Several diffusion-weighted (DW) MRI methods provide estimates of the density of neurites, i.e. axons in white matter (WM) and dendrites in grey matter (GM), modelling them as sticks^1,2 (zero-radius cylinders). This simplification is reasonable in the long diffusion time limit³ and long gradient pulse duration⁴, a condition practically achievable in most brain WM.

However, in spinal cord WM, myelinated axons can have diameters⁵ as large as 10-15 μm, and the diffusion times employed to minimise the echo time T_E of DW spin echo acquisitions may not be sufficiently long to support the stick model.

Here, we investigated whether in clinical settings sub-optimal diffusion times can affect neurite density (ND) estimation in the spinal cord, assessing diffusion time dependency of ND in vivo and corroborating results with simulations.

Simulated signal synthesis The Camino Monte Carlo (MC) simulator⁶ was used to synthesise DW signals from two substrates describing WM characterised by big and small axons (figure 1: BigAxons/SmallAxons, representative of spinal cord⁵ and corpus callosum⁷), made of cylinders with gamma-distributed radii (cylinder volume fraction (CVF) of 0.65, diffusivity inside/outside 1.70 μm²/ms). Four clinically feasible two-shell protocols (b=711 s/mm² and b=2855 s/mm²; 30 and 60 directions; gradient duration δ=18 ms) were synthesised, each characterised by a diffusion time T_d=Δ – δ/3 among {24, 41.3, 58.7, 76} ms (gradient separation Δ was varied).

Simulated signal analysis CVF was estimated with NODDI² on: i) 1000 unique sub-protocols of 25 and 50 directions at b=711 s/mm² and b=2855 s/mm² for infinite signal-to-noise ratio (SNR); ii) 1000 protocols with unique realisations of Rician noise (SNR of 13, 10.25, 8.09, 6.38 for increasing T_d to model the effect of longer T_E, assuming T₂=72 ms and SNR=13 at T_d=24 ms). Signals from substrates BigAxons/SmallAxons were averaged to simulate a mixture of their radius distributions.

In vivo acquisition Three subjects (all aged 27) were scanned axially on a 3T Philips Achieva system (cardiac gated ZOOM-EPI sequence⁸, cervical level C1-C3, resolution 1×1×5mm³, field-of-view 64×48×60mm³, T_R 12RR repeats). Three two-shell protocols (b=711 s/mm² and b=2855 s/mm²; 20 and 40 directions; δ=22 ms) were acquired with T_d ∈ {21.17, 44.67, 68.67} ms, varying Δ. Subjects were scanned twice, with minimum T_E for each T_d in the first session (T_E ∈ {67, 87.20, 111} ms) and fixing T_E=111 ms in the second session, to control for the different T₂-weighting and SNR implied by a variable T_E.

In vivo analysis ND was estimated fitting NODDI after slice-wise motion correction and spinal cord segmentation. We created an average DW image with good GM/WM contrast⁹, where we segmented GM manually and determined WM as the portion of the cord not containing GM. ND was characterised in WM calculating median and interquartile range.

Simulations Figure 2 shows the estimated CVF. At infinite SNR, CVF is underestimated for the BigAxons and mixture BigAxons/SmallAxons substrates, and increasing T_d decreases this bias. CVF shows neither bias nor T_d-dependency for the SmallAxons substrate. Adding noise provides similar trends, but decreases precision.

In vivo ND maps for one slice per volunteer are shown in figures 3 and 4 for the two MRI sessions. In both sessions, ND increases as T_d increases, especially in certain areas as those illustrated. Table 1 reports descriptive statistics of ND in WM and the percentage relative increase of the median ND with respect to the median at T_d=21.17 ms. A trend of higher ND for longer T_d is measured in all subjects and sessions (increase of about 10%).

Here we investigated whether in clinical scenarios sub-optimal diffusion times affect ND estimation in the spinal cord.

MC simulations run with a relatively long gradient pulse duration demonstrated that ND can be underestimated in microstructural geometries plausible in the spinal cord, if inadequately short diffusion times are employed. The underestimation is stronger at shorter diffusion time, but also occurs at longer diffusion time, because of the finite diameter of axons.

In vivo experiments showed a trend of increasing ND in spinal cord WM as the diffusion time increased, not confounded by changes of echo time. This suggests that at the shortest diffusion time we probed, the assumptions of the stick model were not fully met in areas with large axons.

We conclude that careful design of the diffusion time is required for the estimation of ND in the spinal cord. Short diffusion times lead to biased estimates, whereas long diffusion times lead to more accurate but less precise values. A compromise between accuracy and precision needs to be evaluated according to the application.