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. Supplementary Information The online version contains supplementary material available at 10.1007/s12021-023-09630-w.


Section A. Axon Diameter Specificity and Sensitivity
Several studies have suggested that sources of restricted diffusion, other than intraaxonal space may exist (e.g. in extracellular space) that might compromise the specificity of the signal and even mislead the model estimates (Lee et al., 2018(Lee et al., , 2020. Histological analysis of white matter cross section specimens indicates that most of the volume in these areas is occupied by the inner-axonal component (See Figure 1 in (Abdollahzadeh et al., 2019)). While histology might be misleading, since the tissue shrinks dramatically in preparation, especially due to dehydration of the extracellular matrix (Barazany et al., 2009;VIRTANEN et al., 1984), it is still expected that the major part of water signal in diffusion MRI experiments will arise from the intra-axonal compartment. Supporting experimental evidence for this statement comes from water diffusion experiments performed parallel and perpendicular to white matter fascicles, water diffusion experiments on non-myelinated tissue, as well from cortical gray matter area and metabolite (NAA, Choline) diffusion experiments where the extracellular signal is supposedly non-existent ( Fig. S1) (Assaf et al., 2002;Assaf & Cohen, 1998, 2000. This phenomenon, published over 15 years ago, indicates that there are multiple populations of water molecules that are distinguishable by their motion properties (Assaf & Cohen, 2000;Beaulieu et al., 1998;Peled et al., 1999). It appears that white matter tissue exhibits multiple water populations in which diffusion is gradually slowed due to motion hindrance (Fig. S1). Particularly is the apparently endlessly slow diffusing component, which is highly anisotropic, originating mainly from intra-cellular signals and affected tremendously by myelination ( Fig. S1) (Assaf & Cohen, 2000;Beaulieu, 2002;Stanisz et al., 1997;Stanisz & Henkelman, 1998;Yoshiura et al., 2001).

Fig. S1
Water diffusion signal decay for various brain tissue types (cortex, white matter, demyelinated white matter) as well as experimental conditions (measured parallel (‖) or perpendicular (Ʇ) to fiber's long axis. The data is legacy diffusion MRI data, partially published before (Assaf et al., 2002;Assaf & Cohen, 1998, 2000.

Section B
The limiting parameter that controls the experimental conditions in any diffusion MRI experiment is the amplitude of the diffusion gradients (Huang et al., 2020;McNab et al., 2012). Usually, in diffusion MRI, the protocol sets the diffusion gradients to the maximum value and then calculates the other parameters (diffusion time, , diffusion gradients length, ). It has been shown, both in theory and through simulations, that the sensitivity towards axon diameter reduces dramatically when the diffusion gradient length becomes longer than a few milliseconds (Assaf et al., 2008;Assaf & Cohen, 2000;Dyrby et al., 2013;Sepehrband et al., 2016). It was suggested that good estimation of axon diameter could be achievable only in preclinical scanners or clinical scanners with very strong gradient systems (such as the connectome magnet) (Lee et al., 2020;Veraart et al., 2020Veraart et al., , 2021 or even infeasible at all (Paquette et al., 2021). However, experimental evidence suggests that the potential implementation obstacles for axonal diameter estimation from diffusion MRI caused by the empirical factor (solving the Bloch-Torrey equations) and hardware considerations (e.g. gradient strength) are not as severe as suspected.
To better understand this, we need to explore the origins of the methodology limitations. There are three experimental parameters that affect the modeling approach: the diffusion gradient amplitude ( ), the diffusion gradient pulse duration ( ) and the diffusion time ( ). Analytical solutions to the Bloch-Torrey equations for diffusion within cylinders were developed for three experimental conditions: (a) ≪ and Van Gelderen et al., 1994) and (c) ∼ (Neuman, 1974). It has been suggested previously that in-vivo, water exchange between intra-and extra-axonal components, complicates the interpretation of signal decay derived from restricted diffusion (Brabec et al., 2020;Nilsson et al., 2013). Fig. S2 shows data measured in various / (see Fig. S3 for examples) combinations of the corpus callosum of the rat brain, in-vivo and ex-vivo according to these approaches ( Fig. S2a and S2b). Ex-vivo (Fig. S2b), there is a strong effect of the diffusion gradient duration ( ) indicating that indeed this is a critical parameter in the modeling routine affecting which model to choose (Callaghan, Van-Geldern or Neuman). In-vivo (Fig. S2a), however, the dependency of signal decay on the diffusion gradient duration disappears (in both rodents and humans). While the invariance of the signal decay to the gradient duration suggests that the modeling could be dramatically simplified (taking a simple approach out of the three mentioned above, for example eq. 14 in (Van Gelderen et al., 1994)), it might also lead to assume that restricted diffusion is minimal in-vivo. Despite this observation, other experiments suggest that restricted diffusion is significant even in-vivo. In these experiments all conditions are kept similar besides the diffusion time, . Fig. S2c shows variable experiment on the rat corpus callosum measured in-vivo indicating that restricted diffusion affects water motion underscoring the possibility of sensitivity to intra-axonal motion and hence the axon diameter albeit the invariance of the signal to the gradient duration ( ). Moreover, we aimed to separate between the short diffusion time (Δ = 20ms) and the longer ones (Δ>~50ms). As previously shown (Assaf & Cohen, 1998;Kärger, 1996), the effect of the diffusion time of the signal decay reaches a plateau at the longer diffusion times range indicating that above a certain value it becomes insensitive due to restricted diffusion.

