Biophysical compartment models for single-shell diffusion MRI in the human brain: a model fitting comparison

Clinically oriented studies commonly acquire diffusion MRI (dMRI) data with a single non-zero b-value (i.e. single-shell) and diffusion weighting of b=1000 s/mm2. To produce microstructural parameter maps, the tensor model is usually used, despite known limitations. Although compartment models have demonstrated improved fits in multi-shell dMRI data, they are rarely used for single-shell parameter maps, where their effectiveness is unclear from the literature. Here, various compartment models combining isotropic balls and symmetric tensors were fitted to single-shell dMRI data to investigate model fitting optimization and extract the most information possible. Full testing was performed in 5 subjects, and 3 subjects with multi-shell data were included for comparison. The results were tested and confirmed in a further 50 subjects. The Markov chain Monte Carlo (MCMC) model fitting technique outperformed non-linear least squares. Using MCMC, the 2-fibre-orientation mono-exponential ball & stick model (BSME 2) provided artifact-free, stable results, in little processing time. The analogous ball & zeppelin model (BZ2) also produced stable, low-noise parameter maps, though it required much greater computing resources (50 000 burn-in steps). In single-shell data, the gamma-distributed diffusivity ball & stick model (BSGD 2) underperformed relative to other models, despite being an often-used software default. It produced artifacts in the diffusivity maps even with extremely long processing times. Neither increased diffusion weighting nor a greater number of gradient orientations improved BSGD 2 fits. In white matter (WM), the tensor produced the best fit as measured by Bayesian information criterion. This result contrasts with studies using multi-shell data. However, in crossing fibre regions the tensor confounded geometric effects with fractional anisotropy (FA): the planar/linear WM FA ratio was 49%, while BZ2 and BSME 2 retained 76% and 83% of restricted fraction, respectively. As a result, the BZ2 and BSME 2 models are strong candidates to optimize information extraction from single-shell dMRI studies.

Axonal T2 estimation using the spherical variance of the strongly diffusion-weighted MRI signal

In magnetic resonance imaging, the application of a strong diffusion weighting suppresses the signal contributions from the less diffusion-restricted constituents of the brain's white matter, thus enabling the estimation of the transverse relaxation time T2 that arises from the more diffusion-restricted constituents such as the axons. However, the presence of cell nuclei and vacuoles can confound the estimation of the axonal T2, as diffusion within those structures is also restricted, causing the corresponding signal to survive the strong diffusion weighting. We devise an estimator of the axonal T2 based on the directional spherical variance of the strongly diffusion-weighted signal. The spherical variance T2 estimates are insensitive to the presence of isotropic contributions to the signal like those provided by cell nuclei and vacuoles. We show that with a strong diffusion weighting these estimates differ from those obtained using the directional spherical mean of the signal which contains both axonal and isotropically-restricted contributions. Our findings hint at the presence of an MRI-visible isotropically-restricted contribution to the signal in the white matter ex vivo fixed tissue (monkey) at 7T, and do not allow us to discard such a possibility also for in vivo human data collected with a clinical 3T system.

Half Way There: Theoretical Considerations for Power Laws and Sticks in Diffusion MRI for Tissue Microstructure

In this article, we consider how differing approaches that characterize biological microstructure with diffusion weighted magnetic resonance imaging intersect. Without geometrical boundary assumptions, there are techniques that make use of power law behavior which can be derived from a generalized diffusion equation or intuited heuristically as a time dependent diffusion process. Alternatively, by treating biological microstructure (e.g., myelinated axons) as an amalgam of stick-like geometrical entities, there are approaches that can be derived utilizing convolution-based methods, such as the spherical means technique. Since data acquisition requires that multiple diffusion weighting sensitization conditions or b-values are sampled, this suggests that implicit mutual information may be contained within each technique. The information intersection becomes most apparent when the power law exponent approaches a value of 12, whereby the functional form of the power law converges with the explicit stick-like geometric structure by way of confluent hypergeometric functions. While a value of 12 is useful for the case of solely impermeable fibers, values that diverge from 12 may also reveal deep connections between approaches, and potentially provide insight into the presence of compartmentation, exchange, and permeability within heterogeneous biological microstructures. All together, these disparate approaches provide a unique opportunity to more completely characterize the biological origins of observed changes to the diffusion attenuated signal.

DIffusion-Prepared Phase Imaging (DIPPI): quantifying myelin in crossing fibres

PurposeMyelin has long been the target of neuroimaging research due to its importance in brain development, plasticity, and disease. However, most available techniques can only provide a voxel-averaged estimate of myelin content. In the human brain, white matter fibre pathways connecting different brain areas and carrying different functions often cross each other in the same voxel. A measure that can differentiate the degree of myelination of crossing fibres would provide a more specific marker of myelination.Theory & MethodsOne MRI signal property sensitive to myelin is the phase accumulation, which to date has also been limited to voxel-averaged myelin estimates. We use this sensitivity by measuring the phase accumulation of the signal remaining after diffusion weighting, which we call DIffusion-Prepared Phase Imaging (DIPPI). Including diffusion weighting before estimating the phase accumulation has two distinct advantages for estimating the degree of myelination: (1) it increases the relative contribution of intra-axonal water, whose phase is related linearly to the amount of myelin surrounding the axon (in particular the log g-ratio) and (2) it gives directional information, which can be used to distinguish between crossing fibres.ResultsUsing simulations and phantom data we argue that other sources of phase accumulation (i.e., movement-induced phase shift during the diffusion gradients, eddy currents, and other sources of susceptibility) can be either corrected for or are sufficiently small to still allow the g-ratio to be reliably estimated.ConclusionsThis new sequence is capable of providing a g-ratio estimate per fibre population crossing within a voxel.

Optimizing the fitting initial condition for the parallel intrinsic diffusivity in NODDI: An extensive empirical evaluation

PurposeNODDI is widely used in parameterizing microstructural brain properties. The model includes three signal compartments: intracellular, extracellular, and free water. The neurite compartment intrinsic parallel diffusivity (d‖) is set to 1.7 µm2⋅ms−1, though the effects of this assumption have not been extensively explored. This work seeks to optimize d‖ by minimizing the model residuals.MethodsThe model residuals were evaluated in function of d‖ over the range from 0.5 to 3.0 µm2⋅ms−1. This was done with respect to tissue type (i.e., white matter versus gray matter), sex, age (infancy to late adulthood), and diffusion-weighting protocol (maximum b-value). Variation in the estimated parameters with respect to d‖ was also explored.ResultsResults show the optimum d‖ is significantly lower for gray matter relative to 1.7 µm2⋅ms−1 and to white matter. Infants showed significantly decreased optimum d‖ in gray and white matter. Minor optimum d‖ differences were observed versus diffusion protocol. No significant sex effects were observed. Additionally, changes in d‖ resulted in significant changes to the estimated NODDI parameters.ConclusionFuture implementations of NODDI would benefit from d‖ optimization, particularly when investigating young populations and/or gray matter.