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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...
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...
Shearing Stress01:18

Shearing Stress

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.
The average shearing stress can be calculated by dividing the shear by the area of the cross-section.
Transformation of Plane Stress01:18

Transformation of Plane Stress

Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's faces...
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...
Ultrasound II: Endoscopic Ultrasound and FibroScan01:25

Ultrasound II: Endoscopic Ultrasound and FibroScan

Endoscopic Ultrasound (EUS) and FibroScan are valuable diagnostic tools in gastroenterology and hepatology, each with specific applications and techniques.
Endoscopic Ultrasound (EUS):

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Related Experiment Video

Updated: Jun 19, 2026

Viscoelastic Characterization of Soft Tissue-Mimicking Gelatin Phantoms using Indentation and Magnetic Resonance Elastography
07:57

Viscoelastic Characterization of Soft Tissue-Mimicking Gelatin Phantoms using Indentation and Magnetic Resonance Elastography

Published on: May 10, 2022

Cross-plane shear wave elastography for viscoelasticity imaging.

Ryan Patrick Pitsinger1, Murthy N Guddati1

  • 1Department of Civil, Construction, and Environmental Engineering North Carolina State University, Raleigh, NC, United States of America.

Physics in Medicine and Biology
|June 17, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces a novel cross-plane shear wave elastography (SWE) method to image tissue viscosity beyond 2D planes. This advance enables more accurate viscoelasticity mapping for disease progression insights.

Keywords:
cross-plane imagingfull waveform inversionregularizationshear wave elastographyviscosity imaging

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Area of Science:

  • Biomedical Imaging
  • Ultrasound Technology
  • Biophysics

Background:

  • Conventional shear wave elastography (SWE) is limited to 2D planes, hindering comprehensive tissue analysis.
  • Viscosity, a measure of shear wave dissipation, is an emerging biomarker for disease progression, but current SWE lacks sensitivity to it.
  • Extending SWE beyond 2D planes is crucial for advanced viscoelasticity imaging.

Purpose of the Study:

  • To develop and validate a method for extending SWE-based viscoelasticity imaging beyond the 2D measurement plane.
  • To incorporate viscosity measurements as a key biomarker for disease progression.
  • To enhance SWE capabilities for more comprehensive tissue characterization.

Main Methods:

  • A cross-plane acquisition strategy was implemented, recording multiple measurement planes per acoustic radiation force (ARF) push.
  • Full-waveform inversion (FWI) with H1 regularization was employed for stable and accurate reconstruction of elasticity (G) and viscosity (eta).
  • Validation was performed using synthetic datasets with varying parameters and noise levels, employing a multiresolution sequential inversion framework.

Main Results:

  • The cross-plane strategy significantly improved viscosity distribution recovery by capturing inter-plane dissipative behavior.
  • H1 regularization enhanced reconstruction stability and reduced artifacts without compromising resolution.
  • Viscosity reconstructions showed improved boundary fidelity and reduced ambiguity compared to single-plane methods, while elasticity maps remained consistent.

Conclusions:

  • The study demonstrates the feasibility of reconstructing volumetric viscoelastic properties using cross-plane SWE.
  • The developed framework paves the way for true 3D viscoelastic imaging using standard 2D ultrasound acquisitions.
  • This method offers a pathway to improved disease diagnosis and monitoring through enhanced tissue characterization.