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Second Derivatives and the Shape of a Graph

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Related Experiment Video

Updated: May 30, 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 and global measures of shape dynamics.

Meghan K Driscoll1, John T Fourkas, Wolfgang Losert

  • 1Physics Department, University of Maryland, College Park, MD, USA.

Physical Biology
|August 12, 2011
PubMed
Summary

Analyzing cell shape and motion reveals distinct internal processes. This framework quantifies cell dynamics, differentiating contractions from protrusions in Dictyostelium discoideum cells.

Area of Science:

  • Cell biology
  • Biophysics
  • Quantitative biology

Background:

  • Cell shape and dynamics are crucial for understanding cellular functions.
  • Existing methods may not fully capture the complexity of cell shape changes.
  • Dictyostelium discoideum serves as a model organism for studying cell migration.

Purpose of the Study:

  • To introduce a versatile framework for quantifying cell shape and dynamics.
  • To differentiate global and local metrics for analyzing cellular processes.
  • To extract detailed information about cell boundary motion, including protrusions and retractions.

Main Methods:

  • Development of a computational framework for analyzing cell shape and motion.
  • Application of global and local shape metrics to migrating Dictyostelium discoideum cells.

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Measurement of Dynamic Scapular Kinematics Using an Acromion Marker Cluster to Minimize Skin Movement Artifact

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  • Extraction of protrusion and retraction events from boundary motion data.

    • Main Results:

    • Global shape metrics revealed rhythmic oscillations, suggesting cell contractions.
    • Local shape metrics identified wave-like dynamics, indicative of cell protrusions.
    • Protrusions were observed to zigzag, while retractions remained stationary.
    • Cell shape became more elongated with increasing cell speed.
    • Protrusions and retractions exhibited different shapes despite similar areas.

    Conclusions:

    • The developed framework provides distinct insights into cellular processes through global and local shape analysis.
    • Boundary motion analysis successfully quantifies protrusion and retraction dynamics.
    • Cell migration involves complex shape changes, with distinct behaviors for protrusions and retractions.