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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...
Problem Solving on Stress and Strain01:22

Problem Solving on Stress and Strain

Stress is a quantity that describes the magnitude of a force that causes deformation, generally defined as internal force per unit area. When forces pull on an object and cause its elongation, like the stretching of an elastic band, it is called tensile stress. When forces cause the compression of an object, it is known as compressive stress. When an object is being squeezed uniformly from all sides, like a submarine in the depths of the ocean, we call this kind of stress bulk stress (or volume...
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.

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Related Experiment Video

Updated: May 30, 2026

Assessing Collagen and Elastin Pressure-dependent Microarchitectures in Live, Human Resistance Arteries by Label-free Fluorescence Microscopy
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Calculating tissue shear modulus and pressure by 2D Log-Elastographic methods.

Joyce R McLaughlin1, Ning Zhang, Armando Manduca

  • 1Mathematics Department, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA, mclauj@rpi.edu.

Inverse Problems
|August 9, 2011
PubMed
Summary
This summary is machine-generated.

This study introduces a 2D Log-Elastographic algorithm for improved shear modulus imaging. The new method accurately reconstructs tissue properties and enhances image quality compared to existing elastography techniques.

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Area of Science:

  • Medical Imaging
  • Biophysics
  • Computational Mechanics

Background:

  • Elastography, or shear modulus imaging, is crucial for detecting tissue abnormalities.
  • Current methods face challenges in accurately measuring pressure (p) alongside shear modulus (μ).
  • Existing algorithms struggle with numerical error control and reliable pressure reconstruction.

Purpose of the Study:

  • To present a novel 2D Log-Elastographic inverse algorithm.
  • To simultaneously reconstruct shear modulus (μ) and pressure (p) using a first-order partial differential equation system.
  • To improve the accuracy and stability of elastographic imaging.

Main Methods:

  • Developed a 2D Log-Elastographic inverse algorithm.
  • Assumed a 2D plane strain elastic model for tissue displacement.
  • Tested the algorithm on synthetic and in-vivo data.

Main Results:

  • The algorithm successfully reconstructs both shear modulus (μ) and pressure (p).
  • It effectively controls numerical error growth during reconstruction.
  • Demonstrated improved image quality compared to Log-Elastographic and Direct Inversion algorithms.
  • Validated on 2D synthetic and 2D in-vivo data from Mayo Clinic.

Conclusions:

  • The 2D Log-Elastographic algorithm offers a more robust and accurate method for shear modulus imaging.
  • This advancement has the potential to enhance diagnostic capabilities in medical imaging.
  • The reliable reconstruction of pressure (p) provides additional valuable information.