Prediction model for severity of diabetic retinopathy derived from review of endothelial dysfunction and hypoxia markers

Background. According  to a wide  range of authors, eye damage caused by diabetes mellitus accounts for 80–90 % of the total number of disorders. The development of mathematical predictive models allows for a more versatile analysis of experimental and clinical data. The purpose of the study was to develop a model for predicting the severity of diabetic retinopathy based on a review of markers of endothelial dysfunction and hypoxia. Materials and methods. We used a streptozotocin model of type 2 diabetes mellitus. Determined von Willebrand factor,  endothelin-1,  2,3-diphosphoglycerate  are  used  as  variables.  Also,  the  transition  of  the  non-proliferative phase of diabetic  retinopathy  into  the proliferative on  the 180th day of  the experiment was confirmed histologically. Results. We have developed a mathematical model for predicting the studied pathological state based on biochemical blood tests at the early stages of the experiment. We have proven the informative value of endothelial dysfunction markers, von Willebrand factor and endothelin-1, for predicting the transition of non-proliferative diabetic retinopathy into the proliferative phase. We determined the significance of a comprehensive analysis of the level of 2,3-diphosphoglycerate in erythrocytes together with the above markers of the functional status of the endothelium on day 30 for predicting the further course of the disease. Conclusions. We determined the effectiveness of a comprehensive analysis of the level of 2,3-diphosphoglycerate in erythrocytes together with the above markers of the functional status of the endothelium on day 30 for predicting the further course of the pathological process under study.


Introduction
Diabetic retinopathy (DR) is a specific vascular complication of diabetes mellitus (DM) being the major cause of blindness in individuals of active working age in developed economies. According to a wide range of authors, it stands at 80-90 % of total visual disability caused by DM [1,2]. DR pathogenesis has the following phases: progressive hypoxia that stimulates vascular proliferation and results in adipose degeneration and retinal calcification; microangio-pathy of retinal vessels which results in luminal occlusion with hypoperfusion; steal phenomenon with further progression of ischemia that is cause for formation of infiltrates and scars; vascular degeneration with microaneurysms; microinfarctions with exudates, enlargement of proliferating vessels in the retina with shunts and aneurysms; arteriovenous shunts that cause vein dilatation and higher retinal hypoperfusion; retinal detachment due to its ischemic disintegration [3,4]. The key role of endothelial dysfunction in DR occurrence and progression has been currently proved [5].
Late vascular complications appear to be non-fatal if the prevention and treatment are initiated in time and provided properly [6,7]. The course of disease should be appropriately predicted to have pathogenic links effectively adjusted at the early stages. Early detection and prediction of microangiopathies and timely influence on modifying risk factors are extremely essential [8].
Pathogenesis of late DM complications has multifactorial nature. Its simplified model includes glycosylation of cell membranes, basal membranes, and proteins. The significant factors are higher vascular permeability, impaired caloric balance, changed metabolism of cell membranes, and induction of polypeptide growth factors. In each particular case, range and severity of certain late complications vary from their paradoxical, almost complete absence, regardless of long duration of the disease, to combination of every possible variant in a severe form [9,10].
Considering complicated pathogenesis, individual organism specifics, enormous number of factors that diffe rently contribute to pathological growth and closely inte ract with each other, medication strategy and other impacts on pathological process it seems to be a difficult choice to make. The above shows how difficult is to predict the outcome of disease and need to optimise adjustment of the pathological condition with no experimental study or mathematical method involved. The development of mathematical prediction models enables for a more versatile review of experimental and clinical findings which further contributes to higher efficacy in decision making and individual approach in adjustment of pathological conditions [11].
Considering the above, we have developed the prediction mathematical model of DR severity depending on informative biochemistry markers.
The purpose of the study was to develop a prediction model for severity of diabetic retinopathy based on review of endothelial dysfunction and hypoxia markers.

Materials and methods
Type 2 DM and DR were simulated by means of intraperitoneal administration of streptozotocin (Sigma, USA) diluted in 0.1 M citrate buffer with pH 4.5 [12]. Streptozotocin dose of 55 mg per 1 kg of animal weight was divided into two administrations. Streptozotocin use was preceded by a 28-day high-fat diet [13]. On the 30 th day, the levels of von Willebrand factor, endothelin-1, and 2,3-diphosphoglycerate in red blood cells were determined in the blood of this animal group.
A review of transition of non-proliferative phase of diabetic retinopathy into the proliferative one on the 180 th day of the experiment was confirmed histologically.
A situation when an explanatory variable in the model takes only two different values tends to occur under study of impact of some subjective and objective factors on presence or absence of some feature in individuals, households, etc. If a study covers n subjects, i.e. if there are n observations, then the fact of presence or absence of such feature in the i th observation may be easily indexed with figures 1 (feature is present) and 0 (feature is not present). Thereby, an indicative (dichotomic, binary) variable y is determined to obtain y i value in the i th observation. And y i = 1 if a feature is present in the i th subject, y i = 0 means a feature is not present in the i th subject [18].
The task of logistic regression is to explain presence or absence of the feature in question with the values (more precisely, combination of values) of some factors (explanation variables). Accordingly, the task includes assessment of parameters of the binary choice model which in general is as follows: where x i1 , …, x ip is p value of explanation variables in the i th observation; θ 1 , …, θ p are unknown parameters; ε i , …, ε n are random errors that show the impact on presence or absence of the investigational feature in the i th subject of any unaccounted additional factors; G(z) is S-like distribution function. We have chosen the standard logistic distribution function (logit-model) to be G(z) function: We will define a dependent dichotomic variable y as "transition of non-proliferative diabetic retinopathy into the proliferative phase", i.e. y i = 1 with the fact of transition of non-proliferative diabetic retinopathy into the proliferative phase and y i = 0 with no such fact available.
The following three variable factors were used: 1) x 1 as 2,3-diphosphoglycerate in red blood cells; 2) x 2 as endothelin-1; 3) x 3 as von Willebrand factor. The protocol was approved by the Ethics Committee of Ukrainian Research Institute of Transport Medicine (protocol 7, 17.09.2019).

