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Related Concept Videos

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...
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.
Shear and Bending Moment Diagram: Problem Solving01:24

Shear and Bending Moment Diagram: Problem Solving

When analyzing a beam supporting concentrated loads and a distributed load, drawing the shear and bending moment diagrams is essential. These diagrams help understand the internal forces and moments acting on the beam, which is crucial for designing safe and efficient structures. Follow these steps to create the shear and bending moment diagrams:
Draw a Free-Body Diagram: Start by drawing a free-body diagram of the entire beam, including the concentrated loads, distributed load, and reaction...
Mohr's Circle for Plane Strain01:18

Mohr's Circle for Plane Strain

Mohr's circle is a crucial graphical method used to analyze plane strain by plotting strain on a set of cartesian coordinates, where the abscissa is normal strain ∈ and the ordinate is shear strain γ. Similarly to Mohr’s circle for plane stress, two points X and Y are plotted. Their coordinates are (∈x, -γXY) and (∈Y, γXY), respectively.
Mohr's circle visually represents the strain states under various conditions, which is essential for understanding material behavior. The center of Mohr's...
Shearing Stresses in a Beam: Problem Solving01:14

Shearing Stresses in a Beam: Problem Solving

A cantilever beam with a rectangular cross-section under distributed and point loads experiences shearing stresses. The analysis begins by identifying the loads acting on the beam. Then, the reactions at the beam's fixed end are calculated using equilibrium equations. The vertical reaction is a combination of the distributed and point loads, while the moment reaction is the sum of their moments. The shear force distribution along the beam, resulting from these loads, is established by creating...

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

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

Published on: February 9, 2012

Shear modulus decomposition algorithm in magnetic resonance elastography.

Oh In Kwon1, Chunjae Park, Hyun Soo Nam

  • 1Department of Mathematics, Konkuk University, Seoul 143-701, Korea. oikwon@konkuk.ac.kr

IEEE Transactions on Medical Imaging
|September 29, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a novel algorithm for magnetic resonance elastography (MRE) that reduces noise in shear modulus images. The new method enhances image quality without assuming local homogeneity, improving MRE analysis.

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Area of Science:

  • Biomedical Imaging
  • Medical Physics
  • Rheology

Background:

  • Magnetic resonance elastography (MRE) visualizes tissue elasticity using MRI.
  • Current MRE algorithms often assume local homogeneity and struggle with noise.
  • Reducing noise and maintaining contrast in MRE is crucial for accurate mechanical property assessment.

Purpose of the Study:

  • To develop a new MRE algorithm for noise reduction in shear modulus images.
  • To improve the robustness of MRE reconstructions without assuming local homogeneity.
  • To enhance the stability and accuracy of shear modulus determination.

Main Methods:

  • Proposed a novel iterative reconstruction algorithm for MRE.
  • Utilized a decomposition of the stress wave vector based on displacement data.
  • Validated the algorithm using numerical simulations and experimental data (agarose phantoms, human liver).

Main Results:

  • The proposed algorithm demonstrated increased robustness to noise compared to standard methods.
  • Successfully reduced noise amplification in reconstructed shear modulus images.
  • Achieved stable determination of shear modulus without the local homogeneity assumption.

Conclusions:

  • The novel MRE algorithm effectively reduces noise and improves shear modulus image quality.
  • The method offers a more robust and stable approach for MRE analysis, applicable to various tissues.
  • This advancement has the potential to enhance diagnostic capabilities in MRE.