A Revised Model for Estimating g-ratio from MRI (2024)

Journal List
HHS Author Manuscripts
PMC4691384

As a library, NLM provides access to scientific literature. Inclusion in an NLM database does not imply endorsem*nt of, or agreement with, the contents by NLM or the National Institutes of Health.
Learn more: PMC Disclaimer | PMC Copyright Notice

Neuroimage. Author manuscript; available in PMC 2017 Jan 15.

Published in final edited form as:

Neuroimage. 2016 Jan 15; 125: 1155–1158.

Published online 2015 Aug 20. doi:10.1016/j.neuroimage.2015.08.017

PMCID: PMC4691384

NIHMSID: NIHMS717532

PMID: 26299793

Kathryn L. West,^a,^b Nathaniel D. Kelm,^a,^b Robert P. Carson,^c and Mark D. Does^a,^b,^d,^e

Author information Copyright and License information PMC Disclaimer

The publisher's final edited version of this article is available at Neuroimage

Associated Data

Supplementary Materials

Abstract

A key measure of white matter health is the g-ratio, which is defined as the ratio between the inner axon radius and the outer, myelinated, axon radius. Recent methods have been proposed to measure the g-ratio non-invasively using the relationship between two magnetic resonance imaging (MRI) measures. While this relationship is intuitive, it predicates on the simplifying assumption that g-ratio is constant across axons. Here, we extend the model to account for a distribution of g-ratio values within an imaging voxel, and evaluate this model with quantitative histology from normal and hypomyelinated mouse brains.

Keywords: g-ratio, myelin, magnetic resonance imaging, histology

1. INTRODUCTION

Myelin is a critical component of white matter, increasing speed of action potential conduction along axons and improving neurological function. It has been shown that there is a range of values between axon size and myelin thickness for optimal efficiency in healthy tissue (Chomiak and Hu, 2009; Rushton, 1951). The g-ratio describes the relationship between axon size and myelin thickness, and deviations in the g-ratio are thought to be involved in abnormal development and disease (Albert et al., 2007; Fields, 2008; Mason and Langaman, 2001; Paus and Toro, 2009). However, currently, the only way to assess properties of tissue microstructure such as axon diameter, myelin thickness, and g-ratio is through quantitative histology, such as electron microscopy. Such methods are time consuming, expensive, and destructive to the tissue. Magnetic resonance imaging (MRI) methods to measure these microstructural characteristics would be useful to more efficiently study white matter disease processes and treatments and, further, provide the potential for in vivo assessment.

Recently, it has been proposed that two quantitative MRI measures can be combined and interpreted with a geometric model of white matter to provide quantitative estimates of the g-ratio (Stikov et al., 2015, 2011). Specifically, Stikov and colleagues have suggested that using MRI estimates of 1) myelin volume fraction (from, for example, quantitative magnetization transfer measurements), and 2) axon or fiber volume fraction (from, for example, suitable analysis of diffusion-weighted imaging) can be used to estimate the g-ratio. These estimates were termed an “aggregate g-ratio” because the method is predicated on the assumption that the g-ratio is constant for all axons within a voxel, which is known not to be the case in both peripheral nerve (Friede and Beuche, 1985; Rushton, 1951) and central white matter (Berthold et al., 1983; Little and Heath, 1994). Here we extend their model to a more general one that makes no assumption about the distribution of g-ratio values within an imaging voxel, and we demonstrate the model in principal using quantitative evaluations of electron microscopy of the corpus callosum of control and hypomyelinated mice.