Results
Having reviewed a range of studied biochemical blood markers, we determined a relationship between severity of DR and high levels of von Willebrand factor, endothelin-1 (which are common markers for endothelial dysfunction) and 2,3-diphosphoglycerate in red blood cells (hypoxia maker) in the blood of experimental animals.
Let us move to the model analysis. Calculations of the logistic regression parameters and specifications that describe the model adequacy were made in PASW Statistics 18 package. The maximum likelihood estimation was used as loss function; statistical significance of the model was assessed by Chi-square and Hosmer-Lemeshow criteria. P-value by Hosmer-Lemeshow test is equal to 1 which stands for full consistency of the model with really existing rates in the population sample. This means Mìžnarodnij endokrinologìčnij žurnal, ISSN 2224-0721 (print), ISSN 2307-1427 (online) Оригінальні дослідження /Original Researches/ that the part of dispersion that is explained with logistic regression is equal to 100 %. Additionally, the statistical package gives findings for other criteria, more stable than traditional goodness of fit statistics used in logistic regression, especially to study such small population samples as in our case [19]. The determination unit (determination factor) according to Cox and Snell in our model is equal to 0.632 (63.2 %). This criterion shows the share of impact of all factor features on dispersion of the dependent variable. Table 1 gives classification of cases and relevant percentage of correct predictions for presence or absence of the fact of transition of non-proliferative DR into the proliferative phase.
Consequently, we have determined that the model derived can by 100 % correctly predict presence or absence of the fact of transition of non-proliferative DR into the proliferative phase.
The following ( To get the relative likelihood for transition of non-proliferative diabetic retinopathy into the proliferative one (within 0-100 %) using the derived logistic regression function, you should multiply the function value G(z) by 100 %.
By inserting parameter values of a certain animal that is not in the studied group in question, we can determine the risk extent for transition of non-proliferative diabetic retinopathy into the proliferative phase.
Here are some examples of how this equation can be used based on particular clinical parameters determined in tested animals which had further confirmed the fact of transition of non-proliferative diabetic retinopathy into the proliferative phase.
Example with high probability for the fact of transition of non-proliferative diabetic retinopathy into the proliferative phase (laboratory animal No 16

Discussion
DR is a multifaceted disease with a complex network of metabolic and biochemical alterations that remarkably modify the retinal microenvironment [20]. The research has recently revealed the pivotal role of endothelin in the pathogenesis of diabetic complications, particularly in the regulation of the capillary flow which is affected in retinopathy. Although there are several reviews on va rious approaches to the treatment of DM, including normalization of glucose and fat metabolism, no reviews in literature have focused on the endothelin system as a therapeutic target or early indicator of diabetic microangiopathy [21].
In fact, novel genetic strategies to earlier detect the upregulation of endothelin-1, or to assess the wide-ranging downstream effects resulted from the activation of the endothelin system in the course of hyperglycemia are a challenging field for new research. Vascular complications of DM can affect not only large and medium arteries resulting in coronary heart disease and peripheral artery diseases but also small vessels leading to retinopathy and nephropathy. Intercellular adhesion molecule-1, vascular cell adhesion molecule-1, E-selectin, and von Willebrand factor are considered as markers of endothelial dysfunction.
By inserting parameter values of a certain animal that is not in the studied group in question, we may determine the risk extent for transition of non-proliferative DR into the proliferative phase.

Conclusions
1. We have proved the role of endothelial dysfunction in growth of investigational diabetic retinopathy.
2. We have developed a mathematical model for prediction of this pathological condition based on biochemical blood tests at early experimental stages. 4. To get the relative likelihood for transition of nonproliferative diabetic retinopathy into the proliferative one (within 0-100 %) using the derived logistic regression function, you should multiply the function value G(z) by 100 %. 5. We have proved the informative value of the endothelial dysfunction markers, von Willebrand factor and endothelin-1, in predicting transition of non-proliferative diabetic retinopathy into the proliferative phase. 6. We have determined the effectiveness of a comprehensive analysis of the level of 2,3-diphosphoglycerate in red blood cells together with the above markers of the endothelial functional status on the 30 th day for predicting the further course of the pathological process under study.