Biomedical Engineering Reference
In-Depth Information
Fig. 2.4.
Nonlinear propagation of ultrasound through water. Features at peaks
are harmonic components and travel faster than rounded nadirs
was originally considered to propagate by a linear process, meaning that new
frequencies cannot be created. Attenuation may differentially affect some fre-
quencies more than others. Therefore, the spectral content may change with
propagation, but frequencies that were absent in the original wave cannot
subsequently appear. However, it has become apparent recently that there
are nonlinear acoustic effects active in ultrasonography. The nonlinear effects
of the interaction of ultrasound with matter (both on propagation and re-
flection) may create frequencies that were not present in the incident beam.
New harmonics are considered to be generated because water or tissue is not
a completely incompressible medium. Thus at the peaks of pressure, water is
slightly denser than it is at the nadirs of pressure. This change in density also
affects how sound travels through water. Sound travels just a little faster at
the peaks of waves than in the nadirs. This leads to a very slight change in
the shape of the wave as it propagates. At each instant in wave propagation,
an infinitesimal amount of harmonics is generated. Such a shape change is
shown in Fig. 2.4, which reveals that sharp features in the waveforms require
harmonic frequencies beyond the fundamental. As the fundamental frequency
propagates through a compressible medium, nonlinear interactions - i.e., the
generation of harmonic frequencies - occur. The range of frequencies that ac-
cumulate along the distance of propagation change the wave shape to include
sharp features. These sharp features at peaks are harmonic components and
travel faster than rounded nadirs. Anyone who has ever been to a beach has
witnessed a shape change with wave propagation. As the sinusoidal swells
of the ocean move toward the shore, the swells develop into sharp, breaking
waves. The sharp peaks of the waves represent the higher harmonic frequen-
cies, whereas the swells approaching the shoreline represent the fundamental
frequencies.
Two aspects of harmonic generation are critical to their utility in impro-
ving image quality: 1) the growth with distance of propagation; and 2) the
