Bogotá - Ingeniería - Maestría en Ingeniería - Ingeniería Mecánica · 2022
Computational simulation and model of a generalized prototype of an ornamental root
The growth of a healthy and productive plant depends on the correct development of its roots and the surrounding environment. In this context, root growth is crucial because it provides support, anchoring, and feeding characteristics. Multiple reported studies have focused on interpreting and understanding the root behavior, providing different morphological and topological classifications of root archetypes. This document proposes and evaluates two computational models to simulate the root growth. The first model corresponds to the geometrical representation of root growth in 2D and 3D space. In this scheme, four common root archetypes were addressed and considered their tropisms: adventitious, primary root, napiform, and fasciculate. The visual inspection of different root plants such as beans, carrots, and orchids was considered to develop the algorithm. Then, computational simulations were carried out to obtain the desired root archetypes or morphologies. This model has a stochastic factor providing greater versatility in the simulations, similarly to actual roots. The second computational scheme used is Reaction-diffusion Root Branching (RDRB), which models the dynamic root growth using the finite element method (FEM) in 1D for the roots and 2D for the growing media. This model provides a more detailed and more complex description than the first one, considering the reaction-diffusion of the species, representing the biochemical search for nutrients. Additionally, it accounts for an elastic contribution to account for the mechanical effects of root growing and the media interaction. This model involves biochemical, biophysical, and tropism stimuli. The two proposed mathematical/computational models can correctly represent the plant root growth, incorporating geometrical aspects and biophysical and biochemical features. Furthermore, these models have the potential to be adopted to investigate other natural branching phenomena such as slime mold, fractures, circulatory systems, respiratory systems, and thunders.
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Contenido
- 1. INTRODUCTIONp. 20
- Root archetypesp. 20
- Biophysics and biomechanics responsep. 22
- Biochemical responsep. 23
- Computational modelsp. 25
- Proposed Laboratory protocolp. 26
- 1.5.1 Aimp. 26
- 1.5.2 Scopep. 26
- 1.5.3 Target groupp. 27
- 1.5.4 Procedurep. 27
- 1.5.4.1 Equipmentp. 27
- 1.5.4.2 Reagentsp. 27
- 1.5.6 Materialsp. 28
- 1.5.7 Protection elementsp. 29
- 1.5.8 Seed germination procedurep. 29
- 1.5.9 Image analysisp. 30
- MORPHOLOGIES IN PLANTSp. 32
- Materials and methodsp. 32
- Model parametersp. 33
- 2.2.1 Growth algorithmp. 35
- 2.2.2 Simulation conditionsp. 37
- Results and discussionp. 38
- 2.3.1 Simulations in 2Dp. 38
- Adventitious rootp. 38
- Primary rootp. 40
- 2.3.2 Simulations in 3Dp. 41
- Adventitious rootp. 38
- Primary rootp. 40
- Napiform rootp. 42
- Fasciculate rootp. 44
- Conclusionsp. 44
- DIFFUSION MODELp. 46
- 3.1Materials and methodsp. 46
- 3.1.1Reaction - diffusion modelp. 48
- 3.1.2Elastic modelp. 48
- 3.1.3 Internal stimuli in 1D meshp. 49
- 3.1.4 External stimuli in 2D meshp. 50
- 3.1.5 Mechanical stimuli 2D meshp. 51
- 3.1.6 Summary of model parametersp. 51
- Results and discussionp. 38
- 3.1.1 Mesh definitionp. 52
- 3.1.2 Reaction-Diffusion effectp. 52
- 3.1.3 Mechanical effectp. 54
- 3.1.4 Parameter characterizationp. 55
- 3.2.5 Time step stabilizationp. 60
- Conclusionsp. 44
- Future workp. 63
- 4. CONCLUDING REMARKS AND RECOMMENDATIONSp. 64
- 5.REFERENCESp. 65
- APPENDIXp. 70
- root, c. Adventitious root, d. Branching root and e. Fasciculate rootsp. 21
- Figure 3. Assembly of the Rhizoboxes holders inside the Incubatorp. 29
- must be approximately 2 cm to give into the mediump. 30
- The segments can be of different generations (branching order)p. 34
- dt, and the total simulation time is T = (n)dtp. 36
- Photography of actual root of Zea Mays after ten days of growthp. 39
- using the same input parametersp. 40
- Photography of actual root of Phaseolus vulgaris L. after eight days of growthp. 41
- Figure 10. 3D simulation of adventitious root with three generationsp. 42
- Figure 11. 3D simulation of primary root with three different generationsp. 42
- Photography of an actual napiform rootp. 43
- using the same input parametersp. 40
- Photography of an actual fasciculate rootp. 44
- elements are selected from the algorithm of the computational modelp. 50
- corresponds to the nodes with the lowest load responsep. 51
- coarse mesh, b) medium mesh, c) fine meshp. 52
- Emerging branches after simulating the RDRB modelp. 53
- reaction-diffusionp. 54
- this simulation (see Figure 17)p. 55
- Element selection every 50 iterationsp. 61
- simulation (Figure 17)p. 62
- of root (1D mesh)p. 62