scholarly journals Mechanical Properties of Viscoelastic Media by Local Frequency Estimation of Divergence-Free Wave Fields

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
Erik H. Clayton ◽  
Ruth J. Okamoto ◽  
Philip V. Bayly
Keyword(s):  
Mechanical Properties ◽  
Magnetic Resonance ◽  
Shear Modulus ◽  
Rigid Body ◽  
Frequency Estimation ◽  
Magnetic Resonance Elastography ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Wave Fields ◽  
Longitudinal Waves

Magnetic resonance elastography (MRE) is an imaging modality with which mechanical properties can be noninvasively measured in living tissue. Magnetic resonance elastography relies on the fact that the elastic shear modulus determines the phase velocity and, hence the wavelength, of shear waves which are visualized by motion-sensitive MR imaging. Local frequency estimation (LFE) has been used to extract the local wavenumber from displacement wave fields recorded by MRE. LFE -based inversion is attractive because it allows material parameters to be estimated without explicitly invoking the equations governing wave propagation, thus obviating the need to numerically compute the Laplacian. Nevertheless, studies using LFE have not explicitly addressed three important issues: (1) tissue viscoelasticity; (2) the effects of longitudinal waves and rigid body motion on estimates of shear modulus; and (3) mechanical anisotropy. In the current study we extend the LFE technique to (1) estimate the (complex) viscoelastic shear modulus in lossy media; (2) eliminate the effects of longitudinal waves and rigid body motion; and (3) determine two distinct shear moduli in anisotropic media. The extended LFE approach is demonstrated by analyzing experimental data from a previously-characterized, isotropic, viscoelastic, gelatin phantom and simulated data from a computer model of anisotropic (transversely isotropic) soft material.

Magnetic Resonance Elastography for the Measurement of Annulus Fibrosus Material Properties

2011 ◽  
Author(s):  
Daniel H. Cortes ◽  
Lachlan J. Smith ◽  
Sung M. Moon ◽  
Jeremy F. Magland ◽  
Alexander C. Wright ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Magnetic Resonance ◽  
Shear Modulus ◽  
Disc Degeneration ◽  
Annulus Fibrosus ◽  
Pulse Sequence ◽  
Imaging Techniques ◽  
Mechanical Vibration ◽  
Magnetic Resonance Elastography

Intervertebral disc degeneration is characterized by a progressive cascade of structural, biochemical and biomechanical changes affecting the annulus fibrosus (AF), nucleus pulposus (NP) and end plates (EP). These changes are considered to contribute to the onset of back pain. It has been shown that mechanical properties of the AF and NP change significantly with degeneration [1,2]. Therefore, mechanical properties have the potential to serve as a biomarker for diagnosis of disc degeneration. Currently, disc degeneration is diagnosed based on the detection of structural and compositional changes using MRI, X-ray, discography and other imaging techniques. These methods, however, do not measure directly the mechanical properties of the extracellular matrix of the disc. Magnetic Resonance Elastography (MRE) is a technique that has been used to measure in vivo mechanical properties of soft tissue by applying a mechanical vibration and measuring displacements with a motion-sensitized MRI pulse sequence [3]. The mechanical properties (e.g., the shear modulus) are calculated from the displacement field using an inverse method. Since the applied displacements are in the order of few microns, fibers may not be stretched enough to remove crimping. Therefore, it is unknown if the anisotropy of the AF due to the contribution of the fibers is detectable using MRE. The objective of this study is twofold: to measure shear properties of AF in different orientations to determine the degree of AF anisotropy observable by MRE, and to identify the contribution of different AF constituents to the measured shear modulus by applying different biochemical treatments.

A planar reconfigurable linear rigid-body motion linkage with two operation modes

2014 ◽  
Vol 228 (16) ◽  
pp. 2985-2991 ◽  
Author(s):  
Guangbo Hao ◽  
Xianwen Kong ◽  
Xiuyun He
Keyword(s):  
Rigid Body ◽  
Single Mode ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Reference Guide ◽  
Revolute Joints ◽  
Operation Modes ◽  
Straight Line ◽  
Motion Stage ◽  
Motion Mode

A planar reconfigurable linear (also rectilinear) rigid-body motion linkage (RLRBML) with two operation modes, that is, linear rigid-body motion mode and lockup mode, is presented using only R (revolute) joints. The RLRBML does not require disassembly and external intervention to implement multi-task requirements. It is created via combining a Robert’s linkage and a double parallelogram linkage (with equal lengths of rocker links) arranged in parallel, which can convert a limited circular motion to a linear rigid-body motion without any reference guide way. This linear rigid-body motion is achieved since the double parallelogram linkage can guarantee the translation of the motion stage, and Robert’s linkage ensures the approximate straight line motion of its pivot joint connecting to the double parallelogram linkage. This novel RLRBML is under the linear rigid-body motion mode if the four rocker links in the double parallelogram linkage are not parallel. The motion stage is in the lockup mode if all of the four rocker links in the double parallelogram linkage are kept parallel in a tilted position (but the inner/outer two rocker links are still parallel). In the lockup mode, the motion stage of the RLRBML is prohibited from moving even under power off, but the double parallelogram linkage is still moveable for its own rotation application. It is noted that further RLRBMLs can be obtained from the above RLRBML by replacing Robert’s linkage with any other straight line motion linkage (such as Watt’s linkage). Additionally, a compact RLRBML and two single-mode linear rigid-body motion linkages are presented.

