### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4aPAb4. The propagation of ultrasonic waves through a bubbly liquid into
tissue: A linear analysis.

**Quan Qi
**

**
John G. Harris
**

**
**
*Theor. Appl. Mech. UIUC, 216 Talbot Lab., 104 S. Wright St., Urbana, IL
61801
*

*
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**William D. O'Brien
**

**
**
*Elec. Comput. Eng., UIUC, Urbana, IL 61801
*

*
*
The steady-state response induced by an ultrasonic wave in a structure
comprised of two layers, a bubbly liquid, and a viscoelastic solid with a rigid
boundary, is studied in the linear approximation. This structure models a
steadily cavitating liquid in contact with tissue. The upper surface of the
liquid is driven harmonically and models the source. The lower surface of the
solid is rigid and models bone. Though the cavitation processes are nonlinear,
the propagation is approximated as linear. The model of the bubbly liquid is a
simple continuum one, supplemented by allowing for a distribution of different
bubble radii and for damping of the oscillations of each bubble. The model
contains three functions, the probability distribution describing the
distribution of bubble radii, and two functions modeling the mechanical
response of, respectively, the individual bubble and the tissue. Numerical
examples are worked out by adapting data taken from various published sources
to deduce the parameters of these functions. These examples permit an
assessment of the overall attenuation of the structure, and of the magnitude of
the pressure and particle velocity in the bubbly liquid, and of the traction
and the particle displacement in the tissue. [Partial support from Arjo, Inc.,
Morton Grove, IL.]