Keratoconus Disease and Three-Dimensional Simulation of the Cornea throughout the Process of Cross-Linking Treatment
H. Kaya1; A. Çavuşoğlu2; H.B. Çakmak3; B. Şen1; E. Çalık4 1 Yıldırım Beyazıt University, Department of Computer Engineering, Ankara, Turkey
2 Scientific and Technological Research Council of Turkey, Ankara, Turkey
3 Yıldırım Beyazıt University, Atatürk Education and Research Hospital, Ankara, Turkey
4 Karabük University, School of Health Sciences, Karabük, Turkey
Abstract
Keratoconus is a corneal disease characterized by the progressive thinning and tapering of the cornea. Vision gradually decreases as the sphere-shaped cornea becomes more tapered and conical. With corneal cross-linking treatment, which increases the number of cross-links in the connective tissues of the corneal layers, the cornea hardens. The purpose of this chapter is to described the changes in the cornea between the processes before and after the cross-linking treatment. In this study, we used the Cropped Quad-Tree method as the cropping algorithm, Multilayer Perceptron and Logistic Regression methods to prepare the data set, and three-dimensional (3D) imaging methods to model the images in 3D form. With this application, it can be possible to follow up the healing process after the treatment and also monitor whether the treatment has achieved the desired results. This system was developed in order to support eye specialists in the disease diagnosis, treatment, and follow-up stages. It can be seen that the follow-up process of the disease by analyzing two-dimensional (2D) corneal images can be improved by using 3D images.
Acknowledgments
This study is based upon the project supported by T. C. Ministry of Science, Industry, and Technology in the scope of SAN-TEZ Project No. 0477.STZ.2013-2, with Yıldırım Beyazıt University and Akgün Software Company. Also, we would like to thank Yıldırım Beyazıt University, Ataturk Education and Research Hospital board for their permission to use the digital image data with Ethics Committee approval.
1 Introduction
Keratoconus can be defined as the forward extension of the cornea (the transparent, breaker layer, like a watch glass in front of the eye) as it tapers conically (Figure 31.1). This disease is more common among women. Changing the refractive power of the cornea, it causes a moderate or severe degree of irregular astigmatism and blurred vision. In the final stages of keratoconus, corneal swelling and blanching can be seen.
Light enters the eye through the cornea, and because it provides clear vision by breaking or focusing the rays, the cornea is a very important part of the eye. In keratoconus, the shape of the cornea is changed and vision distorted as a result; therefore, it may cause problems with some activities, such as driving a car, using a computer, watching television, and reading. Especially in young people, it may lead to some serious difficulties in their education and work lives. If keratoconus is not treated, it causes serious vision problems. Therefore, early diagnosis and selecting the appropriate treatment is of great importance. Cross-Linking Treatment is suitable for the situation that the patient is in the age group of 15-35, Keratoconus is progressive, patient does not feel comfortable longer with the lenses and the cornea is thicker than 400 micrometers. The purpose of this treatment method is to stop the advance of keratoconus, to improve vision quality by reducing the refractive defect, and to eliminate the need for corneal transplantation (keratoplasty). According to several studies, if the cross-linking treatment is preferred, the progression for the disease can be stopped at the rate of 90%–98%.
The disease is widespread throughout the world, but Turkey is located in the region where the disease is most prevalent. Depending on the high rate of the young population in our country and that existing in the sunny and pollen-rich climate zone, disease can be seen from 2000 to 2500 per person. The disease is genetic, and it can be seen as high astigmatism. In patients, irregular astigmatism or myopia is constantly increasing, and bilateral involvement occurs in time. The majority of patients complain of having to change their eyeglass prescriptions frequently, but eventualy, these glasses will be inadequate and visual impairment will continue that cannot be fixed with glasses. Keratoconus can be associated with corneal injury and systemic diseases. After applying excimer laser surgery to an eye thinner than 400 micrometers, due to the weakening of the vitreous of the eye, keratoconus may occur. In all cases that keratoconus is suspected, doing corneal topography before diagnosis is of great importance (Kocamış, 2011).
