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

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A Revised Model for Estimating g-ratio from MRI (1)

About Author manuscriptsSubmit a manuscriptHHS Public Access; Author Manuscript; Accepted for publication in peer reviewed journal;

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


PMID: 26299793

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

Author information Copyright and License information PMC Disclaimer

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


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


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.


Consider an ensemble of N myelinated fibers with the radius and g-ratio of the ith fiber being Ri and gi, respectively, and axon radius being ri (hence, gi = ri/Ri, see Fig 1e). The total cross-sectional areas of fibers, axons, and myelin, are, respectively,





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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 (gmean), area-weighted mean (gawm), and the square root of the area-weighted g2 (gawmgs). The proposed MRI measure, gMRI, was computed from measures of MVF and AVF.

From here, the ratio of myelin to fiber areas is



In the case that gi = 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



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



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

By starting with the ratio AM/AA, a similar relationship is found, gMRI1/(1+MVF/AVF), 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



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



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.


3.1 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 (AAi, for the ith axon) was computed using a region growing algorithm. This value provided an estimate of axon radius ri=AAi/π, and the sum of all axon areas provided an estimate of AVF. For each axon, the thickness of the surrounding myelin (Δi) was calculated as the average of manual measurements made in two locations, and the g-ratio was estimated as gi = ri/(ri + Δi).

From each image, the MVF and AVF estimates were used to compute gMRI, 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 (gmean), the area-weighted mean (gawm), the square-root of the area-weighted g2 (gawmgs, 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 gi, i = 1 to N, reduced the influence of one or two large axons amongst a relatively small sampling of the population.


Figure 1f displays a representative histogram of the g-ratios obtained from one histology image. Each characterization of the g-ratio (gmean, gawm, gawmgs, and gMRI) is displayed on the histogram. It is apparent that gmean (~0.8) is significantly lower than the area-weighted means and gMRI. 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 gMRI with gmean, gawm, and gawmgs, 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, gMRI shows a reasonable correspondence with all three measures, but the comparisons between gMRI 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.

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Figure 2

Scatter plots of (left) gMRI versus gmean, (middle) gMRI versus gawm, and (right) gMRI versus gawmgs 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 gMRI and the two area-weighted measures, gawm and gawmgs. While theory shows that gMRI = gawmgs for circular geometries, the two experimental measures will deviate for elliptical or other non-cicular axonal shapes. Nonetheless, the close correspondence of gMRI and gawmgs in Fig 2 indicates that this is not a substantial issue. Also, while gawmgs will deviate most from gawm for broad axon diameter distributions with a small mean, the difference between measures of gawm and gawmgs in this study is small (≤ 1.33%). Thus, these three measures are effectively the same and gMRI 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 gMRI 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 gMRI 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 gmean 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 gmean, but that would not change the conclusions of this study.

Table 1

gmean, gawm, gawmgs, and gMRI mean ± SEM from the middle and genu regions of the corpus callosum across all images for control and Rictor CKO mice.


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It is apparent from Table 1 that the two area-weighted measures (gawm, gawmgs) are nearly identical in all cases and similar to gMRI 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, gMRI, which reports a significantly different value than gmean, 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, gMRI 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

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Grant Sponsor: NIH EB001744


MRIMagnetic resonance imaging
MVFmyelin volume fraction
FVFfiber volume fraction
CKOconditional knockout
PBSphosphate-buffered saline
MidCCmidbody of corpus callosum
GCCgenu of corpus callosum


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


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

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

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.

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.

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.

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.

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.

What does a G ratio test results mean? ›

High or low A/G ratios are particularly associated with kidney and liver disease. A low A/G ratio can also indicate chronic infections, cancers, and more. A high A/G ratio is associated with dehydration, malnutrition, and other gastrointestinal conditions.

What is the G ratio of white matter? ›

Abstract. The g-ratio, defined as the inner-to-outer diameter of a myelinated axon, is associated with the speed of nerve impulse conduction, and represents an index of axonal myelination and integrity. It has been shown to be a sensitive and specific biomarker of neurodevelopment and neurodegeneration.

What is the normal range for myelin basic protein? ›

In general, there should be less than 4 ng/mL of myelin basic protein in the CSF. Normal value ranges may vary slightly among different laboratories. Talk to your health care provider about the meaning of your specific test results.

What is neuron refraction ratio? ›

The neuron refraction ratio is defined by the refractory period over the latency period. The refractory period is the time between sending signals and signal latency is the time it takes for information to travel down an axon.

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.

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.

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).

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).

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.

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.

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