## Abstract

We present a theoretical analysis of laser coagulation for diabetic retinopathy (DR) eye surgery procedures. Using a Monte-Carlo multi-layer (MCML) simulation and a finite element model of the human eye, we derive the optimal surgery conditions and address the long standing debate regarding the best laser wavelength to be used. The differences between yellow (577nm) and green (532nm) lasers, which are the commonly used wavelengths for this procedure, have been studied previously, mostly via empirical studies. Here, to the best of our knowledge, we introduce for the first time a quantitative theoretical analysis to determine the best laser wavelength. Using our analysis, we determine optimal laser operation conditions for treating DR with minimal damage to the surrounding tissue. We show that under these conditions, the yellow laser is significantly favorable.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

## 1. Introduction

The retina is the most active tissue metabolically. Its metabolism is regulated by the retinal pigment epithelium (RPE), which is a monolayer barrier tissue that regulates the passage of nutrients to and from the retina. In diabetic patients the RPE function is impaired and the retina is deprived of oxygen and nutrients [1,2]. Therefore angiogenesis occurs i.e., new blood vessels are formed from preexisting blood vessels in order to supply the retina with oxygen and nutrients. These blood vessels are brittle and usually leak causing diabetic retinopathy (DR) and may even cause retinal detachment. DR is a major complication among diabetic patients and is one of the common causes of blindness in patients with diabetes. The common treatment for this condition is panretinal photocoagulation (PRP) [3]. In this procedure laser radiation is used to deliberately heat and destroy newly formed blood vessels and nearby retinal tissues. The overall consequence of which is improved retinal oxygenation and nutrition. Two types of lasers are used for this procedure, green (532nm) lasers and yellow (577nm) lasers. The main advantages of these wavelengths are low intraocular scattering and higher absorption in hemoglobin. These features enable precise treatment using relatively low laser power.

The difference between the green and yellow lasers for diabetic retinopathy eye surgery has been previously investigated [4–7] . Most of the work in this field is experimental and is based on clinical trials on animals and humans. However, no theoretical investigation comparing the two laser types has been carried out. The goal of this research is to investigate which wavelength is more suitable for diabetic retinopathy (DR).

Over the years several clinical trials investigated the differences between the use of yellow and green lasers for treating DR, and the results were inconclusive. Considering the treatment of macular edema using focal/grid laser treatment, the authors in [4] used data from two randomized clinical trials to examine the difference in visual acuity (VA) and optical coherence tomography (OCT) parameters. Meaningful differences between the use of yellow and green lasers were not detected. Ref. [5] reported clinical trials with different trained surgeons and measured VA after 6 -months of focal treatment with green and yellow lasers. The treatment outcome was the same using green and yellow lasers. In a study of the difference between mild coagulation and rupture in rabbits using a yellow laser, the rupture was found to be slightly wider than when using a green laser [6]. The coagulation threshold using the yellow laser was lower than with the green laser, although histologically the lesions were similar. In another clinical research, which was conducted on rabbits [8], using a green laser, the investigators studied the effect of the pulse duration on the size and character of the lesion in retinal photocoagulation. In this study, they found that the lesion size increased linearly with the laser power and logarithmically with the pulse duration. In Ref. [9] the authors evaluated the efficacy and safety of subthreshold micro-pulse yellow laser photocoagulation and found short-term efficacy in the treatment of diabetic macular edema that did not result in retinal damage, and the use of the yellow laser was found to be advantageous. A recent clinical research work [7] studying the patients’ comfort following the treatment of Panretinal Photocoagulation (PRP) for proliferative diabetic retinopathy (PDR), reports on a 10-point pain scale indicates that there is no significant difference in patient comfort during PRP, and that visual acuity is similar for green and yellow wavelengths. The physicians in the study indicated that the yellow laser is easy to use and preferred it over the green one.

