Experimental studies of g-ratio MRI in ex vivo mouse brain

Abstract

This study aimed to experimentally evaluate a previously proposed MRI method for mapping axonal g-ratio (ratio of axon diameters, measured to the inner and outer boundary of myelin). MRI and electron microscopy were used to study excised and fixed brains of control mice and three mouse models of abnormal white matter. The results showed that g-ratio measured with MRI correlated with histological measures of myelinated axon g-ratio, but with a bias that is likely due to the presence of non-myelinated axons. The results also pointed to cases where the MRI g-ratio model simplifies to be primarily a function of total myelin content.

Graphical abstract

1. Introduction

Myelin is a key component of healthy white matter, necessary for efficient action potential conduction along axons. Changes in myelin content and structure occur in several neurodegenerative diseases, such as Multiple Sclerosis (MS) (Lassmann, 2004) and Alzheimer’s disease (Bartzokis, 2004). Additionally, abnormal axon and myelin development cause altered connectivity that may be a key factor in neuropsychiatric disorders such as Autism Spectrum Disorder (Weinstein et al., 2011), Schizophrenia (Mighdoll et al., 2015), and Obsessive Compulsive Disorder (Menzies et al., 2008). Various MRI methods aim to report on the amount of myelin per imaging voxel (Laule et al., 2006, 2007; Alonso-Ortiz et al., 2015; West et al., 2016b), but a measure that reports on the relative myelin to axon volumes may provide a more sensitive and functionally specific evaluation of pathology. The g-ratio of myelinated axons—the ratio of axon diameters to the inner and outer boundaries of myelin—is one such measure that is thought to reflect a physiological optimization of axonal function (Chomiak and Hu, 2009; Rushton, 1951).

The only validated technique to measure the g-ratio is electron microscopy, which allows direct visualization of myelinated axons in cross section. However, this approach is slow, expensive, limited to ex vivo analysis, and not suitable for whole brain analysis. To move beyond the limitations of electron microscopy and extend g-ratio measurements into the MRI domain, Stikov et al. proposed a geometric model that relates myelin, axon, and extra-axon volume fractions (defined here as f_M, f_A, and f_E, respectively) to an aggregate g-ratio index, referred to here as g_MRI, (Stikov et al., 2011, 2015). With f_A + f_E + f_M = 1, any two volume fractions can be used to compute g_MRI, such as,

$$g_{\text{MRI}}=\frac{1}{\sqrt{1+f_{\mathrm{M}}/f_{\mathrm{A}}}}.$$ (1)

This model assumes a constant g-ratio of all axons within a voxel, but West et al. later showed that g_MRI is equal to the square-root of the axon-area weighted mean of g² values from all axons in the voxel (West et al., 2016a). To date, a few combinations of MRI methods for measuring f_M and f_A have been used for g_MRI (Berman et al., 2016; Campbell et al., 2017; Dean et al., 2016; Mancini et al., 2017; Mohammadi et al., 2015; Stikov et al., 2011, 2015) but only one study, involving a single, normal macaque brain, has compared g_MRI data to g-ratio measurements from histology (Stikov et al., 2015).

The present study aimed to fill this gap in experimental work and specifically to evaluate g_MRI as a tool for ex vivo analysis of whole mouse brain. To this end, we analyzed previously-acquired MRI and electron microscopy data from 15 mouse brains, including 3 each from 3 different knockout models that exhibit abnormal myelination. Myelin content was measured using multi-exponential T₂ (MET₂) analysis, as recently evaluated in the same mouse models (West et al., 2016b), and axon content was probed using 2-shell diffusion weighted MRI (DWI) and three different analysis methods. Combinations of these measures were used to make a series of g_MRI maps, which were then quantitatively compared to histological measures of g-ratio.

2. Methods

Most of the experimental methods, including tissue preparation, data acquisition (MRI and electron microcopy) and much of the analysis, have been previously reported in detail (Kaden et al., 2016a; Kelm et al., 2016; West et al., 2016b), and are briefly summarized below.