2. THEORY

Consider an ensemble of N myelinated fibers with the radius and g-ratio of the i^th fiber being R_i and g_i, respectively, and axon radius being r_i (hence, g_i = r_i/R_i, see Fig 1e). The total cross-sectional areas of fibers, axons, and myelin, are, respectively,

$A_{F} = π \sum_{i = 1}^{N} R_{i}^{2}$

$A_{A} = π \sum_{i = 1}^{N} g_{i}^{2} R_{i}^{2} = π \sum_{i = 1}^{N} r_{i}^{2} .$

[1]

$A_{M} = π \sum_{i = 1}^{N} R_{i}^{2} (1 - g_{i}^{2})$

Open in a separate window

Figure 1

Histology analysis methods. a) Demonstration of the middle corpus callosum region chosen for electron microsopy tissue preparation. b) A transmission electron microscope image is acquired from the middle region of the mouse corpus callosum. c) A threshold is applied to separate myelin and non-myelin pixels and obtain a binary myelin mask, providing a myelin volume fraction (MVF). d) A region growing algorithm is used to fill all axon areas, and the sum of all axon areas provides an axon volume fraction (AVF). Myelin thickness is measured manually in two locations per axon. e) Axon radius (r) is derived from the area of each axon, assuming circular geometry. f) The g-ratio is calculated per axon and the histogram of values is fitted to a gamma distribution, from which the following measures are computed: mean (g_mean), area-weighted mean (g_awm), and the square root of the area-weighted g² (g_awmgs). The proposed MRI measure, g_MRI, was computed from measures of MVF and AVF.

From here, the ratio of myelin to fiber areas is

$\frac{A_{M}}{A_{F}} = \frac{\sum_{i = 1}^{N} R_{i}^{2} (1 - g_{i}^{2})}{\sum_{i = 1}^{N} R_{i}^{2}} .$

[2]

In the case that g_i = g for all i = 1 to N, as assumed in the model presented by Stikov et al. (Stikov et al., 2015, 2011), this ratio reduces to

$\frac{A_{M}}{A_{F}} = 1 - g^{2} .$

[3]

Assuming one can measure myelin volume fraction (MVF) and fiber volume fraction (FVF) with MRI, the ratio A_M/A_F can be replaced with MVF/FVF, and the resulting MRI-measured g-ratio is then

$g_{M R I} \equiv \sqrt{1 - M V F / F V F},$

[4]

as previously presented (Stikov et al., 2015, 2011).

By starting with the ratio A_M/A_A, a similar relationship is found, $g_{M R I} \equiv \sqrt{1 / (1 + M V F / A V F)}$ , where AVF is the axon volume fraction as measured by MRI.

However, without the simplifying assumption that g is constant for all axons, Eq [2] can be simply reduced to

$\frac{A_{M}}{A_{F}} = \frac{\sum_{i = 1}^{N} R_{i}^{2} - \sum_{i = 1}^{N} g_{i}^{2} R_{i}^{2}}{\sum_{i = 1}^{N} R_{i}^{2}} = 1 - \frac{\sum_{i = 1}^{N} g_{i}^{2} R_{i}^{2}}{\sum_{i = 1}^{N} R_{i}^{2}} .$

[5]

Again, replacing the A_M/A_F with MVF/FVF and using Eq [4], we get

$g_{M R I}^{2} \frac{\sum_{i = 1}^{N} g_{i}^{2} R_{i}^{2}}{\sum_{i = 1}^{N} R_{i}^{2}},$

[6]

which shows that the squared value of the previously proposed MRI measure of g-ratio is equal to the area-weighted mean of g² values across the N fibers.

