Prediction of the course of primary open-angle glaucoma in combination with diabetic retinopathy using a mathematical model

. It is possible to accurately diagnose diseases in the early stages using optical coherence tomography. A mathematical model has been developed for two diseases: glaucoma and diabetic retinopathy. The model takes into account digital data of ophthalmological equipment obtained from the optic nerve disk and macular area. Criteria that take into account the thickness of the macular zone and the parameters of the optic nerve disc were developed (integral volume and area of the neuroretinal rim, the area of the optic disc excavation). The proposed mathematical model gives the opportunity to predict the development of combined pathology in relation of the integral area of the neuroretinal rim to the integral volume, as well as to a criterion that takes into account the thickness of the macula and the area of excavation of the optic nerve head. The model makes it possible to give a clear risk of developing diseases (low, high) and a significant prognosis of the course of diseases (good prognosis for vision, bad prognosis for vision). The capability of the mathematical model to predict the development of the disease in a patient with type 2 diabetes is demonstrated.


Introduction
The problem of the relationship between primary open-angle glaucoma and diabetes mellitus has been studied worldwide for more than eighty years [1][2][3][4]. Currently, the common pathogenetic mechanisms of the two diseases have been proven. Both glaucoma and diabetic retinopathy affect the internal parts of the retina [5][6][7].
Oxidative stress, hyperglycemia, hypoxia with the release of angiogenic factors play a crucial role [9][10][11][12]. As a result of increased intraocular pressure, the optic disc suffers with mechanical compression of its fibers in the ethmoid plate [13][14][15]. A detailed analysis of the optic nerve disk at the morphological level in the early stages of the disease is provided by a modern optical coherence tomograph [16][17][18][19][20]. The Protocol of analysis of the optic nerve head evaluates the results of measurement of the parameters of the neuroretinal rim. Optical coherence tomography provides objective digital data on the integral area and volume of the neuroretinal rim, the excavation of the optic nerve disk according to the level of retinal pigment epithelium, and also determines the layer of retinal nerve fibers located around the optic nerve disk using circular scans. Both glaucoma and diabetic retinopathy damage the central region of the retina. With glaucoma, Bjerrum scotomas appear in the center, and with diabetic retinopathy, retinal edema occurs in the macular zone. Optical coherence tomography makes it possible to estimate the thickness of the retina in 9 sectors of the macula [21][22][23].
The search for morphological relationships between the optic nerve disk and the macula in the analysis of optical coherence tomography data is of great scientific interest. The found relationships will help to create mathematical models and computer programs not only for diagnostics, but also for the prognosis of two diseases [24,25]. Mathematical modeling and programming are relevant today not only in medicine, but also in other fields of science [26][27][28][29][30].

Problem
To develop a mathematical model for the prognosis of diabetic retinopathy and primary openangle glaucoma based on studies of the macular zone and the state of the optic nerve disk according to optical coherence tomography.

Mathematical processing of digital data of the macular zone thickness based on optical coherence tomography data
To assess the state of the retina, it was decided to develop a criterion that takes into account the thickness of the macular zone. Map of the macula E M5 (figure 1) and a table of thickness of the retina of the macula (figure 2) are the results of the operation of an optical coherent tomography.
A criterion of the influence of retinal thickness, which is characterized by the severity of the volume of edema in the thickness of the retina in 9 sectors of the macular zone, is proposed:     Based on the results of the research, a table that determines the relationship between the developed criteria and the prognosis of the disease was obtained (table 1).  The patient examination data are presented by an optical coherent tomography (table2).

Optic disc parameters Value
Integral area of the neuroretinal rim, m 2 1.732 Integral volume of the neuroretinal rim, m 3 0.253 Optic disc excavation area, m 2 1.242 As a result of the calculation, the program determined the value of the criterion Thus, the proposed mathematical model makes it possible to make a prognosis of diabetic retinopathy and primary open-angle glaucoma simultaneously, both from digital ophthalmological data of the macular zone scanning results and from the examination of the optic nerve disk state. This approach provides more opportunities in comparison with separate studies of fundus structures. The use of a computer program helps to create a system for supporting decision-making by an ophthalmologist, as well as optimize the patient's examination time.

Conclusion
A mathematical model has been created for predicting the development of the combined pathology of diabetic retinopathy and primary open-angle glaucoma. The model makes it possible to provide a clear risk of developing diseases (low, high) and a significant prognosis of the course of diseases (good prognosis for vision, bad prognosis for vision). The model takes into account the clinical and morphofunctional data of the retina, namely, the thickness of the retina in the most important 9 sectors of the macula center, the integral volume of the neuroretinal rim and its area, and the data on the area of the optic disc excavation. The given list of data was combined into a single generalizing criterion The proposed mathematical model for predicting the development of the disease is of great importance for practical health care, as it prevents the development of blindness and low vision in patients with severe form of glaucoma and diabetic retinopathy. This is especially important for patients with glaucoma. Glaucoma has an asymptomatic course and rapid vision loss. The growing intraocular pressure in the eye has a detrimental effect on the fibers of the optic disc, causing the development of compression of axons in the ethmoid plate with the appearance of apoptosis. The proposed model takes into account changes in the structure of the optic nerve disk and provides a prognosis for the development of the disease at an early stage, which allows the patient to preserve vision.
The computer program developed according to the model provides a quick high-quality forecast of the development of the disease and approaches each patient in a personalized way.
The prospect for the development of this scientific direction is the creation of an analysis system and an approach algorithm in the diagnosis and prognosis of combined pathologies of the fundus.