Probing tissue microstructure with restriction spectrum imaging: Histological and theoretical validation

Abstract

Water diffusion magnetic resonance imaging (dMRI) is a powerful tool for studying biological tissue microarchitectures in vivo. Recently, there has been increased effort to develop quantitative dMRI methods to probe both length scale and orientation information in diffusion media. Diffusion spectrum imaging (DSI) is one such approach that aims to resolve such information based on the three-dimensional diffusion propagator at each voxel. However, in practice, only the orientation component of the propagator function is preserved when deriving the orientation distribution function. Here, we demonstrate how a straightforward extension of the linear spherical deconvolution (SD) model can be used to probe tissue orientation structures over a range (or "spectrum") of length scales with minimal assumptions on the underlying microarchitecture. Using high b-value Cartesian q-space data on a rat brain tissue sample, we demonstrate how this "restriction spectrum imaging" (RSI) model allows for separating the volume fraction and orientation distribution of hindered and restricted diffusion, which we argue stems primarily from diffusion in the extraneurite and intraneurite water compartment, respectively. Moreover, we demonstrate how empirical RSI estimates of the neurite orientation distribution and volume fraction capture important additional structure not afforded by traditional DSI or fixed-scale SD-like reconstructions, particularly in gray matter. We conclude that incorporating length scale information in geometric models of diffusion offers promise for advancing state-of-the-art dMRI methods beyond white matter into gray matter structures while allowing more detailed quantitative characterization of water compartmentalization and histoarchitecture of healthy and diseased tissue.

Copyright © 2012 Wiley Periodicals, Inc.

Figures

Figure 1

Restriction spectrum model. The oriented component of the diffusion signal is written a linear mixture (spectrum) of cylindrically symmetric Gaussian response functions R with different fixed transverse diffusivities DT and unknown volume fraction and orientation distribution (f).

Figure 2

RSI analysis for a single horizontal slice taken at the level of the dorsal striatum, hippocampus, and tectum. The diffusion length scale is shown increasing from left to right. Volume fraction maps (top row) are derived from the zeroth‐ordered SH coefficients normalized to sum to one (negative weights set to zero). These maps provide an estimate of the fractional contribution of diffusion at each scale to the total signal, where dark voxels indicate large contributions (volume fractions), and light voxels indicate little or no contribution. Note the apparent bimodal separation of fine (left, red frame) and coarse (right, blue frame) scale diffusion processes, which is consistent with in vivo biexponential models of “slow” and “fast” diffusion, respectively. The FOD spectra for two representative voxels in white and gray matter are shown in rows 2, and 3, respectively. Note the differences in orientation structure at the fine and coarse scale, particularly in gray matter (row 3). All FODs are displayed by subtracting the minimum (which highlights the oriented component of the FOD) and scaling their amplitudes by their relative volume fraction. Values for the geometric tortuosity (λg) were computed directly from the RSI model scale, while the compartment size diameters (d) were estimated using Monte Carlo simulations (see “Compartment Size Diameter Simulation section”). Together, the geometric tortuosity and theoretical compartment size diameter support the hypothesis that the fine‐ and coarse‐scale diffusion processes stem from restricted and hindered diffusion in the intraneurite and extraneurite water compartment, respectively (see “Theoretical and Empirical Support for the Neurite Hypothesis” section). In the “Histological Substrates for the r‐FOD and h‐FOD” section, we compare the restricted (r‐FOD) and hindered (h‐FOD) FOD against histology at the two scales illustrated with arrows. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 3

Comparison of neuronal and glial cell morphologies in the rat cerebral cortex. (A) Confocal image of two‐layer‐V pyramidal neurons [modified from Kalisman et al., 2005, with permission]. (B) Maximum projections of dye‐filled, nonreactive astrocytes in layer IV [reprinted from Wilhelmsson et al., 2006 with permission]. In contrast to pyramidal cell dendrites, astrocytes have a “spongiform” appearance with numerous, highly tortuous, and permeable processes that are not well modeled by piecewise cylindrical elements. As a reference, the maximum length scale probed by our experiment is on the order of ≈ 4μm. Scale bars, 25 μm

Figure 4

Sagittal comparison of RSI and histology in the striatum and globus pallidus. Color‐coded RSI reconstructions of the r‐FOD (left column; A, D) and h‐FOD (right column; C, F) are shown together with myelin stained histological sections (middle column; B, E) from the same specimen. All RSI distributions were scaled to fit within the voxel boundary, while the h‐FOD was further normalized by subtracting the minimum to highlight its preferred orientation. RSI volume fractions are shown as voxel grayscale intensities (dark corresponds to increased volume fraction). The upper left inset indicates position of the sagittal slice. Two regions are compared, one in the dorsolateral striatum (A–C) and one in the globus pallidus (D–F). Arrows on top of the inset images and frames in A and C indicate the position of the coronal slices shown in Figure 5E,H, respectively. The oblique orientation of the elongated dark, myelin stained fibers in B and E correspond well to the anterioposterior (blue) component of the r‐FOD, but less well with the elongated h‐FOD. The r‐FOD volume fractions (grayscale darkening from left to right in D) fit well with the density of myelin labeled fibers in E. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 5

Coronal comparison of RSI and histology in the cerebral cortex and striatum. Presentation as in Figure 4. In addition to the myelin stained histological sections (middle column; C, G) from the same specimen, potassium channel (KChlP1) stains (middle column; B, F, I) are also included from a similar specimen (from http://www.brainmaps.org; see Sample Preparation and Image Acquisition section). Two regions are compared, one in the parietal cortex (A–D) and one in the dorsolateral striatum (E–I). Arrows on top of the inset images and frames in E and H indicate the position of the sagittal slices shown in Figure 4A,C, respectively. In the cortex, the primary orientation of the r‐FOD and h‐FOD are aligned radial to the cortical surface, while the r‐FOD displays additional tangential orientations, which are most prominent in superficial layers I/II. In the striatum, the through‐plane (anterioposterior, blue) r‐FOD and h‐FOD orientations reflect the cross‐sectioned myelin stained fibers passing through the striatum (dark dots in E, light dots in F). Here, again the r‐FOD displays substantial additional in‐plane structure (red and green peaks), which we argue reflects the complex geometry of corticostriatal terminal plexuses (Fig. 6D) and vast networks of dendritic arbors in the region (I). Scale bar 50 μm.