There is not a precise classification method in keratoconus that everyone can agree on. So far, various classification methods are used considering such parameters as conus morphology, clinical findings, visual acuity, disease progression, keratometry, topography-derived values, corneal aberrations alone, or combinations of them. First, classification based on the progression of the disease was made by Amsler (1938) and then similar reclassifications have been made (Hom and Bruce, 2006). Amsler evaluated keratoconus in four stages. For diagnosis and classification of keratoconus, various classification methods obtained from corneal topography systems have been formed. Several researchers have made classifications using corneal topography results (Rabinowitz and Donnell, 1989; Rabinowitz and Rasheed, 1999; McMahon et al., 2006; Mahmoud et al., 2008).
Recently, the possibility of diagnosing the disease with anterior segment parameters using the Scheimpflug camera system was proposed. The Scheimpflug camera system is a next-generation system that can record three-dimensional (3D) images as making rotation to the axis of the eye with its rotating camera. In this kind of systems, in addition to topography maps, corneal volume, anterior chamber angle, anterior chamber volume and anterior chamber depth parameters are also used to diagnose Keratoconus and to evaluate the severity of the disease. (Emre, Doğanay and Yoloğlu, 2007). These devices can record 3D images but offers in two-dimensional (2D) form to the user. Images that were made more understandable by modeling in 3D form in our study were taken from the Scheimpflug camera system.
The importance of correctly identifying and classifying keratoconus is increasing because nowadays, a variety of very effective treatment options are available. Hereafter, treatments such as collagen cross-linking used in progressive keratoconus cases can make it possible to stop the progression of the disease (Kocamış, 2011). The collagen cross-linking method has been used for keratoconus in recent years and is applied to corneas thicker than 400 μm. After treatment, a thin cornea hardens. In this way, sharpness of the cornea and the disease progression can be halted or very decelerated.
Among half of patients treated in this way, the cornea is flattened approximately 2–3 times. Raiskup-Wolf et al. (2008) followed the results of cross-linking on keratoconus cases in a 6-year period. In their study, at the end of the third year, a decrease of 4.84 D in corneal slope and an accompanying increase in best corrected visual acuity was reported. Various studies were conducted on the subject of how to use the treatment, current status, and monitoring of results. A number of studies have shared the effects of the treatment on the disease and the postoperative corneal changes (Utine et al., 2009; Uçakhan Gündüz, 2009; Utine, 2005; Raiskup and Spoerl, 2011; Zhang, 2012; Caporossi et al., 2010; Tahzib et al., 2010). Using the computerized devices benefiting from 3D technologies provides support to the field experts on making the right decisions on the diagnosis in a short time, determining the most effective and results-oriented treatment, and realizing and monitoring the treatment and operations.
Nowadays, 3-D devices increase the success of the monitoring and the treatment processes in Medicine. For an instance, in cancer treatment, healthy cells are prevented from damaging by using 3-D devices because they can clearly determine the accurate tumor localization. As an example of this type of treatment, a 3D imaging device known as the Varian Linear Accelerator started to be used at the Gazi University Faculty of Medicine in order to support target-oriented radiation treatment. It contributed significantly to patients’ comfort and to the treatment. In this treatment method, with the computerized planning device that collects such tumor-related information as the location, size, and precision to make a computerized simulation, it can be possible to mark the tumor and surrounding delicate tissue and determine the treatment doses. Displaying the face in 3D form is recognized as an advance in physical modeling techniques using the engineering methods in medicine. Kumar and Vijai (2012) performed 3D modeling of the face in a different imaging approach.
In this study, a decision support system for the physician was performed on the course of keratoconus to display the cornea in 3D form. Therefore, visibility and readability of the corneal region with keratoconus increased.
