**Purpose.**:
A relationship has been reported between the presence of peripheral neuropathy and the density and shape of corneal nerve fibers. Peripheral neuropathy is a debilitating condition that arises from many common health problems, and its presence is often confirmed with an invasive clinical test called intramuscular electromyography (EMG). In this study, the possibility of developing an alternative or adjunct test to EMG based on the appearance of nerve fibers in corneal micrographs was explored. Since corneal imaging is virtually noninvasive compared with EMG, such a test may be administered more liberally and frequently, before neuropathy symptoms occur.

**Methods.**:
A software program that automatically traces nerve fibers in corneal micrographs and generates measures based on these traces was implemented. This software was applied to a database of images collected by confocal laser scanning corneal microscopy from diabetic subjects whose levels of neuropathy were measured with EMG and from healthy subjects.

**Results.**:
Trends in the nerve fiber density and various measures of shape were calculated and observed, to explore the possibility of using these measures as a clinical tool for corroborating symptoms, confirming an evaluation, or evaluating risk factors for developing neuropathy.

**Conclusions.**:
Preliminary statistical trends show a potential for measuring and observing neuropathy severity or for providing an objective risk measure for a patient's ensuing condition. More work is needed in the development of the measures and in their testing to prove that the measures can be made repeatable in a clinical environment.

^{ 1 }It is among the most common complications of diabetes and is prevalent due to diabetes alone, because diabetes affects ∼8% of the North American population,

^{ 2 }and anyone with diabetes for 25 years has a ∼50% chance of having peripheral neuropathy.

^{ 3 }The most common classification of the condition that occurs in diabetes is distal symmetric polyneuropathy (DSP). The pain and numbness that accompany the condition are often debilitating. It can be dangerous and sometimes life-threatening, because it may affect the autonomous nervous system and thereby may alter physiological functions, most commonly including cardiovascular, gastrointestinal, and genitourinary system functions.

^{ 4 }that implicate potential treatments, such as vascular endothelial growth factor injection.

^{ 5 }One proposed nonpharmaceutical treatment that was tested—frequency-modulated electromagnetic neural stimulation

^{ 6 }—was reported to reverse measurable neuropathic conditions (pain score, tactile perception, and nerve conduction velocity).

^{ 7,8 }The tests reported herein are an early step toward automation of this process and establishing a correlation between quantitative measures of nerve fiber shapes and disease progression. Figures 1 and 2 show example images where the nerve fiber densities, shapes, and other appearance measures differ. These densities, shapes, and appearances are being measured by the software.

^{ 9 }

*P*-values in the statistical significance tests.

^{ 10,11 }The study group contained a large number of volunteers, and for them to be matched according to age and sex, the number of participants would have to increase to an unmanageable size for a first test study. The next step beyond this study will be to perform a rigorously age- and sex-matched study.

*down-up*, TN means

*temporal-nasal*, and R means

*random*. There were 42, 35, 53, 47, 35, and 44 images, respectively, for each of the scans.

*IOVS*2008;49:ARVO E-Abstract 2807),

^{ 8,12 }and the objective in the present study was to see whether the software would show these trends with the automation of nerve fiber detection and the specific measures described later; and (3) to understand the practicalities of usable data acquisition in a clinical environment. To achieve this goal, some parameters reflecting potential repeatability and statistical power were studied.

^{ 13 }The program creates an intensity gradient image, which is used to produce a set of labeled pixels in the image called a ridge map. This operation is followed by execution of rules that automatically edit the ridge map to produce a set of labeled fibers. The ridge map is pruned with morphologic operators

^{ 14 }and further processes follow more rules to find skeletonized branch segments that should be joined together or arranged as having connecting branch points. Counts of branch segments and branch points and measurements of shapes are produced, including those summarized in Table 1 with some of the definitions illustrated in Figures 7 and 8. Later, we refer to these measurements as risk factor measurements.

