Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI

Purpose: Biophysical tissue models are increasingly used in the interpretation of diffusion MRI (dMRI) data, with the potential to provide specific biomarkers of brain microstructural changes. However, the general Standard Model has recently shown that model parameter estimation from dMRI data is ill-posed unless very strong magnetic gradients are used. We analyse this issue for the Neurite Orientation Dispersion and Density Imaging with Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the ill-posedness and increases the accuracy of the parameter estimation. Methods: We analyse theoretically the cumulant expansion up to fourth order in b of SDE and DDE signals. Additionally, we perform in silico experiments to compare SDE and DDE capabilities under similar noise conditions. Results: We prove analytically that DDE provides invariant information non-accessible from SDE, which makes the NODDIDA parameter estimation injective. The in silico experiments show that DDE reduces the bias and mean square error of the estimation along the whole feasible region of 5D model parameter space. Conclusions: DDE adds additional information for estimating the model parameters, unexplored by SDE, which is enough to solve the degeneracy in the NODDIDA model parameter estimation.Comment: 22 pages, 7 figure

Including diffusion time dependence in the extra-axonal space improves in vivo estimates of axonal diameter and density in human white matter

Axonal density and diameter are two fundamental properties of brain white matter. Recently, advanced diffusion MRI techniques have made these two parameters accessible in vivo. However, the techniques available to estimate such parameters are still under development. For example, current methods to map axonal diameters capture relative trends over different structures, but consistently over-estimate absolute diameters. Axonal density estimates are more accessible experimentally, but different modeling approaches exist and the impact of the experimental parameters has not been thoroughly quantified, potentially leading to incompatibility of results obtained in different studies using different techniques. Here, we characterise the impact of diffusion time on axonal density and diameter estimates using Monte Carlo simulations and STEAM diffusion MRI at 7 T on 9 healthy volunteers. We show that axonal density and diameter estimates strongly depend on diffusion time, with diameters almost invariably overestimated and density both over and underestimated for some commonly used models. Crucially, we also demonstrate that these biases are reduced when the model accounts for diffusion time dependency in the extra-axonal space. For axonal density estimates, both upward and downward bias in different situations are removed by modeling extra-axonal time-dependence, showing increased accuracy in these estimates. For axonal diameter estimates, we report increased accuracy in ground truth simulations and axonal diameter estimates decreased away from high values given by earlier models and towards known values in the human corpus callosum when modeling extra-axonal time-dependence. Axonal diameter feasibility under both advanced and clinical settings is discussed in the light of the proposed advances

Direction-averaged diffusion-weighted MRI signal using different axisymmetric B-tensor encoding schemes

Purpose: It has been shown, theoretically and in vivo, that using the Stejskal-Tannerpulsed-gradient, or linear tensor encoding (LTE), and in exhibiting a ’stick-like’ diffusion geometry,the direction-averaged diffusion-weighted MRI signal at high b-values (7000 < b <10000 s=mm2) follows a power-law, decaying as 1=pb. It has also been shown, theoretically,that for planar tensor encoding (PTE), the direction-averaged signal decays as 1=b. We aimedto confirm this theoretical prediction in vivo. We then considered the direction-averaged signalfor arbitrary b-tensor shapes and different tissue substrates to look for other conditions underwhich a power-law exists.Methods: We considered the signal decay for high b-values for encoding geometries rangingfrom 2-dimensional PTE, through isotropic or spherical tensor encoding (STE) to LTE. Whena power-law behaviour was suggested, this was tested using in silico simulations and in vivousing ultra-strong gradients (300 mT/m).Results: Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, ouranalysis showed that using an axisymmetric b-tensor a power-law only exists under very specificconditions: (a) the tissue must have ’stick-like’ geometry; and (b) the waveform must bepurely LTE or purely PTE.Conclusion: A complete analysis of the power-law dependencies of the diffusion-weightedsignal at high b-values has been performed. Only two specific forms of encoding result in apower-law dependency, pure linear and pure planar tensor encoding and when the microstructuralgeometry is ’stick-like’. The different exponents of these encodings could be used toprovide independent validation of the presence of stick-like geometries in vivo

Why diffusion tensor MRI does well only some of the time: Variance and covariance of white matter tissue microstructure attributes in the living human brain

Fundamental to increasing our understanding of the role of white matter microstructure in normal/abnormal function in the living human is the development of MR-based metrics that provide increased specificity to distinct attributes of the white matter (e.g., local fibre architecture, axon morphology, and myelin content). In recent years, different approaches have been developed to enhance this specificity, and the Tractometry framework was introduced to combine the resulting multi-parametric data for a comprehensive assessment of white matter properties. The present work exploits that framework to characterise the statistical properties, specifically the variance and covariance, of these advanced microstructural indices across the major white matter pathways, with the aim of giving clear indications on the preferred metric(s) given the specific research question. A cohort of healthy subjects was scanned with a protocol that combined multi-component relaxometry with conventional and advanced diffusion MRI acquisitions to build the first comprehensive MRI atlas of white matter microstructure. The mean and standard deviation of the different metrics were analysed in order to understand how they vary across different brain regions/individuals and the correlation between them. Characterising the fibre architectural complexity (in terms of number of fibre populations in a voxel) provides clear insights into correlation/lack of correlation between the different metrics and explains why DT-MRI is a good model for white matter only some of the time. The study also identifies the metrics that account for the largest inter-subject variability and reports the minimal sample size required to detect differences in means, showing that, on the other hand, conventional DT-MRI indices might still be the safest choice in many contexts