2 Methodology
2.1 Data
Our study was conducted on 749 digital images of 122 patients recorded by the Scheimpflug camera and the Placido Disc Combination from January 24, 2009, to January 24, 2012. Data were provided from the Yıldırım Beyazıt University Atatürk Education and Research Hospital by the Ethics Committee approval report 43, dated April 25, 2013.
2.2 Application
First, the data set of this study was obtained through 749 2D corneal images that were recorded by the Scheimpflug camera and Placido Disc Combination. After data cleaning and preparing, 144 images had to be discarded because of scanning problems, especially due to closed eyelids, and the final data set had 605 original 2D images. These images were cropped by our application using the Cropped Quad-Tree method. The recorded images have some unnecessary elements, like eyebrows and eyelashes, so these parts were discarded by using this cropping method.
Cropped images were grouped using Multilayer Perceptron and Logistic Regression classification methods using the thickness values that were obtained by our application. With the help of a 3D imaging application developed using the grouped 2D images obtained in the previous step, more easily interpretable 3D maps were obtained.
After modeling the 2D image data set in 3D form, we also developed comparing screens for the physician to see the pre- and post-operational forms of the cornea to follow up the results of the operation.
The steps of our study are detailed in Figure 31.2.
The application architecture of this study is seen in Figure 31.3.
In this application, the Cropped Quad-Tree method was implemented to present the corneal part in the recorded image and crop out the unnecessary parts. By the help of this method, we disregarded the parts that were out of our study’s scope.
A quad-tree is a hierarchical data model that recursively decomposes a map into smaller regions. Each node in the tree has four children nodes, each of which represents one-quarter of the area that the parent represents. So, the root node represents the complete map. This map is then split into four equal quarters, each of which is represented by one child node. Each of these children is now treated as a parent, and its area is recursively split into four equal areas, and so on, until a desired depth is reached. The Cropped Quad-Tree method is the enhanced version of the Quad-Tree method. Here, the minimal screen part where the object is located is determined instead of performing operations on the entire image. Later, division operation is performed only within the window determined previously; in this way, adscititious processes are avoided. Consequently, benefits are obtained in an algorithm in terms of speed depends on the size of the object on the image (Çavuşoğlu et al., 2013). You can see how this method can be implemented in the study in Figure 31.4.
Figure 31.4 corresponds to the following quad-tree in Figure 31.5.
In our study, we applied the Cropped Quad-Tree method to the corneal image as implementing the algorithm:
function CropImage{Takes Points as a Parameter}
Initialize Parameters
Initialize the Reference Height Values(that represents the colour values)
Set Minimum-Maximum X-Y Coordinates
Search for Min-Max X Coordinates for All Points
Search for Min-Max Y Coordinates for All Points
Crop the Image According to the Decision bits
end function
An example screenshot from the screen dividing process can be seen in Figure 31.6. This process was conducted for the purpose of finding which areas were not necessary and cropping these unnecessary areas.
Decision bits on how to crop the image achieved by cropping the screen using the occupied parts can be seen in Figure 31.7. The tree is represented by a series of bits that indicate termination by a leaf with a 0 and branching into child nodes with a 1 based on the occupation situation. We have achieved our desired location (there is no node that is not occupied) in the fifth step, as seen in Figure 31.7.
A multilayer perceptron (MLP) is used in this study as one step of the data mining process. An MLP is a feed-forward artificial neural network model that maps sets of input data onto a set of appropriate outputs. An MLP consists of multiple layers of nodes in a directed graph, with each layer fully connected to the next (Figure 31.8). Except for the input nodes, each node is a neuron (or processing element) with a nonlinear activation function. MLP utilizes a supervised learning technique called back-propagation for training the network. The mathematical expression of each perceptron’s computation can be expressed as
where w is the vector of weights, x is the vector of inputs, b is the bias, and φ is the activation function.