Modeling shear modulus distribution in magnetic resonance elastography with piecewise constant level sets

2012 ◽  
Vol 30 (3) ◽  
pp. 390-401 ◽  
Author(s):  
Bing Nan Li ◽  
Chee Kong Chui ◽  
Sim Heng Ong ◽  
Tomokazu Numano ◽  
Toshikatsu Washio ◽  
...  
Keyword(s):  
Magnetic Resonance ◽  
Shear Modulus ◽  
Level Sets ◽  
Magnetic Resonance Elastography ◽  
Constant Level ◽  
Piecewise Constant

Computation of Nonlinear Response of Hydraulically Actuated Structures

1997 ◽  
Author(s):  
T. D. Burton ◽  
C. P. Baker ◽  
J. Y. Lew
Keyword(s):  
Rigid Body ◽  
Flexible Structures ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Beam ◽  
Test Bed ◽  
Ode Models ◽  
Hydraulically Actuated ◽  
Pressure Dynamics ◽  
Low Order

Abstract The maneuvering and motion control of large flexible structures are often performed hydraulically. The pressure dynamics of the hydraulic subsystem and the rigid body and vibrational dynamics of the structure are fully coupled. The hydraulic subsystem pressure dynamics are strongly nonlinear, with the servovalve opening x(t) providing a parametric excitation. The rigid body and/or flexible body motions may be nonlinear as well. In order to obtain accurate ODE models of the pressure dynamics, hydraulic fluid compressibility must generally be taken into account, and this results in system ODE models which can be very stiff (even if a low order Galerkin-vibration model is used). In addition, the dependence of the pressure derivatives on the square root of pressure results in a “faster than exponential” behavior as certain limiting pressure values are approached, and this may cause further problems in the numerics, including instability. The purpose of this paper is to present an efficient strategy for numerical simulation of the response of this type of system. The main results are the following: 1) If the system has no rigid body modes and is thus “self-centered,” that is, there exists an inherent stiffening effect which tends to push the motion to a stable static equilibrium, then linearized models of the pressure dynamics work well, even for relatively large pressure excursions. This result, enabling linear system theory to be used, appears of value for design and optimization work; 2) If the system possesses a rigid body mode and is thus “non-centered,” i.e., there is no stiffness element restraining rigid body motion, then typically linearization does not work. We have, however discovered an artifice which can be introduced into the ODE model to alleviate the stiffness/instability problems; 3) in some situations an incompressible model can be used effectively to simulate quasi-steady pressure fluctuations (with care!). In addition to the aforementioned simulation aspects, we will present comparisons of the theoretical behavior with experimental histories of pressures, rigid body motion, and vibrational motion measured for the Battelle dynamics/controls test bed system: a hydraulically actuated system consisting of a long flexible beam with end mass, mounted on a hub which is rotated hydraulically. The low order ODE models predict most aspects of behavior accurately.

Structures of the Phosphazenes [ClC(NPCl3)2]+PCl6 − and [CH3C(NPCl3)2]+SbCl6 − at 90 K

1997 ◽  
Vol 53 (6) ◽  
pp. 953-960 ◽  
Author(s):  
F. Belaj
Keyword(s):  
Rigid Body ◽  
Motion Analysis ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Torsion Angles ◽  
Ionic Compounds ◽  
Intramolecular Motions

The asymmetric units of both ionic compounds [N-(chloroformimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachlorophosphate, [ClC(NPCl3)2]+PCl^{-}_{6} (1), and [N-(acetimidoyl)phosphorimidic trichloridato]trichlorophosphorus hexachloroantimonate, [CH3C(NPCl3)2]+SbCl^{-}_{6} (2), contain two formula units with the atoms located on general positions. All the cations show cis–trans conformations with respect to their X—C—N—P torsion angles [X = Cl for (1), C for (2)], but quite different conformations with respect to their C—N—P—Cl torsion angles. Therefore, the two NPCl3 groups of a cation are inequivalent, even though they are equivalent in solution. The very flexible C—N—P angles ranging from 120.6 (3) to 140.9 (3)° can be attributed to the intramolecular Cl...Cl and Cl...N contacts. A widening of the C—N—P angles correlates with a shortening of the P—N distances. The rigid-body motion analysis shows that the non-rigid intramolecular motions in the cations cannot be explained by allowance for intramolecular torsion of the three rigid subunits about specific bonds.

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