Mapping the aggregate g-ratio of white matter tracts using multi-modal MRI Open Access

The g-ratio is a measure of the thickness of the myelin sheath relative to the diameter of the axon and is calculated as the ratio between the inner and outer diameters of the myelin sheath. Myelin plays a vital role in promoting rapid and efficient communication between neurons in the brain through mechanisms such as saltatory conduction, metabolic support, and shorter refractory periods (Khelfaoui et al., 2024). Myelin plasticity is also a mechanism to modulate the precise timing of signals within brain networks to support learning and higher cognitive functions (Xin & Chan, 2020). The g-ratio is one of the primary modulators of axonal conduction velocity, although other features including inter-node length, myelin periodicity, and axon diameter also contribute (Drakesmith et al., 2019). Myelination is a protracted process that peaks around mid-life (Slater et al., 2019), although myelin remains adaptive throughout the lifespan (Xin & Chan, 2020). Demyelination and atypical myelination have been observed in several neurological and psychiatric disorders such as multiple sclerosis (Frohman et al., 2006) and schizophrenia (Davis et al., 2003). Measuring the g-ratio of brain tissue in vivo is thus critical to improve our understanding of how myelination supports brain function during neurodevelopment, aging, and learning, and how dysmyelination alters brain function and behavior.

Histological studies have provided foundational insights into the g-ratio. During human neurodevelopment, axon growth initially surpasses myelination, resulting in a declining g-ratio as myelination progresses (Schröder et al., 1988). The g-ratio of myelinated axons varies with axon diameter, being approximately 0.6 for axons smaller than 5 µm in diameter and greater than 0.6 for axons larger than 5 µm in diameter (Graf von Keyserlingk & Schramm, 1984). These findings align with the concept of an optimal g-ratio, which balances the spatial constraints of the central nervous system and cellular energetics, generally falling within the range of 0.6–0.8 (Chomiak & Hu, 2009). These histological studies were labor-intensive and limited by small fields of view and specific cutting planes (perpendicular to the axon). In vivo measurement techniques are needed to overcome these limitations and further elucidate the role of g-ratio in brain function and pathology.

We can non-invasively estimate the g-ratio in vivo across the whole brain using multi-modal, quantitative magnetic resonance imaging (MRI), though this approach is subject to the limitations and biases of the MRI techniques used (Campbell et al., 2018). Stikov et al. (2015) showed that the aggregate g-ratio of each voxel can be computed from MRI markers of myelin volume fraction (MVF) and intra-axonal volume fraction (AVF) using a simple geometric model, without the need to acquire new MR contrasts. The aggregate g-ratio of a voxel represents a weighted average of the g-ratio of each axon where larger axons will have a greater weight. In this article, we will refer to the “aggregate g-ratio” simply as the “g-ratio”. MRI-based g-ratio mapping methods and applications are reviewed in Campbell et al. (2018) and Mohammadi and Callaghan (2021).

The g-ratio of specific white matter tracts can be estimated using a tractometry pipeline (Bells et al., 2011) where the g-ratio map is projected onto the corresponding streamlines reconstructed from diffusion-weighted MRI using tractography. The mean or median g-ratio value can then be computed across a bundle of streamlines to create a g-ratio tract profile (Yeatman et al., 2012). The mean or median g-ratio can also be computed along the length of the bundle of streamlines representing a white matter tract (Slater et al., 2019). The tracts can be defined using regions of interest for inclusion or exclusion of streamlines or using tract atlases (Radwan et al., 2022). Alternatively, a whole brain structural connectome can be reconstructed where each edge or tract corresponds to the bundle of streamlines connecting two nodes of a cortical and deep gray matter parcellation (Kamagata et al., 2019). However, the true anatomical specificity of tractometry is limited due to the complex wiring geometry of the brain. It is estimated that 60-90% of white matter voxels contain multiple fiber populations at typical diffusion imaging resolutions (Jeurissen et al., 2013), where each fiber may have a different g-ratio. This partial volume effect introduces a bias that is compounded as the g-ratio is averaged along a white matter tract, reducing the specificity of the tract g-ratio measurement and potentially obscuring subtle differences between tracts or individuals.

Despite these limitations, tractometry remains a powerful tool for studying the g-ratio of white matter tracts and networks. Slater et al. (2019) show that g-ratio measurements of white matter tracts in 801 participants aged 7–84 years conformed most closely to a quadratic aging model, with the lowest g-ratios around the third decade of life followed by an increase, indicating thinner myelin sheaths with advancing age. Multiple groups (Berman et al., 2019; Clark et al., 2022; Mancini et al., 2021) also leveraged g-ratio and axon diameter data to estimate conduction velocity and delays. Additionally, tractometry has been used to detect significant increases in brain networks g-ratios of multiple sclerosis patients, particularly in tracts within the motor, the somatosensory, the visual, and the limbic regions (Kamagata et al., 2019).

