Characteristic acoustic parameters of selected substances and tissues at frequency f0 = 1 MHz.
One of the physical phenomena used in medical diagnostics and therapy is ultrasound. We know, for example, ultrasonography, ultrasonic lithotripsy, ultrasonic massages. One of the basic communication channels of humans is sound. The human body is also affected by infrasound. To understand the basic principles of these phenomena, we explain here the origin, properties, and detection of mechanical waves in a matter.
Every continuous medium consists of individual particles (atoms and molecules) that interact with each other. If we do not perceive the microscopic structure, we only see the resulting continuous substance—a
Besides, there act the forces connected with losses of mechanical energy in substances, related to plastic deformation, irradiation, heating, etc. These forces are non-conservative and cause the damping of mechanical waves.
1.1 Propagation of longitudinal deformation in an elastic material
Consider a semi-infinite homogeneous elastic medium with a planar surface. On this surface, we cause mechanical deformation by force with area density
In the medium, we define an elementary cylinder with an axis perpendicular to the surface, the cross-section
Due to the propagation of the deformation of the medium, the bases of the elements move in the longitudinal direction
The motion of an element is described by the equation of mechanical motion
where is the acceleration of the element.
The compressive forces
The resistive force usually has the character of a viscous resistance, which is characterised by a linear dependence on the speed of movement of the element. The bulk density of this force is
Where is the speed of movement of the element and
We express slight differences Δ
The compressive forces
and represents the tensile (mechanical) stress in the deformed medium caused by the propagation of the mechanical deformation.
The motion of an element is described by the equation of mechanical motion (1), which thus has the form
The dynamics of motion of the elements of a continuous elastic medium being described by this partial differential equation.
1.1.1 Longitudinal mechanical waves in a lossless elastic material
The space–time distribution of oscillations of particles (volume elements) of the medium is obtained by solving the differential Eq. (5) under specific initial and boundary conditions.
Let us first consider a simple case of oscillation propagation in a medium with negligible losses (ideal elastic medium). Eq. (5) is simplified by omitting the mean term for
The solution of this equation is a function
which we can be convinced by direct substitution into the Eq. (6).
The shape of the function f is shown in Figure 2.
The elements of the medium oscillate around their equilibrium positions and their movement is described by the displacement
Such a wave both transmits the energy associated with the oscillations of the elements of the substance and transmits information. If we enter a certain disturbance (source signal) at one end of the rod with length
If the medium is solid, the elastic constant
Example 1 Propagation of longitudinal mechanical wave in steel.
Steel, as well as other flexible solids, allows the propagation of longitudinal mechanical waves, for example, ultrasound. For modulus of elasticity value
In other solids, the speed of longitudinal ultrasound is usually lower, around (3 ÷ 5) × 103 m⋅s−1.
1.1.2 Transverse mechanical waves in an elastic medium
In the previous part, we solved an example of the propagation of
The deformation of the medium associated with the propagating wave causes shear stress in the elastic environment
If the wave is undamped or weakly damped, the transverse wave propagates in the medium at a speed
Example 2 Propagation of transverse mechanical wave in steel.
Shear modulus of steel is
Because applies to solid materials
As is clear from the physical origin of the wave, the transverse wave
1.1.3 Propagation of mechanical waves along an elastic string
Another example of a common cause of wave motion is the propagation of transverse excitation along an elastic flexible string.
A string element with a mass d
and in the transverse direction
For very small deviations, it is valid: cos
From the first equation we get
The fibre is stretched with the same force
For small angles
If we express the mass of the element d
where is the speed of propagation of the transverse wave along the string.
The speed of the wave can be changed by changing the line mass density
1.1.4 Mechanical waves in gases
Compression wave propagation takes place in gases. If the pressure increases at a certain point, the change of the pressure gradually propagates through the gas. As the pressure change process is very fast, the adiabatic process is applied (without heat exchange)
If the volume changes according to Figure 1, we get
Substituting into Eq. (12) we have
and the pressure change is
The gas elasticity constant for adiabatic waves is then
Force on the element is
The equation of motion has the form
It is the wave equation of a wave with a speed
Example 3 Sound propagation in the air.
The sound propagates well in the air and thanks to this fact we can communicate and perceive sounds from the surroundings. Under normal conditions (pressure
As we can see from the theoretical result, the speed of sound in the air does not depend on the air pressure, but only on the thermodynamic temperature
1.1.5 Mechanical waves in liquids
Liquids represent a fluid medium in which there is zero shear elasticity. Therefore, liquids
The speed of propagation of a mechanical wave in a liquid is .
