A new method for measuring deformation of folding surfaces during morphogenesis

Area of Science:

• Developmental biology
• Biomechanical engineering
• Cell biology

Background:

• Epithelial tissues undergo complex deformations during embryonic development.
• Quantifying these deformations is challenging due to complex, multivalued surfaces.
• Accurate strain measurements are crucial for understanding morphogenesis.

Purpose of the Study:

• To present a novel method for quantifying deformation in complex epithelial surfaces.
• To enable accurate measurement of surface stretch ratios and shear during morphogenesis.
• To provide a tool for studying the mechanics of embryonic development.

Main Methods:

• Utilizes four-dimensional spatiotemporal coordinates of surface markers.
• Employs straightforward matrix algebra to compute deformation measures.
• Accommodates sparse, randomly scattered marker arrays with potential location errors.
• Examines accuracy using sample problems with exact solutions.

Main Results:

• The method accurately quantifies deformation on complex surfaces.
• Successfully applied to measure surface stretch and shear in chick embryo heart and brain development.
• Demonstrates utility with optical coherence tomography tracking of microspheres.

Conclusions:

• This method offers a robust tool for analyzing epithelial morphogenesis.
• It facilitates quantitative studies of tissue mechanics in developing embryos.
• Provides new insights into the biomechanical processes underlying embryonic shape changes.