To minimize partial volume effects and improve the anatomical specificity tract g-ratio measurements, we use the Convex Optimization Modeling for Microstructure Informed Tractography (COMMIT) framework (Daducci et al., 2014). The original COMMIT implementation estimates the effective intra-axonal cross-sectional area of the biological fibers represented by each streamline in a tractogram, using multi-shell diffusion data. It assumes that the microstructural property, in this case the intra-axonal cross-sectional area, is constant along each streamline and uses whole-brain data for signal fitting. The COMMIT framework can be adapted to other MRI modalities, provided that the signal contributions from the different tracts to a voxel are additive. For instance, COMMIT was used to estimate the myelin volume of white matter tracts from a tractogram and a myelin volume fraction map acquired separately (Schiavi et al., 2022). The COMMIT framework has also been applied to multi-contrast encoding protocols to estimate other tract-specific MR parameters: tract-specific intra-axonal T2 times (Barakovic et al., 2021) and tract-specific magnetization transfer ratio (Leppert et al., 2023).

In this study, we use the COMMIT framework to calculate tract-specific g-ratio. By combining the tract intra-axonal volumes and myelin volumes estimated using COMMIT, tract-specific aggregate g-ratio can be computed. We map the tract-specific g-ratio in 10 healthy participants and compare its spatial distribution, scan-rescan repeatability, and inter-subject variability to state-of-the-art g-ratio tractometry.

This study was approved by the Research Ethics Board of McGill University Health Centre, Canada, and all participants provided written informed consent. Ten participants (six males and four females, 29.2± 6.29 years old) were recruited, all of whom reported no prior history of neurological or psychiatric disorders. Imaging was performed on a Siemens Prisma-Fit 3 Tesla scanner using a 32-channel head coil at the McConnell Brain Imaging Centre of the Montreal Neurological Institute. All 10 participants were rescanned within a 3-week interval.

The MRI acquisition parameters are detailed in Table 1. A 1-mm isotropic T1-weighted anatomical image was acquired using MPRAGE for registration to an atlas, brain tissue segmentation, deep gray matter structure segmentation, and cortical surface extraction. 2.6-mm isotropic diffusion weighted imaging (DWI) data were acquired using a multi-shell 2D diffusion-weighted spin echo EPI sequence for whole-brain tractography and intra-cellular volume fraction mapping. Magnetization transfer saturation (MTsat) maps were computed from an MT-weighted gradient echo (GRE) image, the T1 relaxation time and S0 equilibrium signal maps derived from the MP2RAGE sequence (Marques et al., 2010), and a B1⁺ map using a preconditioning pulse (Chung et al., 2010), as previously described (Rowley et al., 2024). All sequences used the Siemens Prescan Normalize option to generate maps with minimal receive B1^- field bias. A gain factor of 2.5 was applied to the S0 maps from the MP2RAGE protocols to match the receiver gain of the MT-weighted GRE image prior to computing MTsat.

The multi-modal MRI pre-processing pipeline micapipe (v0.1.5) (Cruces et al., 2022) was adapted to preprocess the anatomical and the diffusion data and is described in more detail below.

The T1-weighted MPRAGE image was corrected for intensity nonuniformity, intensity normalized, skull stripped, and cortically segmented using Freesurfer (v6.0) (Dale et al., 1999; Fischl, Sereno, & Dale, 1999; Fischl, Sereno, Tootell, et al., 1999). The subcortical segmentations were performed with FSL (v6.0.3) FIRST (Patenaude et al., 2011), and the tissue types were classified using FSL FAST (Y. Zhang et al., 2001). A five-tissue-type image segmentation was generated for anatomically constrained tractography (R. E. Smith et al., 2012).

Diffusion preprocessing was performed in native DWI space using MRtrix3 (v3.0.3) (Tournier et al., 2019) and proceeded in the following sequence: (1) image denoising (Cordero-Grande et al., 2019; Veraart, Fieremans, et al., 2016; Veraart, Novikov, et al., 2016), (2) Gibbs ringing correction (Lee et al., 2021), (3) four b = 0 s/mm² volumes with reverse-phase encoding were used to correct for susceptibility distortion, head motion, and eddy currents via FSL’s eddy and TOPUP tools (Andersson et al., 2003; Andersson & Sotiropoulos, 2016; Skare & Bammer, 2010; S. M. Smith et al., 2004), and (4) B1 bias-field correction (Tustison et al., 2010). Spatial variations in signal, if uncorrected, will bias the results across the whole brain. The preprocessed DWI was upsampled to 1-mm to match the resolution of the T1-weighted image. The upsampled preprocessed data were used to estimate multi-shell and multi-tissue response functions for constrained spherical deconvolution (Jeurissen et al., 2014; Tournier et al., 2004) followed by intensity normalization (Dhollander et al., 2021; Raffelt et al., 2017). The T1-weighted anatomical images were nonlinearly registered to DWI space using ANTs (Avants et al., 2008).

Anatomically constrained tractography was performed on the normalized white matter fiber orientation distributions (FOD) image using the probabilistic algorithm iFOD2 (R. E. Smith et al., 2012; Tournier et al., 2010). A tractogram of 3 million streamlines was generated using the following parameters: min/max length = 10/400, max angle = 22.5, step = 0.5, cutoff = 0.06, backtrack, crop_at_gmwmi (gray-matter-white-matter interface).

