundaries become less smooth, causing echo reflection in many another result in corresponding brightness changes on directions. A nonspecular reflector represents a bound- the ultrasound display. In general, the echo signal ampli- ary that presents many different angles to the ultra- tude from a tissue or material depends on the number sound beam, and returning echoes have significantly of scatterers per unit volume, the acoustic impedance less intensity (Fig. 1.4). Many organs can be identified differences at interfaces, the sizes of the scatterers, and by a defined “signature” caused by intrinsic structures the ultrasound frequency. Higher scatter amplitude that produce variations in the returning scatter intensity. tissues are called hyperechoic, and lower scatter ampli- Scatter amplitude differences from one tissue region to tude tissues are called hypoechoic relative to the average 6 SECTION 1 Principle of Ultrasound background signal. Scattered echo signals are more prev- Ultrasound µ ≅ 0.5 dB/cm per MHz alent relative to specular echo signals when using higher 1 ultrasound frequencies. 0.9 0.8 Absorption and Attenuation 0.7 Attenuation is the loss of intensity with distance trav- 0.6 eled, caused by scattering and absorption of the incident 0.5 beam. Scattering has a strong dependence on increasing 0.4

ultrasound frequency. Absorption occurs by transferring Relative intensity 0.3 2 MHz energy to the tissues that result in heating or mechanical 0.2 5 MHz 0.1 10 disruption of the tissue structure. The combined effects MHz of scattering and absorption result in exponential atten- 0 0510 15 20 uation of ultrasound intensity with distance travelled as Depth of tissue (cm) a function of increasing frequency. When expressed in Distance traveled = 2 x depth (dB), a logarithmic measure of intensity, atten- Fig. 1.5 Attenuation and relative intensity of ultrasound remain- uation in dB/cm linearly increases with ultrasound fre- ing as a function of depth for 2-, 5-, and 10-MHz beams. quency. An approximate rule of thumb for ultrasound attenuation average in soft tissue is 0.5 dB/cm times the TABLE 1.2 μ (dB/ frequency in MHz. Compared with a 1-MHz beam, a cm-MHz) for Tissues* 2-MHz beam will have approximately twice the attenu- ation, a 5-MHz beam will have five times the attenuation, Tissue μ (1 MHz) and a 10-MHz beam will have ten times the attenuation Air 1.64 per unit distance traveled. Therefore higher-frequency Blood 0.2 ultrasound beams have a rapidly diminishing penetration Bone 7–10 depth (Fig. 1.5), so careful selection of the transducer fre- 0.6 quency must be made in the context of the imaging depth Cardiac 0.52 needed. The loss of ultrasound intensity in decibels can 1.57 be determined empirically for different tissues by mea- Fat 0.48 suring as a function of distance travelled in centimeters Liver 0.5 (cm) and is the attenuation coefficient, , expressed in μ Muscle 1.09 dB/cm. For a given ultrasound frequency, tissues and 4.7 fluids have widely varying attenuation coefficients chiefly resulting from structural and density differences, as indi- Soft tissue (average) 0.54 cated in Table 1.2 for a 1-MHz ultrasound beam. Water 0.0022 *For higher-frequency operation, multiply the attenuation coef- THE ULTRASOUND SYSTEM ficient by the frequency in MHz. PoC ultrasound systems are available from many ven- dors and come with different features and options, Ultrasound Transducer Operation and Beam which depend on acquisition capabilities, number of Properties transducer probes, durability, software functionality, size Ultrasound is produced and detected with a transducer and weight, battery longevity for handheld units, power array, composed of hundreds of ceramic elements with requirements, and other considerations. Although all electromechanical (piezoelectric) properties. Ultrasound ultrasound systems have unique instrumentation, soft- transducers for applications employ a ware, and user interfaces, common components include synthetic piezoelectric ceramic, lead–zirconate–titanate transducer probes, pulser, beam former, scan converter, (PZT), with a crystal structure that generates a sur- processor, display, and user interface for instrumenta- face charge of either negative or positive polarity when tion adjustments and controls. its thickness is expanded under negative pressure or CHAPTER 1 Physics of Ultrasound 7

Near field Far field + V - - V + Beam Electrode Applied diameter wires on voltage surfaces of contracts Expansion Multielement Focal zone transducer or expands transducer thickness thickness excitation Fig. 1.7 The ultrasound beam from a surface has a converging section known as the near field, a diverging section known as the far field, and a focal zone with a minimum beam diameter. In this situation, each transducer element is activated Width simultaneously. The perspective is looking down on the top Equilibrium edge of the transducer multielement array surface. Height

