The effects of axonal beading and undulation on axonal diameter estimation from diffusion MRI: Insights from simulations in human axons segmented from three-dimensional electron microscopy.

The increasing availability of high-performance gradient systems in human MRI scanners has generated great interest in diffusion microstructural imaging applications such as axonal diameter mapping. Practically, sensitivity to axon diameter in diffusion MRI is attained at strong diffusion weightings b , where the deviation from the expected 1 / b scaling in white matter yields a finite transverse diffusivity, which is then translated into an axon diameter estimate. While axons are usually modeled as perfectly straight, impermeable cylinders, local variations in diameter (caliber variation or beading) and direction (undulation) are known to influence axonal diameter estimates and have been observed in microscopy data of human axons. In this study, we performed Monte Carlo simulations of diffusion in axons reconstructed from three-dimensional electron microscopy of a human temporal lobe specimen using simulated sequence parameters matched to the maximal gradient strength of the next-generation Connectome 2.0 human MRI scanner ( ≲ 500 mT/m). We show that axon diameter estimation is accurate for nonbeaded, nonundulating fibers; however, in fibers with caliber variations and undulations, the axon diameter is heavily underestimated due to caliber variations, and this effect overshadows the known overestimation of the axon diameter due to undulations. This unexpected underestimation may originate from variations in the coarse-grained axial diffusivity due to caliber variations. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Tractography passes the test: Results from the diffusion-simulated connectivity (disco) challenge.

Estimating structural connectivity from diffusion-weighted magnetic resonance imaging is a challenging task, partly due to the presence of false-positive connections and the misestimation of connection weights. Building on previous efforts, the MICCAI-CDMRI Diffusion-Simulated Connectivity (DiSCo) challenge was carried out to evaluate state-of-the-art connectivity methods using novel large-scale numerical phantoms. The diffusion signal for the phantoms was obtained from Monte Carlo simulations. The results of the challenge suggest that methods selected by the 14 teams participating in the challenge can provide high correlations between estimated and ground-truth connectivity weights, in complex numerical environments. Additionally, the methods used by the participating teams were able to accurately identify the binary connectivity of the numerical dataset. However, specific false positive and false negative connections were consistently estimated across all methods. Although the challenge dataset doesn't capture the complexity of a real brain, it provided unique data with known macrostructure and microstructure ground-truth properties to facilitate the development of connectivity estimation methods.

Histological validation of per-bundle water diffusion metrics within a region of fiber crossing following axonal degeneration.

Micro-architectural characteristics of white matter can be inferred through analysis of diffusion-weighted magnetic resonance imaging (dMRI). The diffusion-dependent signal can be analyzed through several methods, with the tensor model being the most frequently used due to its straightforward interpretation and low requirements for acquisition parameters. While valuable information can be gained from the tensor-derived metrics in regions of homogeneous tissue organization, this model does not provide reliable microstructural information at crossing fiber regions, which are pervasive throughout human white matter. Several multiple fiber models have been proposed that seem to overcome the limitations of the tensor, with few providing per-bundle dMRI-derived metrics. However, biological interpretations of such metrics are limited by the lack of histological confirmation. To this end, we developed a straightforward biological validation framework. Unilateral retinal ischemia was induced in ten rats, which resulted in axonal (Wallerian) degeneration of the corresponding optic nerve, while the contralateral was left intact; the intact and injured axonal populations meet at the optic chiasm as they cross the midline, generating a fiber crossing region in which each population has different diffusion properties. Five rats served as controls. High-resolution ex vivo dMRI was acquired five weeks after experimental procedures. We correlated and compared histology to per-bundle descriptors derived from three methodologies for dMRI analysis (constrained spherical deconvolution and two multi-tensor representations). We found a tight correlation between axonal density (as evaluated through automatic segmentation of histological sections) with per-bundle apparent fiber density and fractional anisotropy (derived from dMRI). The multi-fiber methods explored were able to correctly identify the damaged fiber populations in a region of fiber crossings (chiasm). Our results provide validation of metrics that bring substantial and clinically useful information about white-matter tissue at crossing fiber regions. Our proposed framework is useful to validate other current and future dMRI methods.

Volume electron microscopy in injured rat brain validates white matter microstructure metrics from diffusion MRI.

Biophysical modeling of diffusion MRI (dMRI) offers the exciting potential of bridging the gap between the macroscopic MRI resolution and microscopic cellular features, effectively turning the MRI scanner into a noninvasive in vivo microscope. In brain white matter, the Standard Model (SM) interprets the dMRI signal in terms of axon dispersion, intra- and extra-axonal water fractions and diffusivities. However, for SM to be fully applicable and correctly interpreted, it needs to be carefully evaluated using histology. Here, we perform a comprehensive histological validation of the SM parameters, by characterizing WM microstructure in sham and injured rat brains using volume (3d) electron microscopy (EM) and ex vivo dMRI. Sensitivity is evaluated by how close each SM metric is to its histological counterpart, and specificity by how independent it is from other, non-corresponding histological features. This comparison reveals that SM is sensitive and specific to microscopic properties, clearing the way for the clinical adoption of in vivo dMRI derived SM parameters as biomarkers for neurological disorders.

The influence of axonal beading and undulation on axonal diameter mapping.

