Matt G. Hall

Orientationally invariant indices of axon diameter and density from diffusion MRI

This paper proposes and tests a technique for imaging orientationally invariant indices of axon diameter and density in white matter using diffusion magnetic resonance imaging. Such indices potentially provide more specific markers of white matter microstructure than standard indices from diffusion tensor imaging. Orientational invariance allows for combination with tractography and presents new opportunities for mapping brain connectivity and quantifying disease processes. The technique uses a four-compartment tissue model combined with an optimized multishell high-angular-resolution pulsed-gradient-spin-echo acquisition. We test the method in simulation, on fixed monkey brains using a preclinical scanner and on live human brains using a clinical 3T scanner. The human data take about one hour to acquire. The simulation experiments show that both monkey and human protocols distinguish distributions of axon diameters that occur naturally in white matter. We compare the axon diameter index with the mean axon diameter weighted by axon volume. The index differs from this mean and is protocol dependent, but correlation is good for the monkey protocol and weaker, but discernible, for the human protocol where greater diffusivity and lower gradient strength limit sensitivity to only the largest axons. Maps of axon diameter and density indices from the monkey and human data in the corpus callosum and corticospinal tract reflect known trends from histology. The results show orientationally invariant sensitivity to natural axon diameter distributions for the first time with both specialist and clinical hardware. This demonstration motivates further refinement, validation, and evaluation of the precise nature of the indices and the influence of potential confounds.

Compartment models of the diffusion MR signal in brain white matter: A taxonomy and comparison

This paper aims to identify the minimum requirements for an accurate model of the diffusion MR signal in white matter of the brain. We construct a taxonomy of multi-compartment models of white matter from combinations of simple models for the intra- and the extra-axonal spaces. We devise a new diffusion MRI protocol that provides measurements with a wide range of imaging parameters for diffusion sensitization both parallel and perpendicular to white matter fibres. We use the protocol to acquire data from two fixed rat brains, which allows us to fit, study and compare the different models. The study examines a total of 47 analytic models, including several well-used models from the literature, which we place within the taxonomy. The results show that models that incorporate intra-axonal restriction, such as ball and stick or CHARMED, generally explain the data better than those that do not, such as the DT or the biexponential models. However, three-compartment models which account for restriction parallel to the axons and incorporate pore size explain the measurements most accurately. The best fit comes from combining a full diffusion tensor (DT) model of the extra-axonal space with a cylindrical intra-axonal component of single radius and a third spherical compartment of non-zero radius. We also measure the stability of the non-zero radius intra-axonal models and find that single radius intra-axonal models are more stable than gamma distributed radii models with similar fitting performance.

From diffusion-weighted MRI to anomalous diffusion imaging

We present a novel interpretation of non‐monoexponential diffusion‐weighted signal decay with b‐value in terms of the theory of anomalous diffusion. Anomalous diffusion is the theory of diffusing particles in environments that are not locally homogeneous, such as brain tissue. In such environments the model of restricted diffusion commonly employed in the analysis of diffusion MR data is not valid, leading to a nonlinear time dependence for the mean‐squared displacement of spins, and to a prediction of a stretched exponential form for the signal decay. We show that this prediction leads directly to a new parameter, the anomalous exponent, which may be measured from scan data and from this we can estimate a fractal dimension, dw, which categorizes the complexity of the excursions of diffusing spins. We construct images of the anomalous exponent and fractal dimension from in vivo human brain data. Distributions of exponents and dimensions are constructed in grey and white matter and cerebrospinal fluid. We observe that these distributions peak at biologically plausible values consistent with previous studies: grey matter dw = 2.366 ± 0.31, white matter dw = 2.587 ± 0.39, CSF dw = 1.970 (mode). Marked contrast is observed between grey and white matter when compared with lateral ventricle CSF. We then consider the anisotropy of the value of the anomalous exponent and define quantities analogous to the mean diffusivity and fractional anisotropy that are commonly generated from diffusion tensor images. Magn Reson Med, 2008.