For water with values
As the soft tissues of the human body have high water content (up to 70%), their mechanical properties are close to water. In such tissues, only ultrasound with longitudinal polarisation propagates and the propagation speed does not differ very much from the value for water, see Table 1.
|Material||Density kg⋅m−3||Phase velocity m⋅s−1||Specific attenuation dB/(m⋅MHz)||Acoustic resistance ×106 kg⋅m4⋅s−1|
|Air at 20°C||340||1.2||—||0.0004|
1.1.6 Wave polarisation
As shown in the previous section, the waves propagate in space at a speed
Table 2 shows some typical values of wave propagation speed with different polarizations in different materials. In fact, the values have a considerable variance for different conditions—the values given are only indicative for creating a basic representation. In fluids (liquids and gases), mechanical waves with transverse polarisation cannot propagate, and in a vacuum, the mechanical wave cannot propagate at all.
|Material||Speed of wave |
|Air (100 kPa, 32°F)||340||—|
|Seismic Rayleigh waves||—||—||3000|
|Tsunami waves on the open seas||—||—||30|
|Guitar string—chamber A||—||500|
1.2 Mechanical behaviour of mechanical waves
1.2.1 Particle displacement and particle velocity
As shown, the elements (particles) of the medium oscillate around their equilibrium positions. The first of the quantities describing their motion is the particle displacement
The movement of medium elements is described by
The particle velocity
1.2.2 Acoustic pressure and acoustic power
The waves are accompanied by local deformation of the elastic medium. As shown in the analysis of the propagation of individual types of waves, for example, Eqs. (4), (10), or (13), mechanical stress or pressure, are directly proportional to the gradient of the particle displacement and their magnitude can be expressed by a quantity of
As a result of this acoustic pressure, the strength limit of the material may be exceeded and thus the material is destroyed, or cavitation (formation of vacuum bubbles) may occur in the liquid. These phenomena are used in ultrasonic cleaning of objects, for example, fine mechanics, surgical instruments, in which the particles of impurities are separated from the cleaned body by the action of ultrasound. The action of intense ultrasound also achieves the spraying of liquids, which use, for example, ultrasonic humidifiers. In technical practice, ultrasonic drills, and cutters suitable for working especially of hard and brittle materials such as ceramics, glass, and porcelain, are used.
In medicine, intensive ultrasound is used in
The device shown in Figure 5 is used for extracorporeal lithotripsy (ultrasound device is outside of the patient body). It also contains an X-ray positioning device, which precisely targets the location of the stone. Due to the very different acoustic impedance of the stone and the surrounding tissue, the ultrasonic pulse will not cause tissue damage. The main advantage is that the procedure is
Intracorporal lithotripsy is also currently used. In Figure 6 is a device that allows lithotripsy by ultrasonic or pneumatic pulse. The thin metallic probe transmitting the ultrasound is introduced through a body orifice (urinary) or a small body cut, tightly to the stone, and large and hard stones are disrupted by intense pressure or pneumatic shock waves with the energy of up to 100 mJ. An ultrasonic probe with a pulse power of up to 150 W and a frequency of approximately 25 kHz crashes the stone and removes soft stones and residues after crushing. This method is very effective, relatively patient-friendly, and requires only minimal surgery to create an incision for the probe.
Another application is in ophthalmic surgery in the process of phacoemulsification. Ultrasound converts the eye lens into an emulsion, which is then aspirated. After this removal of the lens, a new artificial lens is implemented.
Cavitation using intensive ultrasound is also used by cavitation ultrasonic liposuction. Ultrasound disrupts the membranes of fat cells, whereby the liquid contents of the cells enter the intercellular space and from there are washed away by the lymphatic system. It serves for the non-invasive removal of local fat and cellulite and serves to strengthen the subcutaneous muscles.
The exertion of acoustic pressure on moving particles of the medium represents mechanical power, which expresses the
This power is supplied to the mechanical wave by a wave source, and the power propagates in the medium along with the wave. In this way, the mechanical wave can be used to transfer energy, for example, by ultrasonic heating of the tissue. In medical ultrasound applications, for example, in ultrasonic sonography, care must be taken to limit the power used to avoid burns, especially on the surface layers of the body. Mean value of acoustic power
In biomedicine, the power of a focused ultrasound beam is used to destroy a target tissue in the focal point (usually a tumour) by ‘burning’ it. Ultrasonic ablation controlled by magnetic resonance is used, for example, for non-invasive removal of uterine fibroids. Magnetic resonance imaging serves to accurately target the site of the tumour into which the ultrasound beam is focused.
Ultrasound with a frequency of about 20 kHz uses an
Ultrasound therapy is used, for example, in tissue regeneration, promoting the formation of new cells, stimulating blood flow to the tissue, etc. It is used in the treatment of joints, supports the dissolution of fibroblasts, the formation of collagen, reduces tension in the tissue, has an analgesic and anti-inflammatory effect, and positively stimulates wound healing after injuries. It is also used in dermatology and cosmetics.
1.3 Plane harmonic mechanical wave
The function f (
1.3.1 Harmonic mechanical waves
Harmonic waves are generated by a source of harmonic oscillations on the surface of the transmission medium. We express the particle displacement on the surface (
The symbolic-complex method is preferably used to solve time-harmonically dependent functions. In linear systems, all steady-state harmonic response functions have the same time dependence.
