Enrico De Vita^{1,2}, Ruth Oliver^{3}, Chris Sinclair^{4}, David L Thomas^{4}, Xavier Golay^{4}, Simon Mead^{5,6}, and John S Thornton^{1,4}

We here demonstrate how partial volume correction by linear regression in the style originally proposed for arterial spin labelling MRI can be used to perform a simple and effective partial volume correction for Magnetisation Transfer Ratio data.

Magnetisation transfer (MT) acquisitions provide extremey valuable information, most notably for Multiple Sclerosis [vanBuchem1997].The extraction of tissue specific parameters can be confounded by the limited spatial resolution of the images; the partial volume (PV) errors arising from averaging between neighbouring tissues has been discussed early on for MT [Kalkers2001]. With 2D readouts with typical slice thickness of 2-3mm, not sufficient to easily discriminate the contribution to the signal of different tissue types. Methods have recently been suggested to remove the cerebro spinal fluid contamination of the estimated parameters when using quantitative MT protocols by extending the conventional 2-pool model [Deoni2013, Mossahebi2014]. However, for single-offset MT weighted or MT ratio (MTR) acquisitions, when using histograms , the most commonly employed method to reduce PV effects is thresholding partial-volume probability maps [Dehmeshki2003]. However the results are likely to be affected by the threshold chosen, and thecortical ribbon may end up excessively thin. We demonstrate how partial volume correction by linear regression in the style originally proposed for arterial spin labelling MRI [Asllani2008], can be used to perform a simple effective partial volume correction for MTR data.

As proof of principle for this methodology we selected data from 2 subjects enrolled in the UK National Prion Monitoring Cohort, who expressed their informed consent for the study: a 34-year old healthy subject and a 50-year year old patient with inherited prion disease.

**MRI. **Siemens 3T Tim Trio, 32-channel head
coil. Structural imaging (T1w):
3D-MPRAGE, TR=2200ms, TE= 2.9ms, TI=900ms, flip angle (α) 10°, 208 partitions,
(1.1mm)^3 resolution). MT measurement:
3D-FLASH with/without presaturation pulse (10ms Gaussian, 1200Hz offset, α=500°),
yielding Msat (partially saturated) and M0 (equilibrium) images; TR=42ms, TE=3ms,
α=5°, (22.2cm)^2 FoV and an unisotropic spatial resolution of 0.9mm in plane
and 3mm in the ‘slice’ direction (60 partitions).

**Data Processing.** T1w data was simultaneously segmented
and regional labels estimated using a joint multi-atlas and Gaussian mixture
model method [Cardoso 2015], then
affine-registered to the Msat dataset using nifty_reg
[Ourselin 2001]. Fractional probability maps
for grey, white matter and CSF (pGM, pWM,
pCSF) were also downsampled to the MT data space using a point spread function
method [Cardoso 2015b]. The M0 data was rigidly
registered to the Msat data before computing MTR maps as 1-Msat/M0.

**PV correction.** For PV correction we used the linear
regression algorithm described in [Asllani 2008]:
the equation MTR_measured=pGM*MTR_GM + pWM*MTR_WM + pCSF*MTR_CSF) is solved over
a 2 dimensional kernels of 3x3 or 5x5 voxels or a 3D kernel (3x3x3) assuming
local tissue-specific MTR values do not change within the voxel; it is thus possible
to obtain PV corrected (pvc) estimates of MTR_GM and MTR_WM (MTR_ pvcGM, MTR_ pvcWM-)
voxel-by-voxel.
To illustrate the benefits of the PV correction, masks are
generated for pvGM and pvWM values between 0.4-0.5, 0.5-0.6, 0.7-0.8,0.8-0.9, 0.9-1.0,
0.95-1.0; average values of MTR_measured, MTR_ pvcGM, MTR_ pvcWM over these
masks can then be plotted. Histograms of the MTR_ pvcGM and MTR_ pvcWM were
then generated using different PV thresholds and compared to equivalent
histograms for MTR_measured.

The original MTR maps display an approximately linear dependence on PV-fraction for WM, due to the contamination with CSF with extremely low MTR values. The curves for GM are not quite as linear. This is probably due to the contrasting effect of WM contamination (causing an apparent MTR increase) and CSF contamination (causing an apparent MTR decrease). The PV corrected tissue specific MTR values from all 3 kernels used show a much lower dependence on PV-fraction demonstrating a substantial correction of PV effects, especially for PV fractions above 0.7-0.8 (typical threshold used).From Figure 3, 4 it is obvious how the histogram narrow and the PV-threshold dependence is much reduced.

Using the simple PV correction proposed the MTR histograms obtained display a much lower dependnce on PV threshold. This may help in discriminating subtle pathologies. Further work will include testing this methodology in a cohort of MS patients.

Figure 1. Plots of MTR_original MTR_
pvcGM (left) and MTR_ pvcWM (right) for healthy subject (top row) and prion
patient. Plots are shown for the 3 different kernels used: 3x3 (2D), 5x5 (2D)
and 3x3x3 (3D). Bins used were: 0.4-0.5, 0.5-0.6, 0.7-0.8,0.8-0.9, 0.9-1.0,
0.95-1.0.

Figure 2. Shows for the healthy subject (a, top row) and patient (b, bottom row),
from left to right: the MTR_original map; the same map with superimposed slightly
transparent pvGM coloured from 0.5 to 1; the estimated MTR_ pvcGM (2D 5x5
kernel); the estimated MTR_pvcWM (2D 5x5 kernel).

Figure 3. shows GM histograms of patient and control, before (a) and after (b) PV
correction with the 2D 5x5 kernel, using different colours for different
PV-fraction thresholds..

Figure 4. shows WM histograms of patient and control, before (left) and after
(right) PVC, using different colours for different PV-fraction thresholds.