The MP2RAGE-based S0 and T1 maps were fit using a dictionary matching approach that incorporates the B1⁺ map (https://github.com/JosePMarques/MP2RAGE-related-scripts) to extract ΔB1⁺ corrected S0 and T1 maps (Marques & Gruetter, 2013). The MP2RAGE denoised UNI image was registered to the T1-weighted MPRAGE image using ANTS and an affine linear transformation (Avants et al., 2008), and the resulting transformation was subsequently applied to the S0 and T1 maps. Similarly, the MT-weighted GRE was also linearly registered to the MPRAGE space. The MTsat maps were then computed using (Helms et al., 2008):

where α is the excitation flip angle in the MT-weighted image, S_MTw is the MT-weighted signal, and TR is the repetition time of the MT-weighted sequence. A model-based correction was used to correct for ΔB1⁺ (Rowley et al., 2021).

The preprocessed diffusion data at its native resolution were analyzed using the NODDI model (H. Zhang et al., 2012) in the AMICO framework (Daducci et al., 2015) to map the intra-cellular volume fraction (ICVF) and isotropic volume fraction (ISOVF). These maps were subsequently upscaled to a 1-mm resolution to align with the resolution of the T1-weighted image.

To our knowledge, there are currently no histological measurements of the g-ratio in the human splenium. We adopted a g-ratio value of 0.7 for the splenium to align with the calibration approach used in previous MRI-based g-ratio mapping studies (Cercignani et al., 2017; Mancini et al., 2018; Mohammadi et al., 2015; Slater et al., 2019). While this calibration promotes consistency across studies, it underscores the need for more advanced calibration techniques and human histological data to enhance the accuracy of in vivo MRI-based g-ratio estimates. It is important to note that this value serves as a reference point, with the g-ratio being a monotonically increasing function. Thus, while absolute values might vary, the relative differences between regions are expected to remain consistent. Based on the assumption of a group-average g-ratio of 0.7 in the splenium, the MVF of the splenium was estimated using equations 2-3 (Mohammadi et al., 2015; Stikov et al., 2015):

The ROI for the splenium is based on ROI 8 in Fig. 4 of Mohammadi et al. (2015) and was manually delineated in the MNI152 template to include only the central region of the splenium of the corpus callosum, where the g-ratio is notably high. The ROI was then non-linearly transformed into each subject’s DWI space. Within each subject space, voxels with a fractional anisotropy (FA)—which measures the degree of water diffusion in its primary direction—greater than 0.8 were selected for calibration. For each selected voxel, a calibration factor was calculated. The calibration factor was averaged across voxels and participants to determine the global calibration factor, $αcalib$⁠, which was used to derive the MVF:

After calibration, the g-ratio is computed across the whole brain using the MVF and ICVF maps and equations 2 and 3.

The pipelines for tractometry and tract-specific g-ratio mapping are summarized in Figure 1. The tractogram generated from MRTrix3 undergoes a series of processing steps to derive tract-specific g-ratio estimates. First, the tractogram is filtered using COMMIT (v2.1, StickZeppelinBall model, parallel diffusivity of the stick and zeppelin $D∥$ = 1.7E-3 mm²/s, perpendicular diffusivity of the zeppelin $D⊥$ = 0.51E-3 mm²/s, isotropic diffusivity to account for partial voluming with gray matter and cerebrospinal fluids $Diso$ = 1.7E-3, 3.0E-3 mm²/s) to remove implausible streamlines and to generate a volumetric map of tract ICVF.

Assuming a splenium g-ratio of 0.7, the ICVF map generated by COMMIT is used to calibrate the MTsat map to obtain an MVF map. The MVF map and the filtered streamlines were processed through COMMIT (Schiavi et al., 2022) to obtain the myelin cross-sectional area for each streamline, which was then multiplied by the streamline length to calculate the myelin volume (MV). The streamlines with a weight of 0 were removed, as they correspond to tracts deemed implausible by COMMIT.

It is important to note that myelin does not contribute to the diffusion signal due to its very fast T2 decay (Campbell et al., 2018). Consequently, the intra-axonal volume fraction derived solely from DWI will be overestimated, as the myelin contribution is neglected (Stikov et al., 2015). This biased value cannot be directly used to calculate the g-ratio. To address this, the diffusion signal was adjusted to incorporate the myelin signal contribution at the voxel level, enabling the calculation of a more accurate intra-axonal volume fraction, which we refer to as the true intra-axonal volume fraction. Specifically, the diffusion signal $S(q)$ was scaled by a factor of (1−MVF) and normalized by $S(q=0)$ (i.e., the b0 images) at the native DWI resolution. Consequently, the “doNormalizeSignal” option within COMMIT was set to “False”. The scaled diffusion images were upsampled to match the resolution of the T1-weighted image and input into COMMIT to compute each streamline’s true intra-axonal cross-sectional area, calculated as the sum of each streamline’s $Fi$ restricted diffusion (or intra-cellular) compartment signal contribution $fiR$ across all the voxels it traverses using the equation below

where $fiH$ accounts for the hindered diffusion compartment signal contribution in the direction of $Fi$⁠. Additionally, the $R(i)R$ refers to the rotated version of the streamline’s response function, scaled by its length within the voxel. A similar scaling applies to the $R(i)H$ response function. Finally, the isotropic contribution is described by the signal profile $RI(q)$⁠, with $fI$ representing the corresponding volume fraction. The true intra-axonal cross-sectional area is then multiplied by the streamline’s length to obtain the true intra-axonal volume (AV).

