Thomas Kirk^{1,2}, Timothy Coalson^{3}, Flora Kennedy McConnell^{1,2}, and Michael Chappell^{1,2}

Toblerone is a new method for estimating partial volumes on the cortical ribbon using surfaces as input (eg those produced by FreeSurfer). Evaluation has been performed using both simulations and subjects drawn from the Human Connectome Project. The estimates returned differ from those produced by existing tools such as FSL's FAST, which will have implications for the analysis of functional imaging data (notably ASL). A preliminary analysis of an ASL dataset has been performed using Toblerone's PV estimates.

Toblerone has been evaluated
using both simulated cortical surfaces and 50 subjects drawn from the Human
Connectome Project (HCP). For both types of data, PVs were estimated at voxel resolutions of 1 to 3.8mm isotropic, in steps of
0.4mm. For simulations, errors were calculated on a per-voxel and aggregate
basis with reference to ground truth; for HCP subjects, in which context there
is no ground truth, total tissue volume was calculated at each
resolution to assess within-subject consistency across resolutions. Two other methods were also evaluated on
these data (NeuropolyPVE^{6} and the ribbon-constrained method^{7}), and FAST was also used on the structural scans of the HCP subjects from which their surfaces were produced. Finally, PV estimates produced by Toblerone were used in the analysis of an
ASL dataset (multi PLD pcASL, as detailed^{8}, with FreeSurfer as prior step to produce
surfaces). As this method produces estimates for the cortex only, subcortical PV
estimates were filled in using FSL's FAST. FSL’s oxford_asl pipeline (performing subtraction,
calibration, model inversion) was then used to calculate mean GM perfusion in voxels with >80% GM when running on FAST-only or FAST+Toblerone combined PV
estimates.

1 Zhao M et al. A systematic study of the sensitivity of partial volume correction methods for the quantification of perfusion from pseudo-continuous arterial spin labeling MRI, NeuroImage, 2017

2 Asllani I et al. Regression algorithm correcting for partial volume effects in arterial spin labeling MRI, MRM, 2008

3 Zhang Y et al. Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm, IEEE Trans. Med. Imag. 2001.

4 Fischl, B. FreeSurfer, NeuroImage, 2012.

5 Nooruddin et al. Simplification and repair of polygonal models using volumetric techniques, IEEE Trans. Visual. & Comp. Graphics, 2003.

6 Van Assel C et al. Partial volume effect correction for surface-based cortical mapping, Proc. ISMRM, 2017.

7 Glasser M et al. The minimal preprocessing pipelines for the Human Connectome Project, NeuroImage, 2013

8 Mezue M et al. Optimization and reliability of multiple postlabeling delay pseudo-continuous arterial spin labeling during rest and stimulus-induced functional task activation, Jour. Cereb. Blood Flow and Metab. 2014

Standard deviation of per-voxel error in estimated PV, simulated cortical surfaces, across voxel resolutions. Neuro2 refers to the method detailed in 6, RC1/2 to the method detailed in 7.

Cortical GM PV estimates for subject 100307 from the HCP, at 2.2mm isotropic resolution. Note that subcortical GM is not included as surface-based methods are unaware of subcortical structures.

Mean across subjects of difference in total estimated tissue volume at each resolution (using Toblerone's 1mm estimate as reference) for the 50 HCP subjects. FAST's results are incomparable in WM and a mask of the cortex was used to constrain the analysis to consider cortical GM only (so excluding subcortical GM). This mask is imperfectly defined at larger voxel sizes which may cause some positive bias in the FAST results.

Boxplots of mean GM perfusion across the ASL dataset, evaluated using either FAST-only PV estimates or combined FAST+Toblerone.