**3. Physical phenomena elicited by acoustic waves in biological tissues**

#### **3.1. Forms of acoustic waves**

Low-intensity pulsed ultrasound, shock waves and radial pressure waves are different forms of acoustic waves. Their distinct physical parameters are expected to produce different physical phenomena when transmitted into biological tissues.

#### *3.1.1. Low-intensity pulsed ultrasound*

Sound is the vibration (rapid motion) of molecules within a compressible medium such as air or water. It can only propagate in compressible media. When sound waves (acoustic waves) reach molecules, molecules may get closer—compression—or farther—rarefaction. By alternating compression and rarefaction, sound travels in waves transporting energy from one location (transmitter) to another (receiver). Because sound waves produce mechanical motion of molecules, they are mechanical waves. When the frequency of a sound wave is above the typical human audible range (greater than 20 kHz), this sound wave is called ultrasound. Ultrasound is an acoustic radiation that can be transmitted as high-frequency pressure waves (1–12 MHz) [4, 6, 7, 27, 28].

Spatial average temporal average (ISATA) lower than 150 mW/cm2 is generally regarded as the intensity spectrum of LIPUS. ISATA refers to the spatial average intensity over both the on time and the off time of the pulse. Nevertheless, there is no clear-cut upper intensity boundary to define an ultrasound wave as low-intensity ultrasound. LIPUS studies have been conducted with intensity level between 5 and 1000 mW/cm2 , with frequency between 45 kHz and 3 MHz, in continuous or burst mode and with daily exposure times between 1 and 20 min. In spite of that, most used parameters for LIPUS are as originally described by its creator: intensity of 30 mW/cm2 , frequency of 1.5 MHz, pulse (burst mode) of 1 KHz with duty cycle of 20% and daily exposure times of 20 min [4, 29, 30].

#### *3.1.2. Shock waves*

They are also acoustic pressure waves, or sonic pulses. In general, a shock wave can be described as a single pulse with a wide frequency range up to 20 MHz (typically in the range from 16 Hz to 20 MHz), high positive pressure amplitude up to 120 MPa (often 50–80 MPa), low tensile wave up to 10 MPa with short duration (about 1 μs), small pulse width at -6dB, short life cycle of approximately 10 μs and a short rise time of the positive pressure amplitude (lower than 10 ns). The reader may find studies with measured rise times of shock wave devices in the range of 30 ns as a result of the limited time resolution of piezoelectric hydrophones. However, optical hydrophones, which are more sensitive measure devices, displayed measure rise times below 10 ns for electrohydraulic devices [7, 9, 22].

The energy density (maximum amount of acoustical energy transmitted through an area per pulse) of ESWT is up to 1.5 mJ/mm2 and the pulse energy (sum of all energy densities across the beam profile multiplied by the area of the beam profile) is up to 100 mJ. Arbitrarily, energy levels up to 0.08–0.12 mJ/mm2 in the focal zone are defined as low-energy ESWT, energy levels between 0.08 and 0.28 mJ/mm2 are defined as medium-energy ESWT and energy levels greater than 0.28 mJ/mm2 are defined as high-energy ESWT (some authors consider 0.12 mJ/mm2 the cut-off from low- to high-energy ESWT) [7–9, 22, 31, 32].

#### *3.1.3. Ultrasound vs shock waves*

**3. Physical phenomena elicited by acoustic waves in biological tissues**

Low-intensity pulsed ultrasound, shock waves and radial pressure waves are different forms of acoustic waves. Their distinct physical parameters are expected to produce different

Sound is the vibration (rapid motion) of molecules within a compressible medium such as air or water. It can only propagate in compressible media. When sound waves (acoustic waves) reach molecules, molecules may get closer—compression—or farther—rarefaction. By alternating compression and rarefaction, sound travels in waves transporting energy from one location (transmitter) to another (receiver). Because sound waves produce mechanical motion of molecules, they are mechanical waves. When the frequency of a sound wave is above the typical human audible range (greater than 20 kHz), this sound wave is called ultrasound. Ultrasound is an acoustic radiation that can be transmitted as high-frequency pressure waves