2.1. Tissue Preparation

The Vanderbilt University Institutional Animal Care and Use Committee approved all animal studies. The brains of 15 adult mice were perfusion-fixed (2.5% glutaraldehyde + 2% paraformaldehyde), washed of fixative, and loaded (during and following perfusion) with 1.0 mM Gd-DTPA (Magnevist; Berlex, Montville, NJ). The 15 mice included control animals (n = 6) along with two conditional knockout (CKO) models of hypomyelination and one of hypermyelination (n = 3 for each model). In the first model, the Tsc2 gene was deleted (Tsc2 Olig2-Cre CKO, conditional knockout), resulting in an extreme loss of myelinated axons (Carson et al., 2015). The second model targets Rictor (Rictor Olig2-Cre CKO), a key component of the mTORC2 complex, and also displays hypomyelination, but less severe than the Tsc2 model. Previously reported similar models (Tsc1 Emx1-Cre and Rictor Emx1-Cre) showed similar hypomyelination (Carson et al., 2012, 2013). The third model results from the deletion of Pten (Pten Olig2-Cre CKO) leading to activation of the PI3K/Akt signaling pathway and subsequent hypermyelination (Harrington et al., 2010).

2.2. MRI Acquisition

All imaging was performed on a 15.2-T 11-cm horizontal bore Bruker (Rheinstetten, Germany) BioSpec scanner, using a 35-mm diameter Bruker quadrature volume coil for transmission and reception. To provide a signal-free background and prevent tissue dehydration, brains were placed in an MR-compatible tube filled with perfluoropolyether liquid (Fomblin, Solvay Solexis, Thorofarem NJ, USA). Scans were encoded with a matrix size of 128 × 96 × 72 over a 1.92 × 1.44 × 1.08 cm³ FOV, resulting in 150 μm isotropic resolution.

For MET₂ imaging, a 3D multiple spin-echo sequence was used with non-selective excitation and refocusing pulses. Scan parameters were: repetition time (TR) = 520 ms, first echo time (TE) and echo spacing (ESP) = 5.8 ms, echo train length (ETL) = 18, receiver bandwidth = 38.5 kHz, and number of averaged excitations = 6. Total scan time was ≈ 6 hr. Diffusion weighted images were acquired using a 3D diffusion weighted fast spin echo sequence with TR/TE/ESP = 200/19.0/7.1 ms and ETL = 4 (Beaulieu et al., 1993; Kelm et al., 2016). Diffusion weighting was achieved with gradient pulse duration (δ) = 5 ms, diffusion time (Δ) = 12 ms, prescribed b-values = 3000 and 6000 s/mm², 30 directions (Jones et al., 1999), 2 averaged excitations with gradient polarity reversal to mitigate background gradient cross-terms, and five b=0 images. The total scan time was ≈ 12 hr.

2.3. MRI Data Analysis

All data analysis was performed using MATLAB (R2014a-R2017a, The Mathworks, Natick MA) or Python 2.7.6, and MET₂ analyses were performed using the freely available Multi Exponential Relaxation Analysis (MERA) toolbox (Does, 2014) for MATLAB. Prior to Fourier reconstruction, k-space data for all images were apodized using a 3D Tukey window with a 0.25 taper-to-window ratio and zero-padded 2×, resulting in 75 μm nominal isotropic resolution.

For MET₂ analysis, the T₂ spectrum was estimated voxelwise using a linear inverse approach (Whittall and MacKay, 1989) by fitting the spin echo magnitudes to the sum of 100 extended-phase-graph-defined signals (Hennig, 1988) with T₂ values logarithmically spaced between TE/2 and 500 ms, similar to previous work (Prasloski et al., 2012; West et al., 2016b). From each spectrum, the myelin water fraction (MWF) was defined as the fraction of signal components with mean-T₂ < 17 ms (West et al., 2016b).

