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Three-Dimensional Internal Source Plant Root Growth Model Brandy Wiegers University of California, Davis Dr. Angela Cheer Dr. Wendy Silk 2007 RMA World.

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Presentation on theme: "Three-Dimensional Internal Source Plant Root Growth Model Brandy Wiegers University of California, Davis Dr. Angela Cheer Dr. Wendy Silk 2007 RMA World."— Presentation transcript:

1 Three-Dimensional Internal Source Plant Root Growth Model Brandy Wiegers University of California, Davis Dr. Angela Cheer Dr. Wendy Silk 2007 RMA World Conference on Natural Resource Modeling June, 2007 Cape Cod, MA

2 Research Motivation

3 Photos from Silk’s lab

4 How do plant cells grow? Expansive growth of plant cells is controlled principally by processes that loosen the wall and enable it to expand irreversibly (Cosgrove, 1993).

5 Water Potential,  w   w gradient is the driving force in water movement.   w =  s +  p +  m  Gradients in plants cause an inflow of water from the soil into the roots and to the transpiring surfaces in the leaves (Steudle, 2001).

6 Hydraulic Conductivity, K  Measure of ability of water to move through the plant  Inversely proportional to the resistance of an individual cell to water influx  Think electricity  A typical value: K x,K z = 8 x cm 2 s -1 bar -1  Value for a plant depends on growth conditions and intensity of water flow abee/BIOBK/waterflow.gif

7 Relative Elemental Growth Rate, L(z)  A measure of the spatial distribution of growth within the root organ.  Co-moving reference frame centered at root tip.  Marking experiments describe the growth trajectory of the plant through time.  Streak photograph  Marking experiments Erickson and Silk, 1980

8 Relationship of Growth Variables L(z) = ▼· (K·▼  )(1)  Notation:  K x, K y, K z : The hydraulic conductivities in x,y,z directions  f x =  f/  x: Partial of any variable (f) with respect to x  In 2d: L(z) = K z  zz + K x  xx + K z z  z + K x x  xx (2)  In 3d: L(z) = K x  xx +K y  yy +K z  zz +K x x  x +K y y  y +K z z  z (3)

9 Given Experimental Data  Kx, Kz : 4 x10 -8 cm 2 s -1 bar x10 -8 cm 2 s -1 bar -1  L(z) = ▼ · g Erickson and Silk, 1980

10 Boundary Conditions (  Ω)  y = 0 on  Ω  Corresponds to growth of root in pure water  rmax = 0.5 mm  Zmax = 10 mm r max z max

11 Solving for  L(z) =▼·(K·▼  ) (1) L(z) = K x  xx + K y  yy + K z  zz + K x x  x + K y y  y + K z z  z (3) Known: L(z), K x, K y, K z,  on  Ω Unknown:  L ijk = [Coeff]  ijk (4) The assumptions are the key.

12 Osmotic Root Growth Model Assumptions  The tissue is cylindrical beyond the root tip, with radius r, growing only in the direction of the long axis z.  The growth pattern does not change in time.  Conductivities in the radial (K x ) and longitudinal (K z ) directions are independent so radial flow is not modified by longitudinal flow.  The water needed for primary root-growth is obtained only from the surrounding growth medium.

13 3D Osmotic Model Results *Remember each individual element will travel through this pattern*

14 Analysis of 3D Results Model Results  Longitudinal  gradient  Radial  gradient Empirical Results  Longitudinal  gradient has been measured  No radial  gradient has been measured

15 Phloem Source Gould, et al 2004

16 Internal Source Root Growth Model Assumptions  The tissue is cylindrical beyond the root tip, with radius r, growing only in the direction of the long axis z.  The growth pattern does not change in time.  Conductivities in the radial (K x ) and longitudinal (K z ) directions are independent so radial flow is not modified by longitudinal flow.  The water needed for primary root-growth is obtained from the surrounding growth medium and from internal proto-phloem sources.

17 3D Phloem Source Model

18 Comparison of Results Osmotic 3-D Model Results Internal Source 3-D Model Results

19 My Current Work… Sensitivity Analysis Looking at different plant root anatomies, source values, geometry, and initial value conditions.

20 Plant Root Geometry r = 0.3mm:0.5mm:0.7mm

21 Plant Root Geometry Proto-phleom Placement 2.1 mm from tip, 4.1mm, 6.1mm from tip, no source

22 Hydraulic Conductivity Kr: 4 x10 -8 cm 2 s -1 bar -1 Kr: 4 x10 -8 cm 2 s -1 bar x10 -8 cm 2 s -1 bar -1 Source, 4.1 mmNo Source

23 Hydraulic Conductivity Kr: 4 x10 -8 cm 2 s -1 bar -1 Kr: 4 x10 -8 cm 2 s -1 bar x10 -8 cm 2 s -1 bar -1 Source, 2.1 mmNo Source

24 Growth Boundary Conditions Soil vs Water Source, 2.1 mmNo Source

25 Summary: Growth Analysis  Radius: increase in radius results in increase of maximum water potential and resulting gradient  Phloem Placement: The further from the root tip that the phloem stop, the more the solution approximates the osmotic root growth model  Hydraulic Conductivity: Increased conducitivity decreases the radial gradient  Growth Conditions: Soil vs Water Conditions play an important role in comparing source and non source gradients

26 End Goal… Computational 3-d box of soil through which we can grow plant roots in real time while monitoring the change of growth variables.

27 Thank you! Do you have any further questions? Brandy Wiegers University of California, Davis My Thanks to Dr. Angela Cheer, Dr. Wendy Silk, the RMA organizers and everyone who came to my talk today. This material is based upon work supported by the National Science Foundation under Grant #DMS

28 Grid Refinement & Grid Generation

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