Automatic Evaluation of Corneal Nerve Tortuosity in Images from In Vivo Confocal Microscopy

Abstract

Purpose.: An algorithm and a computer program for the automatic grading of corneal nerve tortuosity are proposed and evaluated.

Methods.: Thirty images of the corneal subbasal nerve plexus with different grades of tortuosity were acquired with a scanning laser confocal microscope in normal and pathologic subjects. Nerves were automatically traced with an algorithm previously developed, and a tortuosity measure was computed with the proposed method, based on the number of changes in the curvature sign and on the amplitude (maximum distance of the curve from the underlying chord) of the nerve curves. These measures were evaluated according to their capability to reproduce the expert classification of images into three groups of tortuosity (low, mid, and high). This classification was also compared with measures provided by other methods proposed in the literature to evaluate nerve tortuosity.

Results.: Among all considered methods, the one proposed herein allows a minimum of classification errors (only 2 in 30 images) and the highest Krippendorff concordance coefficient (0.96). Furthermore, it is the only one that can provide a significant difference (P < 0.01) between all pairs of tortuosity classes.

Conclusions.: The results provided by the proposed system confirmed its ability to perform a clinically significant evaluation of corneal nerve tortuosity.

In vivo confocal microscopy of the cornea allows rapid and noninvasive acquisition of images of the various corneal layers, and thus important clinical information on the health status of the cornea can be extracted. ¹ In particular, the images collected at a specific depth, the subbasal layer, allow the visualization of narrow and elongated nerve fiber structures, lying flat inside a thin, 10-μm layer (Fig. 1). These structures have been shown to be important in providing clinical information related to changes caused by aging and a variety of ocular or systemic disorders. Clinical parameters such as length and density of the nerves are essential in collecting objective information related to the cornea's state of health, and the usefulness of measuring nerve tortuosity was recently investigated. ^2,3 An important link has been shown between nerve tortuosity and the severity of diabetic neuropathy, one of the most common and serious long-term complications of diabetes. ^4,5 The subbasal nerve tortuosity coefficient decreased significantly after corneal refractive surgery, ⁶ and nerve fibers appeared shorter and more tortuous in the posttransplantation corneas than in normal corneas. ⁷ Subbasal nerve fibers exhibited increased tortuosity in subjects with keratoconus in comparison with control subjects. ⁸ An abnormal tortuosity has also been found in patients with Sjögren's syndrome ⁹ or pseudoexfoliation syndrome. ¹⁰ Nerve tortuosity and the number of beadlike formations is significantly greater in patients with rheumatoid arthritis. ¹¹  

Almost all of these studies, however, are based on a manual qualitative analysis of nerve tortuosity. An algorithm for the automatic tracing of the subbasal nerve plexus is needed, to obtain an objective and reproducible tortuosity evaluation. An algorithm that implements a clinically meaningful definition of tortuosity is needed, as well. The former has been the goal of some recent research projects. ^12,13 The latter was the purpose of the present work. Starting from nerve segments automatically traced with a system previously developed, ¹³ we designed a new measure that expresses a clinically significant grading of tortuosity in corneal nerves. This proposed measure was evaluated on a set of 30 images, as regards its capability of reproducing the manual classification into three groups of increasing tortuosity. This classification was also compared with the ones obtained by other methods proposed in the literature. 

Methods

Image Acquisition

Thirty images of corneal subbasal nerve plexus with different grades of tortuosity were obtained in normal (6 images, 20%) and pathologic subjects, including diabetes (10 images, 33.3%), pseudoexfoliation syndrome (8 images, 26.7%), and keratoconus (6 images, 20%). In vivo confocal microscopy was performed on all subjects (Rostock Corneal Module of the Heidelberg Retina Tomograph II [HRTII-RCM]; Heidelberg Engineering, Heidelberg, Germany), as described elsewhere. ¹⁰ In brief, after topical anesthesia, the subject was instructed to look straight ahead at a target to make sure that the central cornea was scanned. The objective of the microscope was an immersion lens with 63× magnification (Carl Zeiss Optical, Chester, VA) covered by a polymethylmethacrylate cap (TomoCap; Heidelberg Engineering, Heidelberg, Germany). Each subject was scanned three times at an interval of at least 15 minutes. The laser source is a diode laser with a wavelength of 670 nm. Two-dimensional images, consisting of 384 × 384 pixels covering an area of 400 × 400 μm, were recorded. The best images captured of the subbasal nerve plexus were saved as JPEG compressed, monochrome, digital images. 

