Data-driven quasiconformal morphodynamic flows
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915348574371840 |
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| author | Mosleh, Salem Choi, Gary P. T. Mahadevan, L. |
| author_facet | Mosleh, Salem Choi, Gary P. T. Mahadevan, L. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07073 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Data-driven quasiconformal morphodynamic flows Mosleh, Salem Choi, Gary P. T. Mahadevan, L. Computational Geometry Soft Condensed Matter Biological Physics Quantitative Methods 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. |
| title | Data-driven quasiconformal morphodynamic flows |
| topic | Computational Geometry Soft Condensed Matter Biological Physics Quantitative Methods |
| url | https://arxiv.org/abs/2404.07073 |