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Deformations in a Transverse Cross Section

Deformations in a Transverse Cross Section

When a material is subjected to uniaxial stress, it elongates or contracts in the direction of the applied force, and also undergoes changes in the perpendicular directions. This behavior is crucial for understanding how materials behave under stress and is governed by mechanical properties such as Poisson's ratio v, which measures the ratio of transverse strain to axial strain.
As the material stretches, it expands or contracts in orthogonal directions to the load. This phenomenon varies...

Deformation of Member under Multiple Loadings

Deformation of Member under Multiple Loadings

When a rod is made of different materials or has various cross-sections, it must be divided into parts that meet the necessary conditions for determining the deformation. These parts are each characterized by their internal force, cross-sectional area, length, and modulus of elasticity. These parameters are then used to compute the deformation of the entire rod.
In the case of a member with a variable cross-section, the strain is not constant but depends on the position. The deformation of an...

Three-Dimensional Analysis of Strain

Three-Dimensional Analysis of Strain

Three-dimensional strain analysis is crucial for understanding how materials deform under stress, particularly in elastic, homogeneous materials. This method employs principal stress axes to simplify complex stress states into more understandable forms. Subjected to stress, a small cubic element within a material either expands or contracts along these axes, transforming into a rectangular parallelepiped. This transformation effectively illustrates the material's deformation. The principal...

Transformation of Plane Strain

Transformation of Plane Strain

When analyzing elongated structures like bars subjected to uniformly distributed loads, it is essential to understand the transformation of plane strain when coordinate axes are rotated. This transformation helps to assess how material deformation characteristics vary with orientation, which is crucial in materials science and structural engineering.
Under plane strain conditions, typical for members where one dimension significantly exceeds the others, deformations and resultant strains are...

Deformation of a Beam under Transverse Loading

Deformation of a Beam under Transverse Loading

Understanding beam deflection, particularly for indeterminate beams with overhanging segments and multiple concentrated loads, is crucial for ensuring structural integrity and functionality. The process begins with constructing an accurate free-body diagram, which helps identify the forces and moments acting on the beam. This diagram is vital for visualizing how bending moments vary along the beam's length, influencing its curvature.
The insights from the bending moment diagram extend to...

Deformation in a Circular Shaft

Deformation in a Circular Shaft

One of the distinctive characteristics of circular shafts is their ability to maintain their cross-sectional integrity under torsion. In other words, each cross-section continues to exist as a flat, unaltered entity, simply rotating like a solid, rigid slab. To understand the distribution of shearing stress within such a shaft, consider a cylindrical section inside this circular shaft. This section has a length of L and a radius of R, with one end fixed. The radius of the cylindrical section is...

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Related Experiment Video

Updated: Dec 13, 2025

Author Spotlight: Advancing Hepatic Fibrosis Diagnosis Using Magnetic Resonance Elastography and AI

Author Spotlight: Advancing Hepatic Fibrosis Diagnosis Using Magnetic Resonance Elastography and AI

Published on: July 21, 2023

Divergence-Free Fitting-Based Incompressible Deformation Quantification of Liver.

Tianyu Fu, Jingfan Fan, Dingkun Liu

IEEE Journal of Biomedical and Health Informatics

|August 6, 2020

Summary

This study introduces a novel method for accurately quantifying liver deformation during respiration, ensuring volume preservation. A deep learning framework significantly accelerates this process, achieving over 95% accuracy.

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Measurement of Liver Stiffness Using Atomic Force Microscopy Coupled with Polarization Microscopy

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Published on: July 20, 2022

Area of Science:

Medical Imaging
Computational Anatomy
Biomedical Engineering

Background:

The liver is an incompressible organ, maintaining constant volume during respiratory movements.
Accurate quantification of liver deformation is crucial for effective liver tracking and medical interventions.
Existing methods for enforcing incompressibility during deformation analysis are often time-consuming and can weaken the deformation estimation.

Purpose of the Study:

To develop a rapid and accurate method for quantifying incompressible liver deformation using a divergence-free fitting-based registration approach.
To accelerate the incompressible deformation quantification process through a novel deep learning framework (DLF).

Main Methods:

A divergence-free fitting-based registration method was proposed, mapping deformation to velocity in a diffeomorphic space.
Fast Fourier-based Hodge-Helmholtz decomposition was employed to obtain divergence-free, curl-free, and harmonic fields.
A deep learning framework (DLF) was constructed, utilizing an encoder-decoder network trained on an incompressible respiratory motion model.

Main Results:

The proposed registration method accurately quantified incompressible liver deformation, achieving a mean liver overlap ratio of 95.33%.
The developed deep learning framework (DLF) demonstrated a significant acceleration, being nearly 15 times faster than existing methods.
The DLF effectively learned appearance-velocity correlations at a patch scale for accelerated motion quantification.

Conclusions:

The proposed divergence-free fitting-based registration method offers a rapid and accurate solution for quantifying incompressible liver deformation.
The integration of a deep learning framework substantially enhances the efficiency of liver motion quantification, making it clinically more viable.
This approach provides a robust tool for liver tracking and related medical applications requiring precise deformation analysis.