Fig 1.
Representation of the simulations in which ellipsoids in world space are reconstructed into MR volumes of different resolutions (image space). Orientations were chosen to resemble circumstances in the MRI scanner. The in-plane (x,y-dimension) resolution corresponds to a slice acquired along the scan-direction H-F (slice axis z). Anisotropy (slice thickness) was varied across the slice axis. The long axis of the ellipsoids was either placed parallel, diagonal or orthogonal to the slice axis. Figs for both frequency and image space represent the mid-slice of the reconstructed volume from sagittal view. Here reconstructed images were simulated with a voxel size of 0.5mm isotropic. A = anterior; F = feet; H = head; h = height; L = left; l = length; P = posterior; R = right; V = volume; w = width.
Table 1.
Post mortem hemispheric volume estimates for a number of deep brain stimulation targets.
STN: subthalamic nucleus; GPi: globus pallidus internal segment.
Fig 2.
Sagittal view of central-slice examples from simulated ellipsoids.
Each generated ellipsoid was reconstructed from a k-space transformation using a different in-plane voxel size (mm) and a varying slice thickness (mm). Columns represent the in-plane (xy) voxel size, ranging from left to right with a size of .1, to .2, .5, 1.0, and 2.0mm. Rows represent slice thickness that are proportional to the in-plane resolution, ranging from top to bottom with a factor of 1x (isotropic) to 1.2x, 1.5x, 1.8x, 2x and 3x the in-plane voxel size. For illustration purposes, sagittal slices were used to show the effect of voxel size and slice thickness on the diagonal orientation.
Table 2.
Mask volumes for rater 1 and 2 (R1 and R2) and their conjunct mask.
Labeled volumes were oriented diagonal to the slice axes and were reconstructed from one simulated ellipsoid at different resolutions (x, y, z). Voxel size indicates the fraction of the ground truth volume (164.9mm3) represented by 1 voxel. DCS show a strong overlap (>0.87) between the two raters.
Fig 3.
Psychometric curves used to simulate detection-thresholds and sensitivity in labeling procedures.
Psychometric curves represent the probability (y-axis) that a voxel will be labeled as part of the ellipsoid given its signal intensity (x-axis). Colors represent the liberal human rater (red), the joint-labeling of two human raters (blue), and as a reference, the (average) optimal rater (green). Values are presented on a logarithmic scale.
Fig 4.
Overview of the average percentage deviation in volume for the simulated ellipsoids (n = 100), labeled according to a liberal, a joint, and an optimal rater.
Columns refer to the orientation of the ellipsoid (parallel, diagonal, and orthogonal to the slice axes). Each block of squares represents sizes and shapes as depicted in Fig 2, with increasing in-plane voxel size (0.1 to 2.0mm) from left to the right, and increasing anisotropy (1x to 3x the in-plane voxel size) from top to bottom, with each top row being isotropic. Color intensity indicates the average percentage deviation in volume. Blocks to the right of the dotted lines represent deviations in volume that are > 57% of the ground truth, corresponding in DSC scores < 0.75, as shown in Fig 5 below (see S1 Fig for the relationship between volume deviations and DCS).
Fig 5.
Overview of average shape similarity between the simulated ellipsoids and a high-resolution reference ellipsoid of 0.1 x 0.1 x 0.1mm.
Volumes (n = 100) by all three raters were up-sampled to the reference resolution to create a conjunct mask between the reference volume and the labeled volume. Columns refer to the orientation of the ellipsoid (parallel, diagonal, and orthogonal to the slice axis). Each block of squares represents sizes and shapes as depicted in Fig 2, with increasing in-plane resolution (0.1 to 2.0mm) from left to the right, and increasing anisotropy (1x to 3x the in-plane voxel size) from top to bottom, with each top row being isotropic. Color intensity indicates the average shape similarity expressed in DCS. Blocks to the right of the dotted line represent DCS scores < 0.75.
Fig 6.
Comparison between volume and DCS for isotropic (0.2 x 0.2 x 0.2mm and 1.0 x 1.0 x 1.0mm) and anisotropic (0.1 x 0.1 x 0.8mm and 0.5 x 0.5 x 4.0mm) voxels of the same volume, labeled by the joint rater. Horizontal panels reflect orientations. Error bars indicate standard deviations from the mean.
Fig 7.
Similarity between volumes rated by the joint rater and the high-res (0.1mm) reference volume rated by the optimal rater.
A DCS of 0.75 is considered the lower end of acceptable values [38]. DCS > 0.90 are considered ideal. Different marker symbols refer to the mean DCS for the different in-plane voxel sizes (0.1, 0.2, 0.5, 1.0 and 2.0mm). Isotropic voxel-size have a (rounded) relative volume of respectively 0.0006%, 0.005%, 0.08%, 0.6%, 5% of the ground truth ellipsoid volume (~165.0mm3). The grey area represents standard deviations from the mean. Note that the standard deviations increases for the most anisotropic resolutions due to the increasing PVE for ellipsoids with large voxel sizes and increasing anisotropy. For visualisation purposes, anisotropy factors (x-axis) are plotted on a logarithmic scale. Dashed lines indicate the 0.75 and 0.90 DCS values.