  Many morphogenetic processes involve mechanical rearrangement of epithelial
tissues that is driven by precisely regulated cytoskeletal forces and cell
adhesion. The mechanical state of the cell and intercellular adhesion are not
only the targets of regulation, but are themselves likely signals that
coordinate developmental process. Yet, because it is difficult to directly
measure mechanical stress {\it in vivo} on sub-cellular scale, little is
understood about the role of mechanics of development. Here we present an
alternative approach which takes advantage of the recent progress in live
imaging of morphogenetic processes and uses computational analysis of high
resolution images of epithelial tissues to infer relative magnitude of forces
acting within and between cells. We model intracellular stress in terms of bulk
pressure and interfacial tension, allowing these parameters to vary from cell
to cell and from interface to interface. Assuming that epithelial cell layers
are close to mechanical equilibrium, we use the observed geometry of the two
dimensional cell array to infer interfacial tensions and intracellular
pressures. Here we present the mathematical formulation of the proposed
Mechanical Inverse method and apply it to the analysis of epithelial cell
layers observed at the onset of ventral furrow formation in the {\it
Drosophila} embryo and in the process of hair-cell determination in the avian
cochlea. The analysis reveals mechanical anisotropy in the former process and
mechanical heterogeneity, correlated with cell differentiation, in the latter
process. The method opens a way for quantitative and detailed experimental
tests of models of cell and tissue mechanics.
