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Model-based approachPurpose

Improve understanding

Optimization

Control

Macroscale approach (Ho et al., 2006)Geometry: intact fruit

Gas transport coupled with respiration kinetics

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Gas transport properties of macroscale Assumption

Homogeneous material

Measurement

Biological variability

DCO2 > DO2

Anisotropic diffusivity Apparant values

Deff

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Microscopic overview of tissueParenchyma tissue structure

Grouped cells

Random distribution of cells and pores

Cell wall

Plasma membranes

Transport phenomenaGeometry required

Two phases

Gas

Liquid

Cell membrane

Passive transport

Active transport

Intra-cellular enzymatic reactions Plant Cell wall (Albert et al., 1994)

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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

BIOSYST-MeBioS www.biw.kuleuven.be

Microscale modelling of gas diffusion in fruit tissue

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

IUFoST 13TH WORLD CONGRESS OF FOOD SCIENCE & TECHNOLOGY

Food is Life, 17 -21 September 2006Nantes France

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Geometry model

Light microscopy images (Mebatsion et al, 2006)

Parenchyma tissues of ‘Conference’ pear

Resolution 1pixel~0.735µm

Digitization of image

Geometry model generation (Mebatsion et al, 2006)

Ellipse tessellation algorithm

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Ellipse tesselation

Cell

Cell wall

Intercellular space

TEM image of Conference pear

Cells

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Concept of gas transport

Air filled intercellular space

O2,l

CO2,l

ADP +Pi

ATP synthase

ATP

Work

Mitochondrion

Cytosol

ATP

HCO3-

CO2,g

O2,g

Liquid

Pore

Gas exchange of fruit

At the interface

Intra-cell

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Model of O2 transport in tissue

AssumptionCell wall was assumed gas phase with effective diffusivity DO2,w

Passive gas transport through cell membraneHenry’s law at the inter-phase

Model equation (Fick’s second law of diffusion)

Pore

Cell wall

Cell

2,2, 2,

O gO g O g

CD C

t

2,2, 2,

O gO w O g

CD C

t

2,2, 2, 2,

O lO l O l O l

CD C R

t

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O2 model equation in liquid phase

O2 consumption at intra-cell

Michaelis-Menten reaction

CO2,l can be rewritten in equilibrium gas phase CO2,g

2 2,2

, 2, 2,

mO O lO

m O cell O l

V CR

K C

2,2 2, 2 2, 2

O gO O l O O g O

CR T H D R T H C R

t

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Model of O2 transport in tissue

Model equations Pore

Cell wall

Cell

Flux through cell membrane

2,2, 2,

O gO g O g

CD C

t

2,2, 2,

O gO w O g

CD C

t

2,2 2, 2 2, 2

O gO O l O O g O

CR T H D R T H C R

t

,A mem

mem

DFlux C

L

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Physical parametersLiterature Model

Diffusivity: Pore

Cell

Cell wall

DO2,gas =1.6×10-5 m2/s (1)

DO2,l=2.01×10-9 m2/s (1)

DO2,W = ?

DO2,gas=1.6 ×10-9 m2/s

DO2,l=2.01 ×10-9 m2/s

DO2,W = 5×10-9 m2/s

Cell wall thickness 0.76 µm 0.76 µm

Membrane L =6-10 nm (2)

DO2,membrane =2.91×10-9 m2/s (3)

Permeability

hO2=3.63 ×10-2 m/s

Henry’s constant HO2=0.01371 (mol/m3Pa) (1) HO2=0.01371 (mol/m3Pa)

Source : 1: Lide (1999)

2: Gunning and Steer (1996)

3: Uchida et al. (1992)

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Numerical solution

Meshing125050 elements

SolutionFinite element method

Femlab 3.1 (Comsol AB, Stockholm)

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Estimation of Dtissue, eff

Steady stateBoundary condition

Side 1: C1 ; Side 2: C2

C2

C1

Ltissue

,tissue

tissue eff

Flux LD

C

Isolated boundary

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Simulation result

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Sensitivity analysis

Relative sensitivity of parameter:∆P was taken 10% of value P

Relative change of DO2, tissue corresponded to a relative change of model parameter

,

/

/ 2r P P P PG P

G GG G PJ

P P P G

Parameter Value JDo2,P

Dg (m2/s) 1.6×10-5 1.74×10-4

Dl (m2/s) 2.01×10-9 3.33×10-1

Dw (m2/s) 5×10-9 6.67×10-1

h_coeff (m/s) 3.63×10-2 1.92×10-5

HO2 (mol/m3kPa ) 1.37×10-2 3.33×10-1

Thickness of cell wall (µm ) 0.736 7.21×10-1

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Estimated O2 diffusivity of pear tissue

  DO2, tissue (m2/s)

Micro scale Ellipse Tesselation 3.2×10-10

Measurement (Macro scale)(2.560.48)10-10 (Ho et al., 2005)(4.31.7)10-10 (Schotsmans et al., 2003)

DO2,cell wall =5×10-9 m2/sCell wall thickness= 0.73 µm

(TEM, Mebatsion 2006, unpublished data)

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Upscaling to macroscale

20 kPa O2, 0 kPa CO2, 5°C

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Micro structure and storage disorders

Concentration profile along a line through the tissue at y=1×10-4 m

inside cells

in pores

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3D X-ray microtomography

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Conclusions

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

Macroscopic diffusivity was estimated using microscale simulations

Important consequences for respiration–related disorders

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Thank you