Journal Article

A mathematical framework for modelling cambial surface evolution using a level set method

Damien Sellier, Michael J. Plank and Jonathan J. Harrington

in Annals of Botany

Published on behalf of The Annals of Botany Company

Volume 108, issue 6, pages 1001-1011
Published in print October 2011 | ISSN: 0305-7364
Published online April 2011 | e-ISSN: 1095-8290 | DOI: http://dx.doi.org/10.1093/aob/mcr067
A mathematical framework for modelling cambial surface evolution using a level set method

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  • Ecology and Conservation
  • Evolutionary Biology
  • Plant Sciences and Forestry

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Background and Aims

During their lifetime, tree stems take a series of successive nested shapes. Individual tree growth models traditionally focus on apical growth and architecture. However, cambial growth, which is distributed over a surface layer wrapping the whole organism, equally contributes to plant form and function. This study aims at providing a framework to simulate how organism shape evolves as a result of a secondary growth process that occurs at the cellular scale.

Methods

The development of the vascular cambium is modelled as an expanding surface using the level set method. The surface consists of multiple compartments following distinct expansion rules. Growth behaviour can be formulated as a mathematical function of surface state variables and independent variables to describe biological processes.

Key Results

The model was coupled to an architectural model and to a forest stand model to simulate cambium dynamics and wood formation at the scale of the organism. The model is able to simulate competition between cambia, surface irregularities and local features. Predicting the shapes associated with arbitrarily complex growth functions does not add complexity to the numerical method itself.

Conclusions

Despite their slenderness, it is sometimes useful to conceive of trees as expanding surfaces. The proposed mathematical framework provides a way to integrate through time and space the biological and physical mechanisms underlying cambium activity. It can be used either to test growth hypotheses or to generate detailed maps of wood internal structure.

Keywords: Dynamic model; level sets; surface growth; vascular cambium; wood formation

Journal Article.  8149 words.  Illustrated.

Subjects: Ecology and Conservation ; Evolutionary Biology ; Plant Sciences and Forestry

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