Electroretinogram Analysis In Patients With Non-Proliferative Diabetic Retinopathy

Purpose: Non-proliferative diabetic retinopathy (NPDR) is the earliest stage of diabetic eye disease. Microscopic changes occur in the blood vessels of the eye in NPDR. The changes typically do not produce symptoms and are not visible to the naked eye. This paper aims to investigate a method for distinguishing NPDR based on Electroretinogram (ERG). Method: The ERG responses were recorded in 20 eyes from 14 patients with NPDR and 20 eyes from 20 healthy subjects as the control group. The responses of three standard stimuli were collected for both groups. Time-domain parameters, including amplitudes and implicit time, and a nonlinear criterion, were used to differentiate the groups. Results: This study showed that implicit time and amplitude of b-wave in dark-adapted 10.0 ERG and amplitude and implicit time of light-adapted �icker 30 Hz could distinguish between controls and NPDR groups. Theta values obtained for dark-adapted 10.0 ERG (p=0.0019), light-adapted 3.0 ERG (p=0.0021), and light-adapted �icker 30 Hz (p=0.0023) had signi�cant differences between the groups. Conclusion: The proposed features have made it possible to distinguish between healthy and NPDR eyes. Choosing an appropriate method can effectively evaluate inner retinal dysfunction, especially in diabetic retinopathy.


Introduction
Diabetes is a common type of metabolic disease which is characterized by high blood glucose.Diabetes consists of type 1 or insulin-dependent diabetes, caused by a reduced insulin secretion rate, and type 2 or non-insulin-dependent diabetes, in which body cells do not respond to insulin adequately [1][2].
Hyperglycemia is the main feature of diabetes, and after a while, it causes vascular and neurological changes [3][4][5].
Diabetes has different complications, including cardiovascular disease, kidney, eye, brain, and nerve damages [6][7][8][9][10].Diabetic retinopathy (DR) is the principal cause of vision loss and blindness among people with diabetes, especially working-age adults in developed countries [1,11].Intraretinal uid accumulation and retinal hemorrhage leading to decreased vision are caused by diabetic retinopathy [12].In the advanced stage of the disease, abnormal blood vessels proliferate on the retina's surface, may be associated with vitreous hemorrhage, brous proliferation, and traction retinal detachment [13].
Diabetic retinopathy consists of non-proliferative diabetic retinopathy (NPDR) and proliferative diabetic retinopathy (PDR).NPDR manifests by microaneurysms resulting in leakage of uid and blood into the retina.PDR, which is characterized by neovascularization, is the more advanced DR [14][15].
Although DR involves several stages of severity, even very severe DR can be completely asymptomatic.If diagnosed, the disease can be improved with treatment.Therefore, early diagnosis of the DR is critical, especially in the early stages.Fluorescein angiography, visual evoked potentials (EVP), and electroretinography are usually used to determine if the patient needs treatment [16][17][18].These methods can provide a de nitive study of the visual function and possibly destructive effects of diabetes on the visual system [19].
Electroretinogram (ERG) analysis is usually performed in the time-domain analysis.By measuring the two parameters of implicit time and amplitude of the waves, it is hard or impossible to detect minimal changes caused by NPDR.Biological signals like ERG are complex and have variable dynamics.
Therefore, nding an appropriate method for processing these signals is very di cult.Processing methods attempt to extract the maximum information about the proper functioning or non-functioning of the related organs.Different signal processing methods have been applied to ERG, including timedomain, frequency-domain, and time-frequency domain analyses [20][21][22][23][24][25][26].Besides, nonlinear features have been used to analyze the ERG [27][28].
This article intends to investigate the possibility of differentiating between normal and NDPR groups using a nonlinear feature.

Data description
The Ethics Committee at the Ophthalmic Research Center a liated with Shahid Beheshti University of Medical Sciences Tehran, Iran, approved this study.The study included 20 eyes of 14 patients with NPDR and 20 eyes of 20 healthy subjects as the control group.The control subjects had no known visual system abnormalities, normal ndings in the ophthalmic examination, and normal full-eld ERG (ffERG).The mean statndard deviation (SD) age of the NDPR patients and controls was 62.19 7.33 and 57.24 7.11 years, respectively.
The ERG signals were recorded using Roland Consult (Brandenburg, Germany) from both eyes simultaneously.Pupils were fully dilated using topical tropicamide 1%.Flashes of white light evoked the ERGs.The duration of the ash was 20 s with the interstimulus interval of 1.5 seconds.After 20 minutes of dark adaptation the subjects put their head on Ganzfeld stimulator, and the dark-adapted 10.0 ERG were recorded.In the next step, photopic recordings were preceded after a light adaptation of 10 minutes to a background light of 30 cd/m 2 .
The International Society for Clinical Electrophysiology of Vision (ISCEV) has been continuously standardizing different methods to achieve world-comparable responses [29].The ISCEV standard fulleld ERG [30] includes three responses of dark-adapted 10.0 ERG, light-adapted 3.0 ERG, and lightadapted 30 Hz icker were considered in this study.

