Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion.

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 µm in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

C-Elastography: In Vitro Feasibility Phantom Study.

C-Elastography (CE) is a new ultrasound technique that locally maps the non-linear elasticity of soft tissue using low-frequency (150-250 Hz) shear waves generated by the acoustic radiation force (ARF). CE is based on a recent finding that the magnitude of the ARF in an isotropic tissue-like solid is related linearly to a third-order modulus of elasticity, C, which is responsible for the coupling between deviatoric and volumetric constitutive behaviors. The main objective of the work described here was to examine the feasibility of using and performance of C-elastography in differentiating and characterizing soft tissue via a pilot study on ex vivo tissue and tissue-mimicking inclusions cast in a gelatin block. In this vein, the CE technique deploys a combination of ultrasound motion sensing and 3-D visco-elastodynamic simulation to estimate the non-linear modulus C. As ultrasound focusing inherently confines the ARF to a small region, CE provides the means for measuring C within O(mm3) volumes. Equipped with such data analysis, we performed in vitro CE experiments on agar-based, xenograft and normal breast tissue samples embedded in a gelatin matrix. The compound C-elastograms indicate marked (and sharp) C-contrast, with average values of 1.9 and 5.6 at push points inside the featured soft and hard inclusions, respectively.

Viscoelastic characterization of thin tissues using acoustic radiation force and model-based inversion.

By means of the viscoelastodynamic model for a two-layer solid-fluid system and a detailed account of the locally induced acoustic radiation force, a rational analytical and computational framework is established for the viscoelastic characterization of thin tissues from high-frequency ultrasound (HFUS) measurements. For practical applications, the back-analysis is set up to interpret the frequency response function, signifying the tissue's axial displacement (captured by the imaging transducer) per squared voltage driving the 'pushing' transducer, as experimental input. On parametrizing the tissue's viscoelastic behavior in terms of the standard linear model, the proposed methodology is applied to a set of measurements performed on tissue-mimicking phantom constructs with thicknesses ranging from 0.5 to 4 mm. The results demonstrate that the model-based inversion, which carefully mimics the local boundary conditions and applied ultrasound excitation, yields viscoelastic properties for the phantom that are virtually invariant over the range of specimen thicknesses tested. Beyond its immediate application to in vitro viscoelastic characterization of thin excised tissues and tissue constructs, the proposed methodology may also find use in the characterization of skin or skin lesions over bone in vivo.

Correction to 'A rational framework for dynamic homogenization at finite wavelengths and frequencies'.

[This corrects the article DOI: 10.1098/rspa.2018.0547.].

A rational framework for dynamic homogenization at finite wavelengths and frequencies.

In this study, we establish an inclusive paradigm for the homogenization of scalar wave motion in periodic media (including the source term) at finite frequencies and wavenumbers spanning the first Brillouin zone. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider the projection of germane Bloch wave function onto a suitable eigenfunction as descriptor of effective wave motion. For generality the finite wavenumber, finite frequency homogenization is pursued in R d via second-order asymptotic expansion about the apexes of 'wavenumber quadrants' comprising the first Brillouin zone, at frequencies near given (acoustic or optical) dispersion branch. We also consider the junctures of dispersion branches and 'dense' clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the germane eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points that are relevant to the phenomenon of topological insulation. On the other hand, the effective model for nearby solution branches is found to invariably entail a Dirac-like system of equations that describes the interacting dispersion surfaces as 'blunted cones'. For all cases considered, the effective description turns out to admit the same general framework, with differences largely being limited to (i) the eigenfunction basis, (ii) the reference cell of medium periodicity, and (iii) the wavenumber-frequency scaling law underpinning the asymptotic expansion. We illustrate the analytical developments by several examples, including Green's function near the edge of a band gap and clusters of nearby dispersion surfaces.

On the dynamic homogenization of periodic media: Willis' approach versus two-scale paradigm.

When considering an effective, i.e. homogenized description of waves in periodic media that transcends the usual quasi-static approximation, there are generally two schools of thought: (i) the two-scale approach that is prevalent in mathematics and (ii) the Willis' homogenization framework that has been gaining popularity in engineering and physical sciences. Notwithstanding a mounting body of literature on the two competing paradigms, a clear understanding of their relationship is still lacking. In this study, we deploy an effective impedance of the scalar wave equation as a lens for comparison and establish a low-frequency, long-wavelength dispersive expansion of the Willis' effective model, including terms up to the second order. Despite the intuitive expectation that such obtained effective impedance coincides with its two-scale counterpart, we find that the two descriptions differ by a modulation factor which is, up to the second order, expressible as a polynomial in frequency and wavenumber. We track down this inconsistency to the fact that the two-scale expansion is commonly restricted to the free-wave solutions and thus fails to account for the body source term which, as it turns out, must also be homogenized-by the reciprocal of the featured modulation factor. In the analysis, we also (i) reformulate for generality the Willis' effective description in terms of the eigenfunction approach, and (ii) obtain the corresponding modulation factor for dipole body sources, which may be relevant to some recent efforts to manipulate waves in metamaterials.

