# Global intensity normalisation¶

Several existing DWI models derive quantitative measures by fitting a model to the ratio of the DW signal to the b=0 signal within each voxel. Such a voxel-wise division by the original b=0 signal removes intensity variations due to T2-weighting and RF inhomogeneity. However, unless all compartments within white matter (e.g. intra- and extra-axonal space, myelin, cerebral spinal fluid (CSF) and grey matter partial volumes) are modelled accurately (i.e. with appropriate assumptions/modelling of both the compartment diffusion and T2), the proportion of one compartment in a voxel may influence another. For example, if CSF partial volume (e.g. at the border of white matter and the ventricles) is not taken into account, then a voxel-wise division by the b=0 (which has a long T2 and appears much brighter in CSF than in white matter in the T2-weighted b=0 image), will artificially overreduce the DW signal from the white matter intra-axonal (restricted) compartment, ultimately changing several derived quantitative measures.

A previous work investigating differences in Apparent Fibre Density (AFD) [Raffelt2012] opted to instead perform a global intensity normalisation between subjects. This avoids the aforementioned issues, but also comes with its own set of challenges and assumptions inherent to specific strategies to deal with intensity normalisation for diffusion MRI data. Aside from the problem of how to define a reference region for global intensity normalisation (that is unbiased with respect to the groups in the analysis), the data must also be bias field corrected, to eliminate low frequency (spatially smooth) intensity inhomogeneities across the image.

In theory, an approach to global intensity normalisation could for example be to normalise using the median CSF b=0 intensity for each subject as a reference (under the assumption that the CSF T2 is unlikely to be affected by pathology). However, in practice it is surprisingly difficult to obtain a robust partial-volume-free estimate of the CSF intensity due to the typical low resolution of DW images. For healthy participants less than 50 years old, reasonably small ventricles make it quite difficult to identify pure CSF voxels at 2-2.5mm resolutions. Therefore, performing global intensity normalisation using the median white matter b=0 intensity may be easier to achieve. While the white matter b=0 intensity may be influenced by pathology-induced changes in T2, the assumption then becomes that such changes would be (spatially) quite local and therefore have little influence on the median white matter b=0 value.

The dwinormalise group script is included in MRtrix to perform an automatic global normalisation using the median white matter b=0 intensity. The script input requires two folders: a folder containing all DW images in the study (in .mif format) and a folder containing the corresponding whole brain mask images (with the same filename prefix). The script runs by first computing diffusion tensor Fractional Anisotropy (FA) maps, registering these to a groupwise template, then thresholding the template FA map to obtain an approximate white matter mask. The mask is then transformed back into the space of each subject image and used in the dwinormalise individual command to normalise the input DW images to have the same b=0 white matter median value. All intensity normalised data will be output in a single folder. As previously mentioned, all DWI data must be bias field corrected before applying dwinormalise group, for example using dwibiascorrect. Users are well advised to (manually) check the results of dwinormalise group closely though, as occasional instabilities have been observed in the outcomes of particular subjects.

In case of pipelines that include a multi-tissue spherical deconvolution algorithm yielding compartment estimates for multiple different tissues [Jeurissen2014] [Dhollander2016a], a new command called mtnormalise can be used instead, which performs multi-tissue informed intensity normalisation in the log-domain, correcting simultaneously for both global intensity differences as well as bias fields. The benefit of the mtnormalise command is that normalisation can be performed independently on each subject, and therefore does not require a computationally expensive (and potentially not entirely accurate) registration step to a group template.