Measurement | Description |
---|---|

Number of branch points, N _{b} | Number of branch points in the image. |

Number of branch segments, N _{S} | Number of branch segments in the image. |

Branch segments per branch point N _{S}/N _{b} | Number of branch segments divided by number of branch points. |

Curvature tortuosity 1, T _{C1} | The tortuosity defined in equation 5 and illustrated in Figure 8, left. This parameter is based on the mathematical curvature of the skeleton of the branch segment. |

Curvature tortuosity 2, T _{C2} | The tortuosity defined in equation 8 and derived from T _{C1}. |

Length, L | Path length of the branch segment. |

Length density, D _{L} | Sum of lengths of all branches divided by the area as defined in equation 7. This is, de facto, a measure of total length over the image field. The study could have equivalently recorded the lengths only, because the area divisor is the same for all images, and so dividing by the area has no consequence on the trends. |

Length ratio tortuosity, T _{L} | The tortuosity measurement illustrated on the right of Figure 8. It is the path length of a fiber divided by the distance between its end points. This measure has been called the arch length over length ratio.^{15} |

Signal to background, S/B | Ratio of the mean intensity value within pixels on the fiber to the mean intensity value within surrounding pixels. |

Intensity variance, σ^{2} | Variance of intensity values within pixels on the fiber. |

Width, W | Total fiber area divided by length. |

*x*,

_{n}*y*). This ordered list traces the branch segment's skeleton. A spatial low-pass filter was applied to the function that this list represents to remove rapid shifts from the pixel quantization of the (

_{n}*x*,

_{n}*y*) positions. The resulting filtered sequence is then processed according to the following formulas to form several measurements: and where

_{n}*L*is the length of the segment defined by The length density,

*D*

_{L}, is defined according to where the index

*k*refers to the branch segment being considered and the subscript

*i*refers to the

*i*th image used for the subject being measured.

*T*

_{C1}parameter is called

*curvature tortuosity 1*because it is based on the mathematical curvature of the skeleton of the branch segment.

^{15}This tortuosity is identical with the

*T*c(C) measure that is defined in Hart et al.,

^{16}except that here the term is divided by

*L*which weights it inversely to the length of the branch segment. We also have a

*curvature tortuosity 2*(

*T*

_{C2}) defined according to where

*T*

_{C1k}is the

*T*

_{C1}measured for branch segment

*k*. A third measure, called the length-ratio tortuosity,

^{15}is defined according to where

*L*

_{e}is the distance between the two endpoints of the branch segment.

^{2}was designed to reflect the beading, since as beading increases, the variation of intensities in the fiber appear to increase. The signal-to-background (

*S*/

*B*) was designed to capture the changes in contrast.

*S*/

*B*measurement of <1.25 were rejected, but other than the selection of these thresholds, this rejection process is automated. An obvious idea is to edit the traces by manually drawing missing branches, erasing spurious branches or branch segments, or joining fragmented sections with a point-and-click drawing interface. With the data presented, there was no such operator editing. The software makes errors, as is evident by the missed and spurious fiber identifications in Figures 1 and 2. These errors ought not to be overlooked, and future improved versions of the software algorithms ought to provide more accurate traces. Ways of doing so are suggested later.

^{ 17,18 }has shown that perfect nerve fiber tracing is not possible, either manually or automatically and that attempting to edit the fibers is laborious. Even manual traces, performed by an ophthalmologist and shown in Figure 10, will contain mistakes, equally severe, and will not be perfect, but will have the added variability between ophthalmologists and within the same ophthalmologist at different times. Future improved versions of algorithms will strive to eliminate such automated errors and will have the editing feature as well.

- Group A includes subjects who met either of the following conditions: all nondiabetics older than 55 years or diabetics with no neuropathy according to EMG and no clinical symptoms, and older than 55.
- Group B includes subjects who met the following conditions; diabetics who had an EMG evaluation of mild neuropathy, were clinically symptomatic, and were older than 55 years.

