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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...
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Shearing stress, denoted by the Greek letter tau (τ), is stress caused by forces acting transversely on an object. These forces create internal ones within the entity in the plane where the external forces are applied. The resultant of these internal forces is the shear in the section.
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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...
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In the study of beam mechanics, shear diagrams play a crucial role in understanding the distribution of shear forces along the length of a beam. Consider a beam AB that is supported at both ends and subjected to perpendicular loads.
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Correlation-based full-waveform shear wave elastography.

Abdelrahman M Elmeliegy1,2, Murthy N Guddati1

  • 1North Carolina State University, Raleigh, NC, United States of America.

Physics in Medicine and Biology
|March 10, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new method for creating 2D elasticity maps from ultrasound data, improving shear wave elastography accuracy. The correlation-based approach offers robust and reliable elasticity imaging for soft tissues.

Keywords:
PDE constrained optimizationelastographyinverse modelingultrasoundwave scattering

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Area of Science:

  • Biomedical Engineering
  • Medical Imaging
  • Acoustics

Background:

  • Ultrasound elastography aims to map tissue elasticity for diagnostics.
  • Current methods face challenges with accuracy and robustness in heterogeneous tissues.
  • Reconstructing 3D elasticity maps from 2D ultrasound data is a significant goal.

Purpose of the Study:

  • To develop a novel methodology for inverting 2D elasticity maps from single-line ultrasound particle velocity measurements.
  • To establish a robust inversion framework for shear wave elastography.

Main Methods:

  • Utilized gradient optimization for iterative elasticity map modification.
  • Employed full-wave simulation as the forward model for shear wave propagation.
  • Developed a correlation-based cost functional for inversion, comparing it to least-squares methods.

Main Results:

  • The correlation-based functional demonstrated superior convexity and convergence properties.
  • The method proved robust against noisy measurements and initial guess sensitivity.
  • Successful characterization of homogeneous inclusions and elasticity maps using synthetic data was achieved.

Conclusions:

  • The proposed inversion framework enhances shear wave elastography accuracy.
  • This approach shows promise for obtaining precise shear modulus maps from clinical ultrasound data.
  • The methodology offers a more reliable alternative for soft tissue elasticity imaging.