The shape of kernels and cracks, in a nutshell

We explore the shape of walnut shells and kernels. We analyze 1264 individual 3D X-ray CT scan reconstructions of walnuts, corresponding to 150 walnut accessions. We exploit the nondestructiveness of X-rays to digitally segment and measure the 4 main tissues of interest for each walnut, namely shell, kernel, packing tissue, and sealed air. From these, we extract a total of 38 size- and shape-specific descriptors, many of them unexplored in the current literature. We focus on several allometric relationships of interest, from which we draw theoretical upper and lower bounds of possible walnut and kernel sizes. We then study correlations and variations of these morphological descriptors with qualitative data corresponding to traits of commercial interest like ease of kernel removal and shell strength.

Methods
All plant materials represent walnut breeding lines, germplasm, and cultivars maintained by the Walnut Improvement Program at the University of California, Davis. A total of 150 walnuts accessions were harvested into mesh bags at hull split, oven-dried overnight at 95F, and then air-dried for several weeks before moving into cold storage at 35F. 5 to 16 individuals were selected for each accession, for a total of 1301 individual walnuts to be scanned at Michigan State University. The walnuts were scanned in 171 batches. The scans were produced using the North Star X3000 system and the included efX-DR software. The X-ray source was set at 75 kV and 100~\micro{A}, with 720 projections per scan, at 3 frames per second and with 3 frames averaged per projection. The data was obtained in continuous mode. The 3D X-ray CT reconstruction was computed with the efX-CT software, obtaining voxel-based images with voxel size of 75.9 microns.