Since the previous research regarding which laser wavelength is more suited to this kind of surgery is not fully conclusive, and the clinical and experimental studies were not carried out at optimal laser conditions we assert that further and more extensive research is needed. In this paper we use two simulations tools, Monte-Carlo simulations and finite element method (FEM), to determine the differences between the two. We use these methods to evaluate where in the eye most of the laser radiation is absorbed, what is the resultant temperature increase due to the laser absorption, and what are the optimal laser operation parameters for photocoagulation (i.e., laser energy, pulse duration, and spot size). The Monte-Carlo simulation is used for determining the required laser energy and beam diameter for photocoagulation. The FEM simulation enables us to determine the optimal laser pulse duration.

Numerical methods can provide a deep analysis when presented with a problem that cannot be solved directly; this is done by deriving a suitable model that was designed based on known parameters. In the past such numerical computations were insufficient or, in some cases, not possible at all, but nowadays such solutions can be easily obtained. Numerical modeling of conductive and convective heat transfer in retinal laser applications was suggested [10] and could be considered as a tool for finding optimized treatment under various tissue conditions and laser properties. Good agreement was obtained between numerical results and experimental measurements by using a realistic model. A bio-heat transfer simulation using a FEM model of retinal laser irradiation was conducted [11]; it was used for a PRP procedure using an Argon laser. Optimal parameters were found to achieve a maximal retinal temperature ($60^{\circ } C$). It was concluded that the reduction of laser power can minimize the required retinal temperature and collateral thermal damage of healthy neighboring ocular tissues. Reference [12] investigates the use of FDTD formulation of bio-heat equation using 3D eye model, a validation of the simulation was made in vivo measurements using dog eye, and the results coincide. All measured tissue temperature was found to rise logarithmically versus time.

The absorption spectrum of whole oxygenated blood [13,14] is shown in Fig. 1. The blood has a peak absorption at the 577nm and a slightly lower absorption coefficient at 532nm. Yellow and green lasers are suitable for DR since they are better absorbed in oxyhemoglobin than deoxyhemoglobin and RPE layer. The blood and RPE layer absorption at these wavelengths is higher than for the rest of the tissue; therefore, most of the laser radiation is absorbed in it.

The scattering of yellow wavelengths is lower compared to green (Fig. 2) [13], implying less intraocular scattering and thus enabling the use of lower laser power and preventing additional unnecessary damage.

Table 1 presents the absorption and scattering coefficients of blood and other eye tissues for yellow and green wavelengths.

Photocoagulation is achieved at a tissue temperature of about $60$-$80^{\circ } C$[20] . Temperatures higher than $80^{\circ } C$ can cause severe damage, while for temperatures lower than $60^{\circ } C$ the thermal effect is reversible. Therefore, in order to achieve treatment for DR with minimal peripheral thermal damage we would like to heat the blood vessel to $60$-$80^{\circ } C$. Calculating the temperature rise due to the absorbed laser radiation is done using the thermal properties of the eye tissues (Table 2). These properties allow us to evaluate the temperature needed to achieve a given absorbed energy.

## 2. Monte-Carlo simulation

#### 2.1 Monte-Carlo simulation [MCML]

The Monte-Carlo simulation, used in this paper [MCML] was developed by Wang and Jacques [23,24]. It deals with the transport of an infinitely narrow photon beam perpendicularly incident on a multi-layered tissue. Each layer is infinitely wide, and is described by the following parameters: the thickness, the refractive index, the absorption coefficient $\mu _a$, the scattering coefficient $\mu _s$, and the anisotropy factor $g$. Although the real tissue can never be infinitely wide, it can be so treated if it is much larger than the spatial extant of the photon distribution. The absorption coefficient $\mu _a$ is defined as the probability of photon absorption per unit of infinitesimal path length, and the scattering coefficient $\mu _s$ is defined as the probability of photon scattering per unit infinitesimal path length. Correspondingly, the interaction coefficient means the probability of photon interaction per unit infinitesimal path length. The anisotropy $g$ is the average of the cosine value of the deflection angle. Photon absorption, reflectance and transmittance are the physical quantities to be simulated. The simulation propagates photons in three dimensions, records photons depositions, $A(x,y,z)$ $(J/cm^3)$, due to absorption in each grid element of a spatial array. The laser beam in the simulation is assumed to be Gaussian with a beam waist was chosen according to the literature [8,25,26]. The MCML code does not take into account the pulse duration. Throughout the simulation we assumed the pulse duration to be about $150msec$, which is long enough to create tissue heating.