the near field with a minimum beam diameter at the Thickness focal zone depth and, with further travel, diverging into the far field, as shown inFig. 1.7. The focal zone depth Contraction can be adjusted by introducing brief timing delays of the Single-element Multielement individual element arrays, as discussed later. ABPZT transducer PZT transducers Ultrasound systems have transducer assemblies of Fig. 1.6 (A) A single-element transducer is made of a synthetic many shapes and sizes composed of an array of PZT lead–zirconate–titanate (PZT ) crystal with an internal electrical elements (typically 64–512) categorized into linear and dipole molecular structure that expands and contracts in thick- phased array operation. Common to all transducers are ness mode under a voltage applied to the surfaces via attached a protective housing with a shield to prevent electrical electrodes. (B) Grouped transducer elements create a surface interference, an acoustic damping block to shorten the to expand and contract in the thickness direction of the trans- ducer crystal to introduce mechanical energy into tissues adja- of the piezoelectric elements, a matching cent to the surface. layer to improve the efficiency of ultrasound wave trans- mission to the skin by reducing acoustic impedance compressed under positive pressure due to the internal differences, and a material to absorb backward-directed molecular crystal polarity. Surface electrodes and wires ultrasound energy (Fig. 1.8A). are attached to each element and multiplexed to a trans- Because the transducer array cannot simultaneously mit/receive sensor that measures the surface charge generate and detect ultrasound, a short ultrasound pulse variation when sensing any thickness variations. These is created in the transmit mode with a large applied volt- same wires and attached electrodes generate mechanical age of 100 to 150 volts (V) with a duration equal to about expansion or contraction by applying a voltage of known a millionth of a second (1 μs), causing contraction of the polarity and amplitude from an external power source, transducer elements. Vibration of the crystal occurs at a as illustrated in Fig. 1.6A. By varying the applied voltage natural frequency dependent on its element polarity at a known frequency, the crystal expands and thickness. A short ultrasound pulse is created by the contracts, imparting mechanical energy into the adja- attached damping block, as shown in Fig. 1.8B, which cent medium at the same frequency. Thus each trans- introduces a wide band of higher and lower frequencies, ducer element functions either in an excitation mode to so that most transducers can operate at multiple trans- transmit ultrasound energy or in a reception mode to mit and receive frequencies. Immediately after exci- receive ultrasound energy. In practice, a subset of ele- tation, the transducer elements are switched to receive ments in a linear transducer array, or all elements in a mode to detect the returning ultrasound echoes gen- phased transducer array, are activated, as shown in Fig. erated by reflections from tissue boundaries. A receive 1.6B, to create an ultrasound beam. multiplexer sensor in the ultrasound unit records the The surface vibration and interaction among the indi- voltage signals as a function of time for further pro- vidual elements create a collimated beam converging in cessing. Once all echoes are received from the transmit 8 SECTION 1 Principle of Ultrasound

Transducer wiring

Housing

Absorber Damping block Side view Transducer array Matching layer

Edge view Composite structure A Ultrasound beam direction

Ultrasound spatial pulse length: determined by amount of damping

B Heavy Moderate Light Fig. 1.8 (A) The transducer is composed of a housing, electrical insulation, and a composite of active element layers, including the PZT crystal, damping block and absorbing material on the backside, and a matching layer on the front side of the multielement array. (B) The ultrasound spatial pulse length is based on the damping material causing a ring-down of the element vibration. For imaging, a pulse of two to three cycles is typical, with a broad-frequency bandwidth, whereas for Doppler transducer elements, less damping provides a nar- row-frequency bandwidth. pulse, the process repeats along a slightly different direc- are received from the greatest depths, the next pulse is tion to ultimately cover the volume of interest defined by created by activating another subelement group that is the field of view (FOV). incrementally shifted along the transducer array, and For a given transducer, multifrequency operation the process repeats on the order of thousands of times allows flexibility of the sonographer to interactively per second to generate a rectangular image format with choose the appropriate frequency to emphasize the real-time video image capture. Linear arrays are typi- spatial resolution or depth of penetration based on the cally composed of 256 to 512 transducer elements, are examination, as shown in Fig. 1.9. of smaller form factor, and generally operate at higher frequency ranges (5–15 MHz). Because of the higher Transducer Arrays operating frequency and limited FOV, these transducers Three basic transducer types for PoC ultrasound are suitable for imaging superficial structures such as the include linear, curvilinear, and phased arrays, as shown eyes, joints, muscles, and proximal blood vessels and for in Fig. 1.10. Linear array transducers activate a sub- performing ultrasound-guided procedures. Curvilinear set of elements, producing a single transmit beam at array transducers have 256 to 512 elements in a convex one location, and then listen for echoes in the receive geometry, with a subset of elements activated sequen- mode. Within a fraction of a second, when all echoes tially, like the linear array, producing a trapezoidal CHAPTER 1 Physics of Ultrasound 9

General Penetration (Center frequency) Resolution

Selective transducer bandwidth Overall Response transducer bandwidth

45678910 Frequency (MHz) Fig. 1.9 Multifrequency transducer transmit and receive response to operational frequency bandwidths allows the operator to select an appropriate transmit and receive frequency, depending on the type of exam- ination, type of transducer, transducer bandwidth range, and need for penetration depth (selecting a lower frequency) or spatial resolution (selecting a higher frequency). The transducer response shown has a select- able frequency range of 4 to 10 MHz.