All 30 images in this dataset are publicly available for download (http://bioimlab.dei.unipd.it/, Laboratory of Biomedical Imaging, University of Padua). 

Automatic Nerve Tracing

Nerves were traced with an algorithm designed for the automatic recognition of corneal nerve structures. The method was originally developed for a different confocal microscope and was successfully evaluated on 170 images. ¹³ To use it with images from the retinal tomograph, we modified the algorithm to take into account the different features of these images (e.g., space resolution and contrast). 

The nerve-tracing algorithm returns the list of the nerve segments it was able to detect and track, each one described by a set of ordered pixel coordinates [(x_i , y_i ), i = 1,…, n], with n the number of pixels in the segment. 

Available Tortuosity Measures

The various tortuosity indexes are estimated by using some geometric quantities, which are defined as follows: If a nerve segment s is described by the ordered set of pixels [(x_i, y_i), i = 1,…,n)], chord length L_x, curve length L_c, and curvature K_i (i = 3,…,n) are defined as:  

 

 

 

 

 

where Δx_i = x_i − x_i−1, Δ²x_i = Δx_i − Δx_i−1, Δy_i = y_i − y_i−1, Δ²y_i = Δy_i − Δy_i−1. The main tortuosity indexes are then computed according to the equations described below. 

Arc Length over Chord Length Ratio.

A simple and widely used measure of segment tortuosity is the ratio between its length and the length of the underlying chord ¹⁴ :  

 

 

Absolute Curvature.

Many tortuosity measures involve the use of curvature K_i defined in equation 3. The integral of K_i over the whole segment s is considered to be a measure of the variability of nerve direction ¹⁵ :  

 

 

Absolute Curvature Weighted by Curve Length.

Another tortuosity measure that involves the use of curvature K_i adds to the previous definition the chord length L _c, which weights inversely the tortuosity of segment s. ³ The absolute curvature τ_C(s) and the curve length L _c measured in the segment are used to estimate the segment tortuosity as:  

 

 

First and Second Differences.

This method was recently proposed ⁴ and has been used to quantify nerve tortuosity in confocal images of the cornea also by other authors. ¹⁶ It is based on the first and the second differences of the coordinates of the segment. A straight line is drawn between the endpoints of the segment and it is rotated to align this line with the x-axis. The segment is treated as a mathematical function, and the function first (ƒ′) and second (ƒ″) derivatives are computed. The first derivative ƒ′ is calculated as the difference between two consecutive points on the nerve, divided by the distance between the projections on the x-axis of two consecutive points of the segment (dx). The second derivative ƒ″ is given by the difference of two consecutive values of the ƒ′, divided by dx (in our case dx = 1). The tortuosity coefficient is defined ⁴ as:  

 

 

Proposed Tortuosity Measure

It may be assumed that the greater the number of changes in the curvature sign (twist), the more tortuous the nerve. Moreover, if we define as turn curve that portion s_i of a nerve segment s located between two consecutive twists, we may assume that the greater the amplitude (maximum distance of the curve from the underlying chord) of a turn curve, the greater the tortuosity associated with it. 

The proposed tortuosity measure requires at first a partitioning of the nerve segment s into its m turn curves as defined above:  

 

 

The tortuosity index for the nerve segment s is then computed as ¹⁷ :  

 

 

This tortuosity measure has a dimension of 1/length (in micrometers [μm⁻¹]) and thus may be interpreted as a tortuosity density, allowing its comparison on nerves of different length. 

To derive a tortuosity score for the whole image (which in our data set contains an average of 13 traced nerve segments), we computed the average of the tortuosity measures derived from each segment. This average tortuosity, however, proved to be rather crude and in some cases did not provide a correct estimation of the image tortuosity, vis-à-vis manual evaluation. It may happen, for example, that an image is classified by an expert ophthalmologist as highly tortuous just because it contains only one or two nerves with many little twists. However, when the high tortuosities of these nerves are averaged with the low tortuosities of all other nerves, the resulting average image tortuosity is still low. 