Convergence and Parameter Choice for Monte-Carlo Simulations of Diffusion MRI

This paper describes a general and flexible Monte- Carlo simulation framework for diffusing spins that generates realistic synthetic data for diffusion magnetic resonance imaging. Similar systems in the literature consider only simple substrates and their authors do not consider convergence and parameter optimization. We show how to run Monte-Carlo simulations within complex irregular substrates. We compare the results of the Monte-Carlo simulation to an analytical model of restricted diffusion to assess precision and accuracy of the generated results. We obtain an optimal combination of spins and updates for a given run time by trading off number of updates in favor of number of spins such that precision and accuracy of sythesized data are both optimized. Further experiments demonstrate the system using a tissue environment that current analytic models cannot capture. This tissue model incorporates swelling, abutting, and deformation. Swelling-induced restriction in the extracellular space due to the effects of abutting cylinders leads to large departures from the predictions of the analytical model, which does not capture these effects. This swelling-induced restriction may be an important mechanism in explaining the changes in apparent diffusion constant observed in the aftermath of acute ischemic stroke.

Contrast and stability of the axon diameter index from microstructure imaging with diffusion MRI.

The ActiveAx technique fits the minimal model of white matter diffusion to diffusion MRI data acquired using optimized protocols that provide orientationally invariant indices of axon diameter and density. We investigated how limitations of the available maximal gradient strength (Gmax) on a scanner influence the sensitivity to a range of axon diameters. Multishell high‐angular‐diffusion‐imaging (HARDI) protocols for Gmax of 60, 140, 200, and 300 mT/m were optimized for the pulsed‐gradient‐spin‐echo (PGSE) sequence. Data were acquired on a fixed monkey brain and Monte‐Carlo simulations supported the results. Increasing Gmax reduces within‐voxel variation of the axon diameter index and improves contrast beyond what is achievable with higher signal‐to‐noise ratio. Simulations reveal an upper bound on the axon diameter (∼10 μm) that pulsed‐gradient‐spin‐echo measurements are sensitive to, due to a trade‐off between short T2 and the long diffusion time needed to probe larger axon diameters. A lower bound (∼2.5 μm) slightly dependent on Gmax was evident, below which axon diameters are identifiable as small, but impossible to differentiate. These results emphasize the key‐role of Gmax for enhancing contrast between axon diameter distributions and are, therefore, relevant in general for microstructure imaging methods and highlight the need for increased Gmax on future commercial systems. Magn Reson Med 70:711–721, 2013.

The matrix formalism for generalised gradients with time-varying orientation in diffusion NMR.

The matrix formalism is a general framework for evaluating the diffusion NMR signal from restricted spins under generalised gradient waveforms. The original publications demonstrate the method for waveforms that vary only in magnitude and have fixed orientation. In this work, we extend the method to allow for variations in the direction of the gradient. This extension is necessary, for example to incorporate the effects of crusher gradients or imaging gradients in diffusion MRI, to characterise signal anisotropy in double pulsed field gradient (dPFG) experiments, or to optimise the gradient waveform for microstructure sensitivity. In particular, we show for primitive geometries (planes, cylinders and spheres), how to express the matrix operators at each time point of the gradient waveform as a linear combination of one or two fundamental matrices. Thus we obtain an efficient implementation with both the storage and CPU demands similar to the fixed-orientation case. Comparison with Monte Carlo simulations validates the implementation on three different sequences: dPFG, helical waveforms and the stimulated echo (STEAM) sequence.

Assessment of non-Gaussian diffusion with singly and doubly stretched biexponential models of diffusion-weighted MRI (DWI) signal attenuation in prostate tissue.