The differential Eq. (5), including the damping element, takes the form
We got a regular differential equation that has an exponential solution
From relation [Eq. (19)] we determine the components of the complex wavenumber
For low-loss medium is valid , or for angular frequency ,
we will use simplification for
Using the components of a complex wavenumber, we get a complex deflection form, which is a linear combination of both solutions, (Eq. 18),
or real form of the equation
The first wave function describes an exponentially damped wave propagating in the
The real component of a complex wave number is the
which indicates the distance over which the amplitude of the particle displacement drops to 1/e ≈ 37% of the initial amplitude at the surface.
The harmonic component of the wave function is a periodic function with a period of 2π rad. The expression in parentheses is the phase of the wave,
For the temporal and spatial periods of the wave we have
A certain place of medium with a constant wave phase
The attenuation of ultrasound relates to various physical mechanisms as the intrinsic viscosity, dispersion on inhomogeneities, turbulent losses in gases, etc. The individual influences are frequency dependent, which is described by the frequency dependence of the attenuation coefficient
For air, the characteristic values are
Ultrasound attenuation is significant at the imaging of internal organs using sonography. Since the ultrasound beam reflected from a given organ is used for imaging, the level of the received signal depends on the depth of the organ under the body surface and thus of the total attenuation. The frequency of the ultrasound, therefore, is adopted to the possibilities of signal detection. Frequencies above 10 MHz are used for ophthalmic sonography. In the sonography of obese patients, a lower frequency of about 2 MHz is chosen to reduce the signal attenuation.
1.3.2 Particle displacement and particle velocity of a harmonic wave
Consider a wave with harmonic time dependence with a complex particle displacement
The direction of the phasor
Complex particle velocity is
The particle velocity is also described by a complex harmonic function and its phase shift relative to the particle displacement is π/2 rad.
1.3.3 Acoustic pressure and acoustic power of a harmonic wave
Following the relation [Eq. (14)], we express the acoustic pressure of a harmonic wave
Acoustic pressure is related to particle displacement and particle velocity
The ratio of acoustic pressure and particle velocity is one of the characteristic wave properties of the medium and is called
The complex acoustic impedance has a real component
For low loss or lossless medium, an approximate relationship is valid
Acoustic resistance and acoustic reactance are
The acoustic properties of selected substances and tissues are in Table 1.
The complex power density, see Eq. (15), is expressed by the relation
The real part represents an active power, the imaginary part a reactive power of the wave. The energy transfer by a wave is expressed by the mean value of the active component of the complex power. It is the
where , and are the effective values of particle velocity and acoustic pressure.
The acoustic wave intensity in the medium decreases exponentially after the formula
Attenuation is the result of the conversion of acoustic wave energy into heat. The volume density of the heat created by the attenuation of a wave passing the medium and causing its heating is
where [W⋅m−3] is the heat density at the surface (at the wave source).
The highest heat density is in the surface layer of the medium with a thickness of
Ultrasound is used in medicine to heat the surface layers of tissues. The thickness of the heated layer can be adjusted by changing the frequency of the ultrasound. Warming the tissue increases blood flow and supports regeneration processes, the breakdown of muscle metabolites, etc. Focused ultrasound is also used for hyperthermia and tissue ablation, for example, in the brain in the treatment of Parkinson’s disease. The mechanical pressure, induced by the ultrasonic wave, is also used in
1.4 Wave reflection and dispersion
In a homogeneous medium, the wave proceeds in one direction as a
1.4.1 Reflection of the wave from a planar interface
22.214.171.124 Laws of reflection and refraction
The reflection of waves from the raged interface is complicated. To explain the phenomenon, we use a simple case of wave reflection from the planar interface of two homogeneous media.
To display the propagation of the waves, we use a geometric representation of the rays (Figure 7). In a homogeneous medium, the rays are lines, in a non-homogeneous medium, the rays are curves.
The laws of reflection and refraction are satisfied with the reflection of waves from the interface and the transition through it. For the angle of incidence
126.96.36.199 Total reflection
If the wave passes from a medium with a lower speed to a medium with a higher speed, for example,
Example 4 Total sound reflection at the water/air interface.
The sound propagates in the air at a speed of approximately
188.8.131.52 Energy transfer of wave across the interface
To assess the intensity of the reflected wave and the wave penetrating the second medium, we will use the case of the perpendicular impact of the wave on the interface to simplify the calculations (Figure 8).
Consider the perpendicular incidence of a longitudinally polarised wave at the interface of two media with acoustic impedances
The total sound pressure at the left and right interfaces is the same
the particle velocity at the interface must be the same from the left and the right
According to Eq. (28), there is
Since the impedances are generally complex quantities, the corresponding wave quantities are also complex - phasors.
In the case of a wave incident perpendicularly to the interface, the intensities of the passing and reflected waves are
where , and are the intensities of the incident, reflected, and penetrating wave, respectively.
