Bayesian inference of whole-organ deformation dynamics from limited space-time point data

To understand the morphogenetic mechanisms of organ development and regeneration, it is essential to clarify the inter-hierarchical relationship between microscopic, molecular/cellular activities and organ-level tissue deformation dynamics. While the former have been studied for several decades, the latter - macroscopic geometrical information about physical tissue deformation - is often missing, especially for many vertebrates. This is mainly because live recording of detailed cell behaviors in whole tissues during vertebrate organogenesis is technically difficult. In this study, we have developed a novel method that combines snapshot lineage tracing with Bayesian statistical estimation to construct whole-organ deformation maps from landmark data on limited numbers of space-time points. Following the validation of the method using artificially generated data sets, we applied it to the analysis of tissue deformation dynamics in chick limb development. A quantitative tissue deformation map for St.23-St.24 has been constructed, and its precision has been proven by evaluating its predictive performance. Geometrical analyses of the map have revealed a spatially heterogeneous volume growth pattern that is consistent with the expression pattern of a major morphogen and anisotropic tissue deformation along an axis. Thus, our method enables deformation dynamics analysis in organogenesis using practical lineage marking techniques.