A new method for the in vivo identification of mechanical properties in arteries from cine MRI images: Theoretical framework and validation

Quantifying the stiffness properties of soft tissues is essential for the diagnosis of many cardiovascular diseases such as atherosclerosis. In these pathologies it is widely agreed that the arterial wall stiffness is an indicator of vulnerability. The present paper focuses on the carotid artery and proposes a new inversion methodology for deriving the stiffness properties of the wall from cine-MRI (magnetic resonance imaging) data. We address this problem by setting-up a cost function defined as the distance between the modeled pixel signals and the measured ones. Minimizing this cost function yields the unknown stiffness properties of both the arterial wall and the surrounding tissues. The sensitivity of the identified properties to various sources of uncertainty is studied. Validation of the method is performed on a rubber phantom. The elastic modulus identified using the developed methodology lies within a mean error of 9.6%. It is then applied to two young healthy subjects as a proof of practical feasibility, with identified values of 625 kPa and 587 kPa for one of the carotid of each subject.

In vivo non-invasive high resolution MR-based method for the determination of the elastic modulus of arterial vessels

The mechanical properties of arterial walls have long been recognized to play an essential role in the development and progression of cardiovascular disease (CVD). Early detection of variations in the elastic modulus of arteries would help in monitoring patients at high cardiovascular risk stratifying them according to risk. An in vivo, non-invasive, high resolution MR-phase-contrast based method for the estimation of the time-dependent elastic modulus of healthy arteries was developed, validated in vitro by means of a thin walled silicon rubber tube integrated into an existing MR-compatible flow simulator and used on healthy volunteers. A comparison of the elastic modulus of the silicon tube measured from the MRI-based technique with direct measurements confirmed the method's capability. The repeatability of the method was assessed. Viscoelastic and inertial effects characterizing the dynamic response of arteries in vivo emerged from the comparison of the pressure waveform and the area variation curve over a period. For all the volunteers who took part in the study the elastic modulus was found to be in the range 50-250 kPa, to increase during the rising part of the cycle, and to decrease with decreasing pressure during the downstroke of systole and subsequent diastole.

Thermal Weight Functions and Stress Intensity Factors for Bonded Dissimilar Media Using Body Analogy

In this study, an analytical method is presented for the computation of thermal weight functions in two dimensional bi-material elastic bodies containing a crack at the interface and subjected to thermal loads using body analogy method. The thermal weight functions are derived for two problems of infinite bonded dissimilar media, one with a semi-infinite crack and the other with a finite crack along the interface. The derived thermal weight functions are shown to reduce to the already known expressions of thermal weight functions available in the literature for the respective homogeneous elastic body. Using these thermal weight functions, the stress intensity factors are computed for the above interface crack problems when subjected to an instantaneous heat source.

Modeling of temperature and field-dependent electron mobility in a single-layer graphene sheet

In this paper, we address a physics-based analytical model of electric-field-dependent electron mobility (mu) in a single-layer graphene sheet using the formulation of Landauer and Mc Kelvey's carrier flux approach under finite temperature and quasi-ballistic regime. The energy-dependent, near-elastic scattering rate of in-plane and out-of-plane (flexural) phonons with the electrons are considered to estimate mu over a wide range of temperature. We also demonstrate the variation of mu with carrier concentration as well as the longitudinal electric field. We find that at high electric field (>10(6) Vm(-1)), the mobility falls sharply, exhibiting the scattering between the electrons and flexural phonons. We also note here that under quasi-ballistic transport, the mobility tends to a constant value at low temperature, rather than in between T-2 and T-1 in strongly diffusive regime. Our analytical results agree well with the available experimental data, while the methodologies are put forward to estimate the other carrier-transmission-dependent transport properties.

Transmission of elastic waves through a frictional boundary

Incident energy gets transmitted, reflected and absorbed across an interface in jointed rock mass leading to energy dissipation and alteration of waves. Wave velocities get attenuated during their propagation across joints and this behavior is studied using bender/extender element tests. The velocity attenuation and modulus reduction observed in experimental tests are modeled with three dimensional distinct element code and results are validated. Normal propagation of an incident shear wave through a jointed rock mass cause slip of the rock blocks if shear stress of wave exceeds the shear strength of the joint. As the properties of joint determine the transmission of energy across an interface, a parametric study is then conducted with the validated numerical model by varying the parameters that may determine the energy transmission across a joint using modified Miller's method. Results of the parametric study are analyzed and presented in the paper. (C) 2014 Elsevier Ltd. All rights reserved.