3. MATERIALS AND METHODS

3.1 Tissue Preparation

Animal studies were approved by the Vanderbilt University Institutional Animal Care and Use Committee. Histology was acquired from control and Rictor conditional knockout (CKO) mice, similar to a previously described mouse model of tuberous sclerosis complex (Carson et al., 2013). Six adult mice were anesthetized with isoflurane and sacrificed via transcardial perfusion of 1× phosphate-buffered saline (PBS) wash followed by 2.5% glutaraldehyde + 2% paraformaldehyde in PBS (modified Karnovsky solution). Following perfusion, brains were quickly removed from the skull and immersed in the fixative solution for 1 week. For MRI studies not presented here, the perfusion and immersion solutions included a paramagnetic MRI contrast agent and the fixative was washed out of brains prior to imaging and subsequent histology. For histologic preparation, a 1–2 mm sagittal slice of tissue was cut from the left hemisphere beginning at the mid-brain from each of 6 brains (n=4 control and n=2 CKO). Subsequently, 2 regions of white matter from the corpus callosum (genu- GCC and midbody - MidCC) were cut from each slice. Two regions were analyzed to account for potentially different axon populations between regions of the corpus callosum (Barazany et al., 2009). Tissue samples were then processed for transmission electron microscopy in the Vanderbilt Cell Imaging Shared Resource-Research Electron Microscopy facility. Thick sections (0.5 – 1 µm) were collected using a Leica Ultracut microtome (UC-7), then stained with 1% toluidine blue. Ultra-thin sections (70–80 nm) were then cut and collected on 300-mesh copper grids. Copper grids were post-section stained at room temperature with 2% uranyl acetate (aqueous) for 15 minutes and then with lead citrate for 10 minutes. Ultra-thin sections were imaged on the Philips/FEI Tecnai T12 electron microscope at 15,000× magnification. From each section, six images were acquired using a side-mounted AMT CCD camera, resulting in a total of 6 mice × 2 regions × 6 images/region/mouse = 72 images.

3.2 Data Analysis

The pipeline of histology analysis is summarized in Fig 1. Images were segmented using the histogram of pixel gray scale values, defining the threshold between myelin and non-myelin pixels at the nadir. This provided a binary image where myelin = 1 and non-myelin = 0 (Fig 1c) and an estimate of MVF. From the binary image, each myelinated axon was manually identified and its area (A_Ai, for the i^th axon) was computed using a region growing algorithm. This value provided an estimate of axon radius $r_{i} = \sqrt{A_{A i} / π}$ , and the sum of all axon areas provided an estimate of AVF. For each axon, the thickness of the surrounding myelin (Δ_i) was calculated as the average of manual measurements made in two locations, and the g-ratio was estimated as g_i = r_i/(r_i + Δ_i).

From each image, the MVF and AVF estimates were used to compute g_MRI, as shown above. Also from each image, the N (~50) measures of g were fitted to a gamma distribution as done and observed previously for axon diameter distributions (Assaf et al. 2008, Barazany et al., 2009; Olivares et al., 2001), from which three descriptive measures were calculated: arithmetic mean (g_mean), the area-weighted mean (g_awm), the square-root of the area-weighted g² (g_awmgs, following the right hand side of Eq [6]). Calculating these descriptive measures of g from the fitted gamma distribution parameters rather than directly from the samples g_i, i = 1 to N, reduced the influence of one or two large axons amongst a relatively small sampling of the population.

4. RESULTS AND DISCUSSION

Figure 1f displays a representative histogram of the g-ratios obtained from one histology image. Each characterization of the g-ratio (g_mean, g_awm, g_awmgs, and g_MRI) is displayed on the histogram. It is apparent that g_mean (~0.8) is significantly lower than the area-weighted means and g_MRI. This characteristic will be true in general for distributions of finite width, but will also depend on the skewness of the distribution. For further information on the histology results, including statistical evalutions of fitting axon diameters and g-ratios to gamma distributions, refer to our Data in Brief article, Quantitative Analysis of Mouse Corpus Callosum from Electron Microscopy Images.

Figure 2 displays comparisons of g_MRI with g_mean, g_awm, and g_awmgs, respectively, from left to right. Each point represents the measurements from one image with both MidCC and GCC measures displayed (control = black, CKO = red). The hypomyelination present in the CKO mice is apparent from the generally greater g-ratios. Qualitatively, g_MRI shows a reasonable correspondence with all three measures, but the comparisons between g_MRI and the area-weighted measures are noticeably closer to the line of identity (dashed line). Quantitatively, these differences are reflected in the root mean squared difference (RMSD), between the two measures for each plot.

Open in a separate window

Figure 2

Scatter plots of (left) g_MRI versus g_mean, (middle) g_MRI versus g_awm, and (right) g_MRI versus g_awmgs where black and red points signify control and CKO image measures, respectively. The root mean squared difference (RMSD) between each pair of measures is shown above each plot.

