Optimal data acquisition for application to the continuous time random walk diffusion model

Thomas Richard Barrick^{1}, Andrew Mott^{1}, Diggory North^{1}, and Franklyn Arron Howe^{1}

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 parameters^{2} 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 1.5mm^{2},
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 curves^{1}. Tensor maps were computed^{4} to create mean
eigenvalue maps for individual parameters. Tissue probability maps were
generated from T1-weighted images (1mm^{3} 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.

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.

[1] Ingo et al. Magn Reson Med 71(2):617-27; 2014.

[2] Ingo et al. Entropy 16:5838-5852; 2014.

[3] Yang et al. J Magn Reson Imaging 37: 365–371; 2013.

[4] Hall and Barrick. NMR Biomed. 25(2):286-94; 2012.

[5] Ashburner and Friston. Neuroimage, 26(3):839-851; 2005

Figure 1: Comparison of gold standard and optimised parametric maps for the CTRW model fitting.

Figure 2: Grey and white matter histograms for optimised CTRW model parameters for reduced numbers of b-value compared to the gold standard.

Figure 3: CTRW parameter maps for data acquired without and with inversion recovery diffusion tensor imaging.

Figure 4: Grey and white matter CTRW parameter histograms for data acquired without and with inversion recovery diffusion tensor imaging.

Figure 5: Optimised inversion recovery diffusion tensor acquisition for a suspected gliomatosis cerebri.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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