Myelinated peripheral axons are more vulnerable to mechanical trauma in a model of enlarged axonal diameters.

The velocity of axonal impulse propagation is facilitated by myelination and axonal diameters. Both parameters are frequently impaired in peripheral nerve disorders, but it is not known if the diameters of myelinated axons affect the liability to injury or the efficiency of functional recovery. Mice lacking the adaxonal myelin protein chemokine-like factor-like MARVEL-transmembrane domain-containing family member-6 (CMTM6) specifically from Schwann cells (SCs) display appropriate myelination but increased diameters of peripheral axons. Here we subjected Cmtm6-cKo mice as a model of enlarged axonal diameters to a mild sciatic nerve compression injury that causes temporarily reduced axonal diameters but otherwise comparatively moderate pathology of the axon/myelin-unit. Notably, both of these pathological features were worsened in Cmtm6-cKo compared to genotype-control mice early post-injury. The increase of axonal diameters caused by CMTM6-deficiency thus does not override their injury-dependent decrease. Accordingly, we did not detect signs of improved regeneration or functional recovery after nerve compression in Cmtm6-cKo mice; depleting CMTM6 in SCs is thus not a promising strategy toward enhanced recovery after nerve injury. Conversely, the exacerbated axonal damage in Cmtm6-cKo nerves early post-injury coincided with both enhanced immune response including foamy macrophages and SCs and transiently reduced grip strength. Our observations support the concept that larger peripheral axons are particularly susceptible toward mechanical trauma.

Weighting the structural connectome: Exploring its impact on network properties and predicting cognitive performance in the human brain.

Brain function does not emerge from isolated activity, but rather from the interactions and exchanges between neural elements that form a network known as the connectome. The human connectome consists of structural and functional aspects. The structural connectome (SC) represents the anatomical connections, and the functional connectome represents the resulting dynamics that emerge from this arrangement of structures. As there are different ways of weighting these connections, it is important to consider how such different approaches impact study conclusions. Here, we propose that different weighted connectomes result in varied network properties, and while neither superior the other, selection might affect interpretation and conclusions in different study cases. We present three different weighting models, namely, number of streamlines (NOS), fractional anisotropy (FA), and axon diameter distribution (ADD), to demonstrate these differences. The later, is extracted using recently published AxSI method and is first compared to commonly used weighting methods. Moreover, we explore the functional relevance of each weighted SC, using the Human Connectome Project (HCP) database. By analyzing intelligence-related data, we develop a predictive model for cognitive performance based on graph properties and the National Institutes of Health (NIH) toolbox. Results demonstrate that the ADD SC, combined with a functional subnetwork model, outperforms other models in estimating cognitive performance.

Development of myelination and axon diameter for fast and precise action potential conductance.

Axons of globular bushy cells in the cochlear nucleus convey hyper-accurate signals to the superior olivary complex, the initial site of binaural processing via comparably thick axons and the calyx of the Held synapse. Bushy cell fibers involved in hyper-accurate binaural processing of low-frequency sounds are known to have an unusual internode length-to-axon caliber ratio (L/d) correlating with higher conduction velocity and superior temporal precision of action potentials. How the L/d-ratio develops and what determines this unusual myelination pattern is unclear. Here we describe a gradual developmental transition from very simple to complex, mature nodes of Ranvier on globular bushy cell axons during a 2-week period starting at postnatal day P6/7. The molecular composition of nodes matured successively along the axons from somata to synaptic terminals with morphologically and molecularly mature nodes appearing almost exclusively after hearing onset. Internodal distances are initially coherent with the canonical L/d-ratio of ~100. Several days after hearing onset, however, an over-proportional increase in axon caliber occurs in cells signaling low-frequency sounds which alters their L/d ratio to ~60. Hence, oligodendrocytes initially myelinating axons according to their transient axon caliber but a subsequent differential axon thickening after hearing onset results in the unusual myelination pattern.

A functional account of stimulation-based aerobic glycolysis and its role in interpreting BOLD signal intensity increases in neuroimaging experiments.

