Introduction to Acoustics

transported by those cells and/or retained in particular
tissues or organs.
21.5.6 Interactions Between Ultrasound
and Microbubbles
When exposed to ultrasound at diagnostic frequencies
(1–20 MHz), the contrast bubbles will oscillate at
the driving frequency of the ultrasound, emitting the
fundamental frequency as well as harmonics of the
fundamental frequency. Microbubbles have a natural
resonance frequency, primarily determined by their size,
surface tension, shell rigidity (if any) and the density of
surrounding material. If stimulated at a frequency near
the resonant frequency, the amplitude of oscillations will
be greater. The pressure of the interior gas varies with
volume according to the rules of adiabatic compression
and expansion, at least to the extent that the process
is too fast for heat transfer. Although the waveform of
the oscillation is primarily determined by the waveform
of the driving ultrasound, the surfactant forces also play
a great role in this process. When the ultrasound pressure
is high (for 0.3 µs) the gas compresses, the temperature
raises, the water vapor pressure increases as does the
pressure of other gases. The gas pressures rise above the
surrounding partial pressures of gas, providing a driving
force to move gas out of the bubble into solution. Because
the bubble is small, the surface area available for
heat and mass transfer is small, and the amount of loss of
heat and gas is small. Alternatively, when the ultrasound
pressure is low (the subsequent 0.3 µs), the pressures
and temperature drops, providing driving forces for heat
and gas to enter the bubble. Now the surface area is
large and it is easy for transport into the bubble, leading
to rectified diffusion of gas and heat into the bubble.
At the body temperature of 37 ◦ C, the vapor pressure
of water is 6.2 kPa, 6% of atmospheric pressure.
An acoustic wave of 285 mW/cm 2 SPTP (spatial peak
temporal peak) intensity drops the pressure in a bubble
below the vapor pressure of water (ignoring surface tension)
which will cause the water to vaporize, filling the
bubble with water vapor in addition to the other contained
gasses. The latent heat of evaporation lowers the
temperature of the bubble. On compression, the recondensing
of the water adds heat to the bubble. When the
ultrasound is compressing the bubble, the surfactant acts
as a stable skin. The skin may even exhibit negative surface
tension. Like the hull of a submarine deep in the
ocean, the surfactant may hold the bubble gas pressure
lower than the surrounding pressure. Similarly, when the
ultrasound pressure has dropped below ambient, and the
Medical Acoustics 21.5 Medical Contrast Agents 887
bubble expands to form a larger surface area, the surfactant,
which is often a monolayer of molecules on the
surface, will change in configuration, become patchy and
result in increased surface tension, holding the internal
gas pressure higher than expected from the surrounding
pressure. As there is a driving force for the gaseous
contents of the microbubble to experience rectified diffusion,
there is also a driving force for the surface phase
to experience rectified diffusion, changing the composition
of the surface. A stable molecular monolayer on
the surface of the bubble at one bubble volume will
become compressed when the bubble becomes small,
providing a driving chemical potential to both change
the phase of the monolayer to a multilayer and to drive
some of the surfactant into solution. The monolayer will
be expanded when the bubble becomes large, providing
a driving chemical potential to draw surfactant from
solution. The solution my provide surfactant materials
that are similar to or different from the original surfactant
on the microbubble. Unless the concentration of
potential surfactants in solution is high, this process is
too slow to affect bubble behavior. In experimental solutions,
such concentrations may be low, but the complex
mixture of complex molecules in blood may favor such
a process.
21.5.7 Bubble Destruction
The first experiments with microbubble contrast agents
were disappointing. Contrast agents did not produce reflections
as bright as expected. Increasing the transmit
intensity did not improve the strength of the echoes coming
from the agents. In an effort to improve the signal
strength, broadband ultrasound transducers were used to
form harmonic images. An ultrasound transducer oscillates
at a resonant fundamental frequency determined by
the thickness. The transducer has no efficiency or sensitivity
at double the frequency, although it does have
one-third the efficiency and sensitivity at triple the frequency.
By damping the transducer, a transducer with
a center resonant frequency of 3 MHz can be made
to operate at frequenciesof 1.9–4.1 MHz. In harmonic
imaging to detect contrast bubbles, a 2 MHz transmit
burst is applied to this broadband transducer and the
receiver is tuned to 4 MHz. Echoes from tissue are expected
at 2 MHz, echoes from contrast microbubbles
are expected at 2 MHz and 4 MHz. By selecting only
echoes at 4 MHz, clear visualization of the contrast bubbles
was expected. Unfortunately, for this application,
because ultrasound transmit intensities are so high, ultrasound
transmission in tissue is nonlinear, generating
Part F 21.5