Spatial average temporal average (ISATA) lower than 150 mW/cm2 is generally regarded as the intensity spectrum of LIPUS. ISATA refers to the spatial average intensity over both the on time and the off time of the pulse. Nevertheless, there is no clear-cut upper intensity boundary to define an ultrasound wave as low-intensity ultrasound. LIPUS studies have been

and 3 MHz, in continuous or burst mode and with daily exposure times between 1 and 20 min. In spite of that, most used parameters for LIPUS are as originally described by its creator:

They are also acoustic pressure waves, or sonic pulses. In general, a shock wave can be described as a single pulse with a wide frequency range up to 20 MHz (typically in the range from 16 Hz to 20 MHz), high positive pressure amplitude up to 120 MPa (often 50–80 MPa), low tensile wave up to 10 MPa with short duration (about 1 μs), small pulse width at -6dB, short life cycle of approximately 10 μs and a short rise time of the positive pressure amplitude (lower than 10 ns). The reader may find studies with measured rise times of shock wave devices in the range of 30 ns as a result of the limited time resolution of piezoelectric hydrophones. However, optical hydrophones, which are more sensitive measure devices, displayed measure

The energy density (maximum amount of acoustical energy transmitted through an area per pulse) of ESWT is up to 1.5 mJ/mm2 and the pulse energy (sum of all energy densities across the beam profile multiplied by the area of the beam profile) is up to 100 mJ. Arbitrarily, energy

, frequency of 1.5 MHz, pulse (burst mode) of 1 KHz with duty cycle

in the focal zone are defined as low-energy ESWT, energy levels

, with frequency between 45 kHz

physical phenomena when transmitted into biological tissues.

conducted with intensity level between 5 and 1000 mW/cm2

rise times below 10 ns for electrohydraulic devices [7, 9, 22].

of 20% and daily exposure times of 20 min [4, 29, 30].

**3.1. Forms of acoustic waves**

32 Advanced Techniques in Bone Regeneration

*3.1.1. Low-intensity pulsed ultrasound*

(1–12 MHz) [4, 6, 7, 27, 28].

intensity of 30 mW/cm2

levels up to 0.08–0.12 mJ/mm2

*3.1.2. Shock waves*

Shock waves differ from regular sound waves in that the wave front, where compression takes place, is a region of sudden change in stress and density. Shock waves travel faster than sound, and their speed increases as the amplitude (pressure) is raised. On the other hand, the intensity of a shock wave decreases faster than does of a sound wave. As a consequence, wavelets at high pressure lead to deformation of the wave so that the wave crest assumes a sawtooth appearance, which is different from the sinusoidal appearance of a regular sound wave. Furthermore, shock waves differ from ultrasound waves since the former is uniphasic with high peak pressure (in the order of a hundred MPa), and the latter is biphasic with very low peak pressure (in the order of a hundredth of MPa) [7, 22].

#### *3.1.4. Radial pressure waves*

Considering the physical definition of shock waves, radial pressure waves are wrongly termed unfocused shock waves in the literature. The rise time of the positive pressure waves produced by currently available devices are much greater than 10 ns, varying from 600 to 800 ns. Also, the maximum peak positive pressure of a radial pressure wave device varies from 0.1 to 7 Mpa, and the pulse duration varies from 1 to 5 ms. Since the time taken for the radial wave to rise is too long, the curve of the concave surface of the ray is too wide for it to be possible to focus the energy; therefore, radial waves cannot be focused, unlike ESWT. Moreover, the air pressure-accelerated projectile has a speed from 2 to 20 m/s, which is 2 orders of magnitude slower than sound speed in water or tissue. Shock waves are produced when the projectile speed is comparable or higher than sound speed (i.e. supersonic). In addition, the distinction between RPWT as "low-energy therapy" and ESWT as "high-energy therapy" is not correct. Most protocols of RPWT use energy density lower than 0.20 mJ/mm2 , but the device can reach up to 0.55 mJ/mm2 . Accordingly, ESWT has a wide range of energy density protocols varying from 0.02 mJ/mm2 to more than 0.60 mJ/mm2 [8, 21, 22, 26, 33].