In aerobic glycolysis, oxygen is abundant, and yet cells metabolize glucose without using it, decreasing their ATP per glucose yield by 15-fold. During task-based stimulation, aerobic glycolysis occurs in localized brain regions, presenting a puzzle: why produce ATP inefficiently when, all else being equal, evolution should favor the efficient use of metabolic resources? The answer is that all else is not equal. We propose that a tradeoff exists between efficient ATP production and the efficiency with which ATP is spent to transmit information. Aerobic glycolysis, despite yielding little ATP per glucose, may support neuronal signaling in thin (< 0.5 µm), information-efficient axons. We call this the efficiency tradeoff hypothesis. This tradeoff has potential implications for interpretations of task-related BOLD "activation" observed in fMRI. We hypothesize that BOLD "activation" may index local increases in aerobic glycolysis, which support signaling in thin axons carrying "bottom-up" information, or "prediction error"-i.e., the BIAPEM (BOLD increases approximate prediction error metabolism) hypothesis. Finally, we explore implications of our hypotheses for human brain evolution, social behavior, and mental disorders.

A Method for In-Vivo Mapping of Axonal Diameter Distributions in the Human Brain Using Diffusion-Based Axonal Spectrum Imaging (AxSI).

In this paper we demonstrate a generalized and simplified pipeline called axonal spectrum imaging (AxSI) for in-vivo estimation of axonal characteristics in the human brain. Whole-brain estimation of the axon diameter, in-vivo and non-invasively, across all fiber systems will allow exploring uncharted aspects of brain structure and function relations with emphasis on connectivity and connectome analysis. While axon diameter mapping is important in and of itself, its correlation with conduction velocity will allow, for the first time, the explorations of information transfer mechanisms within the brain. We demonstrate various well-known aspects of axonal morphometry (e.g., the corpus callosum axon diameter variation) as well as other aspects that are less explored (e.g., axon diameter-based separation of the superior longitudinal fasciculus into segments). Moreover, we have created an MNI based mean axon diameter map over the entire brain for a large cohort of subjects providing the reference basis for future studies exploring relation between axon properties, its connectome representation, and other functional and behavioral aspects of the brain.

Temporal Diffusion Ratio (TDR) for imaging restricted diffusion: Optimisation and pre-clinical demonstration.

Temporal Diffusion Ratio (TDR) is a recently proposed dMRI technique (Dell'Acqua et al., proc. ISMRM 2019) which provides contrast between areas with restricted diffusion and areas either without restricted diffusion or with length scales too small for characterisation. Hence, it has a potential for informing on pore sizes, in particular the presence of large axon diameters or other cellular structures. TDR employs the signal from two dMRI acquisitions obtained with the same, large, b-value but with different diffusion gradient waveforms. TDR is advantageous as it employs standard acquisition sequences, does not make any assumptions on the underlying tissue structure and does not require any model fitting, avoiding issues related to model degeneracy. This work for the first time introduces and optimises the TDR method in simulation for a range of different tissues and scanner constraints and validates it in a pre-clinical demonstration. We consider both substrates containing cylinders and spherical structures, representing cell soma in tissue. Our results show that contrasting an acquisition with short gradient duration, short diffusion time and high gradient strength with an acquisition with long gradient duration, long diffusion time and low gradient strength, maximises the TDR contrast for a wide range of pore configurations. Additionally, in the presence of Rician noise, computing TDR from a subset (50% or fewer) of the acquired diffusion gradients rather than the entire shell as proposed originally further improves the contrast. In the last part of the work the results are demonstrated experimentally on rat spinal cord. In line with simulations, the experimental data shows that optimised TDR improves the contrast compared to non-optimised TDR. Furthermore, we find a strong correlation between TDR and histology measurements of axon diameter. In conclusion, we find that TDR has great potential and is a very promising alternative (or potentially complement) to model-based approaches for informing on pore sizes and restricted diffusion in general.

Differential impacts of Cntnap2 heterozygosity and Cntnap2 null homozygosity on axon and myelinated fiber development in mouse.