Similar relationships are found between g_MRI and the two area-weighted measures, g_awm and g_awmgs. While theory shows that g_MRI = g_awmgs for circular geometries, the two experimental measures will deviate for elliptical or other non-cicular axonal shapes. Nonetheless, the close correspondence of g_MRI and g_awmgs in Fig 2 indicates that this is not a substantial issue. Also, while g_awmgs will deviate most from g_awm for broad axon diameter distributions with a small mean, the difference between measures of g_awm and g_awmgs in this study is small (≤ 1.33%). Thus, these three measures are effectively the same and g_MRI can be reasonably interpreted as an axon-area-weighted measure of g, which is somewhat easier to intuit than the square root of the axon-area-weighted g².

Both area-weighted measures show a slight trend toward being underestimated by g_MRI at lower values of g, which may reflect the limitations of the histology analysis. Axons with lower g-ratios tended to be smaller in diameter and more densely packed, which may have resulted in a a tendency to overestimate local MVF due to limitations of the segmentation. This overestimation of MVF would reduce estimates of g_MRI but not affect the other characterizations of g which were derived from direct measures of myelin thickness.

The histology data are also summarized in Table 1, which displays the mean ± standard error of the mean of the four g–ratio measures across the images from each region (MidCC, GCC) for control and CKO mice. The g_mean values from control mice (~0.81) are somewhat higher than the previously predicted optimal value of 0.77 (Chommiak and Hu, 2009) but agree with some previous histological evaluations of the mouse corpus callosum (Arnett et al., 2001; Mason and Langaman, 2001). Because the measures of myelin thickness from histology depended on the the segmentation level, it is possible that a small systematic underestimation of myelin thickness has resulted in overall elevated values of g_mean, but that would not change the conclusions of this study.

Table 1

g_mean, g_awm, g_awmgs, and g_MRI mean ± SEM from the middle and genu regions of the corpus callosum across all images for control and Rictor CKO mice.

Region	g_mean	g_awm	g_awmgs	g_MRI
	Control

MidCC	0.815±0.003	0.848±0.003	0.850±0.003	0.844±0.004
GCC	0.803±0.005	0.847±0.003	0.849±0.003	0.834±0.005

	CKO

MidCC	0.845±0.006	0.873±0.007	0.875±0.007	0.870±0.010
GCC	0.854±0.006	0.880±0.009	0.883±0.009	0.889±0.008

Open in a separate window

It is apparent from Table 1 that the two area-weighted measures (g_awm, g_awmgs) are nearly identical in all cases and similar to g_MRI values. All measures show statistically significant differences (using a two-tailed student’s t-test, α=0.05) between control and CKO mice, demonstrating that for this example, g_MRI, which reports a significantly different value than g_mean, is sufficient to detect differences in microstructure between the control and CKO mice. However, we note the time course of demyeliation and remyelination may not always be well captured by a scalar value, and because of the area-weighting effect, g_MRI in particular will be less sensitive to microstructural changes in smaller axons. For example, a previous study of microstructure in the mouse corpus callosum during and following exposure to cuprizone in the diet (Mason and Langaman, 2001) observed periods with changes in myelin thickness and axon diameter that were not caputured by the mean g-ratio, and found that recovery periods involved preferential remyelination of smaller axons. Perhaps these limitations can be overcome with more sophisticated models that incorporate axon diameter distributions (such as is done with the AxCaliber method, Assaf et al. 2008, Barazany et al. 2009) and established relationships between axon diameter and g-ratio (Berthold et al., 1983; Chomiak and Hu, 2009); however, the practical limits on MRI measures of g-ratio may come from the ability to make robust estimates of MVF and FVF, which remains an area of active study.

4.2 Conclusions

As quantitative MRI methods strive to provide more detailed information about underlying tissue properties, such as the g-ratio, histologic comparisons are vital to understand microstructural meaning of derived imaging measures. We have shown here that the recently proposed approach to estimate the aggregate g-ratio index with MRI will, in principal, provide a measure that is close to the axon-area-weighted measures of g across all axons in a voxel. This measure will naturally be more sensitive to changes or differences in larger diameter axons and should be interpreted with this knowledge.

