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Model-based approach. Purpose Improve understanding Optimization Control Macroscale approach Mannapperuma et al. (1991); Lammertyn et al. (2003) Geometry: intact fruit Gas transport coupled with respiration kinetics. Gas transport properties. Effective parameters. D eff. Liquid phase.

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Model based approach l.jpg
Model-based approach

  • Purpose

    • Improve understanding

    • Optimization

    • Control

  • Macroscale approach

    • Mannapperuma et al. (1991); Lammertyn et al. (2003)

    • Geometry: intact fruit

    • Gas transport coupled with respiration kinetics


Gas transport properties l.jpg
Gas transport properties

Effective parameters

Deff

Liquid phase

1-ε

Ci,l

ε

Ci,g

Gas phase

  • Macroscale approach

    • Volume-averaged parameter

  • Measurement

    • Biological variability

    • DCO2 > DO2

    • Anisotropic diffusivity

    • Apparant values


Microscopic overview of tissue l.jpg
Microscopic overview of tissue

  • Parenchyma tissue structure

    • Grouped cells

    • Random distribution of cells and pores

    • Cell wall

    • Plasma membranes

  • Transport phenomena

    • Geometry required

    • Two phases

      • Gas

      • Liquid

    • Cell membrane

      • Passive transport

      • Active transport

    • Intra-cellular enzymatic reactions

Plant Cell wall (Albert et al., 1994)


Objective l.jpg
Objective

  • To verify the applicability of a microscale modelling approach to the gas transport at tissue level in a multiscale framework

  • To quantify the pathways of gas transport in relation to the microstructure of fruit tissue


Microscale modelling of gas transport in pears l.jpg

Microscale modelling of gas transport in pears

Q. Tri Ho, Hibru K. Mebatsion, Bert E. Verlinden, Pieter Verboven, Stefan Vandewalle and Bart M. Nicolaï


Geometry model l.jpg
Geometry model

  • Light microscopy images

    • Parenchyma tissues of ‘Conference’ pear

    • Resolution 1pixel~0.735µm

    • Digitization of image

  • Geometry model generation (Mebatsion et al, 2006)

    • Ellipse tessellation algorithm


Slide8 l.jpg

TEM image of Conference pear

Cells

  • Ellipse tesselation

Cell

Intercellular space

Cell wall


Concept of gas transport l.jpg
Concept of gas transport

Liquid

Pore

O2,g

ADP

+Pi

O2,l

ATP synthase

Mitochondrion

ATP

Cytosol

CO2,l

Work

ATP

CO2,g

HCO3-

Gas exchange of fruit

Air filled intercellular space

At the interface

Intra-cell


Model of o 2 transport in tissue l.jpg
Model of O2 transport in tissue

  • Assumption

    • Cell wall was assumed gas phase with effective diffusivity DO2,w

    • Passive gas transport through cell membrane

    • Henry’s law at the inter-phase

  • Model equation (Fick’s second law of diffusion)

    • Pore, cell, cell wall (i= pore, cell, cellwall)

    • O2 consumption at intra-cell

      • Michaelis-Menten reaction

    • Flux through cell membrane

      • with C*O2,l the equilibrated O2 concentration outside of the membrane


Model of co 2 transport in tissue l.jpg
Model of CO2 transport in tissue

CO2,l

CO32-

HCO3-

Fraction of spieces

H2CO3

pH

  • Fraction of CO2 spieces in liquid phase


Model of co 2 transport in tissue12 l.jpg
Model of CO2 transport in tissue

O2

Mitochondrion

k1

H2CO3

CO2,l

+ H2O

k2

ka1

HCO3-

+H+

CO2,g

  • In pore, cell wall: the same as Eq of O2

  • In cellular liquid phase


Physical parameters of microscale model l.jpg
Physical parameters of microscale model

(1)Lide (1996), (2) Gunning and Steer (1996), (3) Uchida et al. (1992),

(4)Geers and Gros (2000), (5) Jolly (1991)


Numerical solution l.jpg
Numerical solution

C2

Ltissue

C1

  • Meshing

    • 125050 elements

  • Solution

    • Finite element method

    • Comsol 3.3 (Comsol AB, Stockholm)

  • Estimation of Dtissue, eff

    • Steady state

    • Boundary condition

      • Side 1: C1 ; Side 2: C2

Isolated boundary


Results l.jpg
Results

  • Simulation of O2 transport


Slide16 l.jpg


Effect of vacuole in the model l.jpg
Effect of vacuole in the model

  • Occupy 30-90% of cell volume

  • Storage function

  • Maintain internal acidic pH

  • Lumped pH intra-cell model

    • Constant pH in the cell (DH+=9.3×10-9 m2/s, Geers and Gros, 2000)

    • pHintra-cell=5

  • Model with vacuole

    • Constant pH in the cytoplasm and vacuole

    • Regulation of pH in the cytoplasm and vacuole

    • pHcytoplasm=7, pHvacuole=4.82




Slide20 l.jpg

  • Estimated O including vacuole2 diffusivity of pear tissue

DO2,cell wall =5×10-9 m2/s

Cell wall thickness= 0.73 µm

(TEM, Mebatsion 2006, unpublished data)

9 different geometries


Slide21 l.jpg

Dw, CO2cell= 5×10-9m2/s

Cell wall thickness= 0.73 µm

(TEM, Mebatsion 2006, unpublished data)

9 different geometries


Current work l.jpg
Current work including vacuole

  • Toward 3D model

    • Digitization vs. mapping

X-ray image

Digitial geometry

Mapping parameters

13853 elements

16896 elements


Solution using mapping parameters l.jpg
Solution using mapping parameters including vacuole

Solution based on digitial geometry

DO2=1.29e-9 m2/s

Solution using mapping parameters

DO2=1.33e-9 m2/s


3d geometry based on mapping l.jpg
3D geometry based on mapping including vacuole

  • Geometry information

    • Synchrotron X-ray tomography

    • Resolution 1 pixel~1.4µm

    • Pore distribution


3d geometry based on mapping25 l.jpg
3D geometry based on mapping including vacuole

  • Geometry meshing

    • Lagrange-linear cube

    • Edge dim ~ 2.8µm

    • Nr of elements: 3968750 (3968750 DOFs)

  • Solving

    • Comsol script 1.1 (Comsol 3.3)

    • GMRES

  • HPC Clusters

    • CPU freq: 2000-2400 MHz

    • Used Mem: 5792736kb

    • Processing time: 12.25h


3d geometry based on mapping26 l.jpg
3D geometry based on mapping including vacuole

  • Postprocessing

    • Scripts written in Matlab

    • Running on cluster

    • CPU freq: 2000-2400 MHz

    • Used Mem: 6.5 Mb


Primary 3d simulation l.jpg
Primary 3D simulation including vacuole

CO2,gas (mol/m3)

CO2,l (mol/m3)

  • O2 diffusion in tissue

O2 gas concentration

O2 liquid concentration


Primary 3d simulation28 l.jpg
Primary 3D simulation including vacuole

CO2,gas (mol/m3)

  • O2 diffusion in different tissues

Cortex

Epidermis

Subepidermis


3d diffusivity results l.jpg
3D diffusivity results including vacuole


Conclusions l.jpg
Conclusions including vacuole

  • A model was presented to study gas transport at the microscale

  • O2 mainly transports in the gas phase of intercellular space and cell wall networks

  • CO2 transfer in both gas and liquid phase

  • Macroscopic diffusivity was estimated using microscale simulations

  • Future: 3D simulations based on synchrotron X-ray tomography

500 micron


Slide31 l.jpg

Thank you including vacuole