Energy partition of ultrasonic waves at flat boundaries

Interrelationship Between Control Parameters and Tumor/Bone Conditions for External Ultrasound Hyperthermia

“…The values in Table II can be determined by Snell's law and Mayer (Mayer 1965, which are functions of the angles of the incident wave and the reflected/refracted waves at the interface of soft tissue/bone and the velocities of waves in tissues and the tissue densities. The acoustic and tissue properties used in this study are shown in Table 1.…”

“…Furthermore, the ultrasound wave was assumed to transmit smoothly through the second interface (cortical layer/spongy bone) in the above study and Equation (2b), which neglects the effect of the second interface, was used to describe the absorbed power deposition in the bone region (zb s z s Ze ). When the second interface considered as a sharp change in acoustic impedance and normal incidence for the ultrasound beam, the absorbed power density in the bone region is, (9b) R' is the energy ratio of the reflected wave to the incident wave at the second interface and can be obtained by the densities of cortical layer and spongy/marrow region and the acoustic velocities in the cortical layer and the spongy/marrow region (Mayer 1965. R' is about equal to 0.12 for a 2300 m/s acoustic velocity in the spongy bone and the other parameters are shown in Table I.…”

“…The media of soft tissuebone are modeled as liquid-solid and the soft tissue can be considered as liquid due to the contribution of the shear waves to the heating in the soft tissue is negligible (Haken et al 1992). The interface of soft tissue/bone is regarded as a flat boundary, and the relationship between the incident wave and the reflected/refracted waves at the interface can be determined by Snell's law and Mayer (Mayer 1965 Then, the ultrasonic intensity on the cross-section area of the cone at depth z m is, For 0 5 z < zb (the soft tissue):…”

A model for transient ultrasonic field in solid generated by a transducer in immersion

“…In a fluid, the analytic and exact solution is known [8] and the particle velocity at the interface might be deemed locally to be plane for a point source in a fluid when the local interface area is small enough, compared to the distance to the point source. Using Mayer's formula [19], the contribution at a spatial point in a solid medium carried by a small source in a fluid is obtained. Integrating over the piston, the total field at the spatial point in the solid is obtained.…”

Reflectivity Measurements at the Interface of Two Bonded Solid Halfspaces

“…Theoretica1 ca1cu1ation3 of the ref1ection coefficients have been deve10ped [1][2][3] in case of two elastic solids. The possibi1ity of waves propagating a10ng the interface was shown by Pi1ant [4] and experimenta11y pointed out [5,6].…”