The axon diameter is one of several important measures of the nervous system that provide unique insight into the physiology of information transfer in the brain. While traditionally axonal morphometry could have been measured only by invasive histological procedures, the suggested framework in this paper, AxSI, offers a platform for estimating axonal properties in-vivo and non-invasively. Over the last decade it has been repeatedly shown that diffusion imaging is sensitive to axonal size. While the magnitude of this sensitivity is still under debate, it is agreed that certain experimental conditions may favor this unique axonal characterization. Despite the discussion on how to increase the sensitivity of diffusion imaging to axonal properties, the information embedded in axon diameter estimation using MRI is unequivocal.
However, the ability of AxSI to infer axonal properties relies on several assumptions and modeling approaches that must be well understood before using this method routinely. First, as in any model, the obtained parameters are only estimated and not directly measured. The word ‘estimated’ should be further emphasized, as MRI cannot reach the resolution level that allows visualization of axons, but it infers their existence and size based on the characteristics of water diffusion. As described above, water diffusion in neural matter is a complicated process that occurs in several compartments that may share similar diffusion characteristics (diffusion coefficient, hindrance to diffusion, etc.), therefore the biophysical modeling of axon diameter is challenging and may be considered ill-posed. In addition, while validation of AxCaliber/AxSI against the traditional electron microscopy direct measure of axon diameter has been performed, true validation of this measure in-vivo is obviously out of reach. Yet, previous studies have shown that the estimated axon diameters using AxCaliber fit the expected axonal size variability along the corpus callosum, indicating the sensitivity of this method to known variability [8, 23, 24, 43, 44]. Moreover, correlation with physiological measures, such as conduction velocity, also suggest that this measure of axonal diameter is as physiologically relevant as the traditional electron microscopy measures [7]. Those validations suggest that large population studies are essential to explore new features of brain structure/function relations with AxSI.
Since the first demonstration that diffusion MRI is sensitive to axon diameter over 15 years ago [9], significant limitations and concerns regarding the method have been raised. Additionally, the complicated and somewhat ill-posed modeling framework reduced the applicability of the method to the neuroscientific community. As there are only a few in-vivo markers of brain microstructure properties that have direct physiological meaning, the concerns and obstacles of estimating axonal diameter from MRI should be untangled.
Many papers have dealt with the possible effects of exchange, compartmentalization, and experimental conditions (gradient strength, duration) on the parameters computed from the various frameworks for axon diameter measurement [19, 29, 30, 35, 36, 45–47]. As shown in the supplementary material (section A, B and C), while these effects are meaningful, they cannot completely diminish the observed sensitivity to axon diameter (Fig. S1-3). Taking advantage of some experimental conditions can even favor axon diameter over other factors. As such, the experimental conditions described above provide a diffusion MRI signal that has good specificity and sensitivity to axon diameter.
This experimental optimization still requires a robust and simple modeling framework to increase its applicability and impact. In recent years, the use of machine learning procedures to predict and explain measured signals has become more feasible providing new approaches to estimate free parameters of a model from noisy, sub-sampled data [48–50]. AxSI follows this concept and estimates, per pixel, a set of possible signals that represent different axon diameters. Instead of optimizing the axon diameter directly, AxSI regresses the axon diameter dependent signal library to find the best combination of all possible predictors that explains the measured signal while maintaining smooth weighting distribution function over all possible axon diameters. This approach dramatically simplifies the modeling routine and provides a more robust and stable axon diameter estimation approach.
It should be noted that AxSI, as any other MRI based axon diameter framework, does not directly measure the axon diameter. Rather, it provides a proxy to the diameter via indirect modeling of the diffusion MRI signal. This should not weaken the impact or use of the methodology, since most MRI frameworks suffer from the same indirect interpretation problem: functional MRI does not directly measure brain function but rather susceptibility changes following hemodynamic response to brain activity [3], myelin mapping [51] doesn’t measure myelin but rather relaxometry manifestations of myelination, diffusion MRI doesn’t measure diffusion but rather displacement (39). Following this jargon, AxSI provides a proxy of the axon diameter, and its extracted indices should be indicated as eMAD or estimated axon diameter distribution (eADD).
