During morphogenesis, epithelia (cell sheets) undergo complex deformations as they stretch, bend, and twist to form the embryo. Often these changes in shape create multivalued surfaces that can be problematic for strain measurements. This paper presents a method for quantifying deformation of such surfaces. The method requires four-dimensional spatiotemporal coordinates of a finite number of surface markers, acquired using standard imaging techniques. From the coordinates of the markers, various deformation measures are computed as functions of time and space using straightforward matrix algebra. This method accommodates sparse randomly scattered marker arrays, with reasonable errors in marker locations. The accuracy of the method is examined for some sample problems with exact solutions. Then, the utility of the method is illustrated by using it to measure surface stretch ratios and shear in the looping heart and developing brain of the early chick embryo. In these examples, microspheres are tracked using optical coherence tomography. This technique provides a new tool that can be used in studies of the mechanics of morphogenesis.
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December 2008
Research Papers
A New Method for Measuring Deformation of Folding Surfaces During Morphogenesis
Benjamen A. Filas,
Benjamen A. Filas
Department of Biomedical Engineering,
Washington University
, St. Louis, MO 63130
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Andrew K. Knutsen,
Andrew K. Knutsen
Department of Mechanical, Aerospace and Structural Engineering,
Washington University
, St. Louis, MO 63130
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Philip V. Bayly,
Philip V. Bayly
Department of Mechanical, Aerospace and Structural Engineering,
Washington University
, St. Louis, MO 63130
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Larry A. Taber
Larry A. Taber
Department of Biomedical Engineering,
e-mail: lat@wustl.edu
Washington University
, St. Louis, MO 63130
Search for other works by this author on:
Benjamen A. Filas
Department of Biomedical Engineering,
Washington University
, St. Louis, MO 63130
Andrew K. Knutsen
Department of Mechanical, Aerospace and Structural Engineering,
Washington University
, St. Louis, MO 63130
Philip V. Bayly
Department of Mechanical, Aerospace and Structural Engineering,
Washington University
, St. Louis, MO 63130
Larry A. Taber
Department of Biomedical Engineering,
Washington University
, St. Louis, MO 63130e-mail: lat@wustl.edu
J Biomech Eng. Dec 2008, 130(6): 061010 (9 pages)
Published Online: October 14, 2008
Article history
Received:
January 15, 2008
Revised:
April 11, 2008
Published:
October 14, 2008
Citation
Filas, B. A., Knutsen, A. K., Bayly, P. V., and Taber, L. A. (October 14, 2008). "A New Method for Measuring Deformation of Folding Surfaces During Morphogenesis." ASME. J Biomech Eng. December 2008; 130(6): 061010. https://doi.org/10.1115/1.2979866
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