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Related Concept Videos

Deformation of Member under Multiple Loadings01:11

Deformation of Member under Multiple Loadings

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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...
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Deformations in a Transverse Cross Section01:21

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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.
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Curvilinear Motion: Rectangular Components01:23

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Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector's direction.
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When analyzing the deformation of a symmetric prismatic member subjected to bending by equal and opposite couples, it becomes clear that as the member bends, the originally straight lines on its wider faces curve into circular arcs, with a constant radius centered at a point known as Point C. This phenomenon helps to understand the stress and strain distribution within the member more clearly.
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Plastic Deformations of Members with a Single Plane of Symmetry01:21

Plastic Deformations of Members with a Single Plane of Symmetry

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When a structural member undergoes plastic deformation due to bending, it is crucial to understand the position of the neutral axis and the stress distribution. This member, characterized by a single plane of symmetry, exhibits a uniform stress distribution, with negative stress above the neutral axis and positive stress below. Notably, the neutral axis does not align with the centroid of the cross-section. This misalignment is typical in cases where the cross-section is not rectangular or...
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It is essential to understand how structural members behave under plastic deformation when the bending stress exceeds the material's yield strength. This state of deformation permanently alters the shape of the member, in contrast to the linear elastic behavior observed before yielding. The strain at any point in the member is expressed in terms of maximum strain. Notably, the neutral axis, which coincides with the centroid during elastic bending, shifts away from the centroid under plastic...
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Characterizing interactions between cardiac shape and deformation by non-linear manifold learning.

Di Folco Maxime1, Moceri Pamela2, Clarysse Patrick1

  • 1Univ Lyon, UCBL, Inserm, INSA Lyon, CNRS, CREATIS, UMR5220, U1294,Villeurbanne 69621, France.

Medical Image Analysis
|November 3, 2021
PubMed
Summary

This study uses unsupervised manifold learning to analyze complex cardiac shape and deformation interactions. Our method reveals disease-specific patterns in right ventricular function, outperforming traditional approaches.

Keywords:
Cardiac imagingDimensionality reductionInformation fusionManifold learningMyocardial strain

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Area of Science:

  • Cardiovascular imaging analysis
  • Computational biology
  • Machine learning in medicine

Background:

  • Clinical assessment of cardiac function often simplifies high-dimensional data (shape, deformation) into scalars, limiting disease characterization.
  • Interactions between cardiac descriptors can be complex and disease-dependent, potentially biasing computational analysis.
  • Unsupervised manifold learning offers a potential approach to uncover hidden relationships within complex cardiac data.

Purpose of the Study:

  • To characterize interactions between cardiac shape and deformation descriptors using unsupervised manifold learning.
  • To adapt and validate a sparsified Multiple Manifold Learning (MML) framework for analyzing partially related cardiac descriptors.
  • To compare the proposed manifold alignment approach against other embedding and fusion strategies.

Main Methods:

  • Development and application of a sparsified Multiple Manifold Learning (MML) for latent space alignment of cardiac shape and deformation.
  • Weighting alignment strength based on sample pairs to capture varying interaction intensities.
  • Benchmarking against Diffusion Maps, Multiple Kernel Learning (MKL) fusion, and pairwise correspondence alignment.
  • Validation on a synthetic 0D cardiac model and a real-world dataset of 310 subjects (3D echocardiography).

Main Results:

  • Manifold alignment demonstrated superior performance over fusion methods for characterizing cardiac shape-deformation interactions.
  • The approach successfully identified disease-specific patterns in right ventricular shape and deformation in patients.
  • Experiments confirmed the relevance of jointly analyzing shape and deformation descriptors for improved understanding of cardiac function.

Conclusions:

  • Unsupervised manifold alignment is a powerful tool for characterizing complex interactions between cardiac shape and deformation.
  • This method enhances the understanding of right ventricular diseases by revealing finer-scale characteristic traits.
  • The findings suggest a shift towards more sophisticated, high-dimensional analysis in clinical cardiology.