#### 2.2 Eye multilayer model

We performed a simple Monte-Carlo simulation, where the tissue is assumed to be composed of semi-infinite layers. The eye model is composed of several different tissue layers (Fig. 3) [1,15] , each having different optical and physical properties: refractive index $n$, thickness $d$, absorption $\mu _a$, scattering $\mu _s$, and anisotropy $g$ coefficients. These parameters are well cited in the literature and are shown in Table 1 and Fig. 3. We used a multilayer model Monte-Carlo simulation to calculate the absorbed energy inside the eye. The laser parameters (beam diameter and energy) are modified in order to get the required laser tissue interaction, and the beam diameter is chosen to cover a typical area of the formation of the capillary at the retina ($500\mu m$), which is a conventional parameter according to Ref. [25], and for determining the laser energy $5mJ$ ($50mW$ using $100msec$ pulse duration) [8] . These values are taken as a reference for the preliminary calculations. Time dependent optimization of the pulse duration and heat dissipation is done using FEM simulations (section 3). The resulting laser power is chosen according to the simulation results using optimal energy and pulse duration.

A temperature map can be calculated using the following eye parameters: heat capacity and density. The relationship between the absorbed energy $\Delta E$ to the temperature change $\Delta T$ is given by Eq. (1).

where $\rho [g/cm^3]$ is the mass density, $c[J/g^{\circ } C]$ is the specific heat capacitance and $\Delta T$ is the temperature difference given by Eq. (2). The initial body temperature $T_i=37^{\circ } C$ and the final temperature $T_f$ is the tissue heating temperature. Therefore the final tissue temperature $T_f$ is given by Eq. (3).#### 2.3 Monte-Carlo simulation results

The above tissue parameters were used in the Monte-Carlo simulation to calculate the absorbed energy and the final tissue temperature of each eye layer. In the following analysis we examine the effect of yellow and green laser on a diabetic eye. A diabetic eye has angiogenesis i.e., the formation of new blood vessels inside the retina. We will examine two layers inside the retina, the leaky blood vessel and the retinal peripheral epithelium (RPE). These layers are the cause for the DR and the ones that should be treated. Photocoagulating the blood vessel will cease the leakage into the eye. Coagulation of the RPE layer is crucial in order to cease the angiogenesis in the eye by coagulating deprived retinal area. The initial values of the laser parameters are beam diameter and energy. They were taken from the literature [8,25], beam diameter of $500 \mu m$ and energy of $5mJ$ (using pulse duration of $100msec$). The combination of the exposure time and the power was found to be important [8] and affect the lesion size. The goal of the procedure is to treat the desired area by heating it without damaging nearby healthy tissue. Therefore, the pulse energy must be optimized to heat the tissue to coagulation temperature while keeping the surrounding tissue minimally damaged. Using the MCML algorithm [23,24], the absorbed energy and final temperature were calculated given the laser power, pulse duration, and beam diameter.

#### 2.4 Optimization

In this section, we would like to determine the optimal laser parameters for achieving photocoagulation. The parameters would be determined using an optimization method on the two parameters, by fixing one at a constant standard parameter and varying the other within a reasonable range below and above the standard parameter; this is then repeated for for both yellow and green lasers. Figure 4 shows the maximal temperature of the blood vessel and the RPE as a function of the laser energy for green and yellow lasers for a laser spot size of $500 \mu m$. A linear relation between radiated energy $E_{inc}$ in Joules and the maximum temperature $T_{max}$ can be seen.

Coagulation occurs at tissue temperature between $60^{\circ } C/mJ$ and $80^{\circ } C/mJ$. We define the optimal energy for coagulation as the energy needed for heating the tissue to $65^{\circ } C/mJ$. This temperature is above the threshold and low enough to prevent thermal damage to surrounding tissues. Using Fig. 4 the optimal energy for a desired coagulation temperature using a yellow laser is about $5mJ$, while for the green laser it is about $6.5J$. For these energy values the RPE temperature is $71^{\circ } C$ for the yellow laser and above $80^{\circ } C$ for the green laser. It can be seen that for the green laser the RPE temperature exceeds the coagulation temperature therefore major damage might occur in the tissue.