Modeling the influence of basketball game parameters on the final result in Tokyo 2020 / Modelando a influência dos parâmetros do jogo de basquetebol no resultado final em Tóquio 2020

ABSTRACT This study aims to ascertain the significance of the basketball game parameters which discriminated between winning and losing teams in matches played. The study sample comprises matches played at the men's basketball tournament at the XXXII Olympic Games in Tokyo. Four regression models were formed. Due to the size of the sample, the number of explaining variables was reduced using factor analysis, followed by stepwise regression to ascertain the statistical significance of the obtained models summarily, which were then broken down into individual parameters. This study indicates: (1) one of the four set regression models was summarily highly statistically significant; (2) out of the remaining models, two were eliminated due to the presence of multicollinearity, and one model did not exhibit high statistical significance; (3) the final score was most influenced by the variables of two- and three-point shot percentages, number of three-point shots, turnovers, defensive rebounds, and true shooting percentage. The results of the study corroborated the results of other studies which were carried out in recent years, that the game of basketball is trending towards three-point shots and lay-ups, reduction of turnovers when passing, and defensive rebounds have been confirmed to be greatly significant.

RESUMO Este estudo tem como objetivo verificar a significância dos parâmetros do jogo de basquetebol que discriminam entre equipes vencedoras e perdedoras em partidas disputadas. A amostra do estudo compreende partidas disputadas no torneio de basquete masculino dos XXXII Jogos Olímpicos de Tóquio. Quatro modelos de regressão foram formados. Devido ao tamanho da amostra, o número de variáveis explicativas foi reduzido por meio de análise fatorial, seguida de regressão stepwise para verificar sumariamente a significância estatística dos modelos obtidos, que foram então decompostos em parâmetros individuais. Este estudo indica: (1) um dos quatro modelos de regressão definidos foi sumariamente altamente estatisticamente significativo; (2) dos demais modelos, dois foram eliminados devido à presença de multicolinearidade e um modelo não apresentou alta significância estatística; (3) a pontuação final foi mais influenciada pelas variáveis porcentagem de arremessos de dois e três pontos, número de arremessos de três pontos, turnovers, rebotes defensivos e porcentagem de arremessos verdadeiros. Os resultados do estudo corroboraram os resultados de outros estudos que foram realizados nos últimos anos, que o jogo de basquete está tendendo a arremessos de três pontos e bandejas, redução de turnovers ao passar e rebotes defensivos foram confirmados muito significativo.

Why the high-frequency inverse scattering by topological sensitivity may work.

This study deciphers the topological sensitivity (TS) as a tool for the reconstruction and characterization of impenetrable anomalies in the high-frequency regime. It is assumed that the anomaly is simply connected and convex, and that the measurements of the scattered field are of the far-field type. In this setting, the formula for TS-which quantifies the perturbation of a cost functional due to a point-like impenetrable scatterer-is expressed as a pair of nested surface integrals: one taken over the boundary of a hidden obstacle, and the other over the measurement surface. Using multipole expansion, the latter integral is reduced to a set of antilinear forms featuring Green's function and its gradient. The remaining expression is distilled by evaluating the scattered field on the surface of an obstacle via Kirchhoff approximation, and pursuing an asymptotic expansion of the resulting Fourier integral. In this way, the TS is found to survive upon three asymptotic lynchpins, namely (i) the near-boundary approximation for sampling points close to the 'exposed' surface of an obstacle; (ii) uniform expansions synthesizing the diffraction catastrophes for sampling points near caustic surfaces, lines and points; and (iii) stationary phase approximation. Within the framework of catastrophe theory, it is shown that, in the case of the full source aperture, the TS is asymptotically dominated by the (explicit) near-boundary term-which explains the previously reported reconstruction capabilities of this class of indicator functionals. The analysis further shows that, when the (Dirichlet or Neumann) character of an anomaly is unknown beforehand, the latter can be effectively exposed by assuming point-like Dirichlet perturbation and considering the sign of the leading term inside the reconstruction.

The 'sixth sense' of ultrasound: probing nonlinear elasticity with acoustic radiation force.

Prompted by a recent finding that the magnitude of the acoustic radiation force (ARF) in isotropic tissue-like solids depends linearly on a particular third-order modulus of elasticity-hereon denoted by C, this study investigates the possibility of estimating C from the amplitude of the ARF-generated shear waves. The featured coefficient of nonlinear elasticity, which captures the incipient nonlinear interaction between the volumetric and deviatoric modes of deformation, has so far received only a limited attention in the context of soft tissues due to the fact that the latter are often approximated as (i) fluid-like when considering ultrasound waves, and (ii) incompressible under static deformations. On establishing the analytical and computational platform for the proposed sensing methodology, the study proceeds with applying the prototype technique toward estimating via ARF the third-order modulus C in a series of tissue-mimicking phantoms. To help validate the concept and its implementation, the germane third-order modulus is independently estimated in each phantom via an established technique known as acoustoelasticity. The C-estimates obtained respectively via acoustoelasticity and the new theory of ARF show a significant degree of consistency. The key features of the new sensing methodology are that: (a) it requires no external deformation of a material other than that produced by the ARF, and (b) it estimates the nonlinear C-modulus locally, over the focal region of an ultrasound beam-where the shear waves are being generated.