Over the last decade, a large variety of alterations of the Contactin Associated Protein 2 (CNTNAP2) gene, encoding Caspr2, have been identified in several neuronal disorders, including neurodevelopmental disorders and peripheral neuropathies. Some of these alterations are homozygous but most are heterozygous, and one of the current challenges is to estimate to what extent they could affect the functions of Caspr2 and contribute to the development of these pathologies. Notably, it is not known whether the disruption of a single CNTNAP2 allele could be sufficient to perturb the functions of Caspr2. To get insights into this issue, we questioned whether Cntnap2 heterozygosity and Cntnap2 null homozygosity in mice could both impact, either similarly or differentially, some specific functions of Caspr2 during development and in adulthood. We focused on yet poorly explored functions of Caspr2 in axon development and myelination, and performed a morphological study from embryonic day E17.5 to adulthood of two major brain interhemispheric myelinated tracts, the anterior commissure (AC) and the corpus callosum (CC), comparing wild-type (WT), Cntnap2 -/- and Cntnap2 +/- mice. We also looked for myelinated fiber abnormalities in the sciatic nerves of mutant mice. Our work revealed that Caspr2 controls the morphology of the CC and AC throughout development, axon diameter at early developmental stages, cortical neuron intrinsic excitability at the onset of myelination, and axon diameter and myelin thickness at later developmental stages. Changes in axon diameter, myelin thickness and node of Ranvier morphology were also detected in the sciatic nerves of the mutant mice. Importantly, most of the parameters analyzed were affected in Cntnap2 +/- mice, either specifically, more severely, or oppositely as compared to Cntnap2 -/- mice. In addition, Cntnap2 +/- mice, but not Cntnap2 -/- mice, showed motor/coordination deficits in the grid-walking test. Thus, our observations show that both Cntnap2 heterozygosity and Cntnap2 null homozygosity impact axon and central and peripheral myelinated fiber development, but in a differential manner. This is a first step indicating that CNTNAP2 alterations could lead to a multiplicity of phenotypes in humans, and raising the need to evaluate the impact of Cntnap2 heterozygosity on the other neurodevelopmental functions of Caspr2.

Mapping the human connectome using diffusion MRI at 300 mT/m gradient strength: Methodological advances and scientific impact.

Tremendous efforts have been made in the last decade to advance cutting-edge MRI technology in pursuit of mapping structural connectivity in the living human brain with unprecedented sensitivity and speed. The first Connectom 3T MRI scanner equipped with a 300 mT/m whole-body gradient system was installed at the Massachusetts General Hospital in 2011 and was specifically constructed as part of the Human Connectome Project. Since that time, numerous technological advances have been made to enable the broader use of the Connectom high gradient system for diffusion tractography and tissue microstructure studies and leverage its unique advantages and sensitivity to resolving macroscopic and microscopic structural information in neural tissue for clinical and neuroscientific studies. The goal of this review article is to summarize the technical developments that have emerged in the last decade to support and promote large-scale and scientific studies of the human brain using the Connectom scanner. We provide a brief historical perspective on the development of Connectom gradient technology and the efforts that led to the installation of three other Connectom 3T MRI scanners worldwide - one in the United Kingdom in Cardiff, Wales, another in continental Europe in Leipzig, Germany, and the latest in Asia in Shanghai, China. We summarize the key developments in gradient hardware and image acquisition technology that have formed the backbone of Connectom-related research efforts, including the rich array of high-sensitivity receiver coils, pulse sequences, image artifact correction strategies and data preprocessing methods needed to optimize the quality of high-gradient strength diffusion MRI data for subsequent analyses. Finally, we review the scientific impact of the Connectom MRI scanner, including advances in diffusion tractography, tissue microstructural imaging, ex vivo validation, and clinical investigations that have been enabled by Connectom technology. We conclude with brief insights into the unique value of strong gradients for diffusion MRI and where the field is headed in the coming years.

Does powder averaging remove dispersion bias in diffusion MRI diameter estimates within real 3D axonal architectures?

