Time-dependent diffusion on in vivo human brain data from the Connectom scanner
Uran Ferizi1, Claudia Wheeler-Kingshott2, Daniel Alexander3, and Jose Raya1

1Department of Radiology, New York University School of Medicine, New York, NY, United States, 2Institute of Neurology, University College London, London, United Kingdom, 3Department of Computer Science, University College London, London, United Kingdom


Diffusion MRI models for brain microstructure do not currently incorporate time-dependent diffusivity. Previous studies with ex vivo tissue (muscle and brain) have observed such dependency. The advent of high diffusion gradient scanners have enabled us to probe the tissue to unprecedented. Here we examine and observe the time dependency of the measured diffusion using data from the live human brain.


To show the dependency of the apparent diffusion coefficient (ADC) on diffusion time Δ and gain insight on how multicompartment models depend on diffusion time. In vivo data from the white matter of a human subject was acquired using the high gradient strength (300 mT/m) Connectom scanner.


The Connectom (Siemens Healthcare) scanner uses a custom-built 64-channel coil, capable of |Gmax|=300 mT/m and a slew rate of 200 T/m/s. An 8h PGSE sequence protocol (Ferizi-2014) is used to acquire 48 HARDI shells, each with 90 directions and 10 interwoven b = 0 acquisitions. Every shell has a unique combination of ∆=22, 40, 60, 80, 100, 120 ms, δ=3, 8 ms, and |G|=60, 100, 200, 300 mT/m, giving a bmax= 45,900 s/mm2. The 4mm-thick whole-brain sagittal slices have a 2×2mm2 in-plane resolution. The b=0 image SNR was 35 at TE=49 ms and 6 at TE=152 ms.

A four voxel ROI was selected from the middle of the corpus callosum's genu. The signal from these voxels is then averaged to produce a full dataset (i.e. including all shells and directions). From this dataset, we extract a subset with the diffusion-encoding gradient direction along the fibre, and another with the diffusion gradient running across the fibre. To select these signal subsets we fit the Ball-Stick model, and keep all measurements within 3° of the Stick direction ("axial signal") or orthogonal to it ("radial signal").

To investigate how multicompartment models depend on diffusion time we fitted two multicompartment mode to the full dataset. Both models were selected from previous model comparison studies (Ferizi-2014), the 4 parameter Ball-Stick (Behrens-2003), a simple and relatively low performing two-compartment combination, and the better ranked Zeppelin-Stick, which with different compartmental diffusivities is more complex than Ball and Stick.


Figure 1 shows the dependency of the signal on each diffusion time Δ. The left subplot of short 3ms gradient pulse duration shows that beyond a b-value of about 2,000 s/mm2 the signal along the fibre is clearly non-monoexponential and follows different Δ-specific trajectories; the radial curves also follow different Δ-specific trajectories. These features can be seen better at a larger b-value range in the δ=8ms plot on the right. We note that the radial signal (e.g. Δ=120ms blue curve) continues to attenuate even at the largest of b-values.

In figure 2, the top-left 3D plot shows the dependence of the evaluated ADC on diffusion time Δ and b-value. Here we use only the δ=8ms signal. The 2D projections of this 3D plot are shown in the other three subplots. The ADC vs. b-value map shows a drop, whose rate decreases as the gradient strength increases. The b-value shows the linear dependence on the diffusion time Δ [because b=(γδG)2(Δ-δ/3)]. The bottom-left plot shows the dependence of the evaluated ADC on diffusion time Δ. The ADC drops at variable rates with increasing diffusion time Δ along each |G|-constant curve.

Figure 3 represents the same type of plot as in fig.2, but for the radial part of the signal. As for the axial ADC, the radial ADC decays with diffusion time Δ and with b-value, though within a shorter range of ADC values.

Figure 4 shows how the diffusivity and the volume fraction from the Ball-Stick and Zeppelin-Stick models perform across the Δ range in the full dataset, data which includes all the diffusion sampling directions. As expected, the compartmental volume fraction is broadly constant and shows no particular up/downward trend. The exception here is the highest Δ=120 ms for the Zeppelin-Stick, where the model suffers from the decreasing SNR. Otherwise, the estimated diffusivity, shows dependency on Δ in both models. The downward trend of diffusivity is similar to the trend of decreasing ADC shown in fig.2.


The data in this study uses the unique scanning power afforded by the Connectom scanner to look at the time-dependency of diffusion. This phenomenon could provide an important probe into the tissue microstructure (Novikov-2013). The single-direction datasets, with diffusion gradient oriented along and across the fibre, showed that time-dependent diffusion is a real feature of the signal, and not an artefact of the multicompartment model fitted to the full dataset. Though the current protocol was not designed to specifically look at the time-dependency of diffusion, this work demonstrates that in vivo human white matter shows time-dependent diffusivity, consistent with previous ex vivo experimental results (Kim-2005).


Research reported in this manuscript was supported by the National Institute of Arthritis and Musculoskeletal and Skin Diseases (NIAMS) of the National Insititute of Health (NIH) under award numbers R21AR066897 and RO1 AR067789. The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIH.


Ferizi-2014: Uran Ferizi, Torben Schneider, Thomas Witzel, Lawrence L. Wald, Hui Zhang, Claudia A.M. Wheeler-Kingshott, Daniel C. Alexander, White matter compartment models for in vivo diffusion MRI at 300 mT/m, NeuroImage, Volume 118, September 2015, Pages 468-483

Behrens-2003: Behrens, T.E.J., Woolrich, M.W., Jenkinson, M., Johansen-Berg, H., Nunes, R.G., Clare, S., Matthews, P.M., Brady, J.M. and Smith, S.M. (2003), Characterization and propagation of uncertainty in diffusion-weighted MR imaging. Magn Reson Med, 50: 1077–1088. doi: 10.1002/mrm.10609

Novikov-2014: Novikov, D. S., Jensen, J. H., Helpern, J. A., & Fieremans, E. (2014). Revealing mesoscopic structural universality with diffusion. Proceedings of the National Academy of Sciences, 111(14), 5088-5093.

Kim-2005: Kim S, Chi-Fishman G, Barnett AS, Pierpaoli C (2005) Dependence on diffusion time of apparent diffusion tensor of ex vivo calf tongue and heart. Magn Reson Med 54(6):1387–1396.


Fig.1: Signal decay with increasing b-value. The plot on the left concerns the gradient duration δ=3ms; the plot on the right is for signal of δ=8ms. The axial signal (along the fibre) is shown by the bottom half of the lines; the top half concerns the radial signal. The signal shows dependency on diffusion time Δ.

Fig.2: Gradient duration δ=8ms signal along the axial direction. The top-left 3D subplot shows the dependency of ADC on both b-value and diffusion time Δ. The other three subplots show the 3D subplot as orthogonally projected onto each 2D plane.

Fig.3: As for fig.2, but for signal in the radial direction to the fibre.

Fig.4: Selected estimated parameters of two selected microstructure models for white matter after fitted to the complete dataset (all directions). The models are of varying complexity and construction. They both exhibit reasonably stable compartmental volume fraction; however, the diffusivity is clearly dependent on diffusion time, similarly as for fig.3 (bottom-left subplot).

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