In vivo observation and biophysical interpretation of time-dependent diffusion in human white matter

Highlights

• We measure time-dependent DTI (55 ms – 600 ms) in vivo in human white matter.

• Pronounced longitudinal and weaker transverse time-dependent diffusion is observed.

• Longitudinal time-dependence is attributed to axonal varicosities.

• Transverse time-dependence is attributed to the random axon packing geometry.

• Varying diffusion time may provide a novel microstructural contrast.

Abstract

The presence of micrometer-level restrictions leads to a decrease of diffusion coefficient with diffusion time. Here we investigate this effect in human white matter in vivo. We focus on a broad range of diffusion times, up to 600 ms, covering diffusion length scales up to about 30 μm. We perform stimulated echo diffusion tensor imaging on 5 healthy volunteers and observe a relatively weak time-dependence in diffusion transverse to major fiber tracts. Remarkably, we also find notable time-dependence in the longitudinal direction. Comparing models of diffusion in ordered, confined and disordered media, we argue that the time-dependence in both directions can arise due to structural disorder, such as axonal beads in the longitudinal direction, and the random packing geometry of fibers within a bundle in the transverse direction. These time-dependent effects extend beyond a simple picture of Gaussian compartments, and may lead to novel markers that are specific to neuronal fiber geometry at the micrometer scale.

Introduction

The unique advantage of diffusion-weighted magnetic resonance imaging (dMRI) arises from the sensitivity of water diffusion to the micrometer-level structure of its surrounding environment. In biological tissues, restrictions such as cell walls provide the basis for contrast in dMRI, and particularly, in diffusion tensor imaging (DTI) (Basser, 1995, Beaulieu, 2002). This contrast holds the promise of probing neuronal tissue structure at the scales of about three orders of magnitude below the nominal clinical MRI resolution. From the physics standpoint, this involves quantifying the relevant length scales, such as the compartment (cell) size, or the cell packing correlation length.

There are two physically distinct ways of being sensitive to the cellular length scale: by varying the diffusion wave vector q, or by varying the diffusion time t, as illustrated in Fig. 1 of (Burcaw et al., 2015). The q-method, based on Callaghan's “diffusion diffraction” effect (Callaghan et al., 1991), measures the diffusion signal (the propagator) in the narrow pulse limit as function of q, and the length scale (the fully restricted pore size) is given by the inverse of the characteristic q value for which the propagator experiences oscillations. Unfortunately, given ~ 1 μm-diameter axons and dendrites, the required q values are prohibitively large for in vivo human measurements.

Instead, here our aim is to derive the relevant length scale(s) in human white matter (WM) by varying t, and studying the time-dependence D(t) of the diffusion coefficient (more generally, of the diffusion tensor eigenvalues). This formally amounts to a q → 0 measurement as the diffusion coefficient is proportional to a derivative of the dMRI signal at q = 0, which thereby makes our approach clinically feasible. Since the diffusion coefficient in a given direction $\widehat{x}$ is a measure of the mean squared displacement, i.e. D(t) = 〈(x(t) − x(0))²〉/2t, the length scale probed by water molecules may be adjusted by varying t. With increasing t, water molecules encounter more hindrances and restrictions to their diffusion paths, such as cellular walls and myelin, and therefore the resultant measured diffusion coefficient will decrease (Mitra et al., 1992, Novikov et al., 2014).

