Choice of cross size in stereology - a cautionary note

The stereological method of cross-counting based on the Cavalieri principle is widely used in neuroimaging to estimate the volume of cerebral structures. Although superficially simple, the stereological technique is validated by arcane mathematical proofs, so the cross size is determined by most investigators on a pragmatic basis with the assumption that the volume calculated is independent of the cross size used. We used three cross sizes (8x8, 5x5 and 3x3 voxels) to estimate the brain volume of six healthy control subjects. The volume estimate using a cross size of 3x3 was 9% larger than with a cross size of 5x5 and the latter was 15% larger than with a cross size of 8x8. We conclude that cross size significantly affects whole brain volume estimates and this result is presumably applicable to other structures whose cross-sectional areas form complex shapes. Investigators should be aware of this fact, especially when trying to make direct comparisons between volume estimates derived from the stereological method using different cross sizes.