Figure 6

Axonal architecture in the cerebral cortex and dorsal striatum. Histological images [from the Whole Brain Connectivity Atlas at http://www.rbwb.org, case R606; Zakiewicz et al., 2011] showing specific corticocortical and corticostriatal axonal projections, anterogradely labeled by axonal tracer injection in the primary somatosensory cortex (darkly stained region indicated by asterisk in inset, see “Sample Preparation and Image Acquisition” section). (A) Overview of the secondary somatosensory cortex and dorsal striatum showing the distribution of distinct, darkly labeled axonal plexuses. Note the columnar distribution of labeled fibers in the cerebral cortex, with profuse arborizations in layers I–III and V, and laminar distribution of striatal fiber plexuses (arrowheads) extending in parallel with the overlying external capsule (ec). Frames indicate the position of panels B–D. (B–D) Image magnifications showing detailed fiber architectures in cerebral cortex (B, layer I/II; C, layer IV/V) and dorsal striatum (D). Note the perpendicular fiber orientations in the deeper part of the cortex (C) and striatum (D), which match the r‐FOD in Figure 5A,E, respectively. Also, the more complex fiber orientations in the superficial cortex (B) fit well with the more pronounced tangential r‐FOD peaks in Figure 5A. Scale bars, 500 and 50 μm.

Figure 7

Coronal comparison of RSI estimates of (restricted) neurite volume fraction with histological measures of fiber architecture. The coronal section is the same as in Figure 5 (frames indicate corresponding panels). As expected, the RSI neurite volume fraction is consistent with the combination of both myelinated axons (left panel) and unmyelinated dendrites (right panel). Note also the increased neurite volume fraction in superficial layers of the cerebral cortex (I/II), which are also clearly visible in the potassium channel (KChlP1) stain (right panel). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 8

Axial RSI analysis in the cerebellum. Color‐coded RSI reconstructions of the (A) r‐FOD and (B) h‐FOD are shown for a horizontal cerebellar slice taken at level of lobules 3, 5, and 8, corresponding to a level ∼4.6 mm below bregma, illustrated in the inset atlas diagram redrawn from Figure 201 in Paxinos and Watson 2007 [Paxinos and Watson, 2007]. All distributions were scaled to fit within the voxel boundary, while the h‐FOD was further normalized by subtracting the minimum to highlight its preferred orientation. RSI volume fractions are shown as voxel grayscale intensities (dark corresponds to increased volume fraction). The cerebellar white matter and cortical layers are differentiated by distinct differences in r‐FOD and h‐FOD orientation and volume fraction. White boxes correspond to voxels plotted in Figure 10. Cb, cerebellar lobule, CrusI, crus 1 of the ansiform lobule; CrusII, crus 2 of the ansiform lobule; gcl, granule cell layer; ml, molecular layer; Sim, simple lobule; wm, white matter. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 9

Comparison of RSI with SD and DSI in the cerebral cortex. Color‐coded RSI reconstructions of the (A) r‐FOD and (B) h‐FOD are compared against (C) SD reconstructions of the fixed‐scale FOD (FS‐FOD) and (D) DSI reconstructions of the dODF (DSI‐dODF). The region sampled is the same as in Figure 5A–D. All distributions were scaled to fit within the voxel boundary, while both the h‐FOD and DSI‐dODF were further normalized by subtracting the minimum to highlight their preferred orientation. RSI volume fractions are shown as voxel grayscale intensities (dark corresponds to increased volume fraction). The FS‐FOD and DSI‐dODF are plotted on the r‐FOD volume fraction map. In contrast to the r‐FOD, both the FS‐FOD and DSI‐dODF demonstrate little evidence for the numerous horizontally oriented neurites tangential to the cortical surface (see Fig. 6B,C), and have similar orientation structure to the h‐FOD. I/II, cerebral cortex layer I/II; ec, external capsule. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure 10

Comparison of RSI with SD and DSI in the cerebellum. Color‐coded RSI reconstructions of the r‐FOD and h‐FOD are compared against the FS‐FOD and DSI‐dODF. The sampled voxels are shown as white boxes in Figure 8. In the molecular layer (ml), the r‐FOD shows additional radially (translobularly) oriented green peaks (arrow) that are consistent with the orientation of Purkinje cell dendrites and ascending granule cell axons in the region. These peaks are not evident in either the FS‐FOD or DSI‐dODF. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure A1

RSI model resolution matrix. Each row illustrates the sensitivity of the recovered (estimated) FOD at that scale (row number) to FODs at all other scales (column number). Perfect resolution would result in a diagonal matrix of “cigar‐like” FODs along the horizontal axis (labeled). All FODs are shown unnormalized (without subtracting the minimum) with negative values set to zero. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Figure A2

RSI Monte Carlo simulations. The mean r‐FOD (color‐coded surface) and mean plus standard deviation (gray opaque surface) over 100 Monte Carlo runs are shown for various SNR levels and hindered (h) and restricted (r) volume fractions. The amplitude of the 90° ringing artifact increases both with decreasing SNR and increasing hindered volume fraction. The SNR of our q‐space data in white and gray matter was ≈29.8 and ≈55.1, respectively. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]