The continuous time random walk (CTRW) diffusion model provides an alternative technique for investigation of water diffusion dynamics from diffusion-weighted magnetic resonance imaging (DW-MRI) data.¹ CTRW differs from the standard random walk model by inclusion of probability density functions for spin waiting times and step lengths. These are included as fractional waiting time, α, and step length, β, exponents as follows,

$$ S_b=S_0\sum_{k=1}^\infty \frac{(-D\bar\Delta^\alpha q^\beta)^k}{\Gamma(\alpha k+1)} $$

where $$$\bar\Delta=\triangle-\delta/3$$$, q=γgδ and D is the apparent diffusion coefficient (ADC). Diffusion kurtosis, k, and entropy, H, of the decay curve may be computed from fitted model parameters² for use in clinical imaging biomarker studies. This study aims to optimise the diffusion-weighted MRI (DW-MRI) acquisition to be within clinically acceptable time and to consider the effects of inversion recovery (IR) to null CSF.³

MRI acquisition: Data were acquired at 3T using a single shot EPI DW-MRI acquisition (TE=90ms, TR=6000ms, in-plane resolution 1.5mm², slice thickness 5mm) in 6 non-collinear diffusion directions on 6 healthy volunteers (mean age 22±4.5 years). Optimisation: A “gold standard” acquisition was obtained with 14 diffusion-sensitised images equally spaced between b=0 and 5000 s mm-2 (δ=23.5ms, Δ=43.9ms). Inversion recovery: DW-MRI (δ=22.8ms, Δ=44.6ms) were acquired with IR (TI = 1801ms) and without IR, with b=0, 500, 750, 1000, 1500, 2250, 3500, and 5000 s mm^-2.

Image Analysis: The CTRW model was fitted to each voxel and diffusion direction. Entropy maps were computed to provide a measure of information content of fitted decay curves¹. Tensor maps were computed⁴ to create mean eigenvalue maps for individual parameters. Tissue probability maps were generated from T1-weighted images (1mm³ resolution)⁵ and binary tissue segmentations created to calculate CTRW parameter values in grey and white matter. Permutation analyses with 7, 6, 5 and 4 b-values were performed to optimise similarity between voxel α values in white matter for different b-value combinations compared to the “gold-standard”, using sum of squared difference. Differences between median grey and white matter parameters were assessed using paired t-tests.

Parameter maps and tissue histograms for α, β and H are shown in Figures 1 and 2 for the gold standard compared to the optimal minimum acquisition time of 5.8 mins (4 b-values, b=360, 1080, 4680, 5000 s mm^-2). No significant differences for α, β and H in grey matter, or α and H in white matter were found between the optimised 4 b-value acquisition and the gold standard. Significant differences were found for β (p=0.002) in white matter. Parameter maps and tissue histograms for ADC, α, β and H are shown in Figures 3 and 4. IR reduced the skew of grey-matter ADC. For specific brain regions there were significant differences in deep grey-matter (ADC p<0.001; H p<0.001) and peri-ventricular white matter (ADC p=0.002; α p<0.001; β p<0.001) between IR and non-IR data.

Image acquisition time was minimised while maintaining maximal similarity of parameter maps to the gold standard by a 4 b-value dataset that may be acquired within 5.8 minutes. This represents a clinically acceptable acquisition time for use in patient studies. Furthermore, the majority of parameters were not significantly different to the gold standard. Differences between β parameters in white matter may be due to application of a parameter optimisation on white matter alone.

Results of the IR study show that CSF partial volume effects at the boundary between CSF and grey and white matter significantly affect parameter values. Effects of CSF contamination are unlikely to be an effect of the applied diffusion model and are particularly apparent in ADC measurements. IR DW-MRI is particularly useful for more accurate assessment of grey matter diffusion properties. Future optimisation of data acquisition will simultaneously consider α and β computed from IR DW-MRI in both grey and white matter to ensure optimisation across all tissue types and parameters.

To show the potential utility of coupling the 4 b-value optimised acquisition with IR DW-MRI an example is illustrated for a suspected gliomatosis cerebri patient in Figure 5. The CTRW parameters, particularly anisotropy of α, provide greater tissue contrast than conventional FLAIR, ADC or fractional anisotropy images, potentially revealing extensive, diffuse abnormalities throughout the frontal lobe.