Noninvasive estimation of axon diameter with diffusion MRI holds the potential to investigate the dynamic properties of the brain network and pathology of neurodegenerative diseases. Recent studies use powder averaging to account for complex white matter architectures, but these have not been validated for real axonal geometries from regions that contain fibre crossings. Here, we present 120-304µm long segmented axons from X-ray nano-holotomography volumes of a splenium and crossing fibre region of a vervet monkey brain. We show that the axons in the complex crossing fibre region, which contains callosal, association, and corticospinal connections, exhibit a wider diameter distribution than those of the splenium region. To accurately estimate the axon diameter in these regions, therefore, sensitivity to a wide range of diameters is required. We demonstrate how the q-value, b-value, signal-to-noise ratio and the assumed intra-axonal parallel diffusivity influence the range of measurable diameters with powder average approaches. Furthermore, we show how Gaussian distributed noise results in a wider range of measurable diameter at high b-values than Rician distributed noise, even at high signal-to-noise ratios of 100. The number of gradient directions is also shown to impose a lower bound on measurable diameter. Our results indicate that axon diameter estimation can be performed with only few b-shells, and that additional shells do not improve the accuracy of the estimate. For strong gradients available on human Connectom and preclinical scanners, Monte Carlo simulations of diffusion confirm that powder averaging techniques succeed in providing accurate estimates of axon diameter across a range of diameters, sequence parameters and diffusion times, even in complex white matter architectures. At relatively low b-values, the diameter estimate becomes sensitive to axonal microdispersion and the intra-axonal parallel diffusivity shows time dependency at both in vivo and ex vivo intrinsic diffusivities.

The functional characterization of callosal connections.

The brain operates through the synaptic interaction of distant neurons within flexible, often heterogeneous, distributed systems. Histological studies have detailed the connections between distant neurons, but their functional characterization deserves further exploration. Studies performed on the corpus callosum in animals and humans are unique in that they capitalize on results obtained from several neuroscience disciplines. Such data inspire a new interpretation of the function of callosal connections and delineate a novel road map, thus paving the way toward a general theory of cortico-cortical connectivity. Here we suggest that callosal axons can drive their post-synaptic targets preferentially when coupled to other inputs endowing the cortical network with a high degree of conditionality. This might depend on several factors, such as their pattern of convergence-divergence, the excitatory and inhibitory operation mode, the range of conduction velocities, the variety of homotopic and heterotopic projections and, finally, the state-dependency of their firing. We propose that, in addition to direct stimulation of post-synaptic targets, callosal axons often play a conditional driving or modulatory role, which depends on task contingencies, as documented by several recent studies.

Axon diameter inferences in the human corpus callosum using oscillating gradient spin echo sequences.

Previous methods used to infer axon diameter distributions using magnetic resonance imaging (MRI) primarily use single diffusion encoding sequences such as pulsed gradient spin echo (PGSE) and are thus sensitive to axons of diameters >5 µm. We applied oscillating gradient spin echo (OGSE) sequences to study human axons in the 1-2 µm range in the corpus callosum, which include the majority of axons constituting cortical connections. The ActiveAx model was applied to calculate the fitted mean effective diameter for axons (AxD) and was compared with values found using histology. Axon diameters from histological data were calculated using three different datasets; true diameters (minimum diameter), a combination of minimum and maximum diameters, and diameters measured across a consistent diffusion direction. The AxD estimates from MRI were 1.8 ± 0.1 µm to 2.34 ± 0.04 µm with an average of 2.0 ± 0.2 µm for the ActiveAx model. The histology AxD values were 1.43 ± 0.02 µm when using the true minimum axon diameters, 5.52 ± 0.02 µm when using the combination of minimum and maximum axon diameters, and 2.20 ± 0.02 µm when collecting measurements across a consistent diffusion direction. This experiment demonstrates the first known usage of OGSE to calculate axon diameters in the human corpus callosum on a 1-2 µm scale. The importance for the model to account for axonal orientation dispersion is indicated by histological results which more closely match the MRI model results depending on the direction of axon diameter measurements. These initial steps using this non-invasive imaging method can be applied to future methodology to develop in vivo axon diameter measurements in human brain tissue.

Estimation of electric field impact in deep brain stimulation from axon diameter distribution in the human brain.

