Estimating the number and size of phloem sieve plate pores using longitudinal views and geometric reconstruction

Because it is difficult to obtain transverse views of the plant phloem sieve plate pores, which are short tubes, to estimate their number and diameters, a method based on longitudinal views is proposed. This method uses recent methods to estimate the number and the sizes of approximately circular objects from their images, given by slices perpendicular to the objects. Moreover, because such longitudinal views are obtained from slices that are rather close to the plate centres whereas the pore size may vary with the pore distance from the plate edge, a sieve plate reconstruction model was developed and incorporated in the method to consider this bias. The method was successfully tested with published longitudinal views of phloem of Soybean and an exceptional entire transverse view from the same tissue. The method was also validated with simulated slices in two sieve plates from Cucurbita and Phaseolus. This method will likely be useful to estimate and to model the hydraulic conductivity and the architecture of the plant phloem, and it could have applications for other materials with approximately cylindrical structures.