The result shows that the reflection of the wave from the interface occurs only in the case of a change in acoustic impedance. If the magnitude of the impedance ratio is several orders of magnitude, there is a practically total reflection (with the same or opposite phase).
The principle of wave reflection is used to investigate the structure of bodies. In nature, the reflection of sound is observed as an echo. The use of reflected ultrasound, for example, bats, flaw detectors, or sonar works on the principle of reflection from the inhomogeneous medium. In medicine, ultrasonography works on the principle of ultrasound reflection. Ultrasound is transmitted by a probe into the body, and the signal reflected from individual organs is received. Mirror reflection takes place from the planar interfaces. The flat surface of the reflecting body needs not to be perfectly smooth. If the surface is rough, and the irregularities are considerably smaller than the wavelength of the wave, the surface behaves as planar. If the irregularities are randomly distributed and larger than the wavelength, the waves are reflected in different directions concerning the surface plane. It is called
184.108.40.206 Transmission of wave through an acoustic layer
A significant case represents the transition of a wave through an acoustic layer. The wave propagation through a layer is proper for impedance matching, the formation of reflective or non-reflective layers, or acoustic resonators. The simple model illustrates (Figure 9), which utilises a perpendicular wave impact on the plane-parallel acoustic layer.
The conditions on the interfaces are described in the previous paragraph.
After substituting and editing, we get relationships for complex transition and reflection coefficients
The complex amplification
The input impedance of the layer is
As can be seen from the resulting relations, the quantities
We will identify two extreme cases:
For the case (+) is
For the case (−) is
A room without dispersion elements (bare parallel walls) is a half-wave resonator (for
Next, we see that the layer transforms the impedance from the value
The layer acts as an
The auricle of the outer ear also acts as an adjusting element (sometimes we increase its effect by placing the palm to the ear) (see Figure 10).
The acoustic transformer is also used as a power concentrator (Figure 10(a)). If we generate a wave with intensity
1.4.2 Wave dispersion
When there are small objects compared to the wavelength in the transmission path, the previous idea of reflection from a large area is not applicable. In this case, we consider a wave reflection on the elements of the object surface and the subsequent superposition on elementary reflected waves. It is the diffraction of waves. This phenomenon is called
It follows from Rayleigh’s relationship that small particles disperse waves in all directions
Dispersion of ultrasound with a frequency of about 15 MHz (wavelength of about 100 μm) by red blood cells with a diameter of about 10 μm is used to imaging and measure the speed of blood movement using the Doppler effect.
Ultrasound dispersed on small particles is also used in ultrasonography in the examination of cavities using a contrast medium, which is a liquid with small (micron) particles or microscopic bubbles whose size is smaller than the wavelength of the wave.
1.5 Doppler effect
Several significant applications are related to the
1.5.1 Moving source and static receiver
If the transmitter (source) moves towards the stationary receiver, during time
The receiver thus records the frequency of the incoming wave
The relative frequency change is
As the source approaches the receiver, the frequency increases. If it moves away, the frequency decreases. If the source moves perpendicularly to the source-receiver line, the frequency does not change. By measuring the change in frequency, the velocity
1.5.2 Static source and moving receiver
Now, the source moves towards a stationary receiver at speed
The frequency of the received wave is as follows
The relative frequency change is
If the source approaches the receiver, the received frequency increases, if the receiver moves away, the received frequency decreases. The frequency of the received wave changes only if the distance between the source and receiver changes. If the source moves perpendicularly to the source-receiver connecting line, the received frequency remains the same as that of the source. From the change of received frequency, it is possible to determine the speed
1.5.3 Wave reflection from a moving object
Let us consider the source of the wave with frequency
The relative change of the wave frequency is thus directly proportional to the speed of the object approaching or moving away from the acoustic wave source.
Other acoustic devices utilise the Doppler principle, for example, SONAR (sound navigation and ranging) for the identification of moving objects under the sea level (submarines, flocks of fish), or when using electromagnetic waves to measure the speed of road vehicles, flying aircraft, clouds, etc.
In biomedicine, the Doppler effect is mainly used in ultrasonography, or to measure the velocity of blood flow in blood vessels. Doppler effect is a common phenomenon of all waves irrespective of their physical nature.
Example 5 LIDAR.
LIDAR (Light Radar) is a device that uses the EM waves of a laser beam reflected from a monitored object. RADAR has a wide range of uses, for example, in air traffic, meteorology, etc. LIDAR is used, for example, to control speed in road transport. Older types used microwave radiation; today’s modern devices use optical waves. A narrow beam (3 mrad) of radiation with a wavelength of 905 nm (infrared radiation) is transmitted towards the vehicle in pulses of length
The same principle is used by meteorological radars, which use EM waves of the wavelength of 2–10 cm (microwaves). The result is, for example, maps of clouds movement and precipitation. The radar can also distinguish the type of precipitation (rain, snow).