±
In recent years, different methods for ERG signal processing have been proposed with some advantages and disadvantages.However, the goal of all methods is to nd the best way to analyze the ERG signals.
The standard characteristics of ERG signals, which have been evaluated in most research, include ERG waves' amplitude and implicit time.
The ERG length is normally 200 milliseconds, and the rst 80 milliseconds are the most critical part of the signal; because it contains the main components.Therefore, one of the fundamental challenges of processing ERG is its short length.Nonlinear methods could be the right choice in such signals to represent the signal's dynamic, which cannot be extracted through conventional methods.

Mapping Method
In this method, ERG is mapped to a parabolic curve.Therefore, the pairs of are used to rearrange the points of ERG.The parabolic curve could provide a high resolution for distinguishing between different signals.The distribution of points in the parabolic curve is obtained through a two-degree polynomial equation as follow [28]: 1 The three main parameters of this equation are , , and .The distribution of points in a parabolic curve can have three states.The accumulation of points may be more to the left, right, or approximately divided into both sides equally.An illustration of the possible distribution of signal points on the axis is shown in Fig. 1.
The time series (ERG in our study) may include negative or positive amplitudes.Therefore, based on the the square of the signal causes these parts of the signal to accumulate on the left or right side of the curve.In this way, we can even interpret the positive and negative amplitudes of ERG.
A criterion for measuring the distribution of points on the right or left side of the curve is the angles made by drawing a line from the beginning to endpoints distributed on the parabolic and horizontal axis.If the accumulation of points were on the parabolic curve's right, it indicates that the angle is less than 90 degrees.Such a result means the signal contains positive waves with higher amplitudes.On the other hand, if the accumulation of points were on the left of the parabolic curve, it leads to the angle, which is less than 90 degrees.
Negative angles con rm that signals contain negative waves with higher amplitudes.Signals with small angles (close to zero) indicate the balance between positive and negative waves [28].The calculation of angles and measuring accumulated points on the curve's left or right side is shown in Fig. 2.
The tangent is de ned as the ratio of the opposite side to the adjacent side.Theta is de ned as the inverse of the tangent function, which is the angle whose tangent is a given number: In positive angles, the opposite side is "a," which is a portion of b-wave amplitude, and in the negative angle, the opposite side is "b," which is a portion of a-wave amplitude.In both cases, opposite sides contain more amplitudes than other parts of a-wave and b-wave [28].
There might be cases where several dispersed data far away from the rest of the points open the angle's arc and show a larger Theta.In principle, most of the points have accumulated elsewhere, and if the upper arc angle is considered to be the accumulation of those points, the Theta angle may be smaller.A density criterion can be a solution to this problem.The density of points in the Theta arc can be calculated and multiplied by the Theta angle.Therefore, the density criterion decreases if the accumulation of points is less and the angle is large.On the contrary, the higher the accumulation of points and the smaller the angle, the more robust the density criterion [28].
3 Figure 4 shows the different densities of points in the Theta angle arc for the two sample time series.As can be seen, Figure 3(a) shows the proportional distribution of points and the formation of a corresponding logical angle.However, in Figure (b), two points are located far from the concentration of points, making it a more signi cant angle.This false magni cation of the angle can lead to misjudgment.

Statistical Analysis
The data do not have a normal distribution, and the two studied groups (healthy and NPDR eyes) are independent.Therefore, the Mann-Whitney U test was employed to reveal the signi cance of ERG features.Values are given as the mean ± standard deviation (SD), and the signi cance level is de ned as p < 0.05.Moreover, the effect size statistic for the Mann-Whitney U test is "r" de ned by the following formula: 4 where is the total number of observations, and then runs the test SPSS reports the appropriate value.Effect sizes can be divided in four groups according to their r-values: "small" (0.1<|r|<0.3),"medium" (0.3<|r|<0.5)or "large" (|r|>0.5)[31].

Results
The time-domain method is known as the standard method of ERG analysis.A sample of ERG for healthy normal and NPDR is presented in Fig. 4. Therefore, the implicit time and amplitude of a-and b-waves for all individuals were presented in Table 1.A-wave amplitude did not show any signi cant difference (p < 0.05) in light-adapted 3.0 ERG.In the next step, the parabolic curve parameters ( , , and ) were calculated for all of the six ERG signals.The values obtained for the rst parameter ( ) were all the same for both groups.The other two parameters ( , and ), which represent the parabolic width and its location on the vertical axis, had different values, but no signi cant changes were observed.Theta angles for three studied stimuli are shown in Table 2. Theta values obtained for dark-adapted 10.0 ERG (p = 0.0019), light-adapted 3.0 ERG (p = 0.0021), and light-adapted icker 30 Hz (p = 0.0023) had signi cant differences between the groups.Using the density criterion and its multiplication in the amount of Theta, we found a signi cant difference among dark-adapted 10.0 ERG (p = 0.0012), lightadapted 3.0 ERG (p = 0.0013), and light-adapted 30 Hz icker (p = 0.019).

