3-d computational model of water movement in plant root growth zone
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3-d Computational Model of Water Movement in Plant Root Growth Zone. Brandy Wiegers University of California, Davis Dr. Angela Cheer Dr. Wendy Silk 2007 Joint Mathematics Meeting January 8, 2007 New Orleans, LA. http://faculty.abe.ufl.edu/~chyn/age2062/lect/lect_15/MON.JPG. - PowerPoint PPT PresentationTRANSCRIPT
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3-d Computational Model of Water Movement in Plant Root
Growth Zone
Brandy WiegersUniversity of California, Davis
Dr. Angela Cheer
Dr. Wendy Silk
2007 Joint Mathematics Meeting
January 8, 2007
New Orleans, LA
http://faculty.abe.ufl.edu/~chyn/age2062/lect/lect_15/MON.JPG
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Photos from Silk’s lab
QuickTime™ and aTIFF (LZW) decompressor
are needed to see this picture.
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How do plant cells grow?How do plant cells grow?
Expansive growth of Expansive growth of plant cells is plant cells is
controlled controlled principally by principally by
processes that processes that loosen the wall loosen the wall and enable it to and enable it to
expand expand irreversibly irreversibly
(Cosgrove, 1993).(Cosgrove, 1993).
http://www.troy.k12.ny.us/faculty/smithda/Media/Gen.%20Plant%20Cell%20Quiz.jpg
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Water Potential, Water Potential, ww
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).
http://www.soils.umn.edu/academics/classes/soil2125/doc/s7chp3.htm
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Osmotic Root Growth Osmotic Root Growth Model AssumptionsModel Assumptions
The tissue is cylindrical, 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 (Kx) and longitudinal
(Kz) 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.
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Solving for Solving for
L(z) =·(K· )(1)
L(z) = Kxxx+ Kyyy + Kzzz+ Kxxx +
Kyyy + Kz
zz (2)
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Given Experimental DataGiven Experimental Data
• Kx, Kz : 4 x10-8cm2s-1bar-1 - 8x10-8 8cm2s-1bar-1
• L(z) = · g
Erickson and Silk, 1980
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Boundary Conditions (Boundary Conditions (Ω)Ω)
= 0 on Ω Corresponds to
growth of root in pure water
rmax = 0.4 mm
Zmax = 10 mm
rmax
zmax
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Solving for Solving for
L(z) =·(K· ) (1)
L(z) = Kxxx+ Kyyy + Kzzz+ Kxxx +
Kyyy + Kz
zz (2)
Known: L(z), Kx, Ky, Kz, on ΩUnknown:
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3D Osmotic Model 3D Osmotic Model ResultsResults
*Remember each individual element will travel through this pattern*
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Analysis of 3D ResultsAnalysis of 3D Results
Empirical Results Longitudinal
gradient does exist No radial gradient
Model Results Boyer and Silk, 2004
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Phloem SourcePhloem Source
Gould, et al 2004
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New Model AssumptionsNew Model Assumptions• The tissue is cylindrical, with radius x,
growing only in the direction of the long axis z.
• The growth pattern does not change in time.
• Conductivities in the radial (Kx) and longitudinal (Kz) 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 the phloem sources.
http://home.earthlink.net/~dayvdanls/root.gif
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3D Phloem Source Model3D Phloem Source Model
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Comparison of ResultsComparison of Results
Osmotic 3-D Model Results
Internal Source 3-D Model Results
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My Future Work…My Future Work…
• Sensitivity Analysis: Looking at different plant root anatomies, source values, geometry, and initial value
• Plant Root Micro-Environment
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End Goal…End Goal…
Computational 3-d box of soil through Computational 3-d box of soil through which we can grow plant roots in which we can grow plant roots in real time while monitoring the real time while monitoring the change of growth variables.change of growth variables.
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Thank you! Do you have Thank you! Do you have any further questions?any further questions?
Brandy WiegersUniversity of California, [email protected]://math.ucdavis.edu/~wiegers
My Thanks to Dr. Angela Cheer, Dr. Wendy Silk, the JMM organizers and everyone who came to my talk today.
This material is based upon work supported by the National Science Foundation under Grant #DMS-0135345