Figure 5 shows the maximum temperature at the blood layer and the RPE layer as a function of the beam diameter for a constant laser energy of $5mJ$. It can be seen that in order to reach a coagulation temperature of $65^{\circ } C$, a beam diameter of $500 \mu m$ is needed for the yellow laser and of about $450 \mu m$ for the green one. As the beam diameter increases, the energy density decreases; thus, the temperature decreases and the difference between all the cases become smaller. Again we can see that in the green laser case the RPE layer heats up above the coagulation temperature.

#### 2.5 Simulation using optimal parameters

In the previous section we found that in order to reach the coagulation temperature the yellow laser parameters should be: laser energy $5mJ$ and beam diameter $500\mu m$. The tissue temperature map for yellow laser irradiation using these parameters is shown in Fig. 6. The laser beam has a Gaussian energy distribution. Since the beam energy density (diameter) affects the heated area, and as the beam diameter increases the energy density decreases; therefore, the maximum temperature at the beam center decreases.

The temperature map (Fig. 6) shows that most of the energy is absorbed in the blood vessel and the RPE layer. It can be seen that photocoagulation is achieved in the blood vessels and RPE layer and that the surrounding tissue is unlikely to be damaged during the procedure. The same simulations were done for a green laser and the results were compared with the yellow laser results. For the comparison we assumed that the green laser has the same parameters as the yellow one i.e., $5mJ$ energy and beam diameter $500\mu m$. Figure 7 presents a comparison of the temperature distribution between the two laser types. In the case of the yellow laser the blood vessel heats up to $65^{\circ } C$ due to the high concentration of hemoglobin ($15gr/dl$ in our simulation) [27] and the RPE layer heats about $70^{\circ } C$. In the green laser case the blood vessel heats up to about $60^{\circ } C$ and the RPE layer to almost $80^{\circ } C$, which is the upper value of the photocoagulation range. This is due to the lower absorption coefficient of Hemoglobin in the green. The temperature of the rest of the tissue layers does not exceed the coagulation threshold ($\geq 60^{\circ } C$). When using a yellow laser, the temperature difference between the blood and the RPE is lower, and in both cases does not exceed the coagulation temperature upper range. Therefore less damage to the surrounding tissue might occur. The main differences between the yellow and green lasers is the temperature level. The temperature level in the case of the yellow laser is higher in the blood layer and lower in RPE layer compared to the green one for the same laser parameters. Therefore when operating the laser using optimal parameters the yellow laser is more efficient for this procedure.

Figure 8 shows the temperature distribution as a function of the radial distance from the center of the illumination point at the main absorbing tissues, blood vessel and RPE where the temperature reaches its maximum value for the green and the yellow laser. For the green laser the temperature difference between the RPE layer and blood vessel is about $18^{\circ } C$, while for the yellow laser the difference is much smaller, $5^{\circ } C$. This is due to the larger absorption in the blood in the yellow case. Therefore, using a yellow laser decreases the likelihood of damaging healthy non-diabetic tissue and avoiding severe damage.

We can also conclude from Fig. 8 that in the case of the green laser, higher energy is needed in order to reach the required temperature. However, higher laser energy will also increase the temperature of the RPE layer to above the photocoagulation temperature ($> 80^{\circ } C$) which will cause membrane disruption and critical damage to the tissue.

#### 2.6 Temperature level for different hemoglobin concentrations

The absorption coefficient $\mu _a$ of whole blood can be found using the molar extinction coefficient $\varepsilon$ and the hemoglobin concentration $x$, and is given by Eq. (4).

