Multi-compartmental diffusion characterization of the human cervical spinal cord in vivo using the spherical mean technique

Abstract

The purpose of this work was to evaluate the feasibility and reproducibility of the spherical mean technique (SMT), a multi-compartmental diffusion model, in the spinal cord of healthy controls, and to assess its ability to improve spinal cord characterization in multiple sclerosis (MS) patients at 3 T. SMT was applied in the cervical spinal cord of eight controls and six relapsing-remitting MS patients. SMT provides an elegant framework to model the apparent axonal volume fraction v_ax , intrinsic diffusivity D_ax , and extra-axonal transverse diffusivity D_{ex_perp} (which is estimated as a function of v_ax and D_ax ) without confounds related to complex fiber orientation distribution that reside in diffusion MRI modeling. SMT's reproducibility was assessed with two different scans within a month, and SMT-derived indices in healthy and MS cohorts were compared. The influence of acquisition scheme on SMT was also evaluated. SMT's v_ax , D_ax , and D_{ex_perp} measurements all showed high reproducibility. A decrease in v_ax was observed at the site of lesions and normal appearing white matter (p < 0.05), and trends towards a decreased D_ax and increased D_{ex_perp} were seen. Importantly, a twofold reduction in acquisition yielded similarly high accuracy with SMT. SMT provides a fast, reproducible, and accurate method to improve characterization of the cervical spinal cord, and may have clinical potential for MS patients.

Keywords: axon; diffusion; multiple sclerosis; spherical mean technique; spinal cord; volume fraction.

Figure 1. SMT-Derived Maps and Reproducibility in Controls

From left to right, the averaged map, the standard deviation map, and the histograms of all white mater voxels over all controls for scan 1 and scan 2 are shown for (a) v_ax, (b) D_ax, and (c) D_{ex_perp}.

Figure 2. Example SMT-Derived Maps in MS

Anatomical images (top), SMT-derived maps v_ax (second row), D_ax (third row), and D_{ex_perp} (bottom) are displayed for control (left, 24-years-old) and two patients. MS patient 1 (middle), 46-years-old, EDSS 2 and duration of disease of 17 years, highlights a decreased v_ax, D_ax and increased D_{ex_perp} at the site of the lesion (black arrow) in the left lateral column. MS patient 2 (right), 36-years-old, EDSS 2.5 and duration of disease 8 years, demonstrates similar trends in v_ax and D_ax to the MS patient 1.

Figure 3. Application of SMT in MS Cohort

Boxplots highlighting the median, 25^th and 75^th percentiles over controls (WM) and MS patients (lesions and NAWM) for (a) v_ax, (b) D_ax, and (c) D_{ex_perp}. Mean values from each subject plotted and asterisks indicate significant differences between the groups.

Figure 4. Effect of Reduced Acquisition Schemes on SMT-Derived Parameters

(a) Corresponding v_ax maps for a healthy control for full 18 min acquisition (left), along with reduced data acquisition schemes of 12 minutes, 9 minutes and 6 minutes (right). Bias maps, with respect to full acquisition schemes, are shown below each subsampled scheme and demonstrate that there is an increased bias in v_ax with reduced acquisition times, but with fairly negligible differences between the 2/3 and 1/2 acquisition. (b) Mean root mean squared error (RMSE) for v_ax in white matter over all of the controls, with error bars plotting the inter-subject variability. (c) D_ax maps, with bias maps below, for same reduced acquisition times as shown in (a). (d) RMSE of D_ax increases with reduced acquisition. (e) D_{ex_perp} maps, with bias maps below, for same reduced acquisition times as shown in (a). (f) An increase in RMSE for D_{ex_perp} is observed with reduced acquisition times.

Figure 5. Effect of Reduced Acquisition Schemes on v_ax, D_ax, and D_{ex_perp} in MS Patient

From left to right, the SMT-derived (a) v_ax map, (b) D_ax map, and (c) D_{ex_perp} map are shown with the fully acquired dataset, 2/3 acquisition, 1/2 acquisition, and 1/3 acquisition. With decreases in acquisition time, SMT does not lose sensitivity to distinguish lesions from NAWM. The same patient, as in Figure 2 (MS patient 1), is shown.