Research Article: Size and shape matter: The impact of voxel geometry on the identification of small nuclei

Date Published: April 12, 2019

Publisher: Public Library of Science

Author(s): Martijn J. Mulder, Max C. Keuken, Pierre-Louis Bazin, Anneke Alkemade, Birte U. Forstmann, Niels Bergsland.

http://doi.org/10.1371/journal.pone.0215382

Abstract

How, and to what extent do size and shape of a voxel measured with magnetic resonance imaging (MRI) affect the ability to visualize small brain nuclei? Despite general consensus that voxel geometry affects volumetric properties of regions of interest, particularly those of small brain nuclei, no quantitative data on the influence of voxel size and shape on labeling accuracy is available. Using simulations, we investigated the selective influence of voxel geometry by reconstructing simulated ellipsoid structures with voxels varying in shape and size. For each reconstructed ellipsoid, we calculated differences in volume and similarity between the labeled volume and the predefined dimensions of the ellipsoid. Probability functions were derived from one or two individual raters and a simulated ground truth for reference. As expected, larger voxels (i.e., coarser resolution) and increasing anisotropy results in increased deviations of both volume and shape measures, which is of particular relevance for small brain structures. Our findings clearly illustrate the anatomical inaccuracies introduced by the application of large and/or anisotropic voxels. To ensure deviations occur within the acceptable range (Dice coefficient scores; DCS > 0.75, corresponding to < 57% volume deviation), the volume of isotropic voxels should not exceed 5% of the total volume of the region of interest. When high accuracy is required (DCS > 0.90, corresponding to a < 19% volume deviation), the volumes of isotropic voxels should not exceed 0.08%, of the total volume. Finally, when large anisotropic factors (>3) are used, and the ellipsoid is orthogonal to the slice axes, having its long axis in the imaging plane, the voxel volume should not exceed 0.005% of the total volume. This allows sufficient compensation of anisotropy effects, in order to reach accuracy in the acceptable range (DCS > 0.75, corresponding to >57% volume deviation).

Partial Text

To study the relationship between the structure and function of the brain, it is important to identify the individual anatomical structures and their borders accurately [1]. Additionally, knowledge on the variability in location and shape of small subcortical nuclei, such as the subthalamic nucleus (STN) and the internal segment of the globus pallidus (GPi) is informative for clinical procedures such as deep brain stimulation (DBS) surgery [2,3]. Visualizing and delineating these small nuclei is of great importance for invasive procedures such as DBS in which electrodes are lowered deep into the brain to alleviate disease specific symptoms of movement disorders, such as essential tremor, Parkinson’s disease and dystonia. To accurately plan the trajectory of DBS electrodes, individual anatomical detail is necessary that can be obtained using non-invasive magnetic resonance imaging (MRI; [4])

We simulated the MR reconstruction of 100 mathematical ellipsoids at 30 different resolutions (five in-plane resolutions, and six slice thicknesses) and three different orientations relative to the slice-axis. For each reconstructed ellipsoid, the edge voxels were labeled as part of the volume or not, using psychometric curves of a liberal and joint rater, simulating the detection process of a manual rater. As a reference, we simulated an optimal rater with a labeling threshold which resulted in volumes that were as close as possible to the ground truth volume.

To quantify the effects of the size and shape of voxels on volume estimations and shape similarity of a small region of interest, we generated ellipsoids using different in-plane voxel sizes and varying slice thickness. These were subsequently labeled by simulated raters with different intensity cutoffs (liberal, joint, and optimal rater). For the liberal and joint raters, edge voxels were included based on a probability function derived from a liberal human rater and the joint (conjunct) labeling of two human raters, respectively. For the optimal rater, the decisions were simulated so that edge voxels were included until the labeled volume optimally approximated the ground truth.

Size and shape of a voxel measured with magnetic resonance imaging (MRI) affect the ability to visualize small brain nuclei. In this study, we demonstrate the selective influence of voxel geometry by reconstructing simulated ellipsoid structures with voxels varying in shape and size. As expected, the results show that larger voxels (i.e., coarser resolution) and increasing anisotropy result in increased deviations of both volume and shape measures of the simulated structures of interest. To ensure deviations occur within the acceptable range (DCS > 0.75, corresponding to < 57% volume deviation), the volume of isotropic voxels should not exceed 5% of the total volume of the region of interest. When high accuracy is required (DCS > 0.90, corresponding to a < 19% volume deviation), the volumes of isotropic voxels should not exceed 0.08%, of the total volume. Finally, when large anisotropic factors (>3) are used, under the worst case of the ellipsoid being orthogonal to the slice axes (i.e. having its long axis in the imaging plane), the voxel volume should not exceed 0.005% of the total volume to compensate for anisotropy effects, in order to reach accuracy in the acceptable range (DCS > 0.75, corresponding to >57% volume deviation; see S1 Fig for the relationship between volume deviations and DCS.

 

Source:

http://doi.org/10.1371/journal.pone.0215382

 

Leave a Reply

Your email address will not be published.