title: Modelling the mechanical behaviour of pit membranes in bordered pits with respect to cavitation resistance in angiosperms.
abstract: OBJECTIVE
  Various correlations have been identified between anatomical features of bordered pits in angiosperm xylem and vulnerability to cavitation, suggesting that the mechanical behaviour of the pits may play a role. Theoretical modelling of the membrane behaviour has been undertaken, but it requires input of parameters at the nanoscale level. However, to date, no experimental data have indicated clearly that pit membranes experience strain at high levels during cavitation events.
  
  
  METHODS
  Transmission electron microscopy (TEM) was used in order to quantify the pit micromorphology of four tree species that show contrasting differences in vulnerability to cavitation, namely Sorbus aria, Carpinus betulus, Fagus sylvatica and Populus tremula. This allowed anatomical characters to be included in a mechanical model that was based on the Kirchhoff-Love thin plate theory. A mechanistic model was developed that included the geometric features of the pits that could be measured, with the purpose of evaluating the pit membrane strain that results from a pressure difference being applied across the membrane. This approach allowed an assessment to be made of the impact of the geometry of a pit on its mechanical behaviour, and provided an estimate of the impact on air-seeding resistance.
  
  
  RESULTS
  The TEM observations showed evidence of residual strains on the pit membranes, thus demonstrating that this membrane may experience a large degree of strain during cavitation. The mechanical modelling revealed the interspecific variability of the strains experienced by the pit membrane, which varied according to the pit geometry and the pressure experienced. The modelling output combined with the TEM observations suggests that cavitation occurs after the pit membrane has been deflected against the pit border. Interspecific variability of the strains experienced was correlated with vulnerability to cavitation. Assuming that air-seeding occurs at a given pit membrane strain, the pressure predicted by the model to achieve this mechanical state corresponds to experimental values of cavitation sensitivity (P50).
  
  
  CONCLUSIONS
  The results provide a functional understanding of the importance of pit geometry and pit membrane structure in air-seeding, and thus in vulnerability to cavitation.
authors.affiliation: Clermont Université, Université Blaise Pascal, UMR 547 PIAF, 63000 Clermont-Ferrand, France INRA, UMR 547 PIAF, 63100 Clermont-Ferrand, France.
authors.forename: Aude
authors.initials: A
authors.lastname: Tixier
authors.affiliation: Clermont Université, Université Blaise Pascal, UMR 547 PIAF, 63000 Clermont-Ferrand, France INRA, UMR 547 PIAF, 63100 Clermont-Ferrand, France.
authors.forename: Stephane
authors.initials: S
authors.lastname: Herbette
authors.affiliation: Institute for Systematic Botany and Ecology, Ulm University, Albert-Einstein-Allee 11, D-89081 Ulm, Germany.
authors.forename: Steven
authors.initials: S
authors.lastname: Jansen
authors.affiliation: Université de Toulouse, INPT-CNRS, Institut de Mécanique des Fluides de Toulouse, Allée du Professeur C. Soula, F-31400 Toulouse, France.
authors.forename: Marie
authors.initials: M
authors.lastname: Capron
authors.affiliation: Université de Toulouse, INPT-CNRS, Institut de Mécanique des Fluides de Toulouse, Allée du Professeur C. Soula, F-31400 Toulouse, France.
authors.forename: Philippe
authors.initials: P
authors.lastname: Tordjeman
authors.affiliation: Clermont Université, Université Blaise Pascal, UMR 547 PIAF, 63000 Clermont-Ferrand, France INRA, UMR 547 PIAF, 63100 Clermont-Ferrand, France.
authors.forename: Hervé
authors.initials: H
authors.lastname: Cochard
authors.affiliation: Clermont Université, Université Blaise Pascal, UMR 547 PIAF, 63000 Clermont-Ferrand, France INRA, UMR 547 PIAF, 63100 Clermont-Ferrand, France eric.badel@clermont.inra.fr.
authors.forename: Eric
authors.initials: E
authors.lastname: Badel
mesh_terms: D001696:Biomechanical Phenomena; D002462:Cell Membrane / Q000502:physiology* / Q000648:ultrastructure; D019684:Magnoliopsida / Q000033:anatomy & histology* / Q000502:physiology* / Q000648:ultrastructure; D008954:Models, Biological; D052584:Xylem / Q000033:anatomy & histology* / Q000502:physiology* / Q000648:ultrastructure
keywords: Carpinus betulus; Fagus sylvatica; Populus tremula; Sorbus aria; Tree; air-seeding; beech; bordered pit membrane; cavitation resistance; embolism; hornbeam; mechanical modelling; poplar; strain; whitebeam; wood; xylem anatomy