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Related Concept Videos

Bending of Curved Members - Neutral Surface01:16

Bending of Curved Members - Neutral Surface

In curved beams, unlike straight beams, the stress distribution across the cross-section is not uniform due to the beam's curvature. This non-uniformity arises because the neutral axis, where stress is zero, does not align with the centroid of the section. In a curved beam, the strain varies along the section as a function of the distance from the neutral axis.
Consider the curved member described in the previous lesson. According to Hooke's law, which relates stress to strain within the...
Bending of Curved Members - Strain Analysis01:14

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Simpson's Rule II01:28

Simpson's Rule II

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Deformations in a Symmetric Member in Bending01:18

Deformations in a Symmetric Member in Bending

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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Curvilinear Motion: Rectangular Components01:23

Curvilinear Motion: Rectangular Components

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Deformations in a Transverse Cross Section01:21

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Related Experiment Video

Updated: May 8, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Local shape adaptation for curved slice selection.

Hans Weber1, Martin Haas, Denis Kokorin

  • 1University Medical Center Freiburg, Department of Radiology - Medical Physics, Freiburg, Germany.

Magnetic Resonance in Medicine
|September 6, 2013
PubMed
Summary
This summary is machine-generated.

Multidimensional radiofrequency (RF) excitation with nonlinear spatial encoding enables imaging of curved slices with consistent thickness. This advanced technique allows for local adaptation of slice shape, improving anatomical conformity in medical imaging.

Keywords:
ExLocMRIPatLocmultidimensional excitationnonlinear encoding fieldsspatial encoding

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Area of Science:

  • Magnetic Resonance Imaging (MRI)
  • Radiofrequency (RF) Pulse Design
  • Spatial Encoding

Background:

  • Nonlinear spatial encoding magnetic fields enable excitation and local encoding of curved MRI slices.
  • The inherent nonlinearity of these fields causes variations in slice thickness.
  • A framework for nonlinear receive encoding is extended to multidimensional excitation for pattern determination.

Purpose of the Study:

  • To combine nonlinear spatial encoding with multidimensional RF excitation for local adaptation of curved slice shape.
  • To achieve constant slice thickness in curved slice imaging.
  • To explore modifications of slice shape for enhanced anatomical adaptation.

Main Methods:

  • Utilizing a framework for nonlinear encoding and multidimensional excitation.
  • Acquiring cross-sections of curved slices in phantoms with adapted thickness and curvature.
  • Analyzing voxel shapes to determine the technique's applicability.
  • Applying slice-thickness adaptation to in vivo curved slice imaging.

Main Results:

  • Demonstrated feasibility of local slice thickness adaptation in both phantom and in vivo studies.
  • Achieved local adaptation of slice curvature.
  • Identified limitations including prolonged pulse duration and voxel shape distortion.

Conclusions:

  • Multidimensional excitation facilitates curved slice imaging with uniform thickness.
  • The technique offers potential for further slice shape modifications to better match anatomy.
  • This approach enhances the adaptability of MRI to complex anatomical structures.