1.6 Spectral bands of mechanical waves
The effects and practical use of mechanical waves depend on their frequency. The frequency bands of mechanical waves are defined concerning the frequency band of sound audible by the human ear. For a healthy hearing organ, an audible sound interval is 20 Hz–20 kHz. The music reference tone is
Sound affects the human psyche. The relaxing effects of classical music or, conversely, the excitatory effects of aggressive forms of music are known. These effects are used in sound therapy, sometimes to manipulate masses of people.
The hearing organs of various animals differ and have a different frequency range of sensitivity. For example, the dog hears a sound frequency range of 40 Hz–40 kHz, like a horse. Elephants, on the contrary, perceive vibrations with a frequency of up to 16 Hz. The bats perceive ultrasound with a frequency of up to 150 kHz.
Waves with a frequency
The influence of low-frequency infrasound on the human psyche is used to create specific moods. A typical example is the deep tones of organ pipes, which are supposed to evoke a deeper spiritual experience in cathedrals. On the contrary, the deep tones with high intensity at discotheques intend to put participants into a trance.
Waves with a frequency
The MHz-US probe can be inserted into a vessel using a catheter to dissolve the thrombus by ultrasound support of the thrombolytic drugs.
An important application is transdermal sonophoresis (drug transfer through the top layer of the skin), in which the barrier of the top layer of the skin (
1.7 Sources and detectors of mechanical waves
There is a direct interaction between the oscillations of the particles and the wave. Particle oscillations (dynamic deformation of the medium) are a source of the wave. On the other hand, waves in the medium cause oscillations of particles. It represents the principle of generation and detection of mechanical waves (sound, infrasound, and ultrasound).
A mechanical wave is generated by any time-varying (dynamic) deformation of the elastic or quasi-elastic medium. The sources can be divided according to the physical principle or according to the properties of the waves. According to the physical principle, they can be mechanical, thermal, electro-dynamic, optical, etc. The sources are coherent or incoherent, or from the geometric point of view: dot, line, surface, specially structured, etc. In this part, the sources of mechanical waves are discussed in terms of physical principles. To create a wave in a medium, the initial disturbance of the medium is necessary. According to the mechanism of this disturbance, we know the following sources of mechanical waves, regardless of the time course or geometric structure of the generated field of particle displacement.
In the following section, on the contrary, we describe the physical principles of mechanical wave detection. The wave cause oscillations that can be detected mechanically, electro-dynamically, optically, etc. Accordingly, we distinguish among diverse ways of detection of mechanical waves (infrasound, sound, and ultrasound).
1.7.1 Mechanical sources of mechanical waves
The mechanical excitation of mechanical waves occurs during mechanical excitation of the surface by an external force. A classic example is the collision of two rigid bodies, for example, the impact of a hammer on the anvil. In this way, for example, the sound of musical instruments such as piano or drums is generated. The impact sound is incoherent, but using a resonator, a coherent harmonic component (appropriate tone) can be selected from a wide range of sounds.
The excitation of mechanical waves also occurs due to friction. Sometimes we hear the whistling of vehicle brakes or the sound of a wheel rubbing against the road during heavy braking. Children know the sound of ‘whistling chalk’ on the blackboard, which also results from friction between the chalk and the blackboard. Regarding musical instruments, it is about creating sound in string instruments by rubbing the bow against a string. The vibration of the body can also occur by the friction of the flowing gas. Such oscillates the tongue of reed musical instruments, for example, clarinet or saxophone. We observe this principle even when sound is produced in the
Turbulent flow occurs in the tube when the critical value of the Reynolds number is exceeded. This number gives the formula Re =
There is also turbulent blood flow in the cardiovascular system, audible with a stethoscope. Typical is, for example, examining the heart by listening to the murmur of blood passing through the valves, or the flow of blood in the aorta. Besides the heart and aorta, the flow in healthy vessels is laminar (quiet). However, turbulence can occur when any obstacle occurs. In this way, the arising sound can discover thrombus in a vessel or sclerotic or pressure narrowing an artery. Medical diagnostics use this phenomenon in the
The principle of mechanical excitation of oscillations and mechanical detection of sound use the human hearing organ. The membrane represented by the eardrum oscillates due to the pressure modulation of the air (sound waves). Fine auditory bones (hammer, anvil, and stirrups) in the middle ear transmit the oscillations to the detection system of the inner ear (
1.7.2 Thermic sound excitation
Thermic excitation of mechanical waves arises due to the thermal expansion of the medium during a sudden change of temperature. If a place heats up quickly, it expands due to thermal expansion, causing the medium particles to move. This movement represents excitation, which then propagates like a mechanical wave due to the elasticity of the medium. Depending on the frequency, it is infrasound, sound, or ultrasound. In practice, we observe this phenomenon, for example, in electric discharges in gases. An electric discharge causes a sudden heating of the gas at the point of discharge and thus its expansion. The resulting sound is audible as a crack accompanying the discharge, for example, crackling the very high voltage insulators—400 kV, or thunder accompanying lightning during a storm. This sound is a non-coherent wave. However, there are also coherent spark sources in which the waves are excited by a pulse generator with regularly repeating sparks.
