Characterizing intra-axonal water diffusion with direction-averaged triple diffusion encoding MRI

Integrating multimodality magnetic resonance imaging to the Allen Mouse Brain Common Coordinate Framework

High-resolution magnetic resonance imaging (MRI) affords unique image contrasts to nondestructively probe the tissue microstructure; validation of MRI findings with conventional histology is essential to better understand the MRI contrasts. However, the dramatic difference in the spatial resolution and image contrast of these two techniques impedes accurate comparison between MRI metrics and traditional histology. To better validate various MRI metrics, we acquired whole mouse brain multigradient recalled-echo and multishell diffusion MRI datasets at 25-μm isotropic resolution. The recently developed Allen Mouse Brain Common Coordinate Framework (CCFv3) provides opportunities to integrate multimodal and multiscale datasets of the whole mouse brain in a common three-dimensional (3D) space. The T2*, quantitative susceptibility mapping, diffusion tensor imaging, and neurite orientation dispersion and density imaging parameters were compared with both serial two-photon tomography images and 3D Nissl staining images in the CCFv3 at the same spatial resolution. The correlation between MRI and Nissl staining strongly depends on different metrics and different regions of the brain. Integrating different imaging modalities to the same space may substantially improve our understanding of the complexity of the brain at different scales.

Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI

We enable the estimation of the per-axon axial diffusivity from single encoding, strongly diffusion-weighted, pulsed gradient spin echo data. Additionally, we improve the estimation of the per-axon radial diffusivity compared to estimates based on spherical averaging. The use of strong diffusion weightings in magnetic resonance imaging (MRI) allows to approximate the signal in white matter as the sum of the contributions from only axons. At the same time, spherical averaging leads to a major simplification of the modeling by removing the need to explicitly account for the unknown distribution of axonal orientations. However, the spherically averaged signal acquired at strong diffusion weightings is not sensitive to the axial diffusivity, which cannot therefore be estimated although needed for modeling axons - especially in the context of multi-compartmental modeling. We introduce a new general method for the estimation of both the axial and radial axonal diffusivities at strong diffusion weightings based on kernel zonal modeling. The method could lead to estimates that are free from partial volume bias with gray matter or other isotropic compartments. The method is tested on publicly available data from the MGH Adult Diffusion Human Connectome project. We report reference values of axonal diffusivities based on 34 subjects, and derive estimates of axonal radii from only two shells. The estimation problem is also addressed from the angle of the required data preprocessing, the presence of biases related to modeling assumptions, current limitations, and future possibilities.

Optimized rectification of fiber orientation density function with background threshold

PURPOSE

To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background.

THEORY AND METHODS

The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging.

RESULTS

Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives.

CONCLUSION

Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.

Impact of intra-axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging

PURPOSE

To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI).

THEORY AND METHODS

Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm2 or higher. However, recent work based on numeric simulations shows that diffusion inside axons is non-Gaussian with an intra-axonal kurtosis of ∼ 0.4. Here, the theory underlying FBI is extended to incorporate an intra-axonal kurtosis. This is done to first order in the intra-axonal kurtosis without making assumptions about the details of the diffusion dynamics and to all orders for a specific model based on a gamma distribution of diffusivities. The first order approximation is used to assess the effect of an intra-axonal kurtosis on FBI estimates for the fODF and axonal water fraction. The gamma distribution model is used to test the validity of the approximation.

RESULTS

The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent.

CONCLUSION

The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.

High fidelity fiber orientation density functions from fiber ball imaging

The fiber orientation density function (fODF) in white matter is a primary physical quantity that can be estimated with diffusion MRI. It has often been employed for fiber tracking and microstructural modeling. Requirements for the construction of high fidelity fODFs, in the sense of having good angular resolution, adequate data to avoid sampling errors, and minimal noise artifacts, are described for fODFs calculated with fiber ball imaging. A criterion is formulated for the number of diffusion encoding directions needed to achieve a given angular resolution. The advantages of using large b-values (≥6000 s/mm² ) are also discussed. For the direct comparison of different fODFs, a method is developed for defining a local frame of reference tied to each voxel's individual axonal structure. The Matusita anisotropy axonal is proposed as a scalar fODF measure for quantifying angular variability. Experimental results, obtained at 3 T from human volunteers, are used as illustrations.