We consider the effect of non-cylindrical axonal shape on axonal diameter mapping with diffusion MRI. Practical sensitivity to axon diameter is attained at strong diffusion weightings b, where the deviation from the 1/b scaling yields the finite transverse diffusivity, which is then translated into axon diameter. While axons are usually modeled as perfectly straight, impermeable cylinders, the local variations in diameter (caliber variation or beading) and direction (undulation) have been observed in microscopy data of human axons. Here we quantify the influence of cellular-level features such as caliber variation and undulation on axon diameter estimation. For that, we simulate the diffusion MRI signal in realistic axons segmented from 3-dimensional electron microscopy of a human brain sample. We then create artificial fibers with the same features and tune the amplitude of their caliber variations and undulations. Numerical simulations of diffusion in fibers with such tunable features show that caliber variations and undulations result in under- and over-estimation of axon diameters, correspondingly; this bias can be as large as 100%. Given that increased axonal beading and undulations have been observed in pathological tissues, such as traumatic brain injury and ischemia, the interpretation of axon diameter alterations in pathology may be significantly confounded.

Multi-tensor diffusion abnormalities of gray matter in an animal model of cortical dysplasia.

Focal cortical dysplasias are a type of malformations of cortical development that are a common cause of drug-resistant focal epilepsy. Surgical treatment is a viable option for some of these patients, with their outcome being highly related to complete surgical resection of lesions visible in magnetic resonance imaging (MRI). However, subtle lesions often go undetected on conventional imaging. Several methods to analyze MRI have been proposed, with the common goal of rendering subtle cortical lesions visible. However, most image-processing methods are targeted to detect the macroscopic characteristics of cortical dysplasias, which do not always correspond to the microstructural disarrangement of these cortical malformations. Quantitative analysis of diffusion-weighted MRI (dMRI) enables the inference of tissue characteristics, and novel methods provide valuable microstructural features of complex tissue, including gray matter. We investigated the ability of advanced dMRI descriptors to detect diffusion abnormalities in an animal model of cortical dysplasia. For this purpose, we induced cortical dysplasia in 18 animals that were scanned at 30 postnatal days (along with 19 control animals). We obtained multi-shell dMRI, to which we fitted single and multi-tensor representations. Quantitative dMRI parameters derived from these methods were queried using a curvilinear coordinate system to sample the cortical mantle, providing inter-subject anatomical correspondence. We found region- and layer-specific diffusion abnormalities in experimental animals. Moreover, we were able to distinguish diffusion abnormalities related to altered intra-cortical tangential fibers from those associated with radial cortical fibers. Histological examinations revealed myelo-architectural abnormalities that explain the alterations observed through dMRI. The methods for dMRI acquisition and analysis used here are available in clinical settings and our work shows their clinical relevance to detect subtle cortical dysplasias through analysis of their microstructural properties.

Histological and diffusion-weighted magnetic resonance imaging data from normal and degenerated optic nerve and chiasm of the rat.

Diffusion-weighted magnetic resonance imaging (dMRI) is widely used to infer microstructural characteristics of tissue, particularly in cerebral white matter. Histological validation of the metrics derived from dMRI methods are needed to fully characterize their ability to capture biologically-relevant histological features non-invasively. The data described here were used to correlate metrics derived from dMRI and quantitative histology in an animal model of axonal degeneration ("Histological validation of per-bundle water diffusion metrics within a region of fiber crossing following axonal degeneration" [1]). Unilateral retinal ischemia/reperfusion was induced in 10 rats, by the elevation of pressure of the anterior chamber of the eye for 90 min. Five rats were used as controls. After five weeks, injured animals were intracardially perfused to analyze the optic nerves and chiasm with dMRI and histology. This resulted in 15 brain scans, each with 80 diffusion-sensitizing gradient directions with b = 2000 and 2500 s/mm2 and 20 non-diffusion-weighted images (b = 0 s/mm2), with isometric voxel resolution of 125 µm3. Histological sections were obtained after dMRI. Optical microscopy photomicrographs of the optic nerves (stained with toluidine blue) are available, as well as their corresponding automatic segmentations of axons and myelin.

Estimation of individual axon bundle properties by a Multi-Resolution Discrete-Search method.

A stable, accurate and robust-to-noise method for the estimation of the intra-voxel bundle-wise diffusion properties for diffusion-weighted magnetic resonance imaging is presented. The proposed method overcomes some of the limitations of most of the multi-fiber algorithms in the literature and extends them to estimate the diffusion profiles, improving the estimation of the intra-voxel geometry at challenging microstructure configurations, that is to say: relatively small crossing angles, different voxel-wise anisotropic diffusion profiles and low SNR. The proposed methodology is based on four key novel ideas: (i) A Multi-Resolution Discrete-Search determines the orientation of the fiber bundles accurately and naturally constrains the sparsity on the recovered solutions; (ii) the determination of the number of fiber bundles using the F-test combined with a Rician bias correction; (iii) a Simultaneous Denoising and Fitting procedure that exploits the spatial redundancy of the axon bundles to achieve robustness with respect to noise; and (iv) a general framework for the estimation of the axial and radial diffusivity parameters independently for each voxel. A new useful evaluation metric is also proposed, which combines the information of the success rate in the estimated number of bundles and the angular error, avoiding in this way, some of the limitations these metrics have individually. A novel methodology for the evaluation of the methods on in-vivo data is also proposed. This work presents an extensive evaluation: the proposed methodology has been tested on state-of-the-art biophysical synthetic data for a variety of conditions, on the challenging spatially coherent phantom used on the HARDI reconstruction Challenge 2012, and on the recently released in-vivo MASSIVE data-set. Our results present significant improvements on the estimation of the number and orientation of the fiber bundles over the Spherical Deconvolution algorithm for multi-shell data, which is one of the most widely used multi-fiber algorithm. The results also show that, by the voxel-wise estimation of the diffusion profiles, the axial and radial diffusivity parameters are robustly estimated, being this essential for a better understanding of the individual bundle diffusion properties at challenging structural configurations.