Constructing a statistical atlas of the radii of the optic nerve and cerebrospinal fluid sheath in young healthy adults

Abstract

Optic neuritis is a sudden inflammation of the optic nerve (ON) and is marked by pain on eye movement, and visual symptoms such as a decrease in visual acuity, color vision, contrast and visual field defects. The ON is closely linked with multiple sclerosis (MS) and patients have a 50% chance of developing MS within 15 years. Recent advances in multi-atlas segmentation methods have omitted volumetric assessment. In the past, measuring the size of the ON has been done by hand. We utilize a new method of automatically segmenting the ON to measure the radii of both the ON and surrounding cerebrospinal fluid (CSF) sheath to develop a normative distribution of healthy young adults. We examine this distribution for any trends and find that ON and CSF sheath radii do not vary between 20–35 years of age and between sexes. We evaluate how six patients suffering from optic neuropathy compare to this distribution of controls. We find that of these six patients, five of them qualitatively differ from the normative distribution which suggests this technique could be used in the future to distinguish between optic neuritis patients and healthy controls.

1. INTRODUCTION

The size of the optic nerve (ON) and surrounding cerebrospinal fluid (CSF) have been manually measured[1, 2] previously and have been suggested as a differential diagnosis[3]. Optic neuritis is a sudden inflammation of the ON and is marked by pain on eye movement, and visual symptoms such as a decrease in visual acuity, color vision, contrast and visual field defects [4]. The ON is closely linked with multiple sclerosis (MS) and patients have a 50% chance of developing MS within 15 years [5]. Despite this, there is no radiological biomarker of the ON that predicts eventual development of MS. Furthermore, interventions can now help preserve and/or restore visual function if administered before ON axons are lost, i.e., during the ‘neuroplasticity’ window [6–8]. We hope to better understand ON disease etiology (including MS) using MRI to examine the ON anatomy along the length of the nerve as illustrated in Figure 1.

Figure 1.

Comparison of the ON of a healthy control (A) and an MS patient with severe ON atrophy (B). Red lines in the axial images show the location of the coronal slices to the right.

Manual segmentation with “computer assistance” has been and remains the de facto standard process to characterize the ON on 3-D imaging. Hickman et al. used contouring to identify ON cross-sections in a longitudinal analysis and revealed patterns consistent with acute inflammation followed by long-term atrophy [9, 10]. Combined conventional and magnetization transfer (MT) imaging studies using manual contouring of the ON volume have shown that ON degeneration is associated with persistent functional deficits [11]. These studies have focused on ROIs consisting of the whole ON rather than tract-localized findings. MRI has recently been shown to be accurate at measuring the ON and the CSF sheath using manual observers [12]. Recent efforts have also attempted to automatically segment the ON in MRI but did not segment the sheath or apply to their tool to diseased patients [13]. Recently, we have proposed multi-atlas segmentation pipelines for both CT [14] and MRI[15]. The CSF sheath is not differentiable from the nerve on CT, which is why we choose to focus this effort on MRI.

The goal of this work is to develop a normative distribution of controls using an automated tool to measure the size of the ON and cerebrospinal fluid (CSF) sheath independently for comparison against patient populations. We also present a feasibility study which demonstrates that patient populations may differ from the derived normative distributions which suggests that this technique could be used for differentiating different populations in the future.

2. METHODOLOGY

Our segmentation begins with a previously described multi-atlas segmentation method [14] which automatically segments the orbits, optic chiasm and ON. This method uses 35 manually labeled atlas images which include both healthy controls as well as optic nerve drusen and MS patients. The target image to be segmented is registered to each of the 35 atlas images using an affine registration and non-rigid registration [16]. The manual labels of the atlas images are then transformed to the target space using these registrations and are fused using non-local spatial STAPLE[17, 18]. The segmentation of the ON includes both the ON and CSF sheath and so we must refine our segmentation to separate the two structures and measure them independently.

We utilize a previously described model [19] which can be seen in Equation (1) to fit the ON and CSF sheath in the coronal plane and extract the radii of both. The model is a difference of two Gaussian distributions which matches the intensity profile of the ON in the coronal plane. The second Gaussian is scaled by an exponential term and has a scaling factor on the covariance matrix in the range (0,1) such that the second Gaussian is always smaller than the first Gaussian. The covariance matrix is formulated with the correlation term as a sigmoid function to improve stability later on, during the optimization process.

$$\widehat{I}(x,y)=I_0[N(\stackrel{\rightharpoonup }{\mu },{\mathrm{\sum }}_{xy})-e^{\beta }N(\stackrel{\rightharpoonup }{\mu },{\sigma }_2{\mathrm{\sum }}_{xy})]$$ (1)

$$N(\stackrel{\rightharpoonup }{\mu },{\mathit{\sum }}_{xy})=\frac{1}{2\pi \left|{\mathrm{\sum }}_{xy}\right|}exp\left[-\frac{1}{2}{(X-\mu )}^T{\mathrm{\sum }}_{xy}^{-1}(X-\mu )\right]$$ (2)

$${\mathrm{\sum }}_{xy}=\left[\begin{array}{cc}{\sigma }_x& {\sigma }_x{\sigma }_y\left(\frac{2}{1+e^{-\rho }}-1\right)\\ {\sigma }_x{\sigma }_y\left(\frac{2}{1+e^{-\rho }}-1\right)& {\sigma }_y\end{array}\right]$$ (3)