Objective.Finite element method (FEM) simulations of the electric field magnitude (EF) are commonly used to estimate the affected tissue surrounding the active contact of deep brain stimulation (DBS) leads. Previous studies have found that DBS starts to noticeably activate axons at approximately 0.2 V mm-1, corresponding to activation of 3.4µm axons in simulations of individual axon triggering. Most axons in the brain are considerably smaller however, and the effect of the electric field is thus expected to be stronger with increasing EF as more and more axons become activated. The objective of this study is to estimate the fraction of activated axons as a function of electric field magnitude.Approach. The EF thresholds required for axon stimulation of myelinated axon diameters between 1 and 5µm were obtained from a combined cable and Hodgkin-Huxley model in a FEM-simulated electric field from a Medtronic 3389 lead. These thresholds were compared with the average axon diameter distribution from literature from several structures in the human brain to obtain an estimate of the fraction of axons activated at EF levels between 0.1 and 1.8 V mm-1.Main results. The effect of DBS is estimated to be 47·EF-8.8% starting at a threshold levelEFt0 = 0.19 V mm-1.Significance. The fraction of activated axons from DBS in a voxel is estimated to increase linearly with EF above the threshold level of 0.19 V mm-1. This means linear regression between EF above 0.19 V mm-1and clinical outcome is a suitable statistical method when doing improvement maps for DBS.

Evidence That ITPR2-Mediated Intracellular Calcium Release in Oligodendrocytes Regulates the Development of Carbonic Anhydrase II + Type I/II Oligodendrocytes and the Sizes of Myelin Fibers.

Myelination of neuronal axons in the central nervous system (CNS) by oligodendrocytes (OLs) enables rapid saltatory conductance and axonal integrity, which are crucial for normal brain functioning. Previous studies suggested that different subtypes of oligodendrocytes in the CNS form different types of myelin determined by the diameter of axons in the unit. However, the molecular mechanisms underlying the developmental association of different types of oligodendrocytes with different fiber sizes remain elusive. In the present study, we present the evidence that the intracellular Ca2+ release channel associated receptor (Itpr2) contributes to this developmental process. During early development, Itpr2 is selectively up-regulated in oligodendrocytes coinciding with the initiation of myelination. Functional analyses in both conventional and conditional Itpr2 mutant mice revealed that Itpr2 deficiency causes a developmental delay of OL differentiation, resulting in an increased percentage of CAII+ type I/II OLs which prefer to myelinate small-diameter axons in the CNS. The increased percentage of small caliber myelinated axons leads to an abnormal compound action potentials (CAP) in the optic nerves. Together, these findings revealed a previously unrecognized role for Itpr2-mediated calcium signaling in regulating the development of different types of oligodendrocytes.

Connectome 2.0: Developing the next-generation ultra-high gradient strength human MRI scanner for bridging studies of the micro-, meso- and macro-connectome.

The first phase of the Human Connectome Project pioneered advances in MRI technology for mapping the macroscopic structural connections of the living human brain through the engineering of a whole-body human MRI scanner equipped with maximum gradient strength of 300 mT/m, the highest ever achieved for human imaging. While this instrument has made important contributions to the understanding of macroscale connectional topology, it has also demonstrated the potential of dedicated high-gradient performance scanners to provide unparalleled in vivo assessment of neural tissue microstructure. Building on the initial groundwork laid by the original Connectome scanner, we have now embarked on an international, multi-site effort to build the next-generation human 3T Connectome scanner (Connectome 2.0) optimized for the study of neural tissue microstructure and connectional anatomy across multiple length scales. In order to maximize the resolution of this in vivo microscope for studies of the living human brain, we will push the diffusion resolution limit to unprecedented levels by (1) nearly doubling the current maximum gradient strength from 300 mT/m to 500 mT/m and tripling the maximum slew rate from 200 T/m/s to 600 T/m/s through the design of a one-of-a-kind head gradient coil optimized to minimize peripheral nerve stimulation; (2) developing high-sensitivity multi-channel radiofrequency receive coils for in vivo and ex vivo human brain imaging; (3) incorporating dynamic field monitoring to minimize image distortions and artifacts; (4) developing new pulse sequences to integrate the strongest diffusion encoding and highest spatial resolution ever achieved in the living human brain; and (5) calibrating the measurements obtained from this next-generation instrument through systematic validation of diffusion microstructural metrics in high-fidelity phantoms and ex vivo brain tissue at progressively finer scales with accompanying diffusion simulations in histology-based micro-geometries. We envision creating the ultimate diffusion MRI instrument capable of capturing the complex multi-scale organization of the living human brain - from the microscopic scale needed to probe cellular geometry, heterogeneity and plasticity, to the mesoscopic scale for quantifying the distinctions in cortical structure and connectivity that define cyto- and myeloarchitectonic boundaries, to improvements in estimates of macroscopic connectivity.