A peridynamic theory for linear elastic shells

A state-based peridynamic formulation for linear elastic shells is presented. The emphasis is on introducing, possibly for the first time, a general surface based peridynamic model to represent the deformation characteristics of structures that have one geometric dimension much smaller than the other two. A new notion of curved bonds is exploited to cater for force transfer between the peridynamic particles describing the shell. Starting with the three dimensional force and deformation states, appropriate surface based force, moment and several deformation states are arrived at. Upon application on the curved bonds, such states yield the necessary force and deformation vectors governing the motion of the shell. By incorporating a shear correction factor, the formulation also accommodates analysis of shells that have higher thickness. In order to attain this, a consistent second order approximation to the complementary energy density is considered and incorporated in peridynamics via constitutive correspondence. Unlike the uncoupled constitution for thin shells, a consequence of a first order approximation, constitutive relations for thick shells are fully coupled in that surface wryness influences the in-plane stress resultants and surface strain the moments. Our proposal on the peridynamic shell theory is numerically assessed against simulations on static deformation of spherical and cylindrical shells, that of flat plates and quasi-static fracture propagation in a cylindrical shell. (C) 2016 Elsevier Ltd. All rights reserved.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Elastic-plastic finite element analyses of short cracks

Stress and strain distributions and crack opening displacement characteristics of short cracks have been studied in single edge notch bend and centre cracked panel specimens using elastic–plastic finite element analyses incorporating both a non strain hardening and a power law hardening behaviour. J contour integral solutions to describe stress strain conditions at crack tips for short cracks differ from those for long cracks. The analyses show that (i) short cracks can propagate at stress levels lower than those required for long cracks and (ii) a two-parameter description of crack tip fields is necessary for crack propagation.

The Displacement and Strain Field of Three-Dimensional Rheologic Model of Earthquake Preparation

Based on the three-dimensional elastic inclusion model proposed by Dobrovolskii, we developed a rheological inclusion model to study earthquake preparation processes. By using the Corresponding Principle in the theory of rheologic mechanics, we derived the analytic expressions of viscoelastic displacement U(r, t) , V(r, t) and W(r, t), normal strains epsilon(xx) (r, t), epsilon(yy) (r, t) and epsilon(zz) (r, t) and the bulk strain theta (r, t) at an arbitrary point (x, y, z) in three directions of X axis, Y axis and Z axis produced by a three-dimensional inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model. Subsequent to the spatial-temporal variation of bulk strain being computed on the ground produced by such a spherical rheologic inclusion, interesting results are obtained, suggesting that the bulk strain produced by a hard inclusion change with time according to three stages (alpha, beta, gamma) with different characteristics, similar to that of geodetic deformation observations, but different with the results of a soft inclusion. These theoretical results can be used to explain the characteristics of spatial-temporal evolution, patterns, quadrant-distribution of earthquake precursors, the changeability, spontaneity and complexity of short-term and imminent-term precursors. It offers a theoretical base to build physical models for earthquake precursors and to predict the earthquakes.

Ultrasonic imaging of 3D displacement vectors using a simulated 2D array and beamsteering.

Most quasi-static ultrasound elastography methods image only the axial strain, derived from displacements measured in the direction of ultrasound propagation. In other directions, the beam lacks high resolution phase information and displacement estimation is therefore less precise. However, these estimates can be improved by steering the ultrasound beam through multiple angles and combining displacements measured along the different beam directions. Previously, beamsteering has only considered the 2D case to improve the lateral displacement estimates. In this paper, we extend this to 3D using a simulated 2D array to steer both laterally and elevationally in order to estimate the full 3D displacement vector over a volume. The method is tested on simulated and phantom data using a simulated 6-10MHz array, and the precision of displacement estimation is measured with and without beamsteering. In simulations, we found a statistically significant improvement in the precision of lateral and elevational displacement estimates: lateral precision 35.69μm unsteered, 3.70μm steered; elevational precision 38.67μm unsteered, 3.64μm steered. Similar results were found in the phantom data: lateral precision 26.51μm unsteered, 5.78μm steered; elevational precision 28.92μm unsteered, 11.87μm steered. We conclude that volumetric 3D beamsteering improves the precision of lateral and elevational displacement estimates.

