Shear waves

Abstract: Shear wave elasticity imaging (SWEI) is a new approach to imaging and characterizing tissue structures based on the use of shear acoustic waves remotely induced by the radiation force of a focused ultrasonic beam. SWEI provides the physician with a virtual "finger" to probe the elasticity of the internal regions of the body. In SWEI, compared to other approaches in elasticity imaging, the induced strain in the tissue can be highly localized, because the remotely induced shear waves are attenuated fully within a very limited area of tissue in the vicinity of the focal point of a focused ultrasound beam. SWEI may add a new quality to conventional ultrasonic imaging or magnetic resonance imaging. Adding shear elasticity data ("palpation information") by superimposing color-coded elasticity data over ultrasonic or magnetic resonance images may enable better differentiation of tissues and further enhance diagnosis. This article presents a physical and mathematical basis of SWEI with some experimental results of pilot studies proving feasibility of this new ultrasonic technology. A theoretical model of shear oscillations in soft biological tissue remotely induced by the radiation force of focused ultrasound is described. Experimental studies based on optical and magnetic resonance imaging detection of these shear waves are presented. Recorded spatial and temporal profiles of propagating shear waves fully confirm the results of mathematical modeling. Finally, the safety of the SWEI method is discussed, and it is shown that typical ultrasonic exposure of SWEI is significantly below the threshold of damaging effects of focused ultrasound.

Abstract: Expressions for the velocities of elastic waves in stressed solids are derived using Murnaghan's theory of finite deformations and third-order terms in the energy. For isotropic materials, in addition to the Lam\'e constants $\ensuremath{\lambda}$ and $\ensuremath{\mu}$, three additional constants, $l$, $m$, and $n$, are required to describe the material.By measuring the transmission time of elastic pulses through the material, the velocities of longitudinal and shear waves are determined as a function of applied stress. By subjecting the material to hydrostatic pressure as well as simple compression, it is found that seven functions of the three constants $l$, $m$, and $n$ can be measured and thus numerical values calculated. Results are given for polystyrene, iron, and Pyrex glass.

Abstract: The stability of a liquid layer flowing down an inclined plane is investigated. A new perturbation method is used to furnish information regarding stability of surface waves for three cases: the case of small wavenumbers, of small Reynolds numbers, and of large wavenumbers. The results for small wavenumbers agree with Benjamin's result obtained by the use of power series expansion, and the results for the two other cases are new. The results for large wavenumbers, zero surface tension, and vertical plate contradict the tentative assertion of Benjamin. The three cases are then re‐examined for shear‐wave stability, and the results compared with those for confined plane Poiseuille flow. The comparison serves to indicate the vestiges of shear waves in the free‐surface flow, and to give a sense of unity in the understanding of the stability of both flows. The case of large wavenumbers also serves as a new example of the dual role of viscosity in stability phenomena.The topological features of the ci curves for...

Abstract: Geoacoustic models of the sea floor are basic to underwater acoustics and to marine geological and geophysical studies of the earth’s crust, including stratigraphy, sedimentology, geomorphology, structural and gravity studies, geologic history, and many others A ’’geoacoustic model’’ is defined as a model of the real sea floor with emphasis on measured, extrapolated, and predicted values of those properties important in underwater acoustics and those aspects of geophysics involving sound transmission In general, a geoacoustic model details the true thicknesses and properties of sediment and rock layers in the sea floor A complete model includes water‐mass data, a detailed bathymetric chart, and profiles of the sea floor (to obtain relief and slopes) At higher sound frequencies, the investigator may be interested in only the first few meters or tens of meters of sediments At lower frequencies information must be provided on the whole sediment column and on properties of the underlying rocks Complete geoacoustic models are especially important to the acoustician studying sound interactions with the sea floor in several critical aspects: they guide theoretical studies, help reconcile experiments at sea with theory, and aid in predicting the effects of the sea floor on sound propagation The information required for a complete geoacoustic model should include the following for each sediment and rock layer In some cases, the state‐of‐the‐art allows only rough estimates, in others information may be nonexistent (1) Identification of sediment and rock types at the sea floor and in the underlying layers (2) True thicknesses and shapes of layers, and locations of significant reflectors (which may vary with sound frequencies) For the following properties, information is required in the surface of the sea floor, in the surface of the acoustic basement, and values of the property as a function of depth in the sea floor (3) Compressional wave (sound) velocity (4) Shear wave velocity (5) Attenuation of compressional waves (6) Attenuation of shear waves (7) Density (8) Additional elastic properties (eg, dynamic rigidity and Lame’s constant); given compressional and shear wave velocities and density, these and other elastic properties can be computed There is an almost infinite variety of geoacoustic models; consequently, the floor of the world’s ocean cannot be defined by any single model or even a small number of models; therefore, it is important that acoustic and geophysical experiments at sea be supported by a particular model, or models, of the area However, it is possible to use geological and geophysical judgement to extrapolate models over wider areas within geomorphic provinces To extrapolate models requires water‐mass data (such as from Nansen casts and velocimeter lowerings), good bathymetric charts, sediment and rock information from charts, cores, and the Deep Sea Drilling Project, echo‐sounder profiles, reflection and refraction records (which show detailed and general layering and the location of the acoustic basement), sound velocities in the layers, and geological and geophysical judgement Recent studies have provided much new information which, with older data, yield general values and restrictive parameters for many properties of marine sediments and rocks These general values and parameters, and methods for their derivation, are the main subjects of this paper