In this paper we use AxSI to estimate the MAD and combined it with fiber tracking to visualize tract-specific axonal properties. Each tract shown in Fig. 1–2, was colored according to the mean MAD of the pixels that contribute to the tract (see Methods). Using this visualization procedure, some known neuroanatomical features of axon fascicles become apparent, consequently increasing the validity and impact of the method. For example, the ability to visualize the pattern of axon diameter changes along the corpus callosum (Fig. 2A), highlighting the high MAD in the body of the CC while smaller values in the splenium and genu region, became the hallmark of axon diameter validation [41]. Moreover, the higher MAD values in the cortico-spinal tract compared to other segments of the corona radiata indicate the fast transmission of signal along the motor pathways compared to other fascicles. Noteworthy is the small axon diameter measured at the frontal/temporal transition zone, where the uncinate and inferior fronto-occipital fascicle passes to the frontal lobe, that is in agreement with histological findings [52].
Comparison of AxSI results with histology is limited. First, there is a very limited number of studies measuring axon diameter properties of different fascicles in the human brain [41, 52, 53]. Second, the shrinkage of the tissue in histological preparation underestimates the real axon diameter and probably reduces the variability across fascicles considerably. This stands in contrast to AxSI (and previous methods) that overestimates the axon diameter values. Yet, the above-mentioned observations and comparisons with histology provide sufficient validation to AxSI, thus enabling it to explore other uncharted variations in axonal properties of different tracts. For example, the two massive long-range connections in the human brain: the inferior fronto-occipital fasciculus (IFOF) and superior longitudinal fasciculus (SLF) appear to have sub segments with different axon diameter properties (see Fig. 2C-D). At least for the SLF, these segments resemble that anatomical separation of the SLF into 3 segments. Still, the relevance of these observations should be tested in future studies that will try to relate reaction time or other behavioral aspects that should be related to these fiber-systems across a large population cohort.
The surface presentation of AxSI indicates a unique view of the cortex colored by the eMAD of fibers that project to it. It appears that large fiber fascicles project more frequently to somatosensory and motor areas, as well as to visual and auditory cortices, while lower axon diameter projects to more frontal and anterior temporal regions, probably indicating slower transmission of information to these regions. Such presentation could be the base for connectome analysis integrating axon diameter properties as weights to the edge strength (Fig. 1B). This might provide a more physiological interpretation of the connectome, rather than more spurious measurements such as number of streamline or mean FA [54, 55].
Lastly, we have computed AxSI on 324 random subjects from the HCP database. From these datasets, we were able to create a mean eMAD map in MNI space, providing a reference quantitative map for future studies (see supplementary material Fig. S5). This map allows to explore anatomically the eMAD property of different areas in the WM of the human brain (computed eMAD map is available at: https://github.com/HilaGast/AxSI.git). Moreover, it might provide the basis of an eMAD-based WM atlas. Such an atlas would define different WM anatomical areas based on their microstructural physiology.
While AxSI framework coped with most concerns that were raised over the years, it is still not free from limitations. Aside from conventional MRI limitations that includes signal to noise and resolution issues that need to be sufficient to achieve accurate eMAD modeling there are additional, more specific to the method, limitations. To achieve high sensitivity towards axon diameter it is required to increase the relative weighting of restricted diffusion water populations [8, 9, 24, 28, 56]. Yet, the ability of a diffusion MRI experiment to be sensitive and accurate to restricted diffusion that occurs in a 5 micron and 0.5 micron axon simultaneously depends, in theory, on the experimental conditions [19, 24]. To be sensitive to small-diameter axons there is a need to apply extremely strong diffusion weighting (high-b values) that is achieved by using the shortest possible period of diffusion tagging (termed δ in diffusion MRI pulse sequence) and high amplitude of diffusion gradients (g). There is no magic number for this sensitivity, some simulations suggest that axons with diameter smaller than 5 microns will be indistinguishable, while others indicate 2 microns as the minimum barrier depending on the experimental conditions [28, 36, 57].
The concerns that have been raised over the years regarding the use of diffusion MRI for measuring or estimating axon diameter properties are indeed troubling and hold back the potential uses of this method in neuroscience. All the concerns raised previously (summarized in the introduction and supplementary material) are a result of modeling and simulations and thus, as long as the mathematical description of the diffusion signal is correct, these concerns are valid [45]. However, diffusion MRI is a complicated method to be modeled: First, it measures a stochastic phenomenon; the random motion of water molecules, even for the case of water diffusion within a glass requires several assumptions [58]. Second, the effects of membranes as restrictive or semi-permeable barriers are unknown and hence can only be speculated [59–61]. Third, the ground truth for any axon diameter estimation is histology which may considerably differ from in-vivo conditions [62]. This complexity cannot be resolved by including all possible water pools, biophysical properties (e.g., exchange), and experimental conditions.
Yet, despite the validity and significance of the limitations, none of them, to our understanding, can overrule the sensitivity of diffusion MRI, at specific experimental conditions, to axonal morphometry.