*P*-value shown above each plot was based on a paired

*t*-test. Averaging for each subject was performed by measuring every included branch segment among all included images and then taking the average over that whole population of branch segments.

- Group C was all nondiabetics of all ages.
- Group D was all diabetics with an EMG evaluation of no neuropathy (included both sexes and both asymptomatic and symptomatic disease).
- Group E was all diabetics with EMG evaluation of mild (included both sexes and both asymptomatic and symptomatic disease).

*P*-value shown above each plot is based on ANOVA.

^{ 10,11 }

*L*,

*T*

_{C1},

*T*

_{L}, S/B, σ

^{2}, and

*W*were averaged for the box plots and scatterplots of Figures 9 and 11 to 14 by averaging them over every branch segment within all included images of the subject. The measures

*N*

_{b}and

*N*

_{S}were averaged for these figures by calculating them for every image of the subject and then averaging the value over these images. The length density

*D*

_{L}, as shown by equation 7, was calculated by adding all the lengths of included branch segments of a subject and dividing by the sum of the areas (micrometers squared) of all the images of that subject. This measure is equivalent to calculating the aggregate length of the fibers in each image, and then averaging that aggregate length over the images, since division by the area simply scales the number. The

*k*index of

*T*

_{C2}in equation 8 implies that the calculation is performed over all included branches and all included images. The branch-segment to branch-point ratio was calculated by finding the averages of both

*N*

_{S}and

*N*

_{b}and then taking the ratio.

*t*-test, the measurement calculated for an individual fiber made up the sample point

*L*,

*T*

_{C1},

*S*/

*B*, σ

^{2},

*T*

_{L}, and

*W*. The measurement averaged over an image made up the sample point for

*N*

_{b},

*N*

_{s},

*D*

_{L}, and

*T*

_{C2}. For

*T*

_{C2}, this average followed equation 8. A

*P*-value greater than 0.05 implies that the difference in means is statistically insignificant. Ideally, we would like every entry to have high

*P*-values.

Measure | TN1 vs. TN2 | DU1 vs. DU2 | R1 vs. R2 | |||
---|---|---|---|---|---|---|

% Difference | P | % Difference | P | % Difference | P | |

N _{b} | 13.2 | 0.348 | −10.3 | 0.516 | −21.3 | 0.058 |

N _{S} | 24.6 | 0.016* | 1.8 | 0.879 | −3.3 | 0.695 |

D _{L} | 25.1 | 0.012* | 5.9 | 0.546 | −5.5 | 0.341 |

T _{C2} | 0.72 | 0.844 | −3.4 | 0.25 | 18.0 | 0.054 |

L | 2.6 | 0.649 | 13.4 | 0.062 | −6.0 | 0.375 |

T _{C1} | 2.4 | 0.602 | −3.3 | 0.263 | 10.9 | 0.002* |

S/B | 4.1 | <0.001* | −0.83 | 0.568 | −2.8 | 0.077 |

σ^{2} | 3.3 | 0.469 | 20.0 | 0.001* | −9.7 | 0.072 |

T _{L} | −16.2 | 0.285 | −1.89 | 0.543 | 3.5 | 0.081 |

W | 10.7 | 0.021* | 13.1 | 0.027* | 2.2 | 0.568 |

*N*

_{b},

*T*

_{C2},

*L*, and

*T*

_{L}) showed statistical insignificance in all three tests. For future clinical usage, we think it is important to collect the baseline and follow-up data in the same way. For example, the worst repeatability occurred when comparing the means between DU1 and R1 (not shown in Table 2). In this case, all 10 of the measures had a statistically significant difference. A definitive conclusion about repeatability cannot be arrived at from these tests, but they at least provide some insight, and they imply that, in the clinic, it will be important to define and adhere to collection patterns. We think that other collection patterns and measures could improve repeatability. A thorough repeatability test necessitates compiling a well-defined database that represents a longitudinal study including healthy control subjects, to ensure no change, and subjects who are expected to show a change.