The three DWI data analyses each provided an estimate of the fraction of DWI signal (i.e., excluding myelin signal) resulting from axonal water, called the axon water fraction (AWF). Thus, in our three compartment model, AWF = f_A/(f_A + f_E) and f_A = (1 − f_M) AWF. Method 1: the neurite orientation dispersion and density imaging (NODDI) model (Zhang et al., 2012) was implemented using the AMICO software (Daducci et al., 2015). The fixed model parameters d_iso (diffusion coefficient of the isotropically diffusing compartment) and d_||(unrestricted diffusion coefficient in the intra- and extra-axonal compartments) were set to 2 μm²/ms and 0.35 μm²/ms, respectively. (A range of d_|| were tested and this one resulted in the strongest correlations of g-ratio measurements between MRI and histology.) Then, using standard NODDI notation, AWF = v_ic (1 − v_iso), where v_ic and v_iso are volumes of intra-cellular and isotropically-diffusion water, respectively.

Method 2: the multi-compartment spherical mean (mcSMT) analysis (Kaden et al., 2016a,b) involved computing the mean of the 30 diffusion-weighted signal magnitudes (i.e., the spherical mean) for each b-value, which factored out the effects of crossing fibers and orientation dispersion. The resulting 3-element signal vector was then modeled as the sum of signals from intra- and extra-neurite water compartments, as described previously (Kaden et al., 2016a). Here, the AWF is equal to signal fraction from the intra-neurite component. Method 3: the kurtosis tensor (Jensen and Helpern, 2010) was estimated using a constrained linear least-squares approach (Tabesh et al., 2011) and then the white matter tract integrity (WMTI) model (Fieremans et al., 2011) provided an estimate of AWF as AWF = K_max/(K_max + 3), where K_max is the maximum kurtosis over all directions.

All parameter maps (MWF, and AWF from each DWI analysis method) for a given mouse were co-registered to an arbitrarily chosen reference brain using a combination of rigid affine registration followed by a non-rigid deformable demons registration (Thirion, 1998). The registered MWF maps were converted to myelin volume fraction maps using

$$f_{\mathrm{M}}=\frac{\mathit{MWF}\times {\mathrm{\Phi }}_{{\mathrm{H}}_2\mathrm{O},\text{NM}}}{\mathit{MWF}\times ({\mathrm{\Phi }}_{{\mathrm{H}}_2\mathrm{O},\text{NM}}-{\mathrm{\Phi }}_{{\mathrm{H}}_2\mathrm{O},\mathrm{M}})+{\mathrm{\Phi }}_{{\mathrm{H}}_2\mathrm{O},\mathrm{M}}},$$ (2)

where Φ_H2O,M and Φ_H2O,NM are the water proton pool volume fractions in myelin and non-myelin white matter, respectively (West et al., 2016b). The registered AWF maps were each scaled by (1 − f_M) to generate f_A maps for each DWI analysis method.

From here, Eq (1) was used to generate g_MRI maps for every different DWI analysis method. For comparison, g_MRI maps were also computed using a simplified model that did not require estimates of f_A: assuming zero extra-axonal volume fraction, Eq (1) reduces to $g_{\text{MRI}}{\mid }_{f_{\mathrm{E}}=0}=\sqrt{1-f_{\mathrm{M}}}$. Finally, from a mid-sagittal slice, four white matter ROIs—the genu (GCC), mid-body (MCC), splenium (SCC) of the corpus callosum, and anterior commissure (AC)—were manually defined, and the mean value of each g_MRI measures was tabulated for each ROI and brain.

2.4. Microscopy

After MRI acquisition, from each brain a 1–2 mm thick sagittal section of tissue was cut from the left hemisphere beginning at the inter-hemispheric boundary, and 4 sub-regions corresponding to the 4 ROIs were prepared for ultra-thin sectioning and electron microscopy. Microscopic images were collected using a Philips/FEI Tecnai T12 electron microscope (FEI Company, Hillsboro, OR). For quantification of myelinated axon microstructure, 6–12 15,000× images were acquired per ROI and animal. These images contained a total of N_A ≈ 350, 300, 250, 100 myelinated axons (per ROI and animal) for control, Rictor, Pten, Tsc2 mice, respectively.

