Assessment of myocardial function by speckle-tracking echocardiography

Myocardial deformation or strain is the universal property of contracting cardiac muscle. Deformation is defined in physics as relative change of length (and is therefore unitless and usually given as percentage) and in cardiac imaging it is thus algebraically negative for shortening or positive for thickening. There are several definitions of strain—Lagrangian strain refers to a fixed baseline distance and Eulerian (or natural) strain—to a dynamically changing reference length, representing a time integral of strain rate (which can be obtained by tissue Doppler). Measurements of strains are usually obtained by greyscale image quantification modality—speckle-tracking echocardiography (STE) which analyses myocardial motion by tracking and matching naturally occurring markers of myocardial texture, described as speckles. Echocardiographic speckles represent interference pattern of subtle myocardial scatters and can be followed from frame to frame by dedicated software to define the displacement of the myocardium within the interval between consecutive frames (inverse of frame rate).

Nonuniform Stress Field Determination Based on Deformation Measurement

We demonstrate a technique that, under certain circumstances, will determine stresses associated with a nonuniform deformation field without knowing the detailed constitutive behavior of the deforming material. This technique is based on (1) a detailed deformation measurement of a domain and (2) the observation that for isotropic materials, the strain and the stress, which form the so-called work-conjugate pair, are co-axial, or their eigenvectors share the same direction. The particular measures for strain and stress considered are the Lagrangian strain and the second Piola-Kirchhoff stress. The deformation measurement provides the field of the principal stretch orientation θλ and since the Lagrangian strain and the second Piola-Kirchhoff stress are co-axial, the principal stress orientation θs of the second Piola-Kirchhoff stress is determined. The Cauchy stress is related to the second Piola-Kirchhoff stress through the deformation gradient tensor, which can be measured experimentally. We then show that the principal stress orientation θσ of the Cauchy stress is the sum of the principal stretch orientation θλ and the local rigid-body rotation θq, which is determinable by the deformation gradient through polar decomposition. With the principal stress orientation θσ known, the equation of equilibrium, now in terms of the two principal stresses σ1 and σ2, and θσ, can be solved numerically with appropriate traction boundary conditions. The technique is then applied to the experimental case of nonuniform deformation of a PVC sheet with a circular hole and subject to tension. Limitations and restrictions of the technique and possible extensions will be discussed.

Echocardiographic Assessment of Left Ventricular Remodeling in American Style Footballers

Several athletic programs incorporate echocardiography during pre-participation screening of American Style Football (ASF) players with great variability in reported echocardiographic values. Pre-participation screening was performed in National Collegiate Athletic Association Division I ASF players from 2008 to 2016 at the Division of Sports Cardiology. The echocardiographic protocol focused on left ventricular (LV) mass, mass-to-volume ratio, sphericity, ejection fraction, and longitudinal Lagrangian strain. LV mass was calculated using the area-length method in end-diastole and end-systole. A total of two hundred and thirty players were included (18±1 years, 57% were Caucasian, body mass index 29±4 kg/m2) after four players (2%) were excluded for pathological findings. Although there was no difference in indexed LV mass by race (Caucasian 78±11 vs. African American 81±10 g/m2, p=0.089) or sphericity (Caucasian 1.81±0.13 vs. African American 1.78±0.14, p=0.130), the mass-to-volume ratio was higher in African Americans (0.91±0.09 vs. 0.83±0.08, p<0.001). No race-specific differences were noted in LV longitudinal Lagrangian strain. Player position appeared to have a limited role in defining LV remodeling. In conclusion, significant echocardiographic differences were observed in mass-to-volume ratio between African American and Caucasian players. These demographics should be considered as part of pre-participation screening.

Free-standing Pt and Pd nanowires: strain-modulated stability and magnetic and thermoelectric properties

The concept diagram for (a) when B = 0, the Fermi–Dirac distributions are equal so M = 0 and (b) when the Lagrangian strain is applied, all the anti-parallel spin changes to parallel spins.

Mechanical stabilities and nonlinear properties of monolayer Gallium selenide under tension

The mechanical stabilities and nonlinear properties of monolayer Gallium selenide ( GaSe ) under tension are investigated by using density functional theory (DFT). The ultimate stresses and ultimate strains and the structure evolutions of monolayer GaSe under armchair (AC), zigzag (ZZ) and equiaxial (EQ) tensions are predicted. A thermodynamically rigorous continuum description of nonlinear elastic response is given by expanding the elastic strain energy density in a Taylor series in Lagrangian strain truncated after the fifth-order term. Fourteen nonzero independent elastic constants are determined by least-square fit to the DFT calculations. Pressure-dependent elastic constants (Cij(P)) and pressure derivatives of [Formula: see text] are also calculated. Calculated values of ultimate stresses and strains and the in-plane Young's modulus are all positive. It proves that monolayer GaSe is mechanically stable.

Coherent Lagrangian vortices: the black holes of turbulence

We introduce a simple variational principle for coherent material vortices in two-dimensional turbulence. Vortex boundaries are sought as closed stationary curves of the averaged Lagrangian strain. Solutions to this problem turn out to be mathematically equivalent to photon spheres around black holes in cosmology. The fluidic photon spheres satisfy explicit differential equations whose outermost limit cycles are optimal Lagrangian vortex boundaries. As an application, we uncover super-coherent material eddies in the South Atlantic, which yield specific Lagrangian transport estimates for Agulhas rings.