TubULAR: Tracking in toto deformations of dynamic tissues via constrained maps

A common motif in biology is the arrangement of cells into tubes, which further transform into complex shapes. Capturing the dynamic interplay between cellular behavior and organ shape requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations. Here, we present the Tube-like sUrface Lagrangian Analysis Resource (TubULAR), an analysis framework that builds in toto maps of tissue deformations by following tissue parcels in a static material frame of reference. Our approach then relates in-plane and out-of-plane behaviors and decomposes complex deformation maps into elementary contributions. We demonstrate our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. The method naturally generalizes to in vitro and synthetic systems and provides ready access to the mechanical mechanisms relating genetic patterning to organ shape change.