MLP (Figure 31.8) is a feed-forward network of interconnected neurons that are usually trained using the error back-propogation algorithm. This popular algorithm works by iteratively changing a network's interconnecting weights in proportion to a “training rate” set by the artificial neural network (ANN) method such that the overall error (i.e., between observed values and modeled network outputs) is reduced.
The other step of our study’s data mining part is logistic regression (LR). The purpose of using LR is to establish a least-variable model that is optimum fitting and can define the relationship between dependent and independent variables and that is biologically acceptable (Bircan, 2004). The logistic regression model can be expressed as
where ln is the natural logarithm, logexp, where exp=2.71828..; p is the probability that the event Y occurs; p(Y=1); p/(1-p) is the odds ratio; 
is the log odds ratio, or logit; a is the coefficient on the constant term; B is the coefficients on the independent variable(s); X is the independent variables; and e is the error term.
In our study, we obtained thickness values from 467 points of 605 2D images by analyzing each image with unsupervised MLP and LR methods. A total of 70% of this data are used for training; the remaining 30% of the data is used for testing.
In order to use 3D modeling techniques in our software development process, XNA Framework dynamic-link libraries (DLLs) were added on Microsoft .NET C# platform. Microsoft XNA Framework is a tool that enables software developers developing games using Microsoft Visual Studio C# language on Microsoft Windows and Xbox 360 platforms. Standard game development procedures require a good deal of code and time; XNA Framework is intended to facilitate this process. To bring this idea to fruition, it is presented that the most important thing the programmers should take care of is the code. XNA Framework takes the items on itself that processing and designing periods take time as graphics card, resolution, image processing. Also, it creates a game window for developers. (XNA Framework, 2014). With the help of these DLLs, software codes were developed that supports the 3D transactions in the following ways:
• Creating a height map (terrain) from the red, green, blue (RGB) or grayscale corneal image using the Diamond Square algorithm
• Cleaning the image parts outside the normal range (normalizing the image according to the minimum and the maximum points)
• Terrain texturing
• During the texturing process, if some points cannot be textured due to the irregularities of the height and the slope values, recalculating these values according to the values of the nearest points by scanning the x- and y-axes, respectively
The Diamond Square algorithm that was used in creating the height map in our study includes the following steps:
1. The diamond step: Taking a square of four points, generate a random value at the square midpoint, where the two diagonals meet. The midpoint value is calculated by averaging the four corner values, plus a random amount. This gives you diamonds when you have multiple squares arranged in a grid.
2. The square step: Taking each diamond of four points, generate a random value at the center of the diamond. Calculate the midpoint value by averaging the corner values, plus a random amount generated in the same range as used for the diamond step. This results in squares again.
3. So long as the length of the side of the squares is greater than zero, keep performing the diamond and square steps for each square present and reduce the random number range.
Stages of the normalization process involve finding the points that have minimum and maximum height values, respectively, for the x- and y- axes and displaying after recalculating all points according to these values [Eq. (31.3)]. Normalization formula is as follows:
After normalization and texturing processes on the height map shown in Figure 31.9(c), 3D corneal image in Figure 31.10 was obtained.
Our study was developed in order to provide monitoring and evaluation processes that can be done even by those who are not experienced in dealing with keratoconus, not overlooking any detail in the diagnosis process of the disease, with the help of easily readable and interpretable maps. Thanks to the system that was developed, recorded images for preoperation and postoperation in 2D form were transformed to 3D images (Figure 31.11).
In the next step, to facilitate monitoring the effects of the treatment, images were overlapping (Figure 31.12). In Figure 31.12(b), it can be seen that when the cross-links existing in the corneal layer hardened and became more resistant after the treatment, prolonged tissues were withdrawn.