^{ 11 }Tables 3 and 4 summarize these calculations, which shows the estimated percentage change needed for a statistical power of 0.8, estimated from the DU1 data set. The DU1 set was chosen arbitrarily. Table 3 summarizes the parameters that are averaged over all included fibers. Parameters needed for the Table 3 estimates included the number of fibers (441, taken from the number of fibers automatically identified in DU1), the desired null-hypothesis

*P*-value (0.05), and the desired statistical power (0.8). The required effect size (percentage change over the SD) for this

*P*-value, statistical power, and number of fibers is 0.168. Table 4 summarizes the parameters that are averaged for each included image and then averaged over the images. Parameters needed for the Table 4 estimates include the number of images (42, which is the number of images used for DU1), desired null-hypothesis

*P*-value (0.05), and desired statistical power (0.8). The estimates shown for the mean, standard deviation, and required change in the mean were also calculated from the DU1 data set. The required change in the mean is calculated by multiplying the estimated standard deviation by the required effect size. The required percentage change in the mean is calculated by dividing the required change in the mean by the estimated mean.

Measure | Estimated Mean | Estimated SD | Required Change in the Mean | Required Percentage Change |
---|---|---|---|---|

L | 93.17 | 70.76 | 11.86 | 12.7 |

T _{C1} | 0.139 | 0.048 | 0.008 | 5.8 |

S/B | 1.48 | 0.226 | 0.038 | 2.6 |

σ^{2} | 1198.8 | 770.14 | 129.06 | 10.8 |

W | 5.84 | 3.67 | 0.616 | 10.5 |

Measure | Estimated Mean | Estimated SD | Required Change in the Mean | Required Percentage Change |
---|---|---|---|---|

N _{b} | 5.10 | 3.40 | 1.86 | 36.5 |

N _{S}/N _{b} | 2.85 | 2.14 | 1.17 | 41.2 |

D _{L} | 978.2 | 443.9 | 242.9 | 24.8 |

T _{C2} | 0.13 | 0.017 | 0.009 | 7.0 |

Measure | Range of Required Percentage Change | Percentage Change Estimated from the Difference between Categories A and B in Figure 13 | Percent change Estimated from the Difference between Categories C and E in Figure 14 |
---|---|---|---|

L | 11.8–14.0 | 15.3 | ≈15% |

T _{C1} | 5.1–24.8 | 13.1 | ≈12% |

T _{C2} | 6.5–24.2 | 13.7 | 11.9 |

S/B | 2.3–3.0 | 4.9 | 6.24 |

σ^{2} | 9.3–10.8 | 11.2 | NA |

W | 8.9–11.2 | 10.5 | NA |

N _{b} | 28.5–47.7 | 32.2 | NA |

N _{S}/N _{b} | 24.0–41.2 | 47.7 | NA |

D _{L} | 14.1–24.8 | 15.3 | 11.8 |

^{ 19–24 }This includes the documentation of increased fiber counts (

*N*

_{b}, Fig. 11) in cadaveric skin specimens of human females compared with those in males.

^{ 23 }

^{ 25 }We expected the number of branch segments, branch points, and length density to decrease with age, since we thought that they were indicators of fiber health and further assumed that general health declines with age. On the other hand, we confirmed these trends with the visual appearances of the fibers in the images, and these trends appear to be real. A possible explanation is that the nerve fibers are in continual flux,

^{ 26–28 }and so it is believable that the fibers could generate continually, and the number could, on average, increase over time and thereby over the age of the subject. Before drawing conclusions based on this finding, a regression analysis on a wider range of population has to be performed. Data sets of subjects of age <55 years were not included in Figure 9, because there were no diabetic subjects in this lower age category, and there was a good mix of both diabetics and nondiabetics in the range of 55 years and above. A further corroboration of this trend is provided in Figure 1 in Reinisch et al.,

^{ 25 }where a regression analysis shows an increase in fiber length density (length per unit area) of the subepidermal nerve plexus in diabetic subjects on the order of 50% between the ages of 50 and 90, similar to that shown in Figure 9. The main difference in our data, other than being extracted from different tissue, is that our pool of subjects was a mixture of both diabetics and nondiabetics (although most were diabetic), whereas the data in Reinisch et al.

