Diffusion weighted MR has become a workhorse of neuroimage analysis and increasingly sophisticated acquisitions are acquired in the hope of revealing intricate details of the underlying tissue structure and composition. It is possible to incorporate information from alternative MR imaging modalities to improve structural specificity. In this work we combine a multi-shell diffusion sequence with a multi-echo T2 relaxometry sequence to enhance the estimation of diffusion model parameters. Specifically multi-compartment T2 relaxometry is used to enhance estimation of the free-water volume fraction in a neurite density and dispersion model.We acquire six multi-contrast diffusion imaging datasets. I is acquired on 3 shells, 8 directions at b=300s.mm^-2, 32 directions at b=700s.mm^-2 and 72 directions at b=2000s.mm⁻² with 12 b=0 volumes using a Siemens 3T Trio. Resolution is 2.5mm isotropic. Multi-echo T2 relaxometry data is acquired at 7 echo times sampled at [52,57,67,80,95,110,150]ms in the same space as the diffusion weighted imaging. In addition we use T1-weighted, MPRAGE data to obtain a brain tissue mask and B0 field maps are acquired to guide the transformation between MPRAGE and the diffusion imaging space.

Multi-compartment model fitting of DWI can be carried out using the Neurite Orientation and Density Distribution model (NODDI [1]). The bespoke method we implement here has a couple of differences to the original algorithm. These include parameter initialisation using the diffusion tensor scheme, a finite sampling scheme that is used to estimate the integration over the Watson distribution and a noise model that is Gaussian which empirically assumes a high SNR but which remains likely to provide a reasonable function for minimisation.

The NODDI model attempts to fit the diffusion signal with three volume fractions, v, representing the signal from a free-water volume fraction, A_f, as well as separating out intra-neurite, A_i, and inter-neurite, A_e, signal contributions. These two tissue volume fractions are coupled with a Watson distribution that intrinsically defines how the tissue structure will alter the signal in these two compartments. In this work we add additional information from multi-compartment T2 relaxometry to guide the fitting in regions where these volume fractions are likely to alter the measured tissue T2,. We assume that we have two detectable T2 compartments, one representing a high-diffusivity free-water compartment which is highly likely to have a long T2, and a single compartment containing both intra-and inter neurite volumes with a shorter average T2 [2]. Thus we can modify the multi-compartment diffusion signal equation to take this into account:

$$S=S_0 [(v_i A_i +v_e A_e)e^{-TE/T2_{ie}} + v_fA_fe^{-TE/T2_f}]$$

From the equation above it is possible to see how the multi-compartment diffusion signal overlaps with a simplified multi-component T2 relaxometry model and we further simplify this analysis by only varying the TE of the b=0 images, in which case the equation simplifies in the absence of diffusion-weighting to become a two-component T2 relaxometry fit and we fix the T2 values for tissue to T2_ie=80ms and for free water to T2_f=200ms.

Figure 1 shows intra-neurite volume fraction results for each of the six subjects. The top row of this figure shows the standard fitting results of this implementation of the NODDI algorithm and the bottom rows shows how this parameter is modified using a coupled bi-exponential T2 fit. Although superficially similar, the results show less variability in the fitted vi parameter near regions of CSF.

Figure 2 shows free-water volume fraction results for each of the six subjects. Again, although the results are similar, a more even parameter distribution is obtained in pure CSF regions. Despite the high T2 attributed to CSF, a non-zero volume fraction is uniformly found within the white matter.

We have shown the results of fitting a generalised tissue parametric model for bi-modal MRI imaging contrast. This model has theoretical benefits for the estimation of mixed tissue parameters in regions of partial volume and we have shown some modest benefits. Theoretically a coupled fit such as this could also benefit the estimation of coupled imaging parameters such as the g-ratio which can be estimated from additional short-echo time T2 weighted data. It should be noted that the interpretation of the difference in estimates is complicated slightly by the different treatment of perfusion effects. If these can be neglected, improved model-fitting performance can be achieved; conversely, if these effects cannot be neglected this methodology opens the door to more elaborate models of MR measurement. Results of using this modification would be expected to show improved performance at tissue borders and when using a tissue-type specific T2 value.