Non‐Gaussian diffusion dynamics was investigated in the two distinct water populations identified by a biexponential model of diffusion in prostate tissue. Diffusion‐weighted MRI (DWI) signal attenuation was measured ex vivo in two formalin‐fixed prostates at 9.4 T with diffusion times Δ = 10, 20 and 40 ms, and b values in the range 0.017–8.2 ms/µm2. A conventional biexponential model was compared with models in which either the lower diffusivity component or both of the components of the biexponential were stretched. Models were compared using Akaikes Information Criterion (AIC) and a leave‐one‐out (LOO) test of model prediction accuracy. The doubly stretched (SS) model had the highest LOO prediction accuracy and lowest AIC (highest information content) in the majority of voxels at Δ = 10 and 20 ms. The lower diffusivity stretching factor (α2) of the SS model was consistently lower (range ~0.3–0.9) than the higher diffusivity stretching factor (α1, range ~0.7–1.1), indicating a high degree of diffusion heterogeneity in the lower diffusivity environment, and nearly Gaussian diffusion in the higher diffusivity environment. Stretched biexponential models demonstrate that, in prostate tissue, the two distinct water populations identified by the simple biexponential model individually exhibit non‐Gaussian diffusion dynamics. Copyright

Two-step anomalous diffusion tensor imaging.

We extend the formalism of anomalous diffusion imaging to include directional anisotropy of fitted parameters. The resulting technique is termed anomalous diffusion tensor imaging (aDTI), and allows the directional properties of the distributed diffusion coefficient (α) and the anomalous diffusion exponent, (γ) to be analysed using the same analytical techniques as regular diffusion tensor imaging (DTI). Together, these parameters quantify the rate of diffusion (α) and the complexity of the diffusion environment (γ).

Resolving axon fiber crossings at clinical b-values: An evaluation study

PURPOSE Diffusion tensor magnetic resonance imaging is widely used to study the structure of the fiber pathways of brain white matter. However, the diffusion tensor cannot capture complex intravoxel fiber architecture such as fiber crossings of bifurcations. Consequently, a number of methods have been proposed to recover intravoxel fiber bundle orientations from high angular resolution diffusion imaging scans, optimized to resolve fiber crossings. It is important to improve the brain tractography by applying these multifiber methods to diffusion tensor protocols with a clinical b- value (low), which are optimized on computing tensor scalar statistics. In order to characterize the variance among different methods, consequently to be able to select the most appropriate one for a particular application, it is desirable to compare them under identical experimental conditions. METHODS In this work, the authors study how QBall, spherical deconvolution, persistent angular structure, stick and ball, diffusion basis functions, and analytical QBall methods perform under clinically-realistic scanning conditions, where the b-value is typically lower (around 1000 s∕mm(2)), and the number of diffusion encoding orientations is fewer (30-60) than in dedicated high angular resolution diffusion imaging scans. To characterize the performance of the methods, they consider the accuracy of the estimated number of fibers, the relative contribution of each fiber population to the total magnetic resonance signal, and the recovered orientation error for each fiber bundle. To this aim, they use four different sources of data: synthetic data from Gaussian mixture model, cylinder restricted model, and in vivo data from two different acquisition schemes. RESULTS Results of their experiments indicate that: (a) it is feasible to apply only a subset of these methods to clinical data sets and (b) it allows one to characterize the performance of each method. In particular, two methods are not feasible to the kind of magnetic resonance diffusion data they test. By the characterization of their systematic behavior, among other conclusions, they report the method which better performs for the estimation of the number of diffusion peaks per voxel, also the method which better estimates the diffusion orientation. CONCLUSIONS The framework they propose for comparison allows one to effectively characterize and compare the performance of the most frequently used multifiber algorithms under realistic medical settings and realistic signal-to-noise ratio environments. The framework is based on several crossings with a non-orientational bias and different signal models. The results they present are relevant for medical doctors and researchers, interested in the use of the multifiber solution for tractography.

Two-Compartment Models of the Diffusion MR Signal in Brain White Matter

This study aims to identify the minimum requirements for an accurate model of the diffusion MR signal in white matter of the brain. We construct a hierarchy of two-compartment models of white matter from combinations of simple models for the intra and extracellular spaces. We devise a new diffusion MRI protocol that provides measurements with a wide range of parameters for diffusion sensitization both parallel and perpendicular to white matter fibres. We use the protocol to acquire data from a fixed rat brain, which allows us to fit, study and compare the different models. The results show that models which incorporate pore size describe the measurements most accurately. The best fit comes from combining a full diffusion tensor (DT) model of the extra-cellular space with a cylindrical intra-cellular component.