Predictions using the KZK equation for an HM3-type lithotripter
with a reflector that is made of material that is half pressure-release
and half rigid. For this simulation the centre section is made
of pressure-release material and a outer ring that is rigid. The
first figure shows the propagation curves; that is the pressure
amplitude along the axis; the upper curve is the peak-positive
pressure (P+) and the lower curve the peak-negative pressure (P-).
The geometrical focus of the lithotripter is at 12.8 cm. Note
that both the peak-positive (P+) and peak-negative (P-) pressures
dip dramatically at the focus. This is because of near cancelling,
of the inverted wave from the pressure-release material and the
non-inverted wave fromthe rigid material, in the vicinity of the
focus. On either side there are peaks because the two pulses from
the two materials arrive at different times and do not cancel
- this is classic behaviour in the focussing of a short transient.
The predicted waveforms at three locations are show below -
the pressure is given in MPa. Prefocally (11.3 cm) the negative
pulse from the pressure-release section of the reflector arrives
first. Post-focally (15.8 cm) the positive pulse from the rigid
reflector arives first.
For this simulation the centre section is made of rigid material
and a outer ring is pressure-release. The first figure shows the
propagation curves; that is the pressure amplitude along the axis;
the upper curve is the peak-positive pressure (P+) and the lower
curve the peak-negative pressure (P-). The geometrical focus of
the lithotripter is at 12.8 cm. In this case the structure of
the field is more complicated. The is a small dip in P+ and P-
around 13 cm; however the nature of the pulses involved measn
that they don't cancel as cleanly as in the case of the pressure-release
- rigid scenario.
The predicted waveforms at eight locations along the axis are
show below - the pressure is given in MPa. Prefocally (8.8 cm)
the pulse from the rigid reflector arrives first; the pulse from
the pressure-release is just starting to interact with the tail
of the rigid pulse. Around the geometrical focus the negative
peaks of the two troughs coincide giving a large negative peak.
Just beyond the focus (13.4) the waveforms almost overlap and
provide some sort of cancelling. Post-focally (18.8 cm) the positive
peak from the rigid reflector pulse coincides with positive pulse
from the pressure release reflector superimpose to give a large
positive peak.
See also the acoustic field of a standard lithotripter
This page is maintained by robinc@bu.edu
Last Updated July 1999