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Related Concept Videos

Elastic Strain Energy for Shearing Stresses01:20

Elastic Strain Energy for Shearing Stresses

As discussed in previous lessons, strain energy in a material is the energy stored when it is elastically deformed, a concept crucial in materials science and mechanical engineering. This energy results from the internal work done against the cohesive forces within the material. When a material undergoes shearing stress and corresponding shearing strain, the strain energy density, which is the energy stored per unit volume, is calculated. Within the elastic limit, where the stress is...
Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity01:15

Relation between Poisson's ratio, Modulus of Elasticity and Modulus of Rigidity

Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
Shearing Strain01:20

Shearing Strain

The shearing strain represents a cubic element's angular change when subjected to shearing stress. This type of stress can transform a cube into an oblique parallelepiped without influencing normal strains. The cubic element experiences a significant transformation when exposed solely to shearing stress. Its shape alters from a perfect cube into a rhomboid, clearly demonstrating the effect of shearing strain. The degree of this strain is considered positive if it reduces the angle between the...
Dynamic Modulus of Elasticity of Concrete01:16

Dynamic Modulus of Elasticity of Concrete

The dynamic modulus of elasticity assesses how a concrete structure deforms under impact or dynamic loads. It is typically higher than the static modulus of elasticity, measured under slow, steady loading conditions.
The sonic test is a common method to determine the dynamic modulus. In this test, a concrete beam, sized either 6 x 6 x 30 inches or 4 x 4 x 20 inches, is clamped at its center. Vibrations are initiated at one end of the beam by an electromagnetic exciter unit powered by a...
Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
As the bending moment...
Elastic Strain Energy for Normal Stresses01:22

Elastic Strain Energy for Normal Stresses

Strain energy quantifies the energy stored within a material due to deformation under loading conditions, a fundamental concept in materials science and engineering. The strain energy can be modeled when a material is subjected to axial loading with uniformly distributed stress. In this scenario, the stress experienced by the material is the internal force divided by the cross-sectional area, and the strain induced is directly proportional to this stress through the modulus of elasticity.
If...

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Magnetic Resonance Elastography Methodology for the Evaluation of Tissue Engineered Construct Growth
12:18

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Published on: February 9, 2012

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

Bing Nan Li1, Chee Kong Chui, Sim Heng Ong

  • 1NUS Graduate School for Integrative Sciences & Engineering, National University of Singapore, Singapore. bingoon@ieee.org

Magnetic Resonance Imaging
|January 17, 2012
PubMed
Summary

This study introduces a new method using piecewise constant level sets to improve the analysis of magnetic resonance elastography (MRE) data. This approach enhances the accuracy and reduces variability in interpreting tissue elasticity, aiding clinical applications.

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Area of Science:

  • Biomedical Engineering
  • Medical Imaging
  • Computational Biology

Background:

  • Magnetic resonance elastography (MRE) images soft tissue mechanical properties.
  • Interpreting shear modulus distribution in MRE is challenging and prone to variability.
  • Current methods rely on subjective regional elasticity analysis.

Purpose of the Study:

  • To develop a novel method for remodeling shear modulus distribution in MRE.
  • To improve the accuracy and reduce variability in MRE data interpretation.
  • To enhance the analysis and clinical application of MRE.

Main Methods:

  • Proposed a piecewise constant level set model for shear modulus distribution.
  • Utilized a hybrid level set model with alternating global and local region competitions for segmentation and registration.
  • Applied the model to simulated MRE datasets.

Main Results:

  • Achieved optimal segmentation and registration through the hybrid level set model.
  • Demonstrated mean errors of 11.33% for local frequency estimation and 18.87% for algebraic inversion.
  • Showcased the effectiveness of piecewise constant level set modeling in improving shear modulus distribution quality.

Conclusions:

  • Piecewise constant level set modeling significantly enhances MRE data quality.
  • The proposed method offers a more objective and reliable approach to MRE analysis.
  • This facilitates improved interpretation and clinical utility of MRE in assessing tissue mechanics.