Supplementary Material

Click here to view.^{(26M, zip)}

Acknowledgments

Grant Sponsor: NIH EB001744

Abbreviations

MRI	Magnetic resonance imaging
MVF	myelin volume fraction
FVF	fiber volume fraction
CKO	conditional knockout
PBS	phosphate-buffered saline
MidCC	midbody of corpus callosum
GCC	genu of corpus callosum

Footnotes

Publisher's Disclaimer: This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final citable form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

REFERENCES

Albert M, Antel J, Brück W, Stadelmann C. Extensive cortical remyelination in patients with chronic multiple sclerosis. Brain Pathol. 2007;17:129–138. [PMC free article] [PubMed] [Google Scholar]
Assaf Y, Blumenfeld-Katzir T, Levin G, Yovel Y, Basser PJ. AxCaliber – a method to measure the axon diameter distribution and density in neuronal tissues. Magn Reson Med. 2008;59:1347–1354. [PMC free article] [PubMed] [Google Scholar]
Arnett HA, Mason J, Marino M, Suzuki K, Matsushima GK, Ting JP. TNF alpha promotes proliferation of oligodendrocyte progenitors and remyelination. Nat. Neurosci. 2001;4:1116–1122. [PubMed] [Google Scholar]
Barazany D, Basser PJ, Assaf Y. In vivo measurement of axon diameter distribution in the corpus callosum of rat brain. Brain. 2009;132:1210–1220. [PMC free article] [PubMed] [Google Scholar]
Berthold CH, Nilsson I, Rydmark M. Axon diameter and myelin sheath thickness in nerve fibres of the ventral spinal root of the seventh lumbar nerve of the adult and developing cat. J. Anat. 1983;136:483–508. [PMC free article] [PubMed] [Google Scholar]
Carson RP, Fu C, Winzenburger P, Ess KC. Deletion of Rictor in neural progenitor cells reveals contributions of mTORC2 signaling to tuberous sclerosis complex. Hum. Mol. Genet. 2013;22:140–152. [PMC free article] [PubMed] [Google Scholar]
Chomiak T, Hu B. What is the optimal value of the g-ratio for myelinated fibers in the rat CNS? A theoretical approach. PLoS One. 2009;4 [PMC free article] [PubMed] [Google Scholar]
Fields RD. White matter in learning, cognition and psychiatric disorders. Trends Neurosci. 2008;31:361–370. [PMC free article] [PubMed] [Google Scholar]
Friede R, Beuche W. Combined scatter diagrams of sheath thickness and fibre calibre in human sural nerves: changes with age and neuropathy. J. Neurol. Neurosurg. Psychiatry. 1985;48:749–756. [PMC free article] [PubMed] [Google Scholar]
Little G, Heath J. Morphometric analysis of axons myelinated during adult life in the mouse superior cervical ganglion. J. Anat. 1994;184:387–398. [PMC free article] [PubMed] [Google Scholar]
Mason J, Langaman C. Episodic demyelination and subsequent remyelination within the murine central nervous system: changes in axonal calibre. Neuropathol. Appl. Neurobiol. 2001;27:50–58. [PubMed] [Google Scholar]
Olivares R, Montiel J, Aboitiz F. Species differences and similarities in the fine structure of the mammalian corpus callosum. Brain. Behav. Evol. 2001;57:98–105. [PubMed] [Google Scholar]
Paus T, Toro R. Could Sex Differences in White Matter be Explained by g ratio? Front. Neuroanat. 2009;3:14. [PMC free article] [PubMed] [Google Scholar]
Rushton W. A theory of the effects of fibre size in medullated nerve. J. Physiol. 1951;115:101–122. [PMC free article] [PubMed] [Google Scholar]
Stikov N, et al. Quantitative analysis of the myelin g-ratio from electron microscopy images of the macaque corpus callosum. Data in Brief. 2015 http://dx.doi.org/10.1016/j.dib.2015.05.019. [PMC free article] [PubMed] [Google Scholar]
Stikov N, Perry LM, Mezer A, Rykhlevskaia E, Wandell BA, Pauly JM, Dougherty RF. Bound pool fractions complement diffusion measures to describe white matter micro and macrostructure. Neuroimage. 2011;54:1112–1121. [PMC free article] [PubMed] [Google Scholar]

FAQs

A Revised Model for Estimating g-ratio from MRI? ›

For each axon, the thickness of the surrounding myelin (Δ_i) was calculated as the average of manual measurements made in two locations, and the g-ratio was estimated as g_i = r_i/(r_i + Δ_i).