Thermal excitation can also be achieved by absorbing light radiation. In practice, the excitation of mechanical waves by power pulsed laser radiation is used. If the focused high-power laser beam impacts a certain place on or below the surface of the body, the medium absorbs the radiation, and thus it is locally heated. By the action of a laser beam with pulse modulation, it is possible to excite in the exposed body a mechanical wave with a frequency equal to the repetition rate of the pulse modulation. This phenomenon uses, for example,
In medical practice,
1.7.3 Electrodynamic sources and detectors of mechanical waves
Electrodynamic sources (speakers) and sound detectors (microphones) use the interaction between a moving conductor and a magnet in whose magnetic field it moves. A force d
If the coil is forced to move in the magnetic field of the magnet, or if the magnet moves inside the coil, an electric voltage induces in the coil according to Faraday’s law,
Electrodynamic microphones enable precise recording of sound in a very wide frequency range from infrasound to low-frequency ultrasound (tens of kHz). In addition to their normal use in sound technology, they are also used to measure the level of ‘acoustic pollution’ of the environment, especially in the field of infrasound, which negatively affects the quality of the environment. Similarly, an ultrasound that is inaudible to the human ear can be sensed. Sensitive microphones are also used in the detection of ultrasound, used, for example, by bats or dolphins for spatial orientation.
From a technical point of view, a moving coil system is mainly used in loudspeakers (sound sources), while detectors use a moving magnet and fixed coil arrangement.
If current flows through the coil, the turns of the winding are attracted to each other. During the flowing of alternating current or current pulses, the coil vibrates and generates sound. For example, exciting coils in a magnetic resonance device are very noisy, which is a negative aspect of the MRI investigation.
1.7.4 Electrostatic source and detector of mechanical waves
The electrostatic loudspeaker uses the dependence of the force between two parallel electrodes of a capacitor on the electrical voltage between them. If one electrode is fixed and the other is a fine movable membrane, the effect of the time-varying voltage causes deflection of the membrane. In this way, the membrane oscillations generate a mechanical wave in the surrounding medium. This type of speaker is suitable only for special purposes, for example, as simple sound indicators.
Electrostatic microphones are used more often. The incident mechanical wave deflects the movable flexible electrode (membrane) of the capacitor and changes the capacitance of the capacitor. Keeping the voltage constant, it modulates the current
1.7.5 Magnetostrictive transducer
Magnetostriction is observed in ferromagnetic materials. The external magnetic field changes the orientation of the spontaneous magnetization domains, which is accompanied by a small change in the size of the material sample. In the direction of the magnetic field, the sample dilates in the direction perpendicular to the magnetic field contracts. The alternating magnetic field generated by the current coil, the rod of ferromagnetic material is in, causes the rod to oscillate. The oscillations are transmitted by acoustic coupling to the surrounding environment. The mainly used ferromagnetic material is nickel and its alloys.
Magnetostrictive transducers are used as ultrasound sources in a wide frequency range, or as actuators in automation.
There exists also an inverse magnetoelastic phenomenon. The mechanical deformation of a ferromagnetic rod changes its magnetization. It results in induced voltage in the coil wound around the ferromagnetic rod.
Magnetostrictive transducers are not used in medicine.
1.7.6 Piezoelectric transducer
Piezoelectric transducers are important technical sources and detectors of mechanical waves with lots of applications. The principle is based on a direct or inverse piezoelectric effect. The piezoelectric transducer consists of a plate of piezoelectric material with deposited metallic electrodes, like a parallel-plate capacitor. After connecting the voltage to the electrodes and raising an electric field in the piezoelectric plate, the thickness of the plate changes (inverse piezoelectric effect). By applying a time-varying voltage, the plate mechanically vibrates and generates a mechanical wave in the surrounding medium. Most applications of the piezoelectric transducers are
In the case of mechanical deformation of the plate, for example, by compression, an electric voltage appears directly between the electrodes in direct proportion to the relative change in thickness (direct
The piezoelectric phenomenon occurs in some types of anisotropic crystals, for example, SiO2, LiNbO3, etc. In technical practice are cheaper piezoelectric ceramics Pb (ZrxTi1-x) O3, referred to as PZT (lead zirconium titanate) ceramics, or organic piezoelectric foils, for example, polyvinylidene dihydrochloride (PVDF). Ceramics or organic foils can be easily shaped during production and allow to make various structured transducers. A great advantage of piezoelectric transducers is their very small size, if necessary. It is possible to incorporate them directly into microchips as part of electronic integrated circuits. Structured piezoelectric probes can be composed of piezoelectric segments. It is used, for example, in
Medicine utilises ultrasound very widely. In addition to ultrasonography, which is an important diagnostic tool, ultrasound is used in sonophoresis (incorporation of nutrients or drugs into the skin), deep micro-massage, lipolysis (fat dissolution), deep heating, removal of dental plaque, etc. Intensive ultrasound uses lithotripsy (crushing of kidney, bladder, or gall stones) or ultrasonic scalpels.
