Understanding airspace in leaves: 3D anatomy and directional tortuosity

The leaf intercellular airspace is a tortuous environment consisting of cells of different shapes, packing densities, and orientation, all of which have an effect on the travelling distance of molecules from the stomata to the mesophyll cell surfaces. Tortuosity, the increase in displacement over the actual distance between two points, is typically defined as encompassing the whole leaf airspace, but heterogeneity in pore dimensions and orientation between the spongy and palisade mesophyll likely result in heterogeneity in tortuosity along different axes and would predict longer traveling distance along the path of least tortuosity, such as vertically within the columnar cell matrix of the palisade layer. Here, we compare a previously established geometric method to a random walk approach, novel for this analysis in plant leaves, in four different Eucalyptus species. The random walk method allowed us to quantify directional tortuosity across the whole leaf profile, and separately for the spongy and palisade mesophyll. For all species tortuosity was higher in the palisade mesophyll than the spongy mesophyll and horizontal (parallel to the epidermis) tortuosity was consistently higher than vertical (from epidermis to epidermis) tortuosity. We demonstrate that a random walk approach improves on previous geometric approaches and is valuable for investigating CO₂ and H₂ O transport within leaves.