Linear Curvilinear Phased Fig. 1.10 Linear and curvilinear array transducers activate a subgroup of transducer elements, whereas phased array transducers activate all elements in the array to create a single ultrasound beam in the tissues. Rectangular, trapezoid, and sector beam areas are created, respectively. Location of the beam for linear and curvilinear operation is determined by the active element subgroup across the array, and for the phased array operation by electronic steering of the ultrasound beam. The beam sequentially moves across the field of view in one direction to produce one image frame and then repeats for real-time acquisition. This figure illus- trates only a fraction of the actual number of lines acquired during acquisition. image format with increased FOV at both proximal and at a predetermined depth (or depths), which is oper- distal depths. These transducers are ideal for imaging ator selectable. After excitation, beam direction, and intraabdominal organs such as the liver, spleen, kidneys, beam formation, the phased array is placed in receive and bladder. Lower frequencies (2–5 MHz) are used for mode to listen for echoes. The sequence then repeats depth visualization, but spatial resolution can be lim- along a slightly different beam direction, ultimately ited as a result. Phased array transducers with 64, 128, creating a sector-shaped image format at a frame rate and up to 256 elements use all transducer elements in dependent on the number of lines, depth, and FOV. In the formation of the ultrasound beam. Beam direction the receive mode, returning echoes are detected by all is determined by relatively large incremental delays active transducer elements used in the formation of the for sequential excitation of elements from one side of beam. Phased array transducers typically operate at low the array to the other, effectively steering the beam in frequencies (1–5 MHz), have flexible selection of a nar- a perpendicular direction to the excitation pattern. row to wide FOV by the operator, and provide efficient Along a given direction, small incremental excitation two-dimensional (2D) imaging for heart and thoracic delays in a concave pattern focus the beam diameter imaging requiring small acoustic windows. 10 SECTION 1 Principle of Ultrasound

Intracavitary array probes (not shown) have a con- vex, small footprint and operate like a linear transducer. Because of the proximity of the region to be imaged, a high-frequency range is typically used (5–8 MHz), with a wide FOV and limited range but excellent image Element resolution. These transducers are used in transvaginal, activation patterns ­transrectal, and intraoral applications. Transmit beam focusing at selectable focal distances is achieved by specific timing delays among the active transducer elements, each with a known concave exci- tation profile, as shown in Fig. 1.11. A focal zone close to the transducer surface is produced by initially firing the outer transducer elements in the active array and Selectable depth incrementally firing the inner elements to the center lateral element with slightly longer delays using a concave exci- focusing tation pattern. A more distant focal zone is achieved by reducing the delay time differences among the trans- ducer elements with a shallow concave excitation pat- tern, resulting in beam convergence at a greater depth. The beam former in the ultrasound unit controls the Fig. 1.11 Focal zones can be produced at various depths in tissues by controlling the excitation timing of the transducers excitation patterns, with the focal zone depth select- in a group. Shown are three different focal zones produced by able by the operator. On some advanced ultrasound the system “beam former” to activate the outer elements first, systems, multiple transmit focal zones can be selected followed by successive activation of the inner elements to pro- by repeating the excitation pattern for each focal zone duce a concave excitation of the individual ultrasound pulses. and melding the information from each focal zone into a This is achievable for the element subgroups in a linear/curvi- linear array, as well as for all the elements in a phased array composite image. This does reduce the acquisition frame transducer. rate by a factor equal to the number of focal zones set. Spatial Resolution In ultrasound, the visibility of image detail is determined by three separate factors: (1) in-plane resolution along the direction of beam travel, known as axial resolution; (2) in-plane resolution perpendicular to the direction of beam travel, known as lateral resolution; and (3) out-of- plane resolution perpendicular to the in-plane resolution, Lateral known as elevational or slice-thickness resolution. These constituents of spatial resolution are illustrated in Fig. 1.12. Elevational Axial resolution represents the ability to distinctly separate closely spaced objects in the direction of the ultrasound beam. Returning echoes from adjacent Axial boundaries to be resolved as separate are dependent on the spatial pulse length (SPL), which is the average wavelength times the number of cycles in the pulse. Because distance travelled for a pulse-echo interacting Fig. 1.12 The three components of spatial resolution in the between two adjacent reflectors is twice the separation ultrasound image are shown. Axial, along the beam direction, is constant with depth. Lateral, in-plane and perpendicular to distance, echoes to be recorded as separate signals need the beam direction, varies substantially with depth. Elevational, a spacing just greater than one-half SPL. For example, a perpendicular to the lateral and axial directions, is the slice 5-MHz frequency pulse has a wavelength of 0.31 mm in thickness and varies with depth.