What is the G-ratio in MRI? ›

The g-ratio is a geometrical invariant of axons quantifying their degree of myelination relative to their cross-sectional size. It is computed as the ratio of the inner axonal diameter, or radius, relative to that of the axon plus the myelin sheath that encases it (Fig.

Show Me More ›

How do you calculate myelin G-ratio? ›

By deducting the area occupied by the myelin sheaths from the entire area occupied by both the myelin sheaths and axons, the radius of the axons (r) and the thickness of the myelin sheaths (R-r) were obtained. The G-ratio was obtained by using the following formula: G = r/R.

Learn More Now ›

What is the myelin G-ratio? ›

The g-ratio, equal to the ratio of the inner-to-outer diameter of a myelinated axon, is associated with the speed of conduction, and thus reflects axonal function and integrity.

Explore More ›

What is parallel imaging in MRI? ›

Parallel imaging is a robust method for accelerating the acquisition of magnetic resonance imaging (MRI) data, and has made possible many new applications of MR imaging. Parallel imaging works by acquiring a reduced amount of k-space data with an array of receiver coils.

Know More ›

How serious is high a G ratio? ›

A high A/G ratio may indicate kidney disease, antibody deficiencies, or severe dehydration. A low A/G ratio can also indicate kidney disease as well as liver disease, chronic infections like human immunodeficiency virus (HIV), autoimmune diseases like lupus, and certain cancers.

Can you have too much myelin? ›

New research has found that chronic stress can result in the abnormal overproduction of myelin; a fatty substance that helps speed up the transmission of electrical signals between neurons. Too much myelin can disrupt the brain's sensitive balance of communication.

Show Me More ›

Does more myelin mean faster? ›

By acting as an electrical insulator, myelin greatly speeds up action potential conduction (Figure 3.14). For example, whereas unmyelinated axon conduction velocities range from about 0.5 to 10 m/s, myelinated axons can conduct at velocities up to 150 m/s.

Keep Reading ›

Is the myelin sheath 80%? ›

The myelin sheath is characterized by a high proportion of lipids (70%–85%) and consequently a low proportion of proteins (15%–30%). In contrast, most biological membranes have approximatively equivalent ratio of proteins to lipids (50% lipid/50% protein) [8].

What is the R factor in MRI? ›

The acceleration factor (or reduction factor), R, is defined as the ratio of the amount of k-space data required for a fully sampled image to the amount collected in an accelerated acquisition (if every other line in k-space is collected, the acquisition is accelerated by factor R = 2).

Learn More ›

Which MRI is better plain or contrast? ›

MRIs with and without contrast are both effective, and your doctor will determine which scan you need based on your present condition and your medical and health history. But, if the doctor requires a highly detailed image to assess a specific problem area within your body, they'll typically order the contrast agent.

What are the 3 most common contrast sequences in MRI? ›

In general, T1- and T2-weighted images can be easily differentiated by looking the CSF. CSF is dark on T1-weighted imaging and bright on T2-weighted imaging. A third commonly used sequence is the Fluid Attenuated Inversion Recovery (Flair).

Learn More ›

Is a G ratio 2.3 high? ›

The value of globulin for reference purposes is always set at 1. Therefore, the ratio is presented as the level of albumin in the body. The normal ratio is always more than 1. A ratio of 1.1–2.5 is considered normal.

Explore More ›

What happens if a G ratio is low? ›

A low A/G ratio has been associated with many illnesses, which may be related to inflammation or certain cancer such as myeloma. The A/G ratio can be decreased with short-term problems that cause inflammation, such as tissue trauma or infection, chronic inflammatory conditions, and nutritional problems.

Explore More ›