MV- and AV- weighted connectivity matrices are generated from the filtered streamlines by summing their MV and AV weights. This process is performed using two cortical parcellation resolutions, Schaefer-200 and Schaefer-400 (Schaefer et al., 2017), combined with seven bilateral subcortical regions, including the amygdala, thalamus, caudate, nucleus accumbens, putamen, hippocampus, and pallidum (totaling 214 and 414 nodes, respectively). Lastly, the tract-specific g-ratio connectivity matrix is calculated from the MV- and AV-connectivity matrices using equation 3.

For tractometry, we used the same filtered tractogram as for the tract-specific pipeline, allowing for an equitable comparison between the two techniques. The g-ratio of each streamline was determined by calculating the median g-ratio value sampled along the streamline’s length from the volumetric g-ratio map, as the median is more robust against outliers (Boshkovski et al., 2021). Subsequently, each edge in the connectivity matrix was computed as the mean g-ratio across all the streamlines connecting the respective node pair.

We filtered the edges of the tract-specific connectivity matrix to improve data quality and consistency. First, we removed edges corresponding to the bottom 80% of tract total calibers, calculated as the sum of their true intra-axonal and myelin cross-sectional areas, across the dataset. This step was performed to make the density of the tract-specific connectivity matrix comparable to the values reported by Luppi & Stamatakis (Luppi & Stamatakis, 2021), who used the HCP-1021 template (Van Essen et al., 2013). This process also removed small-caliber tracts with low scan-rescan repeatability. Second, we applied a 50% consensus filter across individuals, retaining only those edges present in at least half of the participants.

We conducted scan-rescan repeatability assessments of the tract-specific g-ratio technique and performed a comparative analysis with tractometry. We also explored the relationship between tract length, caliber, and g-ratio for both techniques.

In the absence of bundle-specific histology, regions containing a single, coherent fiber population can serve as a practical proxy for validating tract-specific g-ratio estimates. To this end, we focused on three subdivisions of the corpus callosum (CC)—the genu, midbody, and splenium—defined using the JHU ICBM labels provided by PreQual (Cai et al., 2021), where the underlying white matter architecture can be modeled as a single fiber bundle. These regions allow voxel-wise g-ratio estimates to act as a stand-in for ground truth when evaluating the accuracy of tractometry and tract-specific methods. To further increase anatomical specificity and ensure that only single-fiber voxels were included, each ROI was eroded and transformed into the subject’s native diffusion space. We further restricted the analysis to voxels with FA greater than 0.7, selecting only highly coherent, single-orientation fiber populations.

Importantly, while the CC ROIs consist of single-fiber voxels, the streamlines traversing these voxels continue into voxels containing multiple crossing fibers. This design allows us to compare the effect of crossing fibers on the g-ratio of our CC-based tracts, facilitating a comparison between the volumetric ground truth and the g-ratio estimates from tractometry and tract-specific methods.

The scan-rescan repeatability results of the connectivity matrix g-ratio estimates derived from the Schaefer-200 parcellation are displayed in Figure 2. While there is a concentration of points along the line of perfect fit, indicating some agreement, the unfiltered results demonstrate overall poor repeatability as evidenced by the low intra-class correlation (ICC) of 0.199 and wide limits of agreement in the Bland-Altman plot. The tracts with low repeatability correspond to those of smaller caliber (shown in Fig. S1). We removed the bottom 80% of tracts based on their caliber which led to an increase in ICC to 0.737, demonstrating that g-ratio estimates of larger caliber tracts are more repeatable. Additionally, this process reduces the connectivity matrix density from 48.24% to 9.91%. Implementing a 50% consensus filter across participants further increases repeatability (ICC = 0.746) and decreases matrix density decreasing to 8.16%. This final density is similar to the 7.40% density of the HCP-1021 template. Similar trends were observed when examining the Schaefer-400 parcellation, as shown in Figure S2, with increased reproducibility following the percentile and consensus filters.

Figure 3 compares the scan-rescan repeatability of tractometry and tract-specific g-ratio results. Tractometry demonstrates a higher ICC than tract-specific g-ratio (ICC = 0.931 and 0.746, respectively) and displays narrower limits of agreement in the Bland-Altman plot. This outcome is anticipated due to the blurring caused by partial volume effects, which increases repeatability across scans.

While the overall topology of the g-ratio-weighted connectome is similar between the two techniques, there are also several differences. The most notable difference is that tract-specific g-ratio estimates are lower, corresponding to thicker myelin sheaths, compared to tractometry (Fig. 4). When calibrating the MVF map using the ICVF maps from NODDI (tractometry) and COMMIT (tract-specific), the calibration factors $αcalib$ differed slightly: 19.28 and 20.00, respectively. This difference in splenium ICVF and thus $αcalib$ is due to the whole-brain optimization used in COMMIT, which assumes the ICVF is constant along a streamline, in contrast to the voxel-based fitting perform by NODDI. Furthermore, the g-ratio histogram is broader for tract-specific estimates compared to tractometry, indicating a greater contrast due to removing partial volume effects. Further analysis examined the voxel-wise percentage difference between the g-ratio map derived from NODDI and the tract-specific volumetric g-ratio map computed using the AVF and MVF maps from COMMIT (Fig. S3). While the percentage difference in voxels along major white matter pathways is low (0-5 %), it increases in areas with partial voluming with the cortex and subcortical regions.