#### **3.2. Attenuation of acoustic energy**

When an acoustic wave is transmitted into a biological tissue, a portion of the acoustic energy is reflected, another portion is attenuated (lost) and the other portion is refracted and continues propagating. Much from the attenuated portion is absorbed by irreversible conversion of acoustical energy into heat mainly via viscous friction, and less is scattered by inhomogeneities within tissue that redirect some sonic energy to regions outside the original wave-propagation path. If the density of the inhomogeneity is high, multiple scattering may occur. Therefore, acoustic energy may scatter several times until it is completely absorbed by tissue and converted to heat [27, 34, 35].

Bone has one of the highest attenuation coefficients among biologic tissues. Besides, as frequency increases, penetration decreases and attenuation increases. Therefore, acoustic waves tend to produce heat preferentially in bones and joints. Accordingly, tissue damage and pain may be produced if the intensity of acoustic energy is high enough. For instance, continuous unfocused ultrasound waves in the range of 4000–5000 mW/cm2 at 1 MHz for 5 min increase temperature by 1.8–4.3° C at different areas of bone within 1–3 cm of distance. On the other hand, ultrasound at intensities of 20–50 mW/cm2 , which is LIPUS, produces negligible variation of tissue temperature (0.01 ± 0.005° C). Moreover, reports using very high ultrasound intensities (5000–25,000 mW/cm2 ) showed delayed bone healing and necrosis, whereas ultrasound at intensities of 200–3000 mW/cm2 has been shown to increase callus formation and accelerate fracture healing [4, 27, 35–38].

Extracorporeal shock waves and radial pressure waves also increase temperature of tissues either by absorption or by cavitation (see Section 3.3). However, no reports were found about temperature raise within biological tissues subjected to ESWT and RPWT. In spite of that, thermal effects may be responsible for decreased cell viability immediately after ESWT with some energy densities and number of impulses [39–44].

#### **3.3. Cavitation bubbles**

When near gas or vapour bubbles, a portion of the refracted acoustic wave may generate cavitation bubbles at locations termed "nucleation sites". Cavitation refers to a range of complex phenomena that involve the creation, oscillation, growth and collapse of bubbles within a liquid or liquid-like medium. Cavitation bubbles have never been confirmed in living tissues; therefore, the following information is based on mathematical simulations and in vitro studies [3, 27, 37].

The occurrence and behaviour of cavitation depend on the acoustic pressure; the existence of microheterogeneities in liquids such as free gas, solid particles or a combination of both; whether the acoustic field is focused or unfocused, or pulsed or continuous; and the nature and state of the material and its boundaries. Cavitation does not occur with ultrasound intensities below 500 mW/cm2 . Consequently, LIPUS does not produce the phenomenon of cavitation. On the other hand, the biological effects of ESWT and RPWT are triggered mainly by the phenomenon of cavitation [4, 27, 30, 38, 45].

Bubbles are gas-filled spheres in a liquid under constant hydrostatic pressure when there are no acoustic waves. In response to a sound field in which the acoustic pressure varies sinusoi‐ dally in time with a given frequency, the bubble radius oscillates (expands and contracts) with radial displacement and velocity, which vary sinusoidally in time with the same frequency of the wave. When there is lower level pressure amplitude in synchrony with bubble motion, the immediately surrounding liquid moves in and out creating a small steady flow of fluid called microstreaming. This is called stable cavitation and may occur with low-energy ESWT and some RPWT. Stable cavitation occurs near a solid boundary (e.g. bone) and creates shear stress near the bubble surface that can also mechanically stimulate cells [7, 45].