Quantifying myelin in crossing fibers using diffusion-prepared phase imaging: Theory and simulations

PURPOSE

Myelin has long been the target of neuroimaging research. However, most available techniques can only provide a voxel-averaged estimate of myelin content. In the human brain, white matter fiber 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 fibers would provide a more specific marker of myelination.

THEORY AND METHODS

One MRI signal property that is sensitive to myelin is the phase accumulation. This sensitivity is used by measuring the phase accumulation of the signal remaining after diffusion-weighting, which is called 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 thickness of the surrounding myelin (in particular the log g-ratio); and (2) it gives directional information, which can be used to distinguish between crossing fibers. Here the DIPPI sequence is described, an approach is proposed to estimate the log g-ratio, and simulations are used and DIPPI data acquired in an isotropic phantom to quantify other sources of phase accumulation.

RESULTS

The expected bias is estimated in the log g-ratio for reasonable in vivo acquisition parameters caused by eddy currents (~4%-10%), remaining extra-axonal signal (~15%), and gradients in the bulk off-resonance field (<10% for most of the brain).

CONCLUSION

This new sequence may provide a g-ratio estimate per fiber population crossing within a voxel.

Magic DIAMOND: Multi-fascicle diffusion compartment imaging with tensor distribution modeling and tensor-valued diffusion encoding

Diffusion tensor imaging provides increased sensitivity to microstructural tissue changes compared to conventional anatomical imaging but also presents limited specificity. To tackle this problem, the DIAMOND model subdivides the voxel content into diffusion compartments and draws from diffusion-weighted data to estimate compartmental non-central matrix-variate Gamma distributions of diffusion tensors. It models each sub-voxel fascicle separately, resolving crossing white-matter pathways and allowing for a fascicle-element (fixel) based analysis of microstructural features. Alternatively, specific features of the intra-voxel diffusion tensor distribution can be selectively measured using tensor-valued diffusion-weighted acquisition schemes. However, the impact of such schemes on estimating brain microstructural features has only been studied in a handful of parametric single-fascicle models. In this work, we derive a general Laplace transform for the non-central matrix-variate Gamma distribution, which enables the extension of DIAMOND to tensor-valued encoded data. We then evaluate this "Magic DIAMOND" model in silico and in vivo on various combinations of tensor-valued encoded data. Assessing uncertainty on parameter estimation via stratified bootstrap, we investigate both voxel-based and fixel-based metrics by carrying out multi-peak tractography. We demonstrate using in silico evaluations that tensor-valued diffusion encoding significantly improves Magic DIAMOND's accuracy. Most importantly, we show in vivo that our estimated metrics can be robustly mapped along tracks across regions of fiber crossing, which opens new perspectives for tractometry and microstructure mapping along specific white-matter tracts.

Double diffusion encoding and applications for biomedical imaging

Diffusion Magnetic Resonance Imaging (dMRI) is one of the most important contemporary non-invasive modalities for probing tissue structure at the microscopic scale. The majority of dMRI techniques employ standard single diffusion encoding (SDE) measurements, covering different sequence parameter ranges depending on the complexity of the method. Although many signal representations and biophysical models have been proposed for SDE data, they are intrinsically limited by a lack of specificity. Advanced dMRI methods have been proposed to provide additional microstructural information beyond what can be inferred from SDE. These enhanced contrasts can play important roles in characterizing biological tissues, for instance upon diseases (e.g. neurodegenerative, cancer, stroke), aging, learning, and development. In this review we focus on double diffusion encoding (DDE), which stands out among other advanced acquisitions for its versatility, ability to probe more specific diffusion correlations, and feasibility for preclinical and clinical applications. Various DDE methodologies have been employed to probe compartment sizes (Section 3), decouple the effects of microscopic diffusion anisotropy from orientation dispersion (Section 4), probe displacement correlations, study exchange, or suppress fast diffusing compartments (Section 6). DDE measurements can also be used to improve the robustness of biophysical models (Section 5) and study intra-cellular diffusion via magnetic resonance spectroscopy of metabolites (Section 7). This review discusses all these topics as well as important practical aspects related to the implementation and contrast in preclinical and clinical settings (Section 9) and aims to provide the readers a guide for deciding on the right DDE acquisition for their specific application.