The data were z-scored (mean and standard deviation computed across all edges and all subjects) to compare the topology of the two g-ratio-weighted connectomes. Each node was also associated with one of seven functional resting-state networks from the Schaefer atlas (Schaefer et al., 2017), with all subcortical nodes grouped together to form a unified subcortical network. The connections between the visual and salience/ventral attention nodes have the lowest g-ratio for tractometry, while the connections within the subcortical network are the highest (Fig. 5). These trends differ from the tract-specific results, where the visual to limbic connections have the lowest network g-ratio, and the highest is observed in the subcortical-somatomotor network connections. Note that the absence of edges connecting the visual and somatomotor nodes does not imply a lack of connections between these two networks; rather, they were filtered out due to low tract caliber and consensus filtering.

The average g-ratio of white matter tracts connected to each cortical node was computed and projected onto the cortical surface to visualize the distribution of g-ratios across different cortical regions (Fig. 5). The surface projections reveal different spatial patterns, with higher g-ratios (indicative of thinner myelin sheaths) in tracts connected to the visual cortex and lower g-ratios in those connected to the parietal regions in tractometry compared to tract-specific. However, both techniques also show similar patterns: high g-ratio values in the motor regions and moderate g-ratio values in the frontal pole.

The voxel-based g-ratio estimates in the CC—where the white matter is dominated by a single fiber bundle—are compared to their tractometry and tract-specific equivalents in Figure 6. The associated streamlines extend beyond these regions into voxels containing crossing fibers. As a result, this allows us to compare how crossing fibers outside the ROIs affects the g-ratio estimates derived from tractometry and tract-specific approaches. The three methods demonstrated a similar pattern of g-ratio variation across the three ROIs. Notably, the median g-ratio values across subjects obtained using the tract-specific approach were closer to the volumetric g-ratio than those derived from tractometry. These results further support the enhanced accuracy of tract-specific g-ratio mapping in comparison to tractometry due to the enhanced anatomical specificity of the approach.

Figure 7 provides whole-brain views of a participant’s tractogram. The z-scored g-ratio maps (top two rows) reveal that both methods consistently highlight high g-ratio values in tracts connecting to motor regions (red arrows) compared to other cortical areas. The corpus callosum (green arrows) demonstrates similar trends across the methods, with the splenium showing slightly higher g-ratio values in the tract-specific approach compared to tractometry. Notable differences appear in connections to the visual regions (yellow arrows), frontal cortex (blue arrows), and temporal regions (purple arrows), where tractometry exhibits higher g-ratio values. The bottom two rows display the same g-ratio-weighted tractograms without z-scoring, showcasing a broader distribution of g-ratio values in the tract-specific method, particularly within the corpus callosum and at major white matter fiber crossings. Additional tractograms from other participants can be found in Figures S5–S6 of the Supplementary Material.

The coefficients of variation (CoVa) of the tract g-ratio estimates across subjects for both techniques are shown in Figure 8. For all subsequent analyses, the edge values were averaged across scan and rescan for each subject. For both techniques, the intra-hemisphere variation is similar to the inter-hemisphere variation. At the resolution of edges, the CoVa for tractometry was lower than for tract-specific g-ratio measurements (Fig. 8A), suggesting that tract-specific g-ratio is more sensitive to inter-individual differences. Regarding network connections, LIMB-LIMB and SUB-SUB edges exhibit the highest CoVa for tractometry, while VIS-SVAN has the lowest CoVa. Conversely, for tract-specific g-ratio, LIMB-LIMB displays the highest coefficient of variation, while the edges connecting the SMN-LIMB have the lowest CoVa (Fig. 8B). The CoVa at the resolution of nodes (i.e., all edges connected to a cortical node across subjects) is higher for the tract-specific results. Tractometry shows a higher CoVa in the occipital lobe compared to the rest of the brain, whereas the tract-specific analysis reveals higher CoVa in the frontal nodes.

Given that several prior MRI-based g-ratio mapping studies have employed tractometry, it is crucial to evaluate whether significant discrepancies exist. In Figure 9, the correlation between tractometry and tract-specific results is depicted.

Inter-hemisphere edges show a higher correlation (0.553) between tractometry and tract-specific g-ratio measurements compared to intra-hemisphere edges (0.360). While most edges demonstrate a positive correlation between the two methods, a few edges have correlations that are close to zero or even negative. Edges connecting the SUB-VIS canonical networks have the lowest correlation but remain positive, while edges connecting LIMB-LIMB and SVAN-LIMB have the highest correlation between the two techniques. The projection onto the cortical surface of the correlation of all edges connected to a node is displayed in Figure 9C. Nodes at the occipital pole, isthmus cingulate cortex, and inferior frontal cortex exhibit lower correlations between the techniques, while those in the temporal and middle and superior frontal lobes show higher correlations.