1.8 Perception of sound by human hearing
Sound represents periodic fluctuations of air pressure. The eardrum hitting a sound wave oscillates. The oscillations are transmitted through a system of fine bones (
The snail channel is a complex acoustic resonator in which the maxima of oscillations with different frequencies are at different places along the channel, as indicated in Figure 11(b) and (c). The snail expands from the oval window, which increases the resonant wavelength and thus decreases the resonant frequency. Since the sound attenuation increases with frequency, the smallest transverse dimension is at the beginning (high tones) and the largest at the end (deep tones). The nerve endings on the perimeter of the snail are sensitive to resonant vibrations at given locations. Each nerve fibre thus transmits a different frequency. The snail is a complex frequency analyser of sound. Bundle of nerve fibres—
A certain minimum of wave intensity is required for nerve excitation. In a healthy ear, the minimum sound pressure at the eardrum required for perception of the sound at a frequency of 1 kHz is on average
The sound perception of the human auditory organ is a
Typical values of the sound intensity level are given in Table 3.
|Sound||Intensity level [dB]|
|Scream, symphonic orchestra||80|
|Rock concert, disco||110|
|Jet aircraft take-off, from the distance of 1 m||120|
|Firecracker, flash grenade||170|
Intensive sound threatens the ear not only by its intensity but also by the time of its action. For example, noise with the intensity level of 80 dB damages the cells of the ear when exposed for more than 8 hours, of the level of 90 dB for only 1 hour, and the level of 120 dB for only 10–16 seconds. Sound of the level of 140 dB and above, damages cells of the ear immediately, and the changes are irreversible. Damage of the cells often accompanies ‘phantom’ sound (tinnitus), such as humming or whistling in the ear. Sound of an intensity level
A person evaluates sound subjectively by its perception by an auditory organ. One perceives the sound with the same intensity differently at different frequencies. The measure of sound perception is
The thick lines correspond to the constant loudness with the values marked on the middle scale (at 1 kHz the values of loudness level are the same as the intensity level on the right scale). The threshold of audibility is lowest at around 3 kHz and increases towards extreme sound frequencies. We hear sound with a frequency of 30 Hz only at an intensity level of around 60 dB. The graph is standardised and corresponds to the average hearing organ of a healthy young person. With increasing age, the ability to hear sound generally decreases, mostly at extreme frequencies.
The volume is also affected by the external auditory canal and the auricle. The auricle is an acoustic transformer that adjusts the ambient impedance to the impedance of the external auditory canal. The effect of the ear can be supported by its effective enlargement using the palm or a funnel, Figure 12.
The auditory meatus is a
1.9 Medical diagnostics using sound and ultrasound
The diagnostic method of
The sound propagates to the inner ear (snail) through the eardrum or a skull bone, Figure 14. The air-conduction hearing test is performed using headphones, bone-conduction by placing the transducer directly on the bone behind the ear. The audiogram shows measurements by air (solid curve) and bone (dashed curve). The audiograms on the right show the airway for the right (red curve) and the left (blue curve) ear. The yellow area shows the intensity and frequency typical for hearing individual sounds of speech. The healthy hearing audiogram (above) provides a comfortable understanding of speech. The audiogram of hearing loss (below) shows hearing that is unable to understand speech—to distinguish the sounds.
Hearing correction is enabled by various instruments, see Figure 15. We often observe that for improving the hearing perception, we tend to put the palm to the ear (left picture). In old films from the 1920s, we can see listening to ‘funnels’. Today, hearing loss is solved by electronic listening aids inserted into the ear canal, the picture on the right.
The classical method of examining body sounds is listening—
Obstruction as a source of murmurs can also be the narrowing of the vessel by the application of lateral pressure. This uses the auscultation method of measuring blood pressure, Figure 16. The cuff around the limb is inflated with a balloon to a pressure higher than the systolic one. The pressure stops flowing blood in the artery, and no sound is heard in the stethoscope applied under the cuff. If the pressure in the cuff drops below the systolic (SYS) one after the cuff slow deflating, blood begins to flow through the constricted artery. The flow is turbulent and is accompanied by murmurs—
In addition to this auscultation method, there also exists an oscillometric method. Because of the blood pressure pulsation, small periodic pressure changes occur in the inflated cuff. The device has a pressure sensor connected with the tube inflating the cuff, which picks up these pressure pulses. The initial cuff inflation realises a built-in compressor. The pressure pulses in the cuff are similar time-course of the murmurs (Figure 16). After the digital processing of the signal of the pressure sensor, the display of the device shows numerical values of the systolic and diastolic pressure and the heart rate. Oscillometric instruments are simple and do not require any special operation. Therefore, they are used for home blood pressure control or continuous pressure monitoring. In the case of a one-time medical examination, doctors prefer the auscultation method because of its better accuracy.