Each image was analyzed semi-automatically, which provided segmentation of each myelinated axon and surrounding myelin, as previously described (West et al., 2016b). Measures of area (a_i) and myelin thickness (ε_i) were computed for the ith myelinated axon, i = 1 to N_A. Using a circular axon model, the g-ratio per myelinated axon was computed as $g_i=\sqrt{a_i}/({\epsilon }_i\sqrt{\pi }+\sqrt{a_i})$. For comparison to g_MRI measures, the histological measure of g-ratio was defined as the root area-weighted mean square value of per-axon g (West et al., 2016a),

$$g_{\text{HIST}}\triangleq \sqrt{\sum _{i=1}^{N_{\mathrm{A}}}{a}_i{g}_i^2/\sum _{i=1}^{N_{\mathrm{A}}}{a}_i},$$ (3)

and was computed for each ROI and brain. Because the non-myelinated axons were not segmented from this analysis, it was not possible to compute histological measures of f_A or f_E (or, consequently, AWF).

3. Results

Example raw and processed histology data are shown in Fig 1. On the top are raw images from the MCC of each of the four different types of mice, in the middle are the corresponding images after segmentation and analysis to determine per-axon measures of g-ratio, and on the bottom are histograms of g-ratio values from all the microscopy images for that brain and ROI. (Note the difference between g_HIST values, which are area-weighted, and the algebraic means.) A summary of the means and standard deviations of g_HIST values from each ROI and mouse type is shown in Fig 2. For comparison to literature, the algebraic mean g-ratio across all control mice and ROIs was 0.72 ± 0.018. This value is slightly lower than previous predictions for rat brain (0.77) (Chomiak and Hu, 2009) or experimental evaluations from mouse corpus callosa (0.76–0.81) (Arnett et al., 2001; Mason et al., 2001). These lower g-ratio values may reflect a systematic overestimation of myelin thickness resulting from the semiautomated segmentation. As expected though, the Tsc2 mice exhibited a substantial loss of myelinated axons while the Rictor and Pten mice differed from controls primarily by having thinner and thicker myelin, respectively. Compared to the control mice, g_HIST was generally greater for the Rictor and Tsc2 mice and lower for the Pten mice. Note that these histology derived measures of g-ratio did not include analysis of non-myelinated axons, which were apparent in all mice and especially abundant in the Tsc2 mice.

Figure 1.

(top) Representative electron microscopy from the MCC of four different mice, one of each type. (middle) The same images after segmentation, with each axon’s fill-color defined by its g-ratio. (bottom) Histograms of g-ratio values of all MCC axons measured from the individual mice corresponding to the histology above. For reference, the g_HIST value is shown for each histogram, and the corresponding algebraic mean g-ratios are 0.72, 0.72, 0.80, and 0.69. For ease of comparison, each histogram has been scaled to have the same peak amplitude.

Figure 2.

Mean ± standard deviation (across animals) of g_HIST from each ROI and mouse model

The MRI measures of f_M have been previously reported and evaluated in comparison to histology, (West et al., 2016b). Briefly, this study showed f_M ≈ 0.05, 0.15, 0.20, and 0.25, for Tsc2, Rictor, control, and Pten mice, respectively, and a strong and accurate linear correlation with histological measures of myelin volume (r² = 0.68). The various DWI derived measures of AWF are shown in Fig 3; however, without a gold-standard measure of AWF from histology, the accuracies of these different methods could be not be quantitatively evaluated. A qualitative evaluation of the histology indicated that across mouse types and ROIs, most of the space between the segmented myelinated axons was filled with non-myelinated axons or other cellular space (see Fig 1), which is most consistent with the relatively high AWF values resulting from mcSMT analysis, and the relatively invariant measures of AWF from both the mcSMT and WMTI analyses.

Figure 3.

Mean ± standard deviation (across animals) of AWF values from each of the three DWI analyses and each mouse model

Representative g_MRI maps of each mouse model and DWI analysis method are shown in Fig 4. (For reference, supplementary Fig S1 shows example f_M and f_A maps.) These g_MRI maps were generated for voxels with f_M values > 0.01 and fractional anisotropy > 0.25 in the control brain shown, and are overlaid on greyscale b = 0 images from the DWI acquisition. Consistent with histology results, these maps show, compared to control mice, relatively higher g-ratio values in Rictor and Tsc2 mice and lower values in the Pten mice.