Strong diffusion gradients allow the separation of intra- and extra-axonal gradient-echo signals in the human brain

The quantification of brain white matter properties is a key area of application of Magnetic Resonance Imaging (MRI), with much effort focused on using MR techniques to quantify tissue microstructure. While diffusion MRI probes white matter (WM) microstructure by characterising the sensitivity of Brownian motion of water molecules to anisotropic structures, susceptibility-based techniques probe the tissue microstructure by observing the effect of interaction between the tissue and the magnetic field. Here, we unify these two complementary approaches by combining ultra-strong () gradients with a novel Diffusion-Filtered Asymmetric Spin Echo (D-FASE) technique. Using D-FASE we can separately assess the evolution of the intra- and extra-axonal signals under the action of susceptibility effects, revealing differences in the behaviour in different fibre tracts. We observed that the effective relaxation rate of the ASE signal in the corpus callosum decreases with increasing b-value in all subjects (from at to at ), while this dependence on b in the corticospinal tract is less pronounced (from at to at ). Voxelwise analysis of the signal evolution with respect to b-factor and acquisition delay using a microscopic model demonstrated differences in gradient echo signal evolution between the intra- and extra-axonal pools

Improving the predictions of computational models of convection-enhanced drug delivery by accounting for diffusion non-gaussianity

Convection-enhanced delivery (CED) is an innovative method of drug delivery to the human brain, that bypasses the blood-brain barrier by injecting the drug directly into the brain. CED aims to target pathological tissue for central nervous system conditions such as Parkinson's and Huntington's disease, epilepsy, brain tumors, and ischemic stroke. Computational fluid dynamics models have been constructed to predict the drug distribution in CED, allowing clinicians advance planning of the procedure. These models require patient-specific information about the microstructure of the brain tissue, which can be collected non-invasively using magnetic resonance imaging (MRI) pre-infusion. Existing models employ the diffusion tensor, which represents Gaussian diffusion in brain tissue, to provide predictions for the drug concentration. However, those predictions are not always in agreement with experimental observations. In this work we present a novel computational fluid dynamics model for CED that does not use the diffusion tensor, but rather the diffusion probability that is experimentally measured through diffusion MRI, at an individual-participant level. Our model takes into account effects of the brain microstructure on the motion of drug molecules not taken into account in previous approaches, namely the restriction and hindrance that those molecules experience when moving in the brain tissue, and can improve the drug concentration predictions. The duration of the associated MRI protocol is 19 min, and therefore feasible for clinical populations. We first prove theoretically that the two models predict different drug distributions. Then, using in vivo high-resolution diffusion MRI data from a healthy participant, we derive and compare predictions using both models, in order to identify the impact of including the effects of restriction and hindrance. Including those effects results in different drug distributions, and the observed differences exhibit statistically significant correlations with measures of diffusion non-Gaussianity in brain tissue. The differences are more pronounced for infusion in white-matter areas of the brain. Using experimental results from the literature along with our simulation results, we show that the inclusion of the effects of diffusion non-Gaussianity in models of CED is necessary, if reliable predictions that can be used in the clinic are to be generated by CED models

Cortical Network for Gaze Control in Humans Revealed Using Multimodal MRI

Functional magnetic resonance imaging (fMRI) techniques allow definition of cortical nodes that are presumed to be components of large-scale distributed brain networks involved in cognitive processes. However, very few investigations examine whether such functionally defined areas are in fact structurally connected. Here, we used combined fMRI and diffusion MRI-based tractography to define the cortical network involved in saccadic eye movement control in humans. The results of this multimodal imaging approach demonstrate white matter pathways connecting the frontal eye fields and supplementary eye fields, consistent with the known connectivity of these regions in macaque monkeys. Importantly, however, these connections appeared to be more prominent in the right hemisphere of humans. In addition, there was evidence of a dorsal frontoparietal pathway connecting the frontal eye field and the inferior parietal lobe, also right hemisphere dominant, consistent with specialization of the right hemisphere for directed attention in humans. These findings demonstrate the utility and potential of using multimodal imaging techniques to define large-scale distributed brain networks, including those that demonstrate known hemispheric asymmetries in human

Subgenual cingulum microstructure supports control of emotional conflict

Major depressive disorder (MDD) is associated with specific difficulties in attentional disengagement from negatively valenced material. Diffusion MRI studies have demonstrated altered white matter microstructure in the subgenual cingulum bundle (CB) in individuals with MDD, though the functional significance of these alterations has not been examined formally. This study explored whether individual differences in selective attention to negatively valenced stimuli are related to interindividual differences in subgenual CB microstructure. Forty-six individuals (21 with remitted MDD, 25 never depressed) completed an emotional Stroop task, using happy and angry distractor faces overlaid by pleasant or unpleasant target words and a control gender-based Stroop task. CBs were reconstructed in 38 individuals using diffusion-weighted imaging and tractography, and mean fractional anisotropy (FA) computed for the subgenual, retrosplenial, and parahippocampal subdivisions. No significant correlations were found between FA and performance in the control gender-based Stroop task in any CB region. However, the degree of interference produced by angry face distractors on time to identify pleasant words (emotional conflict) correlated selectively with FA in the subgenual CB (r = −0.53; P = 0.01). Higher FA was associated with reduced interference, irrespective of a diagnosis of MDD, suggesting that subgenual CB microstructure is functionally relevant for regulating attentional bias toward negative interpersonal stimul