Data-driven quasiconformal morphodynamic flows
<|reference_start|>Data-driven quasiconformal morphodynamic flows: 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 generalises 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 generalised 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 characterise the morphogenesis of a range of surfaces.<|reference_end|>
@article{mosleh2024data-driven,
    title={Data-driven quasiconformal morphodynamic flows},
    author={Salem Mosleh, Gary P. T. Choi, L. Mahadevan},
    journal={arXiv preprint arXiv:2404.07073},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.07073},
    primaryClass={cs.CG cond-mat.soft physics.bio-ph q-bio.QM}
}