We define the error as the sum of squared difference between the model and the image which can be seen in Equation (4). The derivative can be seen in Equation (5) where the last term is the partial derivative with respect to each of the eight model parameters. These partial derivatives are computed analytically and can be seen in Equations (6)(7)(8)(9)(10)(11). Note that the derivatives for σ_y and μ_y are omitted as they are a direct substitutions into equations (6) and (9), respectively. In summary, the complete model is composed of eight terms: Θ = [σ_x, σ_y, σ₂, I₀, μ_x, μ_y, β, ρ].

We then fit the model to the ON in the coronal plane using an iterative conjugate gradient descent optimization method on all eight parameters [20].

$$\mathrm{\epsilon }=\sum {(I(x,y)-\widehat{I}(x,y))}^2$$ (4)

$$\frac{\delta \epsilon }{\delta \mathit{\Theta }}=2\sum _{xy}(I_{xy}-\widehat{\mathrm{I}}(x,y))\frac{-\partial \widehat{\mathrm{I}}}{\partial \mathit{\Theta }}$$ (5)

$$\frac{\partial \widehat{\mathrm{I}}}{\partial {\sigma }_x}=-\widehat{\mathrm{I}}(x,y)\left[\frac{1}{{\sigma }_x}+\frac{\frac{{(x-{\mu }_x)}^2}{{\sigma }_x^3}+\frac{\rho (x-{\mu }_x)(y-{\mu }_y)}{{\sigma }_x^2{\sigma }_y}}{(1-\rho )}\right]$$ (6)

$$\frac{\partial \widehat{\mathrm{I}}}{\partial {\sigma }_2}=\frac{-N_2}{{\sigma }_2}\left[2+\frac{{(X-\stackrel{\rightharpoonup }{\mu })}^T{\mathrm{\sum }}_{xy}^{-1}(X-\stackrel{\rightharpoonup }{\mu })}{(1-\rho )}\right]$$ (7)

$$\frac{\partial \widehat{\mathrm{I}}}{\partial I_0}=\frac{\widehat{\mathrm{I}}(x,y)}{I_0}$$ (8)

$$\frac{\partial \widehat{\mathrm{I}}}{\partial {\mu }_x}=\frac{-\widehat{\mathrm{I}}(x,y)}{(1-\rho )}\left[\frac{\rho (y-{\mu }_y)}{{\sigma }_x{\sigma }_y}-\frac{(x-{\mu }_x)}{{\sigma }_x^2}\right]$$ (9)

$$\frac{\partial \widehat{\mathrm{I}}}{\partial \beta }=-I_0{e}^{\beta }N(\stackrel{\rightharpoonup }{\mu },{\sigma }_2{\mathrm{\sum }}_{xy})$$ (10)

$$\begin{array}{c}\frac{\partial \widehat{\mathrm{I}}}{\partial \rho }=-\widehat{\mathrm{I}}(x,y)\left[\frac{\rho }{1-{\rho }^2}\right]-\left[\frac{(x-{\mu }_x)(y-{\mu }_y)}{\rho {\sigma }_x{\sigma }_y}-2\rho {(X-\mu )}^T{\mathrm{\sum }}_{xy}^{-1}(X-\mu )\right]N(\stackrel{\rightharpoonup }{\mu },{\mathrm{\sum }}_{xy})\\ +\beta \left[\frac{(x-{\mu }_x)(y-{\mu }_y)}{\rho {\sigma }_x{\sigma }_y{\sigma }_2^2}-2\rho {(X-\mu )}^T{\sigma }_2{\mathrm{\sum }}_{xy}^{-1}(X-\mu )\right]N(\stackrel{\rightharpoonup }{\mu },{\mathrm{\sum }}_2{\mathrm{\sum }}_{xy})\end{array}$$ (11)

The model parameters are correlated with the radii of the ON and CSF sheath through a random forest regression[21] using 1.2 million synthetic training images. Six of the eight model parameters are used for the regression, the centroids are omitted as they are dependent solely on field of view. These training images were generated by simulating partial volume effects of imaging two concentric tubular structures with 0.6 mm isotropic voxels using a Monte Carlo simulation. This model is then tilted at varying angles relative to the imaging plane and the size of each of the concentric tubes is varied to generate the training set. The regression is validated using tenfold cross validation which shows the predicted radii to correlate with the true underlying radii with an explanatory R-squared greater than 0.95 for both ON and sheath radii.