Shock waves and radial pressure waves generate cavitation bubbles during the tensile phase of the acoustic wave due to its tensile forces that exceed the dynamic tensile strength of water. During the growth phase of the bubble, a huge amount of energy is delivered to the bubble. Following a number of shock, or radial pressure, wave pulses (sometimes after the first impulse), the bubble collapses (i.e. experiences an extremely rapid contraction), which is called inertial cavitation. As the bubble collapses, four phenomena can be observed [7, 27, 35, 45, 46]:


Additionally, during the positive pressure phase of a second shock, or radial pressure, wave pulse, may also push the liquid of the surrounding medium towards one of the walls of a preformed bubble. That wall goes under deformation and reaches the opposite wall of the same bubble to originate a water jet in the same direction of the propagation of the shock wave. The formation of a water jet usually occurs in the vicinity of boundary areas between materials of differing density, such as bone and cartilage, in the direction of the boundary area. The generated water jet is faster with increasing softness of the interface and more damaging than jets from inertial cavitation. In addition, the presence of a hard biomaterial (e.g. bone and cartilage) causes the bubble to collapse towards it. Besides, as the bubble expands, the interface between the medium and the biomaterial is pushed away from the bubble; however, when the bubble collapses, the interface moves slightly towards the bubble. It should be noted that inertial cavitation bubbles near softer material, such as fat, skin and muscle, tend to collapse by splitting into two or three smaller bubbles without the formation of water jets [7, 21, 38, 46, 47].

#### **3.4. Acoustic radiation pressure**

Bone has one of the highest attenuation coefficients among biologic tissues. Besides, as frequency increases, penetration decreases and attenuation increases. Therefore, acoustic waves tend to produce heat preferentially in bones and joints. Accordingly, tissue damage and pain may be produced if the intensity of acoustic energy is high enough. For instance,

Extracorporeal shock waves and radial pressure waves also increase temperature of tissues either by absorption or by cavitation (see Section 3.3). However, no reports were found about temperature raise within biological tissues subjected to ESWT and RPWT. In spite of that, thermal effects may be responsible for decreased cell viability immediately after ESWT with

When near gas or vapour bubbles, a portion of the refracted acoustic wave may generate cavitation bubbles at locations termed "nucleation sites". Cavitation refers to a range of complex phenomena that involve the creation, oscillation, growth and collapse of bubbles within a liquid or liquid-like medium. Cavitation bubbles have never been confirmed in living tissues; therefore, the following information is based on mathematical simulations and in vitro

The occurrence and behaviour of cavitation depend on the acoustic pressure; the existence of microheterogeneities in liquids such as free gas, solid particles or a combination of both; whether the acoustic field is focused or unfocused, or pulsed or continuous; and the nature and state of the material and its boundaries. Cavitation does not occur with ultrasound

cavitation. On the other hand, the biological effects of ESWT and RPWT are triggered mainly

Bubbles are gas-filled spheres in a liquid under constant hydrostatic pressure when there are no acoustic waves. In response to a sound field in which the acoustic pressure varies sinusoi‐ dally in time with a given frequency, the bubble radius oscillates (expands and contracts) with radial displacement and velocity, which vary sinusoidally in time with the same frequency of the wave. When there is lower level pressure amplitude in synchrony with bubble motion, the immediately surrounding liquid moves in and out creating a small steady flow of fluid called microstreaming. This is called stable cavitation and may occur with low-energy ESWT and some RPWT. Stable cavitation occurs near a solid boundary (e.g. bone) and creates shear stress

near the bubble surface that can also mechanically stimulate cells [7, 45].