220.127.116.11 Basic ultrasonographic imaging
Ultrasonography is a diagnostic method that uses the propagation of ultrasound in substances and its reflection on the impedance interfaces, for example, LABUDA , SHUNG . In technical practice, there exists ultrasonic flaw detection (engineering, construction), which allows the examination of cracks or inhomogeneities in a material. Medical ultrasonography (USG) enables imaging of the internal organs of the body with different acoustic impedance. The ultrasonic transducer generates a short ultrasonic pulse on the surface of the body. It proceeds into the depth of the body, reflects from the impedance interfaces of the organ’s tissue, and returns to the transducer. It now serves as a detector of the reflected pulses. The detected signal is processed by a receiver and then displayed on the screen of the USG device (Figure 17).
The imaging indicated in the figure, in which the magnitude of the reflected signal is displayed by the height of the pulse is called the A-mode (amplitude). Each pulse displays the impedance interface. The time delay
Structured piezoelectric transducers are the main part of the probes with shapes adapted to specific applications. Several examples of USG probes are in Figure 18. The USG probes consist of an array of many small transducers, which allows forming the ultrasound beam.
In the case of 2D imaging, the B-mode (brightness) is used. In this mode, the signal modulates the brightness of the track. An example of comparing A-mode and B-mode is in Figure 19.
If a series of parallel or diverging ultrasonic beams are successively sent into the object under investigation, brightness modulated lines are obtained for each of them. By displaying these lines on the monitor, a 2D brightness modulated profile of the internal structure of the object occurs, Figure 20. Figure 20(a) shows an image of a vessel provided by a series of parallel beams (rectangular image). Figure 20(b) shows a foetus in the body of a mother by a series of diverging beams, arranged in a certain angular sector.
As ultrasonography utilises the principle of ultrasound reflection, it is not suitable for imaging structural parts with an extreme value of the acoustic impedance, gas-filled cavities with a very low impedance, or solid tissues (bones) with a very high impedance. Ultrasound is practically completely reflected from the surface of such objects, and therefore, it is not possible to obtain information about the structures behind these surfaces. The method is suitable for imaging soft tissues, for example, imaging of the heart, kidney, liver, digestive tract, etc. Since ultrasonography has no adverse effects on the human body, it is even used to examine the foetus in the mother’s body, Figure 20(b).
18.104.22.168 Doppler sonography
The Doppler effect is used in acoustic diagnostics to track moving objects, for example, heart, blood flow, etc. When ultrasound reflects from the object that moves in the direction of the ultrasound beam, the frequency of the reflected ultrasound is changed due to the Doppler effect. Doppler sonography device has an electrical circuit for separating signals with the shifted frequency (frequency discriminator), which have been generated by reflection from moving parts of organs, for example, from the beating heart, or from flowing blood. These signals are digitally colour-coded and displayed in a sonogram. Doppler detection also allows suppressing reflections with the original frequency from stationary parts, thus improving the contrast of the image of moving organs. Since the processing of the frequency-shifted signal is time and memory-consuming due to every pixel of the image colour-coding, the Doppler mode is not used for the whole image. The doctor chooses Doppler mode only for a selected demanded part of the image, see Figure 21.
The left image is a picture of blood flow through
The right image is a picture of the blood flow through the ventricle. Current technical means, especially fast computers, allow obtaining an image in a few tenths of a second so that it is possible to observe the motion of the object online. An example of an online Doppler image of the ventricle in motion can be seen at the page http://cs.wikipedia.org/wiki/Soubor:Doppler_mitral_valve.gif.
1.9.4 Ultrasonic measurement of blood flow in vessels
The Doppler effect allows measuring blood flow in vessels. A principle of the device is in Figure 22. It uses a continuous harmonic ultrasonic wave with a frequency of 4–8 MHz, which generates a transmitting transducer T of the probe. Erythrocytes in the blood (the largest blood particles) disperse the ultrasonic wave, and the Doppler-shifted wave returning to the probe detects the receiving transducer R.
The device evaluates the Doppler shift of frequency and displays it in units of blood flow velocity. If we know the cross-section of the vessel, for example, from ultrasonographic measurement, one can determine the volume flow of blood in the vessel. The specific shape of the course of the blood velocity versus time, (Figure 22 right), the leading and trailing edges of the pulses, various maxima, and minima provide information about the state of the vascular system.
The method is relatively simple and therefore is suitable for indicative angiological investigation. The disadvantage of the method is that the probe reads a response from all vessels, and it is problematic to evaluate only the single one. On the other hand, it is advantageous for an examination of vessels with high blood velocity and of subsurface vessels, for example, in dermatology and phlebology.
Labuda M, Vaverka F, Borik S. Ultrasound based distance measurement and assessment of obstacles in the area–a concept for educational purposes. In: 2020 ELEKTRO. IEEE; Žilina: 2020. pp. 1-4
Shung KK. Diagnostic Ultrasound – Imaging and Blood Flow Measurement. Boca Raton: CRC Press; 2006. ISBN: 978-0-8247-4096-2