The present and the future of microstructure MRI: From a paradigm shift to normal science

The aspiration of imaging tissue microstructure with MRI is to uncover micrometer-scale tissue features within millimeter-scale imaging voxels, in vivo. This kind of super-resolution has fueled a paradigm shift within the biomedical imaging community. However, what feels like an ongoing revolution in MRI, has been conceptually experienced in physics decades ago; from this point of view, our current developments can be seen as Thomas Kuhn's "normal science" stage of progress. While the concept of model-based quantification below the nominal imaging resolution is not new, its possibilities in neuroscience and neuroradiology are only beginning to be widely appreciated. This disconnect calls for communicating the progress of tissue microstructure MR imaging to its potential users. Here, a number of recent research developments are outlined in terms of the overarching concept of coarse-graining the tissue structure over an increasing diffusion length. A variety of diffusion models and phenomena are summarized on the phase diagram of diffusion MRI, with the unresolved problems and future directions corresponding to its unexplored domains.

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‐Tanner pulsed‐gradient, or linear tensor encoding (LTE), and in tissue exhibiting a “stick‐like” diffusion geometry, the direction‐averaged diffusion‐weighted MRI signal at high b‐values ( 7000<b<10000s/mm2) follows a power‐law, decaying as 1/b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the direction‐averaged diffusion‐weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction‐averaged signal for arbitrary b‐tensor shapes and different tissue substrates to look for other conditions under which a power‐law exists.

Methods

We considered the signal decay for high b‐values for encoding geometries ranging from 2‐dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power‐law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra‐strong (300 mT/m) gradients.

Results

Our in vivo results confirmed the predicted 1/b power law for PTE. Moreover, our analysis showed that using an axisymmetric b‐tensor a power‐law only exists under very specific conditions: (a) “stick‐like” tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake‐like" tissue geometry and a purely LTE waveform.

Conclusions

A complete analysis of the power‐law dependencies of the diffusion‐weighted signal at high b‐values has been performed. Only three specific forms of encoding result in a power‐law dependency, pure linear and pure PTE when the tissue geometry is “stick‐like” and pure LTE when the tissue geometry is "pancake‐like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo.

Triple diffusion encoding MRI predicts intra-axonal and extra-axonal diffusion tensors in white matter

PURPOSE

To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra-axonal and extra-axonal diffusion tensors in white matter (WM).

METHODS

Using a TDE pulse sequence with an axially symmetric b-matrix, diffusion MRI data were acquired at 3T for 3 healthy adults with an axial b-value of 4000 s/mm² , a radial b-value of 307 s/mm² , and 64 diffusion encoding directions. This acquisition was then repeated with the radial b-value set to 0. A previously proposed theory was applied to these data in order to estimate the intra-axonal diffusivity and axonal water fraction for each WM voxel. Conventional single diffusion encoding data were also obtained with b-values of 1000 and 2000 s/mm² , which provided additional information sufficient for determining both the intra-axonal and extra-axonal diffusion tensors.

RESULTS

From the TDE data, the average intra-axonal diffusivity in WM was found to be 2.24 ± 0.18 µm² /ms, and the average axonal water fraction was found to be 0.60 ± 0.11. From the 2 diffusion tensors, average WM values were estimated for several compartment-specific diffusion parameters. In particular, the extra-axonal mean diffusivity was 1.09 ± 0.19 µm² /ms, the intra-axonal fractional anisotropy was 0.50 ± 0.14, and the extra-axonal fractional anisotropy was 0.23 ± 0.13.

CONCLUSION

By using a simple TDE pulse sequence with an axially symmetric b-matrix, the diffusion tensors for the intra-axonal and extra-axonal spaces can be separately estimated in adult WM. This allows one to determine compartment-specific diffusion properties for these 2 water pools.

Reproducibility of axonal water fraction derived from the spherical mean diffusion weighted signal

Recent years have seen growing interest in measuring axonal water fraction (AWF) using the spherical mean diffusion weighted signal, but information about the reproducibility of this method is needed before applying it in large-scale studies. The current study aims to evaluate the reproducibility of AWF derived from the spherical mean signal method. This retrospective study analyzed the Human Connectome Project (HCP) test-retest diffusion data of ten healthy adults. The diffusion scan was performed two times for each subject. Diffusion tensor imaging-based fractional anisotropy (FA) was calculated with b = 1000 s/mm². AWF was calculated with b = 3000 s/mm² using the spherical mean signal method. Gradient nonlinearities were corrected in both methods. Reproducibility was assessed using the reproducibility error, which is the percent absolute change relative to the mean. The mean reproducibility error of fractional anisotropy (FA) is 9.7 ± 1.0% in white matter and 18.0 ± 2.0% in gray matter. The mean reproducibility error of AWF is 4.6 ± 0.6% in white matter and 7.0 ± 1.5% in gray matter. Spherical mean signal-based AWF is more reproducible than FA for the HCP high resolution, low signal-to-noise ratio diffusion data.