Ultrasonic imaging of 3D displacement vectors using a simulated 2D array and beamsteering

Most quasi-static ultrasound elastography methods image only the axial strain, derived from displacements measured in the direction of ultrasound propagation. In other directions, the beam lacks high resolution phase information and displacement estimation is therefore less precise. However, these estimates can be improved by steering the ultrasound beam through multiple angles and combining displacements measured along the different beam directions. Previously, beamsteering has only considered the 2D case to improve the lateral displacement estimates. In this paper, we extend this to 3D using a simulated 2D array to steer both laterally and elevationally in order to estimate the full 3D displacement vector over a volume. The method is tested on simulated and phantom data using a simulated 6-10 MHz array, and the precision of displacement estimation is measured with and without beamsteering. In simulations, we found a statistically significant improvement in the precision of lateral and elevational displacement estimates: lateral precision 35.69 μm unsteered, 3.70 μm steered; elevational precision 38.67 μm unsteered, 3.64 μm steered. Similar results were found in the phantom data: lateral precision 26.51 μm unsteered, 5.78 μm steered; elevational precision 28.92 μm unsteered, 11.87 μm steered. We conclude that volumetric 3D beamsteering improves the precision of lateral and elevational displacement estimates. © 2012 Elsevier B.V. All rights reserved.

Phonon spectra and thermodynamic properties of rare gas solids based on empirical and semi-empirical (ab initio) two-body potentials : a comparative study /

We study the phonon dispersion, cohesive and thermal properties of raxe gas solids Ne, Ar, Kr, and Xe, using a variety of potentials obtained from different approaches; such as, fitting to crystal properties, purely ab initio calculations for molecules and dimers or ab initio calculations for solid crystalline phase, a combination of ab initio calculations and fitting to either gas phase data or sohd state properties. We explore whether potentials derived with a certain approaxih have any obvious benefit over the others in reproducing the solid state properties. In particular, we study phonon dispersion, isothermal ajid adiabatic bulk moduli, thermal expansion, and elastic (shear) constants as a function of temperatiue. Anharmonic effects on thermal expansion, specific heat, and bulk moduli have been studied using A^ perturbation theory in the high temperature limit using the neaxest-neighbor central force (nncf) model as developed by Shukla and MacDonald [4]. In our study, we find that potentials based on fitting to the crystal properties have some advantage, particularly for Kr and Xe, in terms of reproducing the thermodynamic properties over an extended range of temperatiures, but agreement with the phonon frequencies with the measured values is not guaranteed. For the lighter element Ne, the LJ potential which is based on fitting to the gas phase data produces best results for the thermodynamic properties; however, the Eggenberger potential for Ne, where the potential is based on combining ab initio quantum chemical calculations and molecular dynamics simulations, produces results that have better agreement with the measured dispersion, and elastic (shear) values. For At, the Morse-type potential, which is based on M0ller-Plesset perturbation theory to fourth order (MP4) ab initio calculations, yields the best results for the thermodynamic properties, elastic (shear) constants, and the phonon dispersion curves.

Premartensitic and martensitic phase transitions in ferromagnetic Ni2MnGa

We present an experimental study of the premartensitic and martensitic phase transitions in a Ni2MnGa single crystal by using ultrasonic techniques. The effect of applied magnetic field and uniaxial compressive stress has been investigated. It has been found that they substantially modify the elastic and magnetic behavior of the alloy. These experimental findings are a consequence of magnetoelastic effects. The measured magnetic and vibrational behavior agrees with the predictions of a recently proposed Landau-type model [A. Planes et al., Phys. Rev. Lett. 79, 3926 (1997)] that incorporates a magnetoelastic coupling as a key ingredient.

Premartensitic and martensitic phase transition in ferromagnetic Ni2MnGa

We present an experimental study of the premartensitic and martensitic phase transitions in a Ni2MnGa single crystal by using ultrasonic techniques. The effect of applied magnetic field and uniaxial compressive stress has been investigated. It has been found that they substantially modify the elastic and magnetic behavior of the alloy. These experimental findings are a consequence of magnetoelastic effects. The measured magnetic and vibrational behavior agrees with the predictions of a recently proposed Landau-type model [A. Planes et al., Phys. Rev. Lett. 79, 3926 (1997)] that incorporates a magnetoelastic coupling as a key ingredient.

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.