3. DATA

3.1 Data acquisition

MRI images were obtained with heavily T2-weighted VISTA 3-D spin echo with asymmetric k-space turbo spin echo readout, TR=4s TE=400ms, nominal resolution = 0.6 mm isotropic, ~50 axial slices, SENSE = 2, body coil excitation, and 32 channel receive coil on a 3T Philips Achieva MRI (Philips Medical Systems, Best, The Netherlands). Total scan time was 4.3 min and the field of view included the full optic nerves from the globe to the lateral geniculate nucleus (LGN).

3.2 Demographic Information

Our control population consists of 45 individuals which are young adults with good representation of both male and female subjects. Six relapsing remitting MS patients with optic neuritis were selected to have the worst binocular 1.25% contrast visual acuity to assess whether they were different from the normative distribution.

3.3 Model Application

The model is initialized using the result of a previously described multi-atlas segmentation protocol [14]. Iterative conjugate gradient descent is performed on each slice which contains ON labels from the multi-atlas protocol. Each slice’s optimal parameters are then used in the random forest regression to predict the true underlying radii of the ON and CSF sheath. The results are analyzed along the length of the ON. To make this comparison we interpolate every set of ON measurements to be the same number of samples as the longest one in the data set. The nature of the ONs allows for them to be present in a different number of slices from volume to volume. Interpolation more closely aligns corresponding parts of the ON across subjects. A three-element moving window median filter is also applied within each nerve across slices to reduce noise in the measurements.

4. RESULTS & DISCUSSION

4.1 Normative Distribution Evaluation

Using this framework we examined the normative distribution of controls as a function of normalized length posterior to the globe. Variations in the distribution based on this age range and sex information were investigated and found to be nonexistent. Figure 2 shows the similarity of the distributions across both age and sex. This suggests that although the ON varies widely among healthy controls the variation is not dependent upon age or sex of the subject over this limited age range.

Figure 2.

ON radius with error bars as the standard deviation as a function of normalized slice posterior to the globe illustrating the similarity of distributions regardless of age and sex among the 45 healthy controls.

4.2 Patient Evaluation

We then compare the six selected patients to the normative distribution to see if irregularities became apparent. We would expect patients to fall outside of the normal distribution and it can be seen in Figure 3 that most of them do. From Figure 3 patient 1’s ON appears to be smaller than the normative distribution around the midsection of the ON. This would suggest that this nerve is atrophic while the sheath appears to be approximately of normal size. The star indicates that this slice is shown for comparison in Figure 4 against an age matched control in the first column. The comparison in Figure 4 matches what is observed in the measurements from Figure 3. The sheath appears to be of a similar radius to the age matched control’s sheath while the nerve appears slightly atrophic. Patient 2 appears slightly atrophic through the anterior part of the ON and we see inflammation in the posterior of the ON in both eyes. Patient 3 displays atrophy in both eyes in the anterior region. The right eye remains atrophic for the length of the ON while the left eye appears to approach the normative distribution. Patient 4 appears closest to the normative distribution although the right eye does appear to be slightly atrophic in some regions. Patient 5 shows atrophy in the right ON while the left ON appears highly inflamed. The stars again mark slices which can be seen in Figure 4 for comparison against an age matched control. In this comparison it is very clear the ON is much larger than that of the age matched control. Patient 6 appears atrophic in both eyes with the left being more severe. Once again Figure 4 shows a selected slice and it is clear that the ON is smaller in this patient when compared to the age matched control. These results show promise for this method as a possible tool to differentiate patient and control populations.

Figure 3.

Measurements for the six selected patients as their left and right ONs compare to the normative distribution. Note the asterisks which mark the approximate locations of the visuals from Figure 4.

Figure 4.

Selected comparisons of 3 patients and age matched healthy controls. Patients 1 and 6 are atrophic and patient 5 is hypertrophic.

4.3 Conclusions

We have presented a method for quantitatively measuring the ON and the CSF sheath and have demonstrated its feasibility as a possible tool for differentiating patients with ON atrophy or hypertrophy from healthy subjects. Although this population of healthy control subjects contains a large amount of inter-subject variation the small comparison of patients suggests that there may be information which differs within patients from the normative distribution. This differentiation requires further investigation with a larger patient population to fully understand how patients with varying conditions compare across the length of the ON.

All tools used and developed in this work are available in open source from their respective authors. The tools that implement the ON specific components of analysis are based on the Java Image Science Toolkit (JIST)[22] and NonLocal STAPLE [18]. The ON/sheath characterization code is primarily written in MATLAB (The MathWorks, Inc., Natick, Massachusetts, United States) and bundled into an automated program (i.e., “spider”[23]) that combines these tools using PyXNAT[24] for XNAT[25] and is available in open source through the NITRC project MASIMATLAB (http://www.nitrc.org/projects/masimatlab).

Table 1.

Age demographic information for the 45 controls and six patients

	Controls: 45					Patients: 6
	20–25	25–30	30–35	Over 35	Total	20–25	25–30	30–35	Over 35	Total
Male	5	12	3	1	21	0	0	1	0	1
Female	11	1	10	2	24	1	1	3	0	5
Total	16	13	13	3	45	1	1	4	0	6