Here, we introduce an approach that builds in toto maps of surface deformation by following tissue parcels in the material frame of reference.
capturing the interplay between in-plane and out-of-plane behaviors requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations.
Mapping the full 3D surface to 2D images such that the tissue motion in 2D is minimal enables the user to easily follow the tissue and discern its 3D motion. We then provide a computational framework for linking in-plane and out-of-plane behaviors and decomposing complex deformation maps into elementary contributions
tube-like surfaces deform in 3D space, contracting and dilating inplane while bending out-of-plane in a coupled fashion. Understanding the dynamic mechanisms by which the systems change shape requires not only capturing instantaneous motion in 3D, but also following the material as it deforms to build so-called ‘Lagrangian’ measures of tissue defor...
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