3 Conclusions and Recommendations
Early diagnosis and suitable treatment planning at the right time is extremely important for success in treating keratoconus disease. Because the disease can be treated if diagnosed early, the need for corneal transplantation can be prevented or delayed for many patients through early diagnosis. Keratoconus subsequently occurs in many of the 11-12-year-old amblyopia patients that have astigmatism in one eye and their vision cannot be increased in their past life. Because the disease cannot be identified by routine examination in early stages, special topographic devices are needed to diagnose it. To notice the tapering of the patient's cornea with the naked eye can be available in advanced stages of the disease which require corneal transplantation. Because that special tests are needed to diagnose the disease, large number of patients live without being aware of their disease.
There is a shortage of 3D studies about corneal diseases. Because this disease is very commonly seen and accurate treatment is very important to cure it, we conducted this study. In this study, it was performed to simulate the changes occurred in the cornea by using 3D modeling techniques between preoperational and postoperational periods as selecting from the cornea images of good quality in recording by using data mining methods. With the help of the application developed and discussed here, it was made possible to monitor whether the treatment was successful in achieving the desired results, as well as monitoring the healing process in the posttreatment period. A decision support system was developed by this study for eye specialists in the diagnosis, treatment, and follow-up phases by the established system.
In our study, 605 images were selected from 749 images by data cleaning and preparing steps. Then the images in the data set were cropped using the Cropped Quad-Tree method. This method made our cropping process easier and more accurate. It is also beneficial in studies where speed is important. After the cropping process, thickness values of 467 different points of these 605 cropped images were obtained.
Thickness data obtained from the previous step were analyzed with MLP and LR methods. A total of 424 rows of data were used to train the system, and 181 rows of data were used for the classification process.
Results of the classification methods used in the study are shown in Table 31.1. MP, with an accuracy rate of 97.2376%, is more successful than LR, with an accuracy rate of 87.8453%. A 2D data set grouped with MLP (because it has produced more correctly classified instances) was modeled in 3D form on the .NET C# platform with the help of XNA Framework DLLs. We added this framework to our .NET C# project, and by using the 3D imaging method of consisting of creating a height map, normalizing this map, and applying terrain-texturing process on the height map, we modeled 2D corneal images in 3D form. A directory of corneal images recorded by the Scheimpflug camera system can be given to this system, and it has the potential of performing the following steps:
Table 31.1
Results of Classification Algorithms
| Algorithm | MLP | LR |
| Number of input variables | Total number of instances: 605 Number of training data: 424 (70% of total 605 instances) (This data is not used for classification, only for training the system.) Number of test and classification data: 181 (30% of total 605 instances) (This data is used for classification of the images.) | Total number of instances: 605 Number of training data: 424 (70% of total 605 instances) (This data is not used for classification, only for training the system.) Number of test and classification data: 181 (30% of total 605 instances) (This data is used for classification of the images.) |
| The number of correctly classified instances | 176 instances out of 181 test and classification instances 97.2376% | 159 instances out of 181 test and classification instances 87.8453% |
| The number of incorrectly classified instances | 5 instances out of 181 test and classification instances 2.7624% | 22 instances out of 181 test and classification instances 12.1547% |
| Classification time | 1011.16 s | 6.7 s |
| True classification | Very Good | Good |
1. Prepare the data set so as to select the appropriate ones for the study, cropping and cleaning these images.
2. Classify the images into groups of healthy, keratoconus, other corneal diseases, cross-linking and transplantation operations.
3. Convert the 2D image to a height map using the Diamond Square algorithm.
4. Normalize the height map according to the minimum and the maximum points on the x- and y-axes.
5. Texture these height maps by using the color and height correlation of the Scheimpflug camera system (that the 2D images were recorded by).
6. Give some comparisons of preoperation and postoperation 3D images with the color and height palettes. Also, in the comparison screens, there are camera applications that can change the viewpoint of the users to help them to see the image from different perspectives.
With the help of 3D images, readability of the cornea increased. This study showed that display of the disease and the healing process can be improved by using more interpretable 3D images.