Abstract:Peripheral nerves undulate together, giving them a wavelike appearance. This axonal pattern is also found in one region of the central nervous system, the optic nerve. Undulations provide a degree of compliance, as when a nerve is stretched, they are pulled straight. In the peripheral nervous system, undulations are thought to be conditional on the presence of extrafascicular collagen, which is also present between fascicles in the mammalian optic nerve. The pattern of undulations is described in the rat optic… Show more
“…Note that large axons are present only to a limited extent in the brain but are more common in the spine and for nerves outside the central nervous system. Small axons are found in the corpus callosum, optic nerve, or phrenic nerve (Table ). The second limitation concerns the overestimated spectral width in the 1‐harmonic case for fibers with undulation amplitudes that are large compared with the undulation wavelength ( a /λ ≥ 30 %).…”
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.
K E Y W O R D Saxon diameter, axonal trajectories, diffusion MRI, diffusion spectrum, low frequency, restricted diffusion, time dependence, undulation Abbreviations: dMRI, diffusion MRI; MSE, mean squared error; SNR, signal-to-noise ratio; μOD, microscopic orientation dispersion.
“…Note that large axons are present only to a limited extent in the brain but are more common in the spine and for nerves outside the central nervous system. Small axons are found in the corpus callosum, optic nerve, or phrenic nerve (Table ). The second limitation concerns the overestimated spectral width in the 1‐harmonic case for fibers with undulation amplitudes that are large compared with the undulation wavelength ( a /λ ≥ 30 %).…”
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.
K E Y W O R D Saxon diameter, axonal trajectories, diffusion MRI, diffusion spectrum, low frequency, restricted diffusion, time dependence, undulation Abbreviations: dMRI, diffusion MRI; MSE, mean squared error; SNR, signal-to-noise ratio; μOD, microscopic orientation dispersion.
“…microscopic, mesoscopic and macroscopic; intended to resemble undulation in the optic nerve, the sciatic nerve and fascicle undulation, respectively. On a microscopic scale, undulation with an amplitude on the order of A = 5 µm and a wavelength of about L = 20–30 µm has been reported for axons in the optic nerve . The mean axon diameter in the optic nerve is approximately d = 1 µm .…”
Section: Methodsmentioning
confidence: 99%
“…Undulation on a macroscopic scale with wavelengths up to tens of millimetres and amplitudes as large as the diameter of the nerve has also been reported . The tortuosity factor λ is reportedly up to 1.25 in the optic nerve and in the spinal cord . Four investigations (I–IV) were performed, concerning undulation on microscopic (I, II, III), mesoscopic (II, III) and macroscopic (IV) scales.…”
Section: Methodsmentioning
confidence: 99%
“…Axonal undulation was, in this work, characterised by the undulation wavelength ( L ) and amplitude ( A ), and model structures comprising axons that undulate were studied, using straight axons as reference systems. Undulations on microscopic, mesoscopic and macroscopic scales were considered by investigating structures with L = 24 µm, 300 µm and 5 mm, respectively . These cases were intended to resemble undulation in the optic nerve, the sciatic nerve and fascicular undulation, respectively.…”
Many axons follow wave-like undulating courses. This is a general feature of extracranial nerve segments, but is also found in some intracranial nervous tissue. The importance of axonal undulation has previously been considered, for example, in the context of biomechanics, where it has been shown that posture affects undulation properties. However, the importance of axonal undulation in the context of diffusion MR measurements has not been investigated. Using an analytical model and Monte Carlo simulations of water diffusion, this study compared undulating and straight axons in terms of diffusion propagators, diffusion-weighted signal intensities and parameters derived from diffusion tensor imaging, such as the mean diffusivity (MD), the eigenvalues and the fractional anisotropy (FA). All parameters were strongly affected by the presence of undulation. The diffusivity perpendicular to the undulating axons increased with the undulation amplitude, thus resembling that of straight axons with larger diameters. Consequently, models assuming straight axons for the estimation of the axon diameter from diffusion MR measurements might overestimate the diameter if undulation is present. FA decreased from approximately 0.7 to 0.5 when axonal undulation was introduced into the simulation model structure. Our results indicate that axonal undulation may play a role in diffusion measurements when investigating, for example, the optic and sciatic nerves and the spinal cord. The simulations also demonstrate that the stretching or compression of neuronal tissue comprising undulating axons alters the observed water diffusivity, suggesting that posture may be of importance for the outcome of diffusion MRI measurements.
“…Finally, some axons display a wave-like undulating course, which allow nerves to stretch during motion, such as eye movement and locomotion, without being damaged [46]. Axonal undulation is found generally in extra-cranial white matter, but is also present intracranially, for example, in the optic nerve [47, 48]. Fig.…”
Biophysical models that describe the outcome of white matter diffusion MRI experiments have various degrees of complexity. While the simplest models assume equal-sized and parallel axons, more elaborate ones may include distributions of axon diameters and axonal orientation dispersions. These microstructural features can be inferred from diffusion-weighted signal attenuation curves by solving an inverse problem, validated in several Monte Carlo simulation studies. Model development has been paralleled by microscopy studies of the microstructure of excised and fixed nerves, confirming that axon diameter estimates from diffusion measurements agree with those from microscopy. However, results obtained in vivo are less conclusive. For example, the amount of slowly diffusing water is lower than expected, and the diffusion-encoded signal is apparently insensitive to diffusion time variations, contrary to what may be expected. Recent understandings of the resolution limit in diffusion MRI, the rate of water exchange, and the presence of microscopic axonal undulation and axonal orientation dispersions may, however, explain such apparent contradictions. Knowledge of the effects of biophysical mechanisms on water diffusion in tissue can be used to predict the outcome of diffusion tensor imaging (DTI) and of diffusion kurtosis imaging (DKI) studies. Alterations of DTI or DKI parameters found in studies of pathologies such as ischemic stroke can thus be compared with those predicted by modelling. Observations in agreement with the predictions strengthen the credibility of biophysical models; those in disagreement could provide clues of how to improve them. DKI is particularly suited for this purpose; it is performed using higher b-values than DTI, and thus carries more information about the tissue microstructure. The purpose of this review is to provide an update on the current understanding of how various properties of the tissue microstructure and the rate of water exchange between microenvironments are reflected in diffusion MRI measurements. We focus on the use of biophysical models for extracting tissue-specific parameters from data obtained with single PGSE sequences on clinical MRI scanners, but results obtained with animal MRI scanners are also considered. While modelling of white matter is the central theme, experiments on model systems that highlight important aspects of the biophysical models are also reviewed.
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