Quantification and Visualization of the Three-Dimensional Inconsistency of the Subthalamic Nucleus in the Schaltenbrand-Wahren Brain Atlas

The Schaltenbrand-Wahren (SW) brain atlas has many limitations: the major two are three-dimensional (3D) inconsistency and spatial sparseness. In this work, we quantify and visualize the 3D inconsistency of the subthalamic nucleus (STN). The STN 3D models, 3D-A, 3D-C and 3D-S, are reconstructed from the SW axial, coronal, and sagittal microseries, respectively, by using a shape-based (NURBS) approach. All three models are placed in the SW coordinate system and compared quantitatively in terms of location (centroids), size (volumes), shape (normalized eigenvalues), orientation (eigenvectors), and mutual spatial relationships (overlaps and inclusions). Analysis is done in 3D within each orientation and across them. A dedicated tool is developed for quantitative validation of 3D modeling. The average error achieved is 0.088 mm, which is at the resolution limit of the digital SW atlas. The reconstructed 3D STN models differ in location, size, shape, orientation, overlap size, and inclusion rate. The 3D-S volume is 1.27 times larger than that of 3D-A and 1.38 times larger than that of 3D-C. The highest overlap size is found between 3D-A and 3D-S. The highest inclusion rates of 52.5 and 66.6% are for 3D-A and 3D-S. 3D-C has the lowest overlap size and results in the lowest inclusion rates (around 20–30%), meaning that 3D-C is substantially displaced in comparison to 3D-A and 3D-S. The lateral centroid coordinate of 3D-C is 9.18 mm while that of 3D-S is 12.17 mm. Each of the 3D models has some limitation: 3D-A in orientation, 3D-C in location, and 3D-S in shape realism. The STN in comparison to the actual almond is smaller, and relatively (i.e. normalized to the same height) 2.2–2.4 times wider and 3.7–5.5 times longer. 3D-C becomes more similar to 3D-S by scaling the SW coronal microseries laterally by 1.3257. Then the lateral coordinates of their centroids coincide, the difference between them in orientation is 0.11 mm, and 3D-S is only 1.06 times larger than the scaled 3D-C. This operation substantially improves registration of the SW atlas with the probabilistic functional atlas. However, 3D visualization shows that both 3D-S and scaled 3D-C models are heavily interwoven resulting in low inclusion rates of about 60%. The STN in the SW atlas shows severe 3D inaccuracy within each orientation and across them, and it has to be employed with great care and understanding of its limitations.