Mathematics and Rhizotechnology. Mathematical methods for upscaling of rhizosphere control mechanisms.
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#### Root System Growth Model

We present a root system growth model which is based on L-Systems. The Matlab code RootBox provides tools to easily create time dependent branched geometries of plant root systems. The resulting root systems can be coupled to arbitrary soil as well as nutrient and water uptake models.

#### Key features are:

• Time dependent branched geometries are created from user supplied root parameters.
• Mechanisms included: root turnover, spatial boundaries, geotropism, plagiotropism and coupling to arbitrary soil models.
• Auxiliary Matlab functions to analyse results.
• It is possible to create a finite element mesh (using DistMesh) and import it into Comsol Multiphysics

#### Videos

The following videos give some examples of root system growth models:

The videos were created in Matlab and compressed by VirtualDub using the Xvid Mpeg-4 Codec. If you have problems opening the files we recommend to install the k-lite codec pack.

(23.5.2012): RootBox_v4.zip

(7.1.2010): RootBox_v3.zip
We provide several examples how to use the different tools:

• Introduction to L-Systems: Example_KochCurve.m, Example_Tree2D.m
• How to set up a root system: Example_SingleRoot.m, Example_SingleMaizeRoot.m, Example_Maize.m
• How to choose initial parameters: Example_InitialRoots1.m, Example_InitialRoots2.m
• Further examples: Example_Bounds.m, Example_DensityMap.m
• How to create a mesh around the root system: Example_Mesh.m

There is no user guide, there is only a rather short documentation of each Matlab function. The main dependences and use of the functions are illustrated in this flow chart. Please email comments, questions or bugs (to daniel.leitner(at)boku.ac.at and andrea.schnepf(at)boku.ac.at).

#### References describing the root system growth model

D. Leitner, S. Klepsch, G. Bodner, and A. Schnepf. A dynamic root system growth model based on L-Systems Tropisms and coupling to nutrient uptake from soil. Plant and Soil, 2010, DOI:10.1007/s11104-010-0284-7 (pdf)

D. Leitner, A. Schnepf, S. Klepsch, T. Roose. Comparison of nutrient uptake between 3-dimensional simulation and
an averaged root system model. Plant Biosystems, 2010, DOI: 10.1080/11263501003726334 (pdf)

D. Leitner and A. Schnepf, Root Growth Simulation Using L-Systems. Proceedings of ALGORITMY 2009 Conference on Scientifc Computing, p. 313-320. (pdf)

A. Schnepf and D. Leitner, FEM Simulation of Nutrient Uptake from Soil by a 3-Dimensional Root System Using DistMesh and Comsol Multiphysics. Proceedings of ALGORITMY 2009 - Conference on Scientific Computing, p. 321-330. (pdf)

D. Leitner, A. Schnepf, S. Klepsch, A. Knieß, and T. Roose, The algorithmic beauty of plant roots. Proceedings of Mathmod 2009 - 6th Vienna International Conference on Mathematical Modelling. (jpg)

#### Other relevant references:

P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants. Springer-Verlag, 1999. p. 101–107. (available online)

L. Kutschera: Wurzelatlas mitteleuropäischer Ackerunkräuter und Kulturpflanzen. DLG-Verlag Frankfurt am Main 1960.

T. Roose and A.C. Fowler, A mathematical model for water and nutrient uptake by plant root systems. Journal of Theoretical Biology, 2004. 228(2): p. 173-184.<

T. Roose and A.C. Fowler, A model for water uptake by plant roots. Journal of Theoretical Biology, 2004. 228(2): p. 155-171.

T. Roose, A.C. Fowler, and P.R. Darrah, A mathematical model of plant nutrient uptake. Journal of Mathematical Biology, 2001. 42(4): p. 347-360.

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