The aggregate g-ratio is an intensive characteristic of a white matter tract, presumed to be uniform across the tract cross-sectional area and length. We explore the relationship between g-ratio and extensive tract attributes, length and caliber, across tracts in the brain. Since tract caliber is influenced by node size, it has been scaled by the inverse of the sum of the two node volumes. We used a mixed linear effects model to investigate the fixed effects for caliber and length, as well as random effects for subject ID and for length grouped by subject ID:

Figure 10 depicts the relationship of the g-ratio with tract caliber (above) and tract length (below), for both tractometry and tract-specific methods. For both tractometry and tract-specific g-ratio, the effects of caliber and length were statistically significant (p < 0.001). However, the model fit was better for tractometry (adjusted R² = 0.523) in comparison to the tract-specific (adjusted R² = 0.186).

In the tract-specific analysis, the model predicts a negative $β1 (−7.46×10−3)$⁠, suggesting that larger caliber tracts tend to have lower g-ratios, that is, thicker myelin sheaths relative to axon diameter. Conversely, tractometry reveals the opposite trend, with a positive $β1 (2.63×10−3)$⁠, indicating that g-ratios increase as tract caliber increases.

When examining the relationship between g-ratio and tract length, both methods again show opposing patterns. For tract-specific g-ratio, the model predicts a positive $β2 (4.04×10−4)$ where g-ratio increases as tract length increases. In contrast, tractometry predicts a negative $β2 (−1.79×10−4)$ where the g-ratio decreases as a function of length. These findings highlight fundamental differences in how each method captures the relationship between g-ratio and the structural characteristics of the tracts.

Tractometry, the current state-of-the-art, has limited anatomical specificity (Schiavi et al., 2022). It samples each voxel traversed by a streamline, then takes the mean or median to estimate the streamline’s g-ratio. Most of the traversed voxels contain multiple fiber populations, each with specific microstructural properties, which leads to partial volume effects that are compounded along the length of the streamline. This introduces a bias and reduces the anatomical specificity of tract g-ratio estimates obtained from tractometry. To address this issue, this study expands on the COMMIT framework, previously used to derive tract-specific intra-axonal and myelin volumes, to estimate the tract-specific aggregate g-ratio. Since the g-ratio is not additive, the COMMIT framework cannot be applied directly to the g-ratio map. Instead, the g-ratio is computed at the bundle level using MV and AV estimates derived from MTsat and DWI data, respectively using COMMIT. This approach effectively mitigates the partial volume effects caused by crossing fibers. An alternative method involves generating a voxel-wise AV fraction map from the NODDI ICVF map and calculating the tract AV using the COMMIT bundle approach (Schiavi et al., 2022) has been discussed in the Supplementary Material.

The tract-specific g-ratio estimates are highly repeatable across scanning sessions in larger tracts, as evidenced by an ICC of 0.737 at the Schaefer-200 resolution. However, when looking at all tracts, the ICC decreases considerably to 0.198, indicating that the g-ratio estimates of small caliber tracts are less repeatable. The estimates for true intra-axonal cross-sectional area and myelin cross-sectional area in smaller tracts are particularly prone to noise-related errors. Although these estimates demonstrate high ICC values of 0.856 and 0.838, respectively, the noise amplifies variance in the g-ratio calculation, making it less reliable. Applying a 50% edge consensus filter across participants increases the confidence of the remaining tracts and further increases the ICC to 0.746.

The tract-specific g-ratio pipeline can be applied to higher parcellation resolutions (i.e., resulting in smaller caliber tracts), albeit with slightly reduced ICC values (e.g., 0.637 for the filtered Schaefer-400 results), or coarser parcellations, such as the Desikan-Killiany or Schaefer-100 atlases, to improve repeatability.

Using a more accurate tractogram may improve the repeatability of the techniques, especially for smaller tracts. The first iteration of COMMIT filters the streamlines that do not fit the model to the DWI data to remove false positive streamlines. However, the technique is unable to eliminate all false positives and cannot correct for false negatives, and its effectiveness relies on the quality of the input tractogram (Schiavi et al., 2020).

Theoretically, both methods would yield equivalent results in the absence of crossing fibers. However, at a typical DWI resolution of 2 mm isotropic, approximately 90% of voxels contain crossing fibers (Jeurissen et al., 2013). As a result, isolating a tract connecting two gray matter regions that does not cross another fiber along its trajectory is effectively not possible.

Tract-specific and tractometry aggregate g-ratio estimates align closely with previous neuroimaging literature examining whole-brain voxel-wise aggregate g-ratio estimates (Mohammadi et al., 2015), typically ranging from 0.5 to 0.8. Our tract-specific g-ratio estimates tend to be lower, indicating thicker myelin sheaths relative to axon diameter, than those observed in tractometry, accompanied by a much broader distribution of g-ratio values. This discrepancy partially arises from differences in how COMMIT and NODDI handle partial voluming with gray matter. Additionally, the resolution mismatch between DWI (2.6 mm) and MTsat (1 mm) images—MTsat typically offering higher resolution than DWI—may introduce interpolation artifacts in voxels near the cortex and subcortical gray matter. These factors influence the voxel’s ICVF and, consequently, the g-ratio calculation.

