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Related Concept Videos

Deformations in a Transverse Cross Section01:21

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...

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Related Experiment Video

Updated: Jun 27, 2026

Visualization of Cortical Modules in Flattened Mammalian Cortices
08:49

Visualization of Cortical Modules in Flattened Mammalian Cortices

Published on: January 22, 2018

Discrete conformal methods for cortical brain flattening.

Monica K Hurdal1, Ken Stephenson

  • 1Department of Mathematics, Florida State University, Tallahassee, FL 32306-4510, USA. mhurdal@math.fsu.edu

Neuroimage
|December 4, 2008
PubMed
Summary

This study introduces conformal flattening, a distortion-free method for mapping brain surfaces. This technique, using circle packing, enables better comparison of functional brain activity across individuals.

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How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index
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Last Updated: Jun 27, 2026

Visualization of Cortical Modules in Flattened Mammalian Cortices
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How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index
09:57

How to Measure Cortical Folding from MR Images: a Step-by-Step Tutorial to Compute Local Gyrification Index

Published on: January 2, 2012

Area of Science:

  • Neuroimaging
  • Computational Geometry
  • Medical Image Analysis

Background:

  • Comparing functional brain activity across subjects is challenging due to individual variations in cortical folding.
  • Cortical surface flattening (flat mapping) aids in identifying structural and functional relationships.
  • Existing metric flattening methods minimize but do not eliminate distortion.

Purpose of the Study:

  • To introduce the mathematical principles of conformal mapping for cortical surface flattening.
  • To present conformal mapping as a superior alternative to metric flattening for neuroimaging.
  • To demonstrate the practical application of conformal mapping using MRI data.

Main Methods:

  • Exploration of the mathematical impossibility of distortion-free metric flattening.
  • Introduction to the mathematical possibility and advantages of conformal flattening (zero angular distortion).
  • Application of discrete conformal mapping via circle packing, realizing the Riemann Mapping Theorem.

Main Results:

  • Conformal maps offer versatility, rich mathematical theory, and respect canonical coordinates for intersubject registration.
  • Circle packing enables practical computation of conformal maps, overcoming previous limitations.
  • Demonstrated generation of conformal flat maps from human cerebral cortex and cerebellum MRI data.

Conclusions:

  • Conformal flattening provides distortion-free maps essential for accurate intersubject comparison of brain activity.
  • Circle packing-based discrete conformal mapping is a practical and powerful tool for neuroimaging analysis.
  • This approach enhances the ability to study structural and functional brain organization.