Kavli Affiliate: L. Mahadevan
| First 5 Authors: Salem Mosleh, Gary P. T. Choi, L. Mahadevan, ,
| Summary:
Temporal imaging of biological epithelial structures yields shape data at
discrete time points, leading to a natural question: how can we reconstruct the
most likely path of growth patterns consistent with these discrete
observations? We present a physically plausible framework to solve this inverse
problem by creating a framework that generalizes quasiconformal maps to
quasiconformal flows. By allowing for the spatio-temporal variation of the
shear and dilatation fields during the growth process, subject to regulatory
mechanisms, we are led to a type of generalized Ricci flow. When guided by
observational data associated with surface shape as a function of time, this
leads to a constrained optimization problem. Deploying our data-driven
algorithmic approach to the shape of insect wings, leaves and even sculpted
faces, we show how optimal quasiconformal flows allow us to characterize the
morphogenesis of a range of surfaces.
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