Discussion
In this study, a nonlinear criterion was used to evaluate the ERG of NPDR and healthy eyes.This article aimed to investigate the ability of nonlinear features to differentiate the changes in eyes with NPDR compared with normal eyes.
ERG has valuable characteristics that can be used as an independent diagnostic method.Retinal function, retinal disease progression, or even control in some retinal diseases can be well assessed using an ERG signal.The ERG changes with some retinal diseases, such as retinitis pigmentosa (RP) or central retinal vein occlusion (CRVO), are so signi cant that their effects on implicit time and amplitude are apparent.However, in some cases or the early stages of the disease, little difference occurs with the normal state due to minimal changes in the ERG's amplitude and implicit time.However, these changes have led to changes in ERG dynamics and will undoubtedly be detectable using a sensitive feature to even small changes.
Various nonlinear features have been applied to ERG signals so far.These features include the Lyapunov exponent, Hurst exponent, approximate entropy, and fractal dimension.Nonlinear features have made a good distinction between healthy and abnormal groups [27].Another feature that could show the dynamic of ERG in CRVO patients was mapping the ERG to a parabolic curve and extracting an angle criterion based on the arrangement of points on a new curve [28].Due to the short length of the ERG, geometric features or signal mapping can create a different point of view to the distribution of time series points, and perhaps the hidden dynamics of the signal can be detected.
NPDR has a more negligible effect on the ERG signal than the proliferative stage diabetic retinopathy.
Therefore, in this study, we tried to investigate the potential of mapping features in this type of diabetes.Since the standard criteria for ERG analysis refer to the amplitude and implicit time of the ERG components, we compared the two groups with the time-domain characteristics before evaluating the nonlinear method.B-wave amplitudes were signi cantly lower in the NPDR group [32].The b-wave amplitude is believed to be a good indicator of retinal circulation.Therefore, our results con rmed the insu ciency in the retinal circulation of the NPDR group.
The implicit times of the a-and b-wave were increased in the NPDR group.Previous research has also reported the delay in the a-and b-wave in various retinal diseases [33][34].The increase in the implicit time in b-wave has already been con rmed in various retinal diseases [35][36].It was reported that hat delays in the development of b-wave in patients with CRVO could manifest the disease progression and the occurrence of retinal neovascularization [36].This similarity between the results and PDR nature, characterized by neovascularization, could be an essential point.It may help the ophthalmologists to early diagnose the progress of NPDR and its advance towards PDR.
In the Theta angle criterion, the accumulation of points on the right-hand side is somehow an indicator of the b-wave amplitude.Past studies have shown that if the ERG b-wave generated in the neural retinal layers becomes very small in the eye with CRVO, it can be concluded that the overall retinal ischemia is very severe [37][38][39][40][41].The Theta angle of the NPDR group for dark-adapted 10.0 was negative and reduced dramatically in the NPDR group.A negative angle refers to the a-wave.So, it seems that bipolar cells are disrupted.In some NPDR patients, Theta-angle changes were smaller.This difference could be attributed to the severity of DR.This idea can be further explored by examining patients with PDR comparing the angle differences observed in this group with the non-proliferative group.

Conclusion
Although various imaging techniques have always been reliable to diagnose retinal diseases and monitor their progression, such methods are also more expensive than a signal recording method.The nonlinear criterion evaluated in this study showed that selecting the appropriate feature to extract the ERG signal dynamics can increase the chance of detection and more accurate investigations based on this signal.
The Theta criterion can be a practical feature for diagnosing DR, and it can be a valuable method in other retinal diseases.This criterion provided helpful information about photoreceptors and different layers of the retina.
In this study, we examined the ERG signals of NPDR patients.It is suggested that Theta can be used to evaluate other types of diabetic retinopathy.Positive and negative angle index in the parabolic map The density of points in the arc of Theta angle

Figure 5
Figure 5 indicates an example of Theta angle in dark-adapted 3.0 ERG for (a) NPDR and (b) normal eyes.It can be seen that the value of the Theta angle in the NPDR eye has decreased compared to a normal eye.

Figures Figure 1
Figures

Figure 4 Sample
Figure 4

Table 1
Time-domain characteristics of the non-proliferative diabetic and normal eyes

Table 2 :
The mean and standard deviation of Theta feature for non-proliferative diabetic retinopathy and the normal eyes in six ERG signals recorded with different stimulus