To solve this problem, we devised an algorithm more refined than simple averaging, which accounts for the fact that the very high tortuosity of only a few nerves must be capable of boosting the overall image tortuosity. In each identified nerve segment, the ratio between the number of twists and the length of the segment is evaluated. By applying an empirically determined threshold to these ratios, segments with a high value for this ratio are identified and counted. This count is then combined with the average tortuosity, so as to derive an overall image tortuosity index that effectively captures the clinical perception of tortuosity and addresses the problem outlined above, when high tortuosity segments are present in the image. 

Results

A manual grading of the 30 images was performed by one of the authors (XZ), based on the nerve tortuosity in each. Each image was classified as having low, mid, or high tortuosity, and Figure 1 reports the representative images for each class of tortuosity (this classification is also publicly available for download at http://bioimlab.dei.unipd.it). The algorithm for the automatic nerve tracing is then applied to these images, and the tortuosity measure is computed with the proposed method. Manual grading and automatic values of tortuosity are reported in Table 1. 

Figure 1.

 

Representative images in the low tortuosity group (left), mid tortuosity group (center), and high tortuosity group (right).

Table 1.

 

Manual Grading and Automatic Measure for Corneal Nerve Tortuosity

Image	Manual Grading	Automatic Measure (μm−1)	Image	Manual Grading	Automatic Measure (μm−1)
1	Low	0.18	16	Mid	2.47
2	Low	0.18	17	Mid	2.55
3	Low	0.60	18	High	5.12
4	Low	0.92	19	Mid	2.58
5	Low	1.01	20	Mid	2.68
6	High	4.96	21	Mid	3.28
7	Low	1.02	22	Mid	3.57
8	Low	1.08	23	Mid	3.61
9	Low	1.21	24	High	4.05
10	Low	1.24	25	Mid	4.26
11	Low	1.41	26	High	4.74
12	Mid	1.68	27	High	4.90
13	High	1.79	28	High	5.38
14	High	4.71	29	High	5.68
15	Mid	2.41	30	High	6.80

Images are then ordered by increasing automatic tortuosity, and the result is compared with the expert manual classification. Results are shown in Figure 2, top, where the manual grading is reported on the x-axis and the automatic tortuosity measure on the y-axis. 

Figure 2.

 

Manual and automatic grading of tortuosity. Top: tortuosity for all images is derived from automatically traced images; two classification errors are present in the automatic grading: for image 13 and for image 24 or 25. Bottom: tortuosity for image 13, 24, and 25 is derived from manually traced images.

We also computed the tortuosity measure according to the other methods described in the literature and for each of them and for our own proposed method, we computed the thresholds for minimal classification error between low, mid, and high tortuosity. As shown in Table 2, our proposed method resulted in a minimum of classification errors and the highest Krippendorff concordance coefficient. ¹⁸  

Table 2.

 

Minimum Number of Classification Errors, Krippendorff Concordance Coefficient, and Differences between Groups

Method	Classification Errors	Concordance Coefficient	P *
			Low vs. High	Low vs. Mid	Mid vs. High
Proposed method	2	0.96	0.00008	0.00006	0.0035
Arc length over chord length ratio	11	0.85	0.0317	0.0088	0.9605
Absolute curvature	15	0.55	0.5060	0.0742	0.1032
Absolute curvature weighted with curve length	15	0.72	0.1254	0.0324	0.2672
First and second differences	14	0.67	0.0935	0.0697	0.1197

*  Differences between groups.

Statistical tests were also applied to check the capability of the different methods to correctly reproduce the expert manual classification of images into the three groups. A two-tailed paired t-test was used to estimate the statistical significance of the difference between the tortuosity values assigned to the images of two different classes. The obtained P values, also reported in Table 2, show that our proposed method is the only one able to provide a significant difference (P < 0.01) between all pairs of classes. 

Discussion

The proposed algorithm provides a completely automatic measure of corneal nerve tortuosity, using a new criterion to express it. It is worth noting that this criterion estimates the global nerve tortuosity by summing local contributions, assessing how much each turn curve is different from a smooth curve. This procedure is at variance with other methods that evaluate tortuosity by using a geometric quantity for the entire nerve. 

To evaluate the reliability of the tortuosity estimated by our automated system, we compared it against the manual assessment performed by a cornea expert. At variance with automatic systems, however, the manual analysis is not capable of expressing a quantitative estimation of tortuosity, but only of providing a qualitative assessment such as low, mid, or high. By ordering the numerical tortuosities according to the increasing values estimated by the automated systems, it is possible to reproduce the manual classification. Our method achieved by far the lowest number of wrong classifications and the best concordance coefficient and class separation. 

