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Data-driven quasi-conformal morphodynamic flows
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AI
DOI：10.1098/rspa.2024.0527.png)
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Abstract
En 中文
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 quasi-conformal maps to quasi-conformal flows. By allowing the spatio-temporal variation of the shear and dilation 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 quasi-conformal flows allow us to characterize the morphogenesis of a range of surfaces.
Keywords:
quasi-conformal flow
mathematical modelling
morphodynamics
growth
Journal
P
IF:
3
Papers:
403
Citations:
2.5W
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