Full-field MRI measurements of in-vivo positional brain shift reveal the significance of intra-cranial geometry and head orientation for stereotactic surgery

Positional brain shift (PBS), the sagging of the brain under the effect of gravity, is comparable in magnitude to the margin of error for the success of stereotactic interventions (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sim $$\end{document}∼ 1 mm). This non-uniform shift due to slight differences in head orientation can lead to a significant discrepancy between the planned and the actual location of surgical targets. Accurate in-vivo measurements of this complex deformation are critical for the design and validation of an appropriate compensation to integrate into neuronavigational systems. PBS arising from prone-to-supine change of head orientation was measured with magnetic resonance imaging on 11 young adults. The full-field displacement was extracted on a voxel-basis via digital volume correlation and analysed in a standard reference space. Results showed the need for target-specific correction of surgical targets, as a significant displacement ranging from 0.52 to 0.77 mm was measured at surgically relevant structures. Strain analysis further revealed local variability in compressibility: anterior regions showed expansion (both volume and shape change), whereas posterior regions showed small compression, mostly dominated by shape change. Finally, analysis of correlation demonstrated the potential for further patient- and intervention-specific adjustments, as intra-cranial breadth and head tilt correlated with PBS reaching statistical significance.


Correction
Prone Supine None 1.88 ± 0.34 mm 1.40 ± 0.36 mm Scanner default 1.32 ± 0.11 mm 1.31 ± 0.33 mm gradunwarp 1.25 ± 0.10 mm 1.30 ± 0.20 mm Table 1. Differences between scans acquired with the 7T and 3T scanners for both prone and supine positioning prior to correction and after correction with the scanner default software and with gradunwarp. Differences are represented in terms of average and standard deviation magnitude of the warp field in the brain area.
L-R angle P-A angle I-S angle L-R translation P-A translation I-S translation Table 2. Rotation and translation values tested for the validation of the skull alignment.
The accuracy of this initial step was evaluated by calculating the Dice coefficient, given by 11 : where skull original represents the original skull segmentation and skull registered the skull segmentation after registration of the synthetic images. Fig. 1 shows the dice coefficient averaged among the subjects for each of the registration methods tested. ANTs performed best given the outliers showed by elastix (reported in the zoom out box in the bottom-right part of the figure), and was therefore used throughout the study.

Elastic Registration
Three state of the art registration algorithms for neuroimaging were optimised and then compared in order to gauge their accuracy in measuring a synthetic displacement field replicating PBS. The extensive comparisons by Klein et al. 12 , Ou et al. 13 and Murphy et al. 14 put SyN 15 , elastix 10 and DRAMMS 16 at the top for best performance. Registration methods based on mechanical models were discarded not to impose any a priori constraints on the deformation 17,18 . A realistic displacement field was generated through a biofidelic finite element simulation of PBS ( Fig. 2) 19 . This displacement field was characterised by a magnitude of 0.60 ± 0.26 mm, azimuth angle of −89.70 ± 11.98 • and elevation angle of 1.27 ± 11.46 • . The warp field was applied to the supine scans of 8 participants and these registered back to the original using each of the selected methods. Parameters controlling for the transformation model and the similarity measure were optimised, leaving the others as default in order to reduce the number of combinations to test (Table 3). Regarding the call to elastix, a similar parameter file as in Staring et al. 20 was used. Computations were run on a cluster at Cardiff University Brain Research Imaging Centre (CUBRIC). First, the root mean square error (RMSE) between the estimated warp and the ground truth was extracted in the brain area, as well as at some regions of interest (ROI). Sensitivity analysis (MATLAB R2020, Mathworks, Natick, MA) was then used to assess the influence of parameters based on partial correlation with Spearman ranks. Results are reported in Table 4, showing that the most influencing parameters for all methods were the ones controlling for the spacing of control points of the transformation models. Furthermore, a score-based system was implemented, where a parameter's performance was calculated, for every value, as sum of the rank of each optimisation run in terms of accuracy. This was done to avoid any averaging among subjects or ROI (Fig. 4, 8, 6). The optimal set was therefore chosen as the one achieving the smallest RMSE, alongside guaranteeing that the parameter with the greatest sensitivity on the error had the lowest rank score (Fig. 3, 7, 5).

2/9
ANTs     Table 4. Sensitivity analysis showing, for each registration method, the influence of parameters on the error. Table 5 shows the best parameter set for each method, with the corresponding RMSE. Fig. 9 shows the boxplot of the error at different ROI corresponding to the best parameter set for each method. The distribution of the error for one of the subjects is reported on an axial slice in Fig. 10 for the three methods. SyN showed the best performance and was therefore used throughout the study. Evaluating accuracy on synthetic data represents a best case-scenario 21 , as synthetic warp field, interpolation and noise pattern cannot reproduce the realistic conditions fully. However, given the lack of ground truth to test the accuracy on and the lack of expertise in identifying / placing fiducial landmarks, any further attempt in assessing the accuracy of the method were considered out of scope.      Figure 10. Distribution of the mean squared error corresponding to the best parameter set over the brain area for one subject.
Colour bar represents values in [mm].

8/9
Method Name Value mean ± std (5 th percentile, 95 th percentile) error  Table 5. Best parameter set for each registration methods with the corresponding error averaged over the brain area.