Gas transport modelling of pear - KU Leuven › LCMC › archive › activities › ... · Light...

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Applied research

Application of fundamental research to problems in agro-food sector

Application areasEgg quality and incubation (Josse De Baerdemaeker)

Food quality (Jeroen Lammertyn)

Predictive microbiology and risk analysis (Annemie

Geeraerd)

Agrofood process design (Josse De Baerdemaeker)

Postharvest technology (Bart Nicolaï)

Precision mechanics (Herman Ramon)

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0.00E+00

1.00E-08

2.00E-08

3.00E-08

4.00E-08

5.00E-08

6.00E-08

0.15 0.17 0.19 0.21 0.23

DO

2(m

2/s)

VmO2 (mmol/m3.s)

Jonagold

Conference

Cameo

Kanzi

Biophysics

Biology

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TemperatureO2

CO2

Full factorial screening design23+1=9 combinations

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Full factorial response surface design33=27 combinations

TemperatureO2

CO2

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BIOSYST-MeBioS www.biw.kuleuven.be

Multiscale modelling of gas transport in plant tissue

Bart M. Nicolaï

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Continuum model

States: O2, CO2 and N2

Enzyme kinetics: Michaëlis-MentenInhibition by CO2

Vmax dependent on temperature according to Arrhenius

Transport: diffusion + permeation

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2

2 2

2

OO O

O

C Lflux D D fluxL C

Δ= ⇒ =

Δ

L

5% O2

15% O2

Brown, 1827; Fick,1855; Einstein,1905.Ho et al. Postharvest Biol Technol, 41:113-120.

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2

2 2

2

OO O

O

C Lflux D D fluxL C

Δ= ⇒ =

Δ

L

5% O2

15% O2

Brown, 1827; Fick,1855; Einstein,1905.Ho et al. Postharvest Biol Technol, 41:113-120.

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Lammertyn et al. 2003. Postharvest Biol Technol 30: 29-42Ho et al. 2006. J. Exp. Bot. 57, 4215-4224.Ho et al. 2008. PLoS Computational Biology 4(3): e1000023 doi:10.1371/journal.pcbi.1000023

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Validation: gas partial pressure in jar with pear

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ProblemsFit reasonable but not perfectApparent model parametersSimulations do not provide direct information about gas related disorders

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ProblemsFit reasonable but not perfectApparent model parametersSimulations do not provide direct information about gas related disorders

Multiscale model

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Multiscale modelling

1 cm 100 μm 10 μm 100 nm

Fruit Cell Membrane Plasmodesmaton

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2

2 2

2

OO O

O

C Lflux D D fluxL C

Δ= ⇒ =

Δ

L

5% O2

15% O2

L

5% O2

15% O2

2-D Microscale model

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Light microscopy image and ellipse tesselation of apple cortex tissueMebatsion et al. (2008) Computational Modeling in Engineering and Sciences 14, 1-14; Trends in Food Science & Technology 19(2), 59-66

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Microscale O2 transport in apple cortex tissueHo et al. (2008) New Phytologist, 182: 163–174

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Diffusivity (m2 s-1):

Cell 2.01×10-9

Air 1.6×10-5

Cell wall 4.25×10-9

⇒ Cell wall porous ?

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Diffusivity (m2 s-1):

Cell 2.01×10-9

Air 1.6×10-5

Cell wall 4.25×10-9

⇒ Cell wall porous ?

Plant Cell wall Albert et al., 1994)

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Flatland (1884)E. A. Abbot

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X-Ray micro computed tomography (MTM K.U.Leuven)

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Micro CT image of apple parenchyma tissue Mendoza et al., Planta 226, 559-570

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European Synchrotron Radiation Facility (ESRF)

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3-D rendering of the void network of apple (A) and pear (B) fruit cortexVerboven et al. Plant Physiol. 2008;147:518-527

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3-D microscale modelModel:

Pore, cell: Fick’s second law of diffusionIntracellular respiration: Michaelis Menten Kinetics Interface between gas and liquid phase: Henry’ s law

Finite volume discretisation~ 2 106 or 4 106 control volumesAlgebraic multigrid solver

Solution on cluster computerAMD Opteron cluster16 Gb RAM

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Epidermis and sub-epidermis

E1 E2

mol m-3

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Parenchyma tissue

mol m-3

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Vascular bundles regionmol m-3

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Simulation Experiment Reference

Epidermis /  8.5×10‐10―1.9×10‐10 1.9×10‐10―3.3×10‐10  Ho et al. (2006)

hypodermis Schotsmans et al. (2003)

Cortex parenchyma 3.6×10‐10―2.7×10‐8  2.8×10‐10 ―5.6 ×10‐10 Ho et al. (2006)

Schotsmans et al. (2003)

Brachysklereids 1.48×10‐10

Vascular tissue 3.45×10‐8

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Conclusions

O2 transport is mainly through the intercellular space3D modelling necessaryMacroscopic diffusivity depends to a large extent on microstructureMeasured and predicted diffusion coefficients are in the same range

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Outlook

Smaller scales ?Coupling with metabolic pathway modelsTransport of other species (water, ethanol, ethylene)ValidationVirtual plant

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AcknowledgementsWendy SchotsmansJeroen LammertynFernando MendozaQuang Tri HoPieter VerbovenHibru MebatsionBert VerlindenGreet KerckhofsTuan PhamNguyen Trung AnhNico ScheerlinckJustyna CybulskaStijn Verlaak