The molecular weight of Hb is $64,500$ grams per mole and typically there are $150$ grams of Hb per one liter of blood. The refractive index of whole blood also changes according to the hemoglobin concentration [18]. The absorption of whole blood and the maximum temperature at the retina using the yellow laser with a beam diameter of $500\mu m$ and energy of $5mJ$ are shown in Table 3. The normal hemoglobin levels for males are $14$ to $18$ $gr/dl$, and for females are $12$ to $16$ $gr/dl$.As the hemoglobin concentration increases the absorption increases; therefore, the maximum temperature increases. A linear relation between the hemoglobin concentration and the maximum tissue temperature was found using curve fitting (Eq. (5)).

where $x$ is the hemoglobin concentration and $T_{max}$ is the maximum temperature at the retina.## 3. Finite element method

In order to be more accurate and to take into account heat transfer and time dependent phenomena we used the Comsol Multiphysics simulation package. This simulation package enables us to model and solve physical phenomena based on is based on finite element methods. Using this method we built a 3D model of the eye using the eye real physical size, and physical and optical properties as listed above.

#### 3.1 Eye 3D model

Figure 9(a) shows a 3D model of the eye, which was created using the Comsol Multiphysics software package. The model is composed of different media, each with its own optical and thermal properties, that are shown in more details in Fig. 9(b). The model is symmetrical with respect to the optical axis; thus, the laser beam propagates through the lens in the z-direction all the way to the vitreous and finally reaches the retina. Therefore, the beam is distributed symmetrically along the retina surface.

This numerical model is solved using a Bio-heat transfer model with Penne’s approximation [28], and the Henyey-Greenstein phase function [29] is employed for scattering. The solution is time dependent and shows the temperature distribution, heat gain and dissipation over time. In the simulation, we use a typical $TEM_{00}$ Gaussian Laser with power that is equal to the product of pulse duration $t$, and optimal energy $E$ (found in section 2). The hemoglobin concentration was taken as $15gr/dl$.

#### 3.2 Finite element method results

Using the Bio-heat transfer physics module of Comsol Multiphysics it is possible to calculate the heat transfer resulting from the laser heating. Figure 10 shows the temperature distribution resulting from yellow laser heating. As can be seen, the blood vessel in the retina is heated above the coagulation temperature, while the surrounding tissue is left undamaged.

The main advantage of FEM is the possibility it affords to evaluate the temperature distribution over time and in 3D space. The tissue is heated using laser radiation through the lens in the z direction, and some of the heat is dissipated into the surrounding tissue due to conduction and convection. The maximum and minimum temperature of the eye as a function of time, beginning from the laser irradiation, is shown in Fig. 11 , where the ambient temperature is set to $20^{\circ } C$ and the body temperature is set to $37^{\circ } C$. It takes the laser about $150msec$ to heat the blood vessel to the coagulation temperature. If the laser pulse is longer than $200msec$ for the yellow laser then the temperature will rise above $70^{\circ } C$ and the surrounding tissue might be damaged. Note that the temperature slope decreases over time, since some of the heat dissipates to the surrounding tissue. The coagulation threshold starts at $60^{\circ } C$; this occurs for the yellow laser at $120msec$ and for the green laser at $160msec$. In a clinical study [25] it has been concluded that shortening exposure time of retinal laser procedures reduces the pain significantly and is still equally effective. Therefore, the use of a yellow laser is expected to cause less pain to the patient. The temperature difference between the yellow and green lasers increases for longer pulse durations.

Table 4 compares the Monte-Carlo Simulations and the FEM simulation results. It can be seen that the calculated temperature are very close, for the same laser parameters - power, beam diameter and exposure time. However, using the FEM simulation, we can take into account heat dissipation to the surrounding tissue and calculate the temperature increase over time, thus better determining the laser pulse duration. The time dependence of the FEM simulation, along with the heat dissipation, is the cause for the temperature differences between the two simulation methods.

## 4. Conclusions

Using two different simulation tools we have shown that the yellow laser is better suited for DR due to its higher absorption in hemoglobin and lower scattering in the eye tissues. Our research provides quantitative numerical analysis that shows that a yellow laser makes it possible to use lower power in order to get the same results as with the green laser, thus preventing thermal damage to neighboring tissues. The MCML and FEM simulations yield similar results, with a slight difference in terms of absorbed temperature. Our numerical results suggest a new surgery protocol, where the recommended parameters for retinal eye surgeries are: wavelength $577nm$, peak power $50mW$, beam diameter $500\mu m$ and pulse duration $150msec$ for a single pulse. If necessary, additional pulses of the laser can be delivered in order to gradually heat the tissue and cause coagulation.

Finally