Quantification and visualization of three-dimensional inconsistency of the ventrointermediate nucleus of the thalamus in the Schaltenbrand-Wahren brain atlas

Background. This work quantifies and visualises 3D inconsistencies of the ventrointermediate nucleus (VIM) of the thalamus, including the VIM externum (VIMe) and VIM internum (VIMi), in the Schaltenbrand-Wahren (SW) brain atlas. Method. For each VIM, VIMe, VIMi the 3D models, 3D-A, 3D-C and 3D-S were reconstructed from the SW axial, coronal and sagittal microseries, respectively, by applying a shape-based method. All 3D models, placed in the SW coordinate system, were compared quantitatively in terms of location (centroids), size (volumes), shape (normalised eigen values), orientation (eigen vectors), and mutual spatial relationships (overlaps and inclusions). Findings. The reconstructed 3D models differ significantly in location, size, shape, and inclusion rate. The centroid of 3D-A/VIM differs considerably from those of 3D-C/VIM and 3D-S/VIM. The difference between the centroids of 3D-C/VIM and 3D-S/VIM is in laterality only: that of 3D-C/VIM is located more medially (11.85 mm) than that of 3D-S/VIM (14.62 mm). 3D-A/VIM has the smallest volume (69.00 mm³); 3D-C/VIM is 3.71 and 3D-S/VIM 3.89 times larger. The overlap is also highly variable: 104.88 mm³ for 3D-C/VIM with 3D-S/VIM, and very low (3.22 and 7.45 mm³) when 3D-A/VIM is involved. The highest inclusion rate is for 3D-C/VIM with 3D-S/VIM (39.10 and 40.97%) and the lowest for 3D-A/VIM with 3D-C/VIM (1.26 and 4.66%). The centroid of 3D-A/VIMe differs noticeably from those of 3D-C/VIMe and 3D-S/VIMe. The difference between the centroids of 3D-C/VIMe and 3D-S/VIMe is mainly in laterality: that of 3D-C/VIMe is located more medially (12.91 mm) than that of 3D-S/VIMe (16.65 mm). 3D-A/VIMe has the smallest volume (49.87 mm³); 3D-S/VIMe is 3.24 and 3D-C/VIMe 3.36 times larger. The overlap sizes are low: 32.72 mm³ for 3D-C/VIMe with 3D-S/VIMe, and very low (1.32 and 2.01 mm³) when 3D-A/VIMe is involved. The inclusion rates are also low: the highest is for 3D-C/VIMe with 3D-S/VIMe (19.53 and 20.29%) and the lowest for 3D-A/VIMe with 3D-C/VIMe (1.19 and 4.01%). Lateral scaling of the coronal microseries by 1.2897 to match the 3D-C/VIMe and 3D-S/VIMe centroids increases the inclusion rates for the sagittal microseries by more than twice. The volume of scaled 3D-C enlarges to 216.24 mm³ which is 1.34 bigger than that of 3D-S. There are substantial differences among the centroids of 3D-A/VIMi, 3D-C/VIMi and 3D-S/VIMi. The centroid of 3D-A/VIMi is located more anteriorly (-1.92 mm) than that of 3D-C/VIMi (-5.02 mm). The centroid of 3D-A/VIMi is located more ventrally (2.88 mm) than those of 3D-C/VIMi and 3D-S/VIMi (each at 5.34 mm). 3D-A/VIMi has the smallest volume (19.75 mm³); 3D-S/VIMi is 3.23 and 3D-C/VIMi 4.30 times larger. 3D-A/VIMi practically does not overlap with 3D-C/VIMi and 3D-S/VIMi. The inclusion rates for 3D-C/VIMi with 3D-S/VIMi are medium (32.63 and 43.43%). Conclusion. Each VIM, VIMe, VIMi as reconstructed from the SW atlas has a significant 3D inaccuracy within each orientation and across them. Therefore, absolute and direct reliance on the original SW atlas is unreliable and unsafe, and this atlas has to be used with great care and understanding of its strengths and limitations.