Figure 4.

Representative g-ratio maps for each mouse type and DWI analysis method.

Across all brains and ROIs, Fig 5 shows scatter plots and linear correlations of each g_MRI measure with g_HIST. In all cases, the linear correlations are statistically significant (p ≪ 0.01) and adjusted R² values (shown on plots in blue) are similar across methods (≈ 0.3). For all methods, the differences in g-ratios between animal models is apparent, and it is clear that results from Tsc2 mice did not follow the same linear relationship. This is demonstrated on each plot by the best-fit line and adjusted R² value (gray) when the Tsc2 mice were not included in the regression. It is also noteworthy that all three DWI analyses and analysis using f_E = 0 provided similar quality correspondence of g_MRI and g_HIST, suggesting the the correlations were driven primarily by the measure of f_M.

Figure 5.

Scatter plots of MRI vs histological measures of g-ratio for each of the three DWI analysis protocols and analysis assuming f_E = 0. Shown in each frame is the best linear fit (blue), the best linear fit excluding Tsc2 mice (gray), and the line of unity (dash-dot).

4. Discussion

Figures 4 and 5 demonstrate potential of 3D g_MRI mapping of ex vivo mouse brains. In general, the g_MRI maps are relatively smooth and show widespread amplitude variations that are consistent with histology and known white matter characteristics of these mouse models. Likewise, the g_MRI scatter plots show a moderate linear correspondence to g_HIST. However, Fig 5 also reveals shortcomings. Across all animals and methods, g_MRI generally overestimates g_HIST, especially so for the Tsc2. Also, in terms of g_MRI serving as a correlative measure of g_HIST, the analysis based on f_M maps alone (i.e., assuming f_E = 0) worked approximately as well as any of the methods that used DWI-derived estimates of AWF.

The general overestimation of g_MRI compared to g_HIST may be due to a few factors. One possible source of this difference is the different definitions of the two measures. The analysis of histology did not include quantitation of non-myelinated axons, and so g_HIST reflects only measures of g-ratio from the myelinated axons. In contrast, to the extent that a given DWI measure of AWF includes at least some portion of non-myelinated axons, this signal will also contribute to g_MRI. In other words, g_MRI may include a weighting of g = 1 from some or all the non-myelinated axons and will then be greater than g_HIST, by definition. Another potential source of difference comes from the limitations of the DWI analysis methods. For example, the methods used here assume that extra-axonal water diffusion is Gaussian. However, with large b-values and tightly packed axons, this assumption may not be valid, which would then lead to an overestimation of axonal water fraction and, in turn, g-ratio.

These systematic inaccuracies may or may not be a problem for a particular study. For example, in comparing the control, Rictor, and Pten mice, despite the overestimation of g_MRI for myelinated axon g-ratio, the correlation between g_MRI and g_HIST for all analyses was moderately strong. However, this linear correlation broke down for the Tsc2 mice. It cannot, for example, be discerned from g_MRI that the g-ratio values of myelinated axons in the Tsc2 mice is near normal and similar to those of the Rictor mice.

In addition to the effect of non-myelinated axons on g_MRI, the data in Fig 5 also point to another systematic characteristic of g_MRI that may be important. Comparing g_MRI results across the different DWI analysis methods reveals the greatest inter-method variation for the Pten mice, the least for the Tsc2 mice, and intermediate amounts for the control and Rictor mice. This may be surprising given that the AWF estimates themselves (Fig 3) were not especially more variant for any one mouse type, but did differ substantially between methods. The explanation, again, lies in the definition of g_MRI. Consider this reformulation of Eq (1),

$$g_{\text{MRI}}=\sqrt{\frac{f_{\mathrm{A}}}{f_{\mathrm{A}}+f_{\mathrm{M}}}}=\sqrt{\frac{\mathit{AWF}(1-f_{\mathrm{M}})}{\mathit{AWF}(1-f_{\mathrm{M}})+f_{\mathrm{M}}}}.$$ (4)

