ArticleJournal of mathematical biology2014
Surface growth kinematics via local curve evolution.
Article in Journal of mathematical biology, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 7 papers.
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Who cites it
7 citing papers in PubMed.
- Riemannian L-systems: modelling growing forms in curved spaces.Quantitative plant biology · 2025Review
- Possible roles of Wnt in the shell growth of the pond snail Lymnaea stagnalis.Scientific reports · 2024Article
- A multiscale computational framework for the development of spines in molluscan shells.PLoS computational biology · 2024Article
- Pseudo null growth model and its classifications based on generalized vortex filament equation.Heliyon · 2022Article
- The physical basis of mollusk shell chiral coiling.Proceedings of the National Academy of Sciences of the United States of America · 2021Article
- Mechanics unlocks the morphogenetic puzzle of interlocking bivalved shells.Proceedings of the National Academy of Sciences of the United States of America · 2020Article
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Authors and funding
2 authors.
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Abstract
A mathematical framework is developed to model the kinematics of surface growth for objects that can be generated by evolving a curve in space, such as seashells and horns. Growth is dictated by a growth velocity vector field defined at every point on a generating curve. A local orthonormal basis is attached to each point of the generating curve and the velocity field is given in terms of the local coordinate directions, leading to a fully local and elegant mathematical structure. Several examples of increasing complexity are provided, and we demonstrate how biologically relevant structures such as logarithmic shells and horns emerge as analytical solutions of the kinematics equations with a small number of parameters that can be linked to the underlying growth process. Direct access to cell tracks and local orientation enables for connections to be made to the underlying growth process.
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