Scan-rescan repeatability of axonal imaging metrics using high-gradient diffusion MRI and statistical implications for study design.

Axon diameter mapping using diffusion MRI in the living human brain has attracted growing interests with the increasing availability of high gradient strength MRI systems. A systematic assessment of the consistency of axon diameter estimates within and between individuals is needed to gain a comprehensive understanding of how such methods extend to quantifying differences in axon diameter index between groups and facilitate the design of neurobiological studies using such measures. We examined the scan-rescan repeatability of axon diameter index estimation based on the spherical mean technique (SMT) approach using diffusion MRI data acquired with gradient strengths up to 300 mT/m on a 3T Connectom system in 7 healthy volunteers. We performed statistical power analyses using data acquired with the same protocol in a larger cohort consisting of 15 healthy adults to investigate the implications for study design. Results revealed a high degree of repeatability in voxel-wise restricted volume fraction estimates and tract-wise estimates of axon diameter index derived from high-gradient diffusion MRI data. On the region of interest (ROI) level, across white matter tracts in the whole brain, the Pearson's correlation coefficient of the axon diameter index estimated between scan and rescan experiments was r = 0.72 with an absolute deviation of 0.18 µm. For an anticipated 10% effect size in studies of axon diameter index, most white matter regions required a sample size of less than 15 people to observe a measurable difference between groups using an ROI-based approach. To facilitate the use of high-gradient strength diffusion MRI data for neuroscientific studies of axonal microstructure, the comprehensive multi-gradient strength, multi-diffusion time data used in this work will be made publicly available, in support of open science and increasing the accessibility of such data to the greater scientific community.

The variability of MR axon radii estimates in the human white matter.

The noninvasive quantification of axonal morphology is an exciting avenue for gaining understanding of the function and structure of the central nervous system. Accurate non-invasive mapping of micron-sized axon radii using commonly applied neuroimaging techniques, that is, diffusion-weighted MRI, has been bolstered by recent hardware developments, specifically MR gradient design. Here the whole brain characterization of the effective MR axon radius is presented and the inter- and intra-scanner test-retest repeatability and reproducibility are evaluated to promote the further development of the effective MR axon radius as a neuroimaging biomarker. A coefficient-of-variability of approximately 10% in the voxelwise estimation of the effective MR radius is observed in the test-retest analysis, but it is shown that the performance can be improved fourfold using a customized along-tract analysis.

Axon diameter index estimation independent of fiber orientation distribution using high-gradient diffusion MRI.

Axon diameter mapping using high-gradient diffusion MRI has generated great interest as a noninvasive tool for studying trends in axonal size in the human brain. One of the main barriers to mapping axon diameter across the whole brain is accounting for complex white matter fiber configurations (e.g., crossings and fanning), which are prevalent throughout the brain. Here, we present a framework for generalizing axon diameter index estimation to the whole brain independent of the underlying fiber orientation distribution using the spherical mean technique (SMT). This approach is shown to significantly benefit from the use of real-valued diffusion data with Gaussian noise, which reduces the systematic bias in the estimated parameters resulting from the elevation of the noise floor when using magnitude data with Rician noise. We demonstrate the feasibility of obtaining whole-brain orientationally invariant estimates of axon diameter index and relative volume fractions in six healthy human volunteers using real-valued diffusion data acquired on a dedicated high-gradient 3-Tesla human MRI scanner with 300 mT/m maximum gradient strength. The trends in axon diameter index are consistent with known variations in axon diameter from histology and demonstrate the potential of this generalized framework for revealing coherent patterns in axonal structure throughout the living human brain. The use of real-valued diffusion data provides a viable solution for eliminating the Rician noise floor and should be considered for all spherical mean approaches to microstructural parameter estimation.

