In vascular plants, from a physical point of view, xylem sap transport can be limited by cavitation (breakage of water columns) and by the collapse of cell walls. Cavitation has been more documented than collapse of cell walls but recent work has demonstrated the existence of cell wall collapse in lignin deficient Arabidopsis (Taylor et al., 1999) but also in not mutant structures like xylem of pine needles (Cochard et al, 2004). Studying cell wall collapse in 4 pine species (P. cembra, P. mugo, P. sylvestris and P. nigra) revealed an inter-specific variability of collapse vulnerability. It was also demonstrated that collapse onset starts before the cavitation process, raising a possible role of cell wall collapse for protection from cavitation (Cochard et al., 2004). In 2001, Hacke et al., proposed the risk of conduit collapse to be related to the dimensions of cell: Pcollapse=f(t2/b2) with t the size of the lumen and b the thickness of the cell wall. Applying Hacke et al. equation on data pine needles xylem, lead as expected, to a negative correlation between Pcollapse and tracheids anatomy but the correlation was weak; moreover the Pcollapse values obtained using cell geometry as a predictor were two to six times more negative than the measured ones. This discrepancy suggested that it was necessary to take cellular structure of xylem and heterogeneities of tracheids into account because the collapse may rely on cell geometry but also on a structure effect i.e. an effect of the arrangement of cells.
In this work, we modelled the xylem collapse of pine needles. Xylem of four different pine species were digitised and imported in a finite elements code. The choice of the finite elements software relied on a central question: is the observed collapse of xylem is an elastic buckling or a progressive deformation leading to the collapse? Analysis of experimental results led to conclude that the collapse was more a progressive deformation than a real buckling process, except for Pinus mugo. Because of heterogeneity of sensibility to collapse between cells in a given xylem structure, the finite element software was chosen in order to take into account possible local increase of rigidity because of contact between cell walls when some cells get their collapsed state.
In order to choose the appropriate Young moduli the two modelled tissues (cell walls and parenchyma), we ran the model with different values of Young moduli for each tissue in order the isoperimetric coefficient to match the experimental observed values for Pinus nigra. In general, at the first order geometrical effects explain most of the mechanical behaviour so that in first approximation, the same value of elastic moduli will be taken equal for every cell and in the xylem structures of the fourth studied species. In first approximation we will not consider possible heterogeneities of negative pressures between cells.
The validation of such a model is a difficult issue because it is not possible to measure the successive strain states on the same xylem structure. In a first time, we will proceed to a “global” validation of the model by comparing the average isoperimetric coefficient computed on a modelled xylem and the one measured of real xylem. This work will present first modelling outputs and the comparison of modelled and measured datas.