at 1 MHz for 5

C at different areas of bone within 1–3 cm of distance. On

) showed delayed bone healing and necrosis, whereas

. Consequently, LIPUS does not produce the phenomenon of

C). Moreover, reports using very high ultrasound

has been shown to increase callus formation and

, which is LIPUS, produces negligible

continuous unfocused ultrasound waves in the range of 4000–5000 mW/cm2

min increase temperature by 1.8–4.3°

34 Advanced Techniques in Bone Regeneration

intensities (5000–25,000 mW/cm2

**3.3. Cavitation bubbles**

studies [3, 27, 37].

intensities below 500 mW/cm2

by the phenomenon of cavitation [4, 27, 30, 38, 45].

variation of tissue temperature (0.01 ± 0.005°

ultrasound at intensities of 200–3000 mW/cm2

accelerate fracture healing [4, 27, 35–38].

the other hand, ultrasound at intensities of 20–50 mW/cm2

some energy densities and number of impulses [39–44].

This is the proposed mechanism by which LIPUS stimulates living tissues. The authors also believe this is the main mechanism by which ESWT and RPWT stimulate living tissues. Acoustic radiation pressure tends to increase in proportion to intensity, is generally relatively small in magnitude and produces forces and motions at much lower frequencies than those of the incident acoustic wave. While the tensile phase of the shock and radial pressure waves generates cavitations, the positive pressure phase of those waves produces acoustic radiation pressure [9, 35, 37, 45].

Radiation pressure is a universal phenomenon in any wave motion involving sound. It is exerted on surface or media interfaces and acts in the direction of propagation of the wave thereby producing direct and indirect mechanical stress. Direct mechanical stress is produced by strain. Following mechanical deformation, bone exhibits electrical activity and cellular activation. It is unclear, however, whether the main responsible for bone electrical activity is piezoelectricity, streaming potentials, or ion channels and ATP receptor activities (see 3.4.1) [4, 28, 34, 45].

Indirect mechanical stress is produced by acoustic streaming and modal conversion. When acoustic waves are refracted from water to soft tissues, waves propagate longitudinally (in the same direction of the beam source) due to impedance similarity. Differently, when acoustic waves are refracted to materials with impedance mismatch, such as bones, modal conversion occurs, that is, shear waves (waves at right angles to the direction of the beam source) are produced along with longitudinal waves. Shear waves may produce direct mechanical deformation to tissue, called shear stress [7, 27, 36, 45].

Acoustic radiation pressure decreases with the distance of the wave from its source; hence, radiation pressure gradients are formed within the fluid. As a result, fluid flow originates, which is called acoustic streaming. The flow is directed away from the transducer with gradual build up of the axial streaming speed with distance from the transducer and a peak of velocity in the focal region. The fluid flow continues beyond the focal region and returns to the transducer as recirculation vortices. Fluid flow can also build up again in the acoustic beam after a membrane. Acoustic streaming and microstreaming are often used as synonyms in the literature. Although both produce fluid flow which can modulate osteogenesis, they are distinct phenomena. As described above, acoustic streaming results from radiation pressure gradients, whereas microsteaming is generated by stable cavitation bubbles. Furthermore, not only mechanical deformation but also acoustic streaming increases cell membrane permea‐ bility and generates streaming potentials. It has not been shown, however, whether acoustic streaming directly affects cell membrane permeability, or triggers cellular reactions that increase membrane permeability [30, 37, 45, 48]. For a detailed explanation of streaming potentials, see reference [3].

#### *3.4.1. Electric potentials*

Bone exhibits electrical activity when subjected to mechanical forces. The opposite is also true: bone undergoes deformation when exposed to electric potentials. For instance, ESWT induces transient cell membrane hyperpolarization. There are three possible contributors to electric potentials on bone. First, mechanically induced activity of ion channels and ATP receptors promotes ion transport between the intra and extracellular environments resulting in mem‐ brane action potentials; second, piezoelectricity, which is the generation of electricity when asymmetric crystalline materials—as those that form the extracellular matrix of bone—are subjected to strain; and finally, streaming potentials that result from mechanically induced flow of fluid containing high conductivity ions [3, 4, 44, 49].