Nonivasive quantification of axon radii using diffusion MRI.

Axon caliber plays a crucial role in determining conduction velocity and, consequently, in the timing and synchronization of neural activation. Noninvasive measurement of axon radii could have significant impact on the understanding of healthy and diseased neural processes. Until now, accurate axon radius mapping has eluded in vivo neuroimaging, mainly due to a lack of sensitivity of the MRI signal to micron-sized axons. Here, we show how - when confounding factors such as extra-axonal water and axonal orientation dispersion are eliminated - heavily diffusion-weighted MRI signals become sensitive to axon radii. However, diffusion MRI is only capable of estimating a single metric, the effective radius, representing the entire axon radius distribution within a voxel that emphasizes the larger axons. Our findings, both in rodents and humans, enable noninvasive mapping of critical information on axon radii, as well as resolve the long-standing debate on whether axon radii can be quantified.

Time-dependent diffusion in undulating thin fibers: Impact on axon diameter estimation.

Diffusion MRI may enable non-invasive mapping of axonal microstructure. Most approaches infer axon diameters from effects of time-dependent diffusion on the diffusion-weighted MR signal by modeling axons as straight cylinders. Axons do not, however, propagate in straight trajectories, and so far the impact of the axonal trajectory on diameter estimation has been insufficiently investigated. Here, we employ a toy model of axons, which we refer to as the undulating thin fiber model, to analyze the impact of undulating trajectories on the time dependence of diffusion. We study time-dependent diffusion in the frequency domain and characterize the diffusion spectrum by its height, width, and low-frequency behavior (power law exponent). Results show that microscopic orientation dispersion of the thin fibers is the main parameter that determines the characteristics of the diffusion spectra. At lower frequencies (longer diffusion times), straight cylinders and undulating thin fibers can have virtually identical spectra. If the straight-cylinder assumption is used to interpret data from undulating thin axons, the diameter is overestimated by an amount proportional to the undulation amplitude and microscopic orientation dispersion of the fibers. At higher frequencies (shorter diffusion times), spectra from cylinders and undulating thin fibers differ. The low-frequency behavior of the spectra from the undulating thin fibers may also differ from that of cylinders, because the power law exponent of undulating fibers can reach values below 2 for experimentally relevant frequency ranges. In conclusion, we argue that the non-straight nature of axonal trajectories should not be overlooked when analyzing and interpreting diffusion MRI data.

ActiveAxADD : Toward non-parametric and orientationally invariant axon diameter distribution mapping using PGSE.

PURPOSE: Non-invasive axon diameter distribution (ADD) mapping using diffusion MRI is an ill-posed problem. Current ADD mapping methods require knowledge of axon orientation before performing the acquisition. Instead, ActiveAx uses a 3D sampling scheme to estimate the orientation from the signal, providing orientationally invariant estimates. The mean diameter is estimated instead of the distribution for the solution to be tractable. Here, we propose an extension (ActiveAxADD ) that provides non-parametric and orientationally invariant estimates of the whole distribution. THEORY: The accelerated microstructure imaging with convex optimization (AMICO) framework accelerates mean diameter estimation using a linear formulation combined with Tikhonov regularization to stabilize the solution. Here, we implement a new formulation (ActiveAxADD ) that uses Laplacian regularization to provide robust estimates of the whole ADD. METHODS: The performance of ActiveAxADD was evaluated using Monte Carlo simulations on synthetic white matter samples mimicking axon distributions reported in histological studies. RESULTS: ActiveAxADD provided robust ADD reconstructions when considering the isolated intra-axonal signal. However, our formulation inherited some common microstructure imaging limitations. When accounting for the extra axonal compartment, estimated ADDs showed spurious peaks and increased variability because of the difficulty of disentangling intra and extra axonal contributions. CONCLUSION: Laplacian regularization solves the ill-posedness regarding the intra axonal compartment. ActiveAxADD can potentially provide non-parametric and orientationally invariant ADDs from isolated intra-axonal signals. However, further work is required before ActiveAxADD can be applied to real data containing extra-axonal contributions, as disentangling the 2 compartment appears to be an overlooked challenge that affects microstructure imaging methods in general.