Diffusion time dependence of microstructural parameters in fixed spinal cord

Abstract

Biophysical modelling of diffusion MRI is necessary to provide specific microstructural tissue properties. However, estimating model parameters from data with limited diffusion gradient strength, such as clinical scanners, has proven unreliable due to a shallow optimization landscape. On the other hand, estimation of diffusion kurtosis (DKI) parameters is more robust, and its parameters may be connected to microstructural parameters, given an appropriate biophysical model. However, it was previously shown that this procedure still does not provide sufficient information to uniquely determine all model parameters. In particular, a parameter degeneracy related to the relative magnitude of intra-axonal and extra-axonal diffusivities remains. Here we develop a model of diffusion in white matter including axonal dispersion and demonstrate stable estimation of all model parameters from DKI in fixed pig spinal cord. By employing the recently developed fast axisymmetric DKI, we use stimulated echo acquisition mode to collect data over a two orders of magnitude diffusion time range with very narrow diffusion gradient pulses, enabling finely resolved measurements of diffusion time dependence of both net diffusion and kurtosis metrics, as well as model intra- and extra-axonal diffusivities, and axonal dispersion. Our results demonstrate substantial time dependence of all parameters except volume fractions, and the additional time dimension provides support for intra-axonal diffusivity to be larger than extra-axonal diffusivity in spinal cord white matter, although not unambiguously. We compare our findings for the time-dependent compartmental diffusivities to predictions from effective medium theory with reasonable agreement.

Recent Developments in Fast Kurtosis Imaging

“…Determining which of these two "branches" yields physically correct parameter estimates has been subject of some debate [38,73,74] and is not yet fully resolved. In Hansen et al [38] affected parameters are reported for both branches.…”

“…The solutions for the two branches are much more obvious than in conventional WMTI, where the sign choice is only known to be stable over diffusion encoding directions for the branch defined by D a ≤ D e,|| [2]. WMTI analysis based on modest data makes it feasible to experimentally investigate the unresolved branch duality-e.g., using data acquisitions employing varying diffusion times as in Jespersen et al [73] which would have been prohibitively time consuming with conventional WMTI. Similarly, the increase in acquisition speed facilitates high resolution data acquisitions for validation purposes or for in vivo applications.…”

“…For axially symmetric systems specifically, these are p 2 and p 4 , the two lowest nontrivial Legendre expansion coefficients of the fODF [73]. Hence in general, there are more unknowns than equations.…”

“…Hence in general, there are more unknowns than equations. However, if a one parameter fODF, such as the Watson distribution, can be assumed, p 2 and p 4 become interdependent and the number of unknowns equals the number of equations, facilitating fast axisymmetric WMTI in the presence of dispersion [73]. Figure 7A (upper row) shows estimates of the time-dependent dispersion [Watson concentration parameter κ (kappa)] of both branches (labeled + and −, shown on the left and right, respectively) measured using such an approach with data acquired from a stimulated echo diffusion-weighted sequence in four regions of interest (ROIs) in in pig spinal cord white matter.…”

“…Figure 7A (upper row) shows estimates of the time-dependent dispersion [Watson concentration parameter κ (kappa)] of both branches (labeled + and −, shown on the left and right, respectively) measured using such an approach with data acquired from a stimulated echo diffusion-weighted sequence in four regions of interest (ROIs) in in pig spinal cord white matter. The data is from Jespersen et al [73] with ROI labels matching that work. Figure 7B (lower row) plots time dependence of intra-axonal diffusivity of both branches (again + branch on the left and − branch on the right).…”