While time-dependence of the diffusion coefficient in mammalian WM has been clearly demonstrated at short times (~ 1 ms) (discussed in more detail below), in vivo evidence for the time-dependence using pulse gradient spin echo (PGSE) methods over clinically feasible diffusion time ranges (t > 20 ms) has been inconsistent. In vivo studies of brain, such as healthy and ischemic feline brain tissue (van Gelderen et al., 1994) yielded no change in the mean diffusivity with respect to t for a wide range encompassing 20–2000 ms. Nor was time-dependence observed in vivo in the mean diffusivity of human genu at relatively short times (t = 8 – 80 ms) (Clark et al., 2001) or in the longitudinal or transverse diffusivity within the human corticospinal tract for even longer times (t = 64 – 256 ms) (Nilsson et al., 2009). On the other hand, time-dependent diffusion has been observed in vivo in the corpus callosum, corona radiata, and brainstem of human subjects at times ranging from 40 to 800 ms (Horsfield et al., 1994). Furthermore, ex vivo studies in frog sciatic nerve with diffusion times of 2 ms and 28 ms (Beaulieu and Allen, 1996), bovine optic nerve with diffusion times ranging from 8 to 30 ms (Stanisz et al., 1997), optic and sciatic nerves with diffusion times from 3.7 ms to 99.3 ms (Bar-Shir and Cohen, 2008), as well as bovine optic nerve and rat spinal cord and brain with diffusion times from 40 to 250 ms (Assaf and Cohen, 2000) have shown a clear dependence of D(t) on time in longitudinal and/or transverse direction. More recently, Kunz et al. (2013) imaged the rat corpus callosum in vivo at t ranging from 9 to 24 ms and found time-dependent diffusion in both longitudinal and transverse directions.

Oscillating gradient spin echo (OGSE) diffusion-weighted sequences are able to probe shorter diffusion times compared to conventional PGSE, and have demonstrated time-dependent diffusion in the brain. An in vivo oscillating gradient study of the rat cortex (Does et al., 2003) at frequencies up to 500 Hz, which correspond to very short t ≳ 1 ms, shows a clear time-dependence in the mean diffusivity in both normal live and post-mortem globally ischemic rat cortex. Later work using OGSE with corresponding effective diffusion times (1 – 5 ms) also demonstrated time-dependence in ex vivo rat WM tracts (Xu et al., 2014). In humans, Baron et al. (Baron and Beaulieu, 2014) combined OGSE (25 and 50 Hz) and PGSE methods (t = 20 and 40 ms) for a total diffusion time range of 4 to 40 ms, and found eight major WM tracts and two deep gray matter areas to exhibit time-dependent diffusion. Van et al. (2014) have seen a similar effect with OGSE in human corpus callosum in the frequency range 18–63 Hz. Furthermore, recent work using double PFG MR indirectly points at the possibly non-Gaussian (time-dependent) nature of diffusion in the extracellular space of WM with increasing diffusion times from 25 to 100 ms (Shemesh and Cohen, 2011).

Here we report the observation of time-dependent diffusion in vivo for relatively long diffusion times, t = 45 – 600 ms, on a standard clinical scanner using STimulated Echo Acquisition Mode (STEAM)-DTI, and discuss the biophysical origin of this phenomenon. STEAM-DTI measurements were performed on 5 healthy volunteers and were calibrated on a gel phantom over the whole time range. Pronounced time-dependence in the longitudinal diffusivity and less pronounced time-dependence in the transverse diffusivity were found in both anatomically based WM regions and in fractional anisotropy (FA) thresholded regions.

The biophysical origin of the observed time-dependence, as discussed below, reflects the non-Gaussian nature of diffusion in at least one tissue compartment (in either direction). In all cases, both longitudinal and transverse diffusivities approach a finite tortuosity limit (i.e. diffusion is not anomalous (Bouchaud and Georges, 1990)), with a slow transient part that is best described by a power-law behavior (Novikov et al., 2014, Burcaw et al., 2015). We argue that the origin of this behavior is likely due to randomly placed (short-range disordered) hindrances and restrictions to diffusion in both parallel and transverse directions. Interestingly, the biological sources of this short-range disorder may be qualitatively distinct: structural disorder along the axons such as, e.g., varicosities for diffusion in the longitudinal direction, and the random packing geometry of fibers within a bundle for diffusion in the transverse direction. This picture is corroborated by the estimated correlation length scales in the range of a few microns in both directions.