176
5 Acoustics in Biology and Medicine
that of water: c h ≈ 1 cal/gm-deg = 4.18 /J gm-deg and ρ ≈ 1.0 gm/cm 3 . For pulseecho ultrasonic imaging, typically, I us may reach as high as 500 mW/cm 2 but with
a pulse duration of only 2 μs. At a frequency of 5 MHz, α L ≈ 0.25/cm, we find that
T ≤ 0.12 ◦ C. For a continuous wave with intensity of 1 W/cm 2 , T ≤ 0.12 ◦ C in
1 s.
Commercial non-Doppler ultrasound devices operating with pulsed waves have
averaged intensities ranging from 0.001 to more than 0.20 W/cm 2 . Pulsed Doppler
waves used for imaging can reach time-averaged intensities as high as 1.9 W/cm 2
next to the probe. Thus, the probe transducer for these intensities should not be held
in one place on the body more than a few seconds.
Cavitation
Strong negative gauge pressure (i.e. absolute pressure minus ambient pressure) in
short times can produce bubbles in liquids and viscoelastic solids. These bubbles
will contain the liquid vapor. As the pressure increases, the bubbles tend to drop
to zero volume (or collapse in times shorter than the period of the sound wave).
Bubble formation is strongly dependent on the existence of ‘nucleation’ sites, where
the phase change from liquid to gas occurs with less negative pressure than in the
bulk of the liquid. Small particles and surfaces with micro-indentations can act as
nucleation locations. The presence of various salt ions also enhances cavitation.
When a cavitation bubble forms and when it collapses, it may disrupt a cell structure.
Cavitation bubbles oscillate in size and position in response to the ultrasonic
wave. These oscillating micro-bubbles can rupture membranes, including cell walls.
They also cause stronger absorption of the wave intensity, through conversion of
mechanical work into scattered sound energy and heat. More details on bubble
vibrations can be found in Sect. D.3 of Appendix D.
If there were no dissolved gases or nucleation sites, the theoretical value of
negative pressure to cause water cavitation is in the range of 100,000 atmospheres.
The presence of nucleation sites (within the water or on a bounding surface) drops
the required negative pressure to about 50 atmospheres. For water saturated with
oxygen, only negative pressures >0.1 atm are needed to cause gas bubble cavitation.
Mammalian nervous system tissue is damaged by cavitation when exposed to
sound of intensities greater than 1000 W/cm 2 (δp rms = 39 atm) 30 for at least 1 μs.
Mice suffer lung damage due to cavitation if the sound has pressure variations above
8 atm at 1 MHz.
30 The connection between intensity I and RMS pressure
(δp) 2
is given in Eq. (5.33), namely
I =
(δp) 2
/(ρv), where ρ is the material density and v the speed of sound in the material.
5 Acoustics in Biology and Medicine
that of water: c h ≈ 1 cal/gm-deg = 4.18 /J gm-deg and ρ ≈ 1.0 gm/cm 3 . For pulseecho ultrasonic imaging, typically, I us may reach as high as 500 mW/cm 2 but with
a pulse duration of only 2 μs. At a frequency of 5 MHz, α L ≈ 0.25/cm, we find that
T ≤ 0.12 ◦ C. For a continuous wave with intensity of 1 W/cm 2 , T ≤ 0.12 ◦ C in
1 s.
Commercial non-Doppler ultrasound devices operating with pulsed waves have
averaged intensities ranging from 0.001 to more than 0.20 W/cm 2 . Pulsed Doppler
waves used for imaging can reach time-averaged intensities as high as 1.9 W/cm 2
next to the probe. Thus, the probe transducer for these intensities should not be held
in one place on the body more than a few seconds.
Cavitation
Strong negative gauge pressure (i.e. absolute pressure minus ambient pressure) in
short times can produce bubbles in liquids and viscoelastic solids. These bubbles
will contain the liquid vapor. As the pressure increases, the bubbles tend to drop
to zero volume (or collapse in times shorter than the period of the sound wave).
Bubble formation is strongly dependent on the existence of ‘nucleation’ sites, where
the phase change from liquid to gas occurs with less negative pressure than in the
bulk of the liquid. Small particles and surfaces with micro-indentations can act as
nucleation locations. The presence of various salt ions also enhances cavitation.
When a cavitation bubble forms and when it collapses, it may disrupt a cell structure.
Cavitation bubbles oscillate in size and position in response to the ultrasonic
wave. These oscillating micro-bubbles can rupture membranes, including cell walls.
They also cause stronger absorption of the wave intensity, through conversion of
mechanical work into scattered sound energy and heat. More details on bubble
vibrations can be found in Sect. D.3 of Appendix D.
If there were no dissolved gases or nucleation sites, the theoretical value of
negative pressure to cause water cavitation is in the range of 100,000 atmospheres.
The presence of nucleation sites (within the water or on a bounding surface) drops
the required negative pressure to about 50 atmospheres. For water saturated with
oxygen, only negative pressures >0.1 atm are needed to cause gas bubble cavitation.
Mammalian nervous system tissue is damaged by cavitation when exposed to
sound of intensities greater than 1000 W/cm 2 (δp rms = 39 atm) 30 for at least 1 μs.
Mice suffer lung damage due to cavitation if the sound has pressure variations above
8 atm at 1 MHz.
30 The connection between intensity I and RMS pressure
(δp) 2
is given in Eq. (5.33), namely
I =
(δp) 2
/(ρv), where ρ is the material density and v the speed of sound in the material.