Optimization of data acquisition and analysis for fiber ball imaging

The inverse Funk transform of high angular resolution diffusion imaging (HARDI) data provides an estimate for the fiber orientation density function (fODF) in white matter (WM). Since the inverse Funk transform is a straightforward linear transformation, this technique, referred to as fiber ball imaging (FBI), offers a practical means of calculating the fODF that avoids the need for a response function or nonlinear numerical fitting. Nevertheless, the accuracy of FBI depends on both the choice of b-value and the number of diffusion-encoding directions used to acquire the HARDI data. To inform the design of optimal scan protocols for its implementation, FBI predictions are investigated here with in vivo data from healthy adult volunteers acquired at 3 T for b-values spanning 1000 to 10,000 s/mm², for diffusion-encoding directions varying in number from 30 to 256 and for TE ranging from 90 to 120 ms. Our results suggest b-values above 4000 s/mm² with at least 64 diffusion-encoding directions are adequate to achieve reasonable accuracy with FBI for calculating axon-specific diffusion measures and for performing WM fiber tractography (WMFT).

Comparison of NODDI and spherical mean signal for measuring intra-neurite volume fraction

PURPOSE

Neurite orientation dispersion and density imaging (NODDI) is a clinically feasible approach to measure intra-neurite volume fraction (fin). However, the sophisticated fitting procedure takes several hours. And the NODDI model relied on several questionable assumptions. Recent analytical work demonstrated that fin could be simply calculated from the spherical mean signal (MEANS) averaged over all gradient directions with a more solid theoretical foundation. The current study aims to compare NODDI and MEANS for measuring fin in human brain and investigate the potential of MEANS as a fast approach in clinics.

METHODS

NODDI fin and MEANS fin were measured and compared on the same dataset. NODDI fin was obtained using the NODDI MATLAB Toolbox. MEANS fin is the product of the spherical mean signal and 2bD/π, where D is the intra-neurite intrinsic diffusivity.

RESULTS

NODDI fin and MEANS fin maps are similar. The voxel-by-voxel correlation suggests that NODDI fin and MEANS fin are approximately equivalent to each other.

CONCLUSION

MEANS may have potential to serve a fast and simple approach to estimate fin in clinics.

Measuring intra-axonal T2 in white matter with direction-averaged diffusion MRI

PURPOSE

To demonstrate how the T₂ relaxation time of intra-axonal water (T_2a ) in white matter can be measured with direction-averaged diffusion MRI.

METHODS

For b-values larger than about 4000 s/mm² , the direction-averaged diffusion MRI signal from white matter is dominated by the contribution from water within axons, which enables T_2a to be estimated by acquiring data for multiple TE values and fitting a mono-exponential decay curve. If given a value of the intra-axonal diffusivity, an extension of the method allows the extra-axonal relaxation time (T_2e ) to be calculated also. This approach was applied to estimate T_2a in white matter for 3 healthy subjects at 3 T, as well as T_2e for a selected set of assumed intra-axonal diffusivities.

RESULTS

The estimated T_2a values ranged from about 50 ms to 110 ms, with considerable variation among white matter regions. For white matter tracts with primarily collinear fibers, T_2a was found to depend on the angle of the tract relative to the main magnetic field, which is consistent with T_2a being affected by magnetic field inhomogeneities arising from spatial differences in magnetic susceptibility. The T_2e values were significantly smaller than the T_2a values across white matter regions for several plausible choices of the intra-axonal diffusivity.

CONCLUSION

The relaxation time for intra-axonal water in white matter can be determined in a straightforward manner by measuring the direction-averaged diffusion MRI signal with a large b-value for multiple TEs. In healthy brain, T_2a is greater than T_2e and varies considerably with anatomical region.