In the absence of histological ground truth, we compared the tract-derived g-ratio values to those from the volumetric map to validate our technique. Since we can model each region of the corpus callosum (genu, body, and splenium) as a single fiber population, the volumetric g-ratio mapping of those ROIs is used as a reference for evaluating tract-based methods. Our analysis showed that the tract-specific g-ratio aligned with the volumetric estimates, while tractometry exhibited greater deviations. This finding highlights a key advantage of the tract-specific approach: by computing tract-specific metrics rather than averaging across all voxels the tract crosses, tract-specific g-ratio retains more anatomically specific microstructural information and is less influenced by signal contributions from crossing fibers. However, validation using histology would further increase confidence in these methods.

Furthermore, the coefficient of variation across subjects for tract-specific g-ratio is much higher than that of tractometry. This difference is likely partially due to the partial volume effect observed along the length of the tracts in tractometry, which also contributes to an increased scan-rescan repeatability compared to the tract-specific technique. The coefficients of variation in g-ratio tractometry are mostly below 0.3, in line with previous g-ratio research (Cercignani et al., 2017; Mohammadi et al., 2015). However, for tract-specific g-ratio, the variability between participants tends to be much more pronounced, a trend seen in previous tract-specific microstructure mapping studies (Leppert et al., 2023; Nelson et al., 2023). The increased dynamic range observed in tract-specific results has also been observed in prior studies that address partial voluming (De Santis et al., 2016; Leppert et al., 2021, 2023; Schiavi et al., 2022). Prior MRI-based g-ratio mapping studies employed tractometry (Cercignani et al., 2017; Mancini et al., 2018; Slater et al., 2019) and reported a high degree of variability across individuals of similar age within the same tract, suggesting that the inter-subject variability seen in tract-specific g-ratio is an inherent characteristic of the data. To investigate the relationship between tractometry and tract-specific results, we conducted a correlation analysis to assess the level of agreement between the two techniques. Most edges in the Schaefer-200 parcellation exhibit a positive correlation, indicating that both methods generally agree on whether a subject’s g-ratio is higher or lower relative to others. However, some correlations approach zero or become negative, suggesting that certain tracts may intersect or cross other tracts, causing individual tract characteristics to be biased by partial volume effects. When examining inter- and intra-hemisphere results, the correlation between tractometry and tract-specific g-ratio values is positive (0.36 for intra-hemisphere and 0.55 for inter-hemisphere), further demonstrating overall agreement between the two approaches.

When we explored the relationship of tract g-ratio with tract length and caliber, we found contrasting patterns between the two techniques. Tractometry shows a positive effect of tract caliber on g-ratio estimates and a negative effect of length. In contrast, tract-specific analysis reveals the opposite polarity: a negative effect of tract caliber on the g-ratio and a positive effect of tract length. This suggests that while the agreement between tractometry and tract-specific analysis holds at the broader, cross-subject level, when we delve deeper into specific tract attributes, the differences between the two techniques become more pronounced. Tractometry shows a relatively constant g-ratio as tract length increases, while tract-specific g-ratio values rise with increasing tract length. Interestingly, even though the mixed-effects linear model for both techniques shows opposite trends with length, both techniques agree that as tract length increases, the adjusted g-ratio approaches 0.6 to 0.7—values considered optimal for signal conduction (Smith & Koles, 1970). These findings suggest that the relationship between tract g-ratio and length may be more nuanced than previously modeled. The tractometry results show that the g-ratio varies slightly across tracts of varying lengths, yet the tract-specific method reveals a different pattern. These findings could have important implications for computational models of the spatio-temporal dynamics of neuronal activity in brain network that include conduction delays estimated from tract length and microstructural properties (Drakesmith et al., 2019). Future work should investigate whether these observed trends hold across different datasets and populations. Additionally, the impact of image resolution on these findings warrants further investigation, as the lower resolution of conventional diffusion MRI data may introduce partial volume effects—especially of smaller tracts—which could bias the whole-brain fitting of the COMMIT framework. Replication across various resolutions will be essential to confirm the robustness of these trends.The volumetric percentage difference map between the two techniques reveals 0-5% absolute differences in g-ratio of major white matter pathways, indicating a good agreement for longer tracts. However, larger differences are found near the cortex and in subcortical regions, suggesting that these areas contribute to the overall shift in g-ratio distribution. Taken together, these observations imply that part of the difference between the two techniques stems from tracts traversing voxels with gray matter partial volume for a significant portion of their length, such as tracts neighboring deep gray matter structures or shorter fibers, including U-fibers.

The tract-specific aggregate g-ratio mapping technique was developed to improve anatomical specificity in comparison to conventional tractometry. There is unfortunately no ground truth from large-scale histological studies to validate our findings. We, therefore, compared the tract-specific results to voxels that contain a single fiber as a form of validation.

Our tract-specific g-ratio mapping method uses the COMMIT framework to first disentangle the axonal and myelin volumes of crossing tracts in the brain. We are thus limited by the assumption that the microstructural properties of these tracts are constant along their length. This assumption may not always hold true, particularly in pathology such as focal white matter lesions. Ongoing work is focused on adapting the framework to account for these lesions and integrate them into the analysis (Bosticardo et al., 2023). Additionally, similar to the voxel-wise aggregate g-ratio, the tract’s aggregate g-ratio is a weighted average of the g-ratios of individual axons, where larger axons contribute more weight.