From here, it is easy to appreciate that when f_M ≪ AWF, g_MRI → 1 and will be relatively insensitive to the AWF value. Hence, for the Tsc2 and Rictor mice (f_M ≈ 0.05 and 0.15, respectively), in particular, g_MRI had relatively little dependence on AWF, and for the Pten mice (f_M ≈ 0.25) the effect of AWF on g_MRI was the greatest. This characteristic, coupled with the fact that f_M varied considerably more across mouse types than did AWF (by any DWI analysis method) also explains the g_MRI results obtained using the simplified model with f_E = 0 (right panel of Fig 5). That is, for this study, the observed correlations between g_MRI and g_HIST were driven primarily by variations in f_M between mouse types. The same situation will be true for any condition that does not include substantial changes in f_E—because AWF will also be relatively invariant, there will be little benefit in measuring it.

Although general conclusions can be drawn from the mathematical nature of the g_MRI model, generalizations about the data reported here should be done with caution. All of the data used in this study came from the mid-sagittal plane, where, perhaps, the dense packing of axons results in g_MRI or g_HIST values that are systematically different than in other regions. Ideally, MRI offers the potential for 3D volumetric g-ratio imaging, but comparisons to histology at arbitrary locations will be a challenge. Also, the MRI measurements were performed on excised, chemically-fixed, and contrast-enhanced samples, which introduces a number of potential variations.

The relatively low concentration of Gd (1 mM) loaded into the brains in this study is not expected to significantly alter the DWI (D’Arceuil et al., 2007) or MET₂ data (West et al., 2016b), but this has not been rigorously tested for exactly the sample preparations and MRI studies used here. For example, as discussed previously (West et al., 2016b), while f_M from MET₂ measurements works effectively in these samples, its use for human studies may be limited by scan time/signal-to-noise ratio and possibly more affected by inter-compartmental water exchange. Use of quantitative magnetization transfer (qMT) to measure f_M, which has its own challenges with regard to calibration and specificity, may offer a more efficient alternative. For comparison, supplementary Fig S2 shows the g_MRI vs g_HIST plots for the case that f_M is derived from qMT, as previously described (West et al., 2016b). Also previously discussed (Kaden et al., 2016a), these fixed tissues exhibit relatively high residual DWI signal for gradient directions parallel to the fiber orientation, indicating the presence of slowly diffusing water that was not incorporated into any of the DWI analysis models used here. Although not shown, variations of the NODDI and mcSMT models with the addition of a stationary, or “dot”, signal component (Alexander et al., 2010), were implemented as part of this study, but they did not result in stronger correlations between g_MRI and g_HIST.

It is also important to remember that g_MRI is an axon area-weighted measure (West et al., 2016a). Therefore, during diseases targeting either large (e.g., amyotrophic lateral sclerosis (Nguyen et al., 2000)) or small axons (e.g., the cuprizone model of demyelination (Jelescu et al., 2016; Mason et al., 2001; Thiessen et al., 2013)) or changes during development where large axons are typically myelinated first (Matthews and Duncan, 1971; Remahl and Hildebrand, 1982), the observed g_MRI will more heavily reflect changes in the larger axons. In addition, the g-ratio is not constant across axon size, with larger axons generally having higher g-ratios (Berthold et al., 1983); hence, if the distribution of axons in tissue changes, a different g_MRI may be detected.

5. Conclusion

Experimental MRI and electron microscopy studies of excised and fixed mouse brains provide the most extensive comparisons to date of g_MRI to histology. The results demonstrate moderate linear correlations between g_MRI and corresponding measures of myelinated axon g-ratio from histology (g_HIST), but the presence of non-myelinated axons also causes g_MRI to be systematically greater than g_HIST. Also, the observations and consideration of the model led to the conclusion that g_MRI reduces to be well approximated by only myelin content for cases of relatively low myelin content or any case where little variation of extra-axonal volume fraction exists.