Fig. S2
Controlled parameters experiment for AxSI framework validation. (a-b) Plots (upper panel) and heatmaps (lower panel) of signal decay in the CC of 4 different scan protocols (Experiment 1, 3, 4 & 5 in Table S1), along ascending b-values, for in-vivo (a) and ex-Vivo (b) rat brain scans. (c) A plot (upper panel) and a heatmap (lower panel) of signal decay for experiment with controlled and changing , along ascending bvalues to examine the ability of the diffusion signal to be sensitive to intra-axonal water motion

Fig. S3
Examples of in-vivo diffusion MRI signal decay for different experimental conditions at the same b-value range.

Section C: Axon Diameter Estimation in Pre-Clinical Scanner
Clearly, the estimated axon diameter value might deviate from real numbers due to water exchange and other experimental limits (sections A and B) but it can be considered a marker or indicator of intra-axonal diameter. Fig. S4 demonstrates this ability where the axon diameters along the corpus callosum of the rat brain were measured in the most optimal experimental conditions compared with clinical conditions. As indicated from Fig. 4, the in-vivo experimental conditions do not affect the extracted axon diameter trends and appear to linearly shift it towards smaller values. Mantel test for distance comparisons was done to compare the resemblance of the distributions, between each protocol parameters and the optimal protocol (Δ/δ = 120/1.3 ms). Resulted correlations were significant for all comparisons. P-value were corrected for multiple comparisons using Bonferroni correction. Results are for the correlation between the mentioned protocol and optimal protocol: r60/2 = 0.63, p < 0.01, r40/3 = 0.57, p < 0.01, r40/12 = 0.52, p < 0.01, r25/12 = 0.51, p < 0.01. Even though we demonstrate a single sample for each protocol parameters and therefore, no statistical analysis performed to measure it, all experimental conditions resembled the known trend of ADD along the CC (Suzuki et al., 2016). The above-mentioned experimental drill-down indicates that axon diameter estimation with diffusion MRI is feasible. While absolute measurement of the exact diameter distribution in a region or fiber bundle could be limited due to biophysical and experimental limitations, the numerical values do represent intra-axonal morphology (Fig. S4).

Fig. S4
Mean Axon Diameter Distribution, as resulted from the AxSI analysis for five different protocol parameters, marked with different colors (see Table S1 Experiments 1-5 in Methods). Dot markers represent an average value around a voxel in the skeleton of CC and the solid lines are the corresponding third-degree polynomial functions.

Supplementary methods:
Data: Rats were scanned at a 7T Bruker 70/30 Biospec system. The imaging protocol consisted of a series of diffusion weighted echo planar images with experimental parameters summarized in Table 1 to control for the effects of gradient pulse duration ( ) and gradient separation (diffusion time, ). In all scans the diffusion gradients were applied perpendicular to the corpus callosum.
Measures of ADD distribution along the CC axis: CC masks for mid-sagittal slices in rat scans were created using automatic region-ofinterest selection based on DWI scan intensity. A skeleton was extracted for each scan protocol (Experiment 1-5 in Table S1) and 23 equally spaced points along the skeleton were chosen. Then, each voxel in the CC mask was associated with the closest point to it and the values were averaged to represent the mean value of each of the 23 points. Finally, a third-degree polynomial distribution was matched to each experiment's values.

Comparing along CC distributions:
Mantel test (N Mantel, 1967) was conducted to compare distance matrices between protocols. First, the distance matrix of each protocol was calculated as the difference between each pair of values along the skeleton (as shown in the graph Fig. S4). Then, Mantel test was conducted on each distance matrix with the distance matrix of Δ/δ = 120/1.3 ms. The resulted p-values were corrected using Bonferroni correction for the 4 comparisons.

Table S1
Experimental parameters for diffusion scans of Rat experiments.