The coarse spatial resolution of the DWI dataset (2.6 mm isotropic) limited the reliable reconstruction of the smaller caliber tracts. To reduce noise, we applied an aggressive tract filtering strategy that specifically excluded these smaller tracts, as they tended to be the most poorly reproducible connections—such as those linking the VIS and SMN networks. While this approach enhances the robustness of the analysis, it also underrepresents or entirely omits known pathways. In future work, we plan to investigate the impact of acquiring higher-resolution diffusion data using advanced imaging techniques such as gslider-SMS (Setsompop et al., 2018) and 3D MERMAID (Feizollah & Tardif, 2025). These acquisitions are expected to improve tractography sensitivity and reproducibility (Jones et al., 2020), potentially reducing the need for such aggressive filtering and allowing better characterization of smaller tracts in tract-specific g-ratio mapping. Continued improvements in tractography algorithms more broadly will also help address these limitations.

Furthermore, it is well known that MRI-based tractography has inherent limitations, particularly in generating false positive streamlines (Maier-Hein et al., 2017). Determining the appropriate matrix density remains a point of contention due to the lack of consensus and absence of a definitive ground truth (Schiavi et al., 2020). This point further underscores the complexity of filtering streamlines and edges to achieve both accuracy and completeness of structural networks.

Tract-specific g-ratio mapping can be carried out using widely available MRI techniques. In this study, MTsat was employed to evaluate tract myelin volume, but other myelin-sensitive methods such as myelin water imaging (Schiavi et al., 2022) or inhomogeneous magnetization transfer (Berg et al., 2022) are also effective alternatives. There are, however, two main limitations in modeling the ICVF. First, both the NODDI and the COMMIT model fix diffusivities. While these values can vary slightly between tracts (Vos et al., 2012), they also change with age (Hasan et al., 2014) or in the presence of pathology (Chung et al., 2017). Implementing the standard model (Novikov et al., 2019) into COMMIT for diffusivity estimation could help address this issue. Second, NODDI and the StickZeppelinBall model used in COMMIT output T2-weighted signal fractions for the stick compartment, but we have treated them as volume fractions (as is commonly the practice). These models do not account for compartment-specific T2 relaxation times (Papazoglou et al., 2024) which can bias g-ratio estimates (Gong et al., 2020). This limitation becomes more pronounced in pathological conditions, where T2 times can significantly differ from those in healthy white matter (Udaka et al., 2002). To accurately measure compartment volume fractions, a diffusion-relaxometry acquisition with multiple echo times is needed (Barakovic et al., 2021).

Tract-specific g-ratio mapping could contribute to a better understanding of brain network microstructure during neurodevelopment, aging, and in disease. Using g-ratio-weighted connectivity matrices, the impact of myelin g-ratio on the relationship between network structure and function can be studied, providing a more comprehensive understanding of brain network organization and dynamics. This technique holds potential to study the impact of adaptive myelination on brain network function (Knowles et al., 2022), and can provide insights into the characteristics of white matter tracts and networks in various disorders such as autism or Alzheimer’s disease.

This study presents a novel method for calculating the aggregate g-ratio of individual white matter tracts using the COMMIT framework, aimed at improving anatomical specificity. By filtering out false positive streamlines and small-caliber edges, the approach ensures repeatable g-ratio estimates and enhances contrast between tracts and individuals compared to tractometry. Validation of this method in the corpus callosum using a volumetric map demonstrated that the tract-specific results closely matched the volumetric g-ratio measurements, reinforcing the enhanced anatomical specificity of the approach. This technique advances tract-specific analysis by reducing biases from the complex network of crossing white matter fibers. This tract-specific approach is critical to study the impact of the g-ratio on the spatio-temporal patterns of brain network function.

The full pipeline is available on Github: https://github.com/TardifLab/mwcpipe/tree/Mapping-the-aggregate-g-ratio-of-white-matter-tracts-using-multi-modal-MRI. The data supporting the findings of this study are available from the corresponding author upon request.

W.L.: writing, idea implementation, and data analysis. M.C.N.: analysis and visualization code, image acquisition, and manuscript editing. I.L.R.: image acquisition and manuscript editing. J.S.W.C.: discussion and manuscript edit. S.S.: support for COMMIT framework and manuscript editing. G.B.P.: discussion and manuscript edit. C.D.R.: sequence implementation and manuscript editing. A.D.: support for COMMIT framework and manuscript editing. C.L.T.: idea, financial support, manuscript editing, and supervision.

The authors have nothing to declare.

This work was supported by the following funding sources: Canadian Neurodevelopmental Research Training Platform (CanNRT), Natural Sciences and Engineering Research Council of Canada (NSERC), Brain Canada, Fonds de Recherche du Québec—Santé (FRQS), CFREF Healthy Brains Healthy Lives, and the Killam Trusts.

Supplementary material for this article is available with the online version here: https://doi.org/10.1162/IMAG.a.49