title: Inferring cellular forces from image stacks.
abstract: Although the importance of cellular forces to a wide range of embryogenesis and disease processes is widely recognized, measuring these forces is challenging, especially in three dimensions. Here, we introduce CellFIT-3D, a force inference technique that allows tension maps for three-dimensional cellular systems to be estimated from image stacks. Like its predecessors, video force microscopy and CellFIT, this cell mechanics technique assumes boundary-specific interfacial tensions to be the primary drivers, and it constructs force-balance equations based on triple junction (TJ) dihedral angles. The technique involves image processing, segmenting of cells, grouping of cell outlines, calculation of dihedral planes, averaging along three-dimensional TJs, and matrix equation assembly and solution. The equations tend to be strongly overdetermined, allowing indistinct TJs to be ignored and solution error estimates to be determined. Application to clean and noisy synthetic data generated using Surface Evolver gave tension errors of 1.6-7%, and analyses of eight-cell murine embryos gave estimated errors smaller than the 10% uncertainty of companion aspiration experiments. Other possible areas of application include morphogenesis, cancer metastasis and tissue engineering.This article is part of the themed issue 'Systems morphodynamics: understanding the development of tissue hardware'.
authors.affiliation: Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
authors.forename: Jim H
authors.initials: JH
authors.lastname: Veldhuis
authors.affiliation: Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
authors.forename: Ahmad
authors.initials: A
authors.lastname: Ehsandar
authors.affiliation: Department of Genetics and Developmental Biology, Institut Curie, 26 rue d'Ulm, 75248 Paris Cedex 05, France.
authors.forename: Jean-Léon
authors.initials: JL
authors.lastname: Maître
authors.affiliation: Developmental Biology Unit, European Molecular Biology Laboratory, Meyerhofstraße 1, 69117 Heidelberg, Germany.
authors.forename: Takashi
authors.initials: T
authors.lastname: Hiiragi
authors.affiliation: Department of Mathematics, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK.
authors.forename: Simon
authors.initials: S
authors.lastname: Cox
authors.affiliation: Department of Civil and Environmental Engineering, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 brodland@uwaterloo.ca.|Centre for Bioengineering and Biotechnology, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.
authors.forename: G Wayne
authors.identifier: http://orcid.org/0000-0002-3775-2121
authors.initials: GW
authors.lastname: Brodland
mesh_terms: D000818:Animals; D015509:Developmental Biology / Q000295:instrumentation / Q000379:methods*; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D008954:Models, Biological; D009024:Morphogenesis
keywords: CellFIT; CellFIT-3D; cell mechanics; force inference; interfacial tensions; video force microscopy (VFM)