^{ 25 }are from diabetic persons only.

^{ 29 }and many inflammatory diseases including lupus erythematosus and Sjögren's syndrome, vitamin deficiencies, HIV (Sabato L, et al.

*IOVS*2008;49:ARVO E-Abstract 2804), chemotherapy, and others. As explained in Scarpa et al.,

^{ 12 }corneal surgical interventions, including LASIK, photorefractive keratectomy, and transplantation disrupt the integrity of the nerve fibers, and regeneration of these fibers occurs after surgery (Midena E, et al.

*IOVS*2008;49:ARVO E-Abstract 2261). The capability of automatically identifying nerve fibers and measuring them may provide an objective means of evaluating reinnervation after these surgeries.

^{ 26–28 }It is possible that, in some subjects, good sampling over all regions of the cornea was not obtained. Considering that the nerve fiber numbers and shapes change across the cornea positions, especially radially, a better collection scheme would use a pattern like one of those illustrated in Figures 5a, 5b, and 6, and would collect a whole stack (i.e., axially) at each location. The ideal would be to image exactly the same fields between baseline and follow-up visits and thereby ensure that the same fibers are measured. One may think of ways of doing so, but there is one problem that is impossible to circumvent. The nerve fibers are not stationary. They are in continual flux, moving and changing shape from one visit to the other.

^{ 26–28 }The best hope is to strive for stationary statistics by using schemes like those shown in Figures 5 and 6. The schemes in Figure 6 are better for more thorough sampling of the cornea, but work is needed on the software that automates the collection of these patterns. The schemes are difficult to execute manually because it is hard to determine a reference point on the cornea, and it requires a relatively long time to collect. With a contact microscope, the schemes in Figure 5 are more practical because they require shorter contact time with the cornea. The scheme of Figure 5c was used for collecting the data pools of Figures 13 and 14. All three of the schemes in Figure 5 were used to examine repeatability.

^{ 17,18 }These mistakes probably do not contribute significantly to difficulties in establishing trends, because such mistakes are repeatable and systematic and because the other sources of variability are obvious and significant. It is an obvious suggestion to place a human operator in the process by editing the nerve tracings as discussed earlier in the Automated Measurements section, but doing so may reduce repeatability and, as a result, the capability of detecting trends and thereby recognizing progression of a condition.

*P*-values in Table 2. Higher

*P*-values are needed in more of the entries, which would indicate that the means of the measures are virtually unchanged (statistically speaking) from one data collection (i.e., examination) to the next. By “work” we mean that the following factors should to be designed, implemented, and tested. Better patterns (e.g., Figs. 5, 6) are needed that provide repeatability measurement means. Variants on measures, besides those in Figures 13 and 14, may provide smaller effect sizes. There are many measures that we thought about after completing this study. One such measure is a fragmentation measure that counts the number of fragmented branch segments after automatically detecting and rejoining branches that have been segmented due to contrast degradation. Another such measure is a linear combination of several of the existing measures.

**T. Holmes**, Lickenbrock Technologies, LLC (E);

**M. Pellegrini**, Lickenbrock Technologies, LLC (F);

**C. Miller**, Lickenbrock Technologies, LLC (E);

**T. Epplin-Zapf**, Lickenbrock Technologies, LLC (E);

**S. Larkin**, Lickenbrock Technologies, LLC (E);

**S. Luccarelli**, None;

**G. Staurenghi**, Lickenbrock Technologies, LLC (F)

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