Only 2 classification errors in 30 images were made by the proposed system (Fig. 2, top): Image 13 and either image 24 or 25 had an automatic tortuosity index that classified them in a group different from the one assigned by manual grading. A close inspection of the processed images revealed that in these images some nerve fibers were not completely traced by the automatic nerve-tracking algorithm. To understand the impact of these tracing errors, a manual tracing was performed on images 13, 24, and 25, and the proposed automatic tortuosity measure was computed again on the manually traced images. The results are reported in Figure 2, bottom, where no classification errors are present. The tortuosity indexes derived from the manually traced image 13 (6.59) and image 24 (7.59) are within the range of the high tortuosity group, as in the manual assessment, confirming that the previous misclassification was due to an incomplete nerve tracing. For image 25, the tortuosity measure derived from the manual tracing is very similar to that obtained from the automatic tracing (4.26 and 4.34, respectively). In this case the automatic tracing outlined all the significant nerves in the image. Therefore, the proposed algorithm for automatic tortuosity estimation appears to be, at least in our 30-image dataset, correct and reliable. 

In this study, nerves were traced by an automatic algorithm, which proved to be able to correctly trace, on average, more than 80% of nerve fibers recognizable in the images. ¹³ As noted above, in 2 (<7%) of 30 images, the outcome of the tortuosity estimation algorithm appeared to be affected by the insufficient extension of nerve tracing. This outcome may be due in general to several reasons, related to the patients' characteristics or to acquisition procedure features. With regard to the latter, nerve fibers may sometimes appear out of focus in an image, because the depth of field of the instrument is very narrow (∼5 μm). An effective improvement of this aspect might be to use an image preprocessing technique such as one recently proposed, ¹⁹ which extracts the nerve fiber 3D course from a volume scan of several imaging planes and therefore effectively sums the information from all of them. If the possibly incomplete nerve tracing is a serious concern for the user, a user-friendly manual image editor could be included in the system, so as to allow close to 100% of true nerve recognition with very short (30–60 seconds) user interaction. In this way, an objective, precise, and complete tracing of corneal nerves could be obtained. 

To further assess the reliability of the automatic tortuosity estimation, we measured for all the subjects the corneal sensitivity using the Cochet-Bonnet esthesiometer. ¹⁰ Figure 3 shows these values plotted against the automatic tortuosity values, with the tortuosity manual grading represented by different symbols. Being that both high tortuosity and low sensitivity are in principle related to the presence or level of pathology, the good correlation between the increase in automatic tortuosity and the decrease in corneal sensitivity, as evidenced by visual examination of the scatterplot and a Pearson correlation coefficient of 0.783, provides a further confirmation of the clinical validity of the proposed tortuosity measure. 

Figure 3.

 

Scatterplot of automatic tortuosity of corneal nerves versus corneal sensitivity measured by Cochet-Bonnet esthesiometer. The different symbols indicate the manual tortuosity grading: low (♦), mid (■), and high (▴).

A further, mandatory step before the clinical application of the proposed system is the evaluation of the repeatability of the tortuosity measure, along the same lines proposed in ad hoc studies for automated estimation of endothelial cell density ²⁰ or semiautomated nerve fiber length measurement. ²¹ Since the variability of the tortuosity measurement in subbasal layer images from different central areas of the same cornea are due not only to the physiological variation of this parameter, but also to the random presence of noise and artifacts, an effective improvement in repeatability might be to use the already mentioned image preprocessing technique, ¹⁹ which may help to reduce the variability in nerve appearance across images from the same area. 

In summary, we developed a novel automatic grading method for subbasal corneal nerve plexus tortuosity. It has been successfully used on 30 images and the results compared with other tortuosity estimation methods proposed in the literature. The results indicate that our new method is able to better represent the clinical evaluation of tortuosity in corneal nerves. Work is currently in progress to evaluate the repeatability of the proposed method across different images of the same subject, to develop a clinically applicable version of this automatic analysis of nerve fiber tortuosity. 

As a possible final step in the development of a complete system for the clinical description of subbasal nerve fibers, additional parameters, such as fiber density, average fiber diameter, number of bifurcations, and number of hyperreflective beads, could be quantitatively measured and added to the information provided to the clinical user. 

Footnotes

 Disclosure: F. Scarpa, None; X. Zheng, None; Y. Ohashi, None; A. Ruggeri, None