Introduction

The hippocampus is implicated in numerous neurological disorders, including temporal lobe epilepsy (TLE) and Alzheimer’s disease (AD), and the ability to detect subtle or focal hippocampal abnormalities earlier could significantly improve the treatment of patients. Ex vivo studies with ultra-high field have revealed that diffusion MRI (dMRI) can reveal microstructural variations within the hippocampal subfields and lamina, and may also be sensitive to intra-hippocampal pathways ¹. However, in vivo dMRI studies of the hippocampus are challenging due to its complicated geometry. In addition to its small size, the hippocampus, similar to the cortex, shows gyrification (or digitations) across its structure. Further, the hippocampus has a curled or folded configuration. One novel way to overcome these obstacles is by transforming the usual cartesian coordinates in a MRI image to coordinates that are mathematically crafted to curve themselves according to the complicated geometry of the hippocampus ². This allows us to virtually flatten the hippocampus into a thin sheet. A particularly unique aspect of our proposed approach is to project the diffusion data onto this sheet, carefully adjusting the diffusion directions from the original acquisition to be compatible with the sheet.

Methods

We used data from four participants in the Human Connectome Project (HCP) Young Adult 3T study ³. We begin by a manual segmentation of both hippocampi. This is followed by solving Laplace’s equation, $\nabla^2 \phi =0$, in 3-dimensions on the underlying cartesian grid with coordinates $x,y$ and $z$ native to the MRI scan; denoted the ‘native space’. The Laplace’s equation is solved three times to provide three new anatomical coordinates $u, v$ and $w$, using boundary conditions as depicted in Figure 1a. The resulting coordinate fields are shown in Figure 1b,c,d, where bright yellow is 1 and dark blue is 0. Next, we reparameterize the new coordinates with the arc length. At this stage we can ‘unfold’ the hippocampus by going in to the domain of the new coordinates, the ‘unfolded space’. The coordinate fields $u(x,y,z)$, $v(x,y,z)$ and $w(x,y,z)$ allow us to map data from the native space to the unfolded space. The novel contribution in this work is to also map vector data to the unfolded space, which is essential for properly handling diffusion gradient directions. We use the Jacobian to correctly ‘push’ the diffusion directions and corresponding signal intensities to the the unfolded space. This allows us to generate a diffusion-weighted volume, resampled in the unfolded space, with the Jacobian encoding the unfolding transformation. Several existing tools for fitting already can make use of a Jacobian to account for gradient non-linearities (e.g. FSL FDT ⁴), and thus can be used directly for fitting and tractography in the unfolded space. We utilized the inherent correspondence across subjects in the unfolded space to define subfield labels in our participants using average labels defined previously at 7T². We used these to perform probabilistic tractography (FSL PROBTRACKX ⁵), all voxels were taken as seeds tagged with the subfield they belong to and 5000 samples were used.

Results

The visualizations of fibre orientation maps in Figure 2 demonstrates how unfolding provides an holistic visualization of the entire extent of the hippocampus, and reveals patterns in fibre orientation and anisotropy that are more difficult to discern in the native space. A validation of the ability of the unfolding approach to preserve orientation information is shown in Figure 3, with angle errors from fits in the native space compared to fits performed in unfolded space and mapped back to the native space. Figure 4 shows that fractional anisotropy has some subfield specificity, with subiculum significantly different than all other subfields. Figure 5 shows the intra-hippocampal connectivity for all 8 hippocampi, revealing consistent patterns that are consistent with connections related to the tri-synaptic pathway.

Discussion

A benefit of the unfolded space is that the orthogonal axes now represent anatomically relevant axes: longitudinal (anterior to posterior), laminar (deep to superficial), and lamellar (proximal to distal). These are notably the axes in which axonal projections generally follow anatomically, so tractography in this space could be constrained more effectively. This advantage could also be employed to inform novel microstructural models of cortical tissue, which future work will explore. One limitation of the current work is the need for manual segmentations, and thus was limited to a small number of subjects, however, semi-automated methods are currently in development, and this technique can also be applied more generally to any cortical structure.

Acknowledgements

This work was supported by a BrainsCAN Stimulus grant from the Canada First Research Excellence Fund, Brain Canada, and a Project Grant from the Canadian Institutes of Health Research (CIHR). We thank Kayla Ferko for assisting with hippocampal subfield segmentation.