A Comprehensive Review on the Viscoelastic Parameters Used for Engineering Materials, Including Soft Materials, and the Relationships between Different Damping Parameters.

Although the physical properties of a structure, such as stiffness, can be determined using some statical tests, the identification of damping parameters requires a dynamic test. In general, both theoretical prediction and experimental identification of damping are quite difficult. There are many different techniques available for damping identification, and each method gives a different damping parameter. The dynamic indentation method, rheometry, atomic force microscopy, and resonant vibration tests are commonly used to identify the damping of materials, including soft materials. While the viscous damping ratio, loss factor, complex modulus, and viscosity are quite common to describe the damping of materials, there are also other parameters, such as the specific damping capacity, loss angle, half-power bandwidth, and logarithmic decrement, to describe the damping of various materials. Often, one of these parameters is measured, and the measured parameter needs to be converted into another damping parameter for comparison purposes. In this review, the theoretical derivations of different parameters for the description and quantification of damping and their relationships are presented. The expressions for both high damping and low damping are included and evaluated. This study is considered as the first comprehensive review article presenting the theoretical derivations of a large number of damping parameters and the relationships among many damping parameters, with a quantitative evaluation of accurate and approximate formulas. This paper could be a primary resource for damping research and teaching.

Displacement of a bubble located at a fluid-viscoelastic medium interface.

A model for estimating the displacement of a bubble located at a fluid-viscoelastic medium interface in response to acoustic radiation force is presented by extending the model for a spherical object embedded in a bulk material. The effects of the stiffness and viscosity of the viscoelastic medium and the amplitude and duration of the excitation force on bubble displacement were investigated using the proposed model. The results show that bubble displacement has a nonlinear relationship with excitation duration and viscosity. The time at which the steady state is reached increases with increasing medium viscosity and decreasing medium stiffness.

Displacement of a bubble by acoustic radiation force into a fluid-tissue interface.

Microbubbles in an ultrasound beam experience a primary Bjerknes force, which pushes the microbubbles against a fluid-tissue interface and deforms the tissue. This interaction has been used to measure tissue elasticity and is a common interaction in many therapeutic and diagnostic applications, but the mechanisms of deformation, and how the deformation dynamic depends on the bubble and ultrasound parameters, remain unknown. In this study, a mathematical model is proposed for the displacement of a bubble onto a fluid-tissue interface and the tissue deformation in response to the primary Bjerknes force. First, a model was derived for static loading and the model's prediction of bubble-mediated tissue displacement and stresses in tissue were explored. Second, the model was updated for dynamic loading. The results showed that the bubble is both displaced by the applied force and changes its shape. The bubble displacement changes nonlinearly with the applied force. The stress values in tissue are quite high for a distance within one radius of the bubble from the bubble surface. The model proposed here is permissible in human tissue and can be used for biomedical ultrasound applications, including material characterization.

The effects of ultrasound parameters and microbubble concentration on acoustic particle palpation.

The elasticity of tissue-an indicator of disease progression-can be imaged by ultrasound elasticity imaging technologies. An acoustic particle palpation (APP) has recently been developed-the use of ultrasonically driven acoustic particles (e.g., microbubbles)-as an alternative method of tissue deformation. APP has the potential to improve the resolution, contrast, and depth of ultrasound elasticity imaging; but the tissue displacement dynamics and its dependence on acoustic pressure, center frequency, and microbubble concentration remains unknown. Here, displacements of at least 1 µm were produced by applying ultrasound onto a microbubble solution (concentration: 10 × 106 microbubbles ml-1) placed within a tunnel surrounded by a 5% gelatin phantom. Displacements of more than 10 µm were produced using a 1, 3.5, or 5 MHz center frequency pulse with peak-rarefactional pressures of 470, 785, and 1210 kPa, respectively. The deformation of the distal wall varied spatially and temporally according to the different parameters investigated. At low pressures, the deformation increased over several milliseconds until it was held at a nearly constant value. At high pressures, a large deformation occurred within a millisecond followed by a sharp decrease and long stabilization. Ultrasound exposure in the presence of microbubbles produced tissue deformation (p < 0.05) while without microbubbles, no deformation was observed.

Elastic Deformation of Soft Tissue-Mimicking Materials Using a Single Microbubble and Acoustic Radiation Force.

Mechanical effects of microbubbles on tissues are central to many emerging ultrasound applications. Here, we investigated the acoustic radiation force a microbubble exerts on tissue at clinically relevant therapeutic ultrasound parameters. Individual microbubbles administered into a wall-less hydrogel channel (diameter: 25-100 µm, Young's modulus: 2-8.7 kPa) were exposed to an acoustic pulse (centre frequency: 1 MHz, pulse length: 10 ms, peak-rarefactional pressures: 0.6-1.0 MPa). Using high-speed microscopy, each microbubble was tracked as it pushed against the hydrogel wall. We found that a single microbubble can transiently deform a soft tissue-mimicking material by several micrometres, producing tissue loading-unloading curves that were similar to those produced using other indentation-based methods. Indentation depths were linked to gel stiffness. Using a mathematical model fitted to the deformation curves, we estimated the radiation force on each bubble (typically tens of nanonewtons) and the viscosity of the gels. These results provide insight into the forces exerted on tissues during ultrasound therapy and indicate a potential source of bio-effects.

Acoustic Streaming in a Soft Tissue Microenvironment.

We demonstrated that sound can push fluid through a tissue-mimicking material. Although acoustic streaming in tissue has been proposed as a mechanism for biomedical ultrasound applications, such as neuromodulation and enhanced drug penetration, streaming in tissue or acoustic phantoms has not been directly observed. We developed a material that mimics the porous structure of tissue and used a dye and a video camera to track fluid movement. When applied above an acoustic intensity threshold, a continuous focused ultrasound beam (spatial peak time average intensity: 238 W/cm2, centre frequency: 5 MHz) was found to push the dye axially, that is, in the direction of wave propagation and in the radial direction. Dye clearance increased with ultrasound intensity and was modelled using an adapted version of Eckart's acoustic streaming velocity equation. No microstructural changes were observed in the sonicated region when assessed using scanning electron microscopy. Our study indicates that acoustic streaming can occur in soft porous materials and provides a mechanistic basis for future use of streaming for therapeutic or diagnostic purposes.

Acoustic particle palpation for measuring tissue elasticity.

We propose acoustic particle palpation-the use of sound to press a population of acoustic particles against an interface-as a method for measuring the qualitative and quantitative mechanical properties of materials. We tested the feasibility of this method by emitting ultrasound pulses across a tunnel of an elastic material filled with microbubbles. Ultrasound stimulated the microbubble cloud to move in the direction of wave propagation, press against the distal surface, and cause deformations relevant for elasticity measurements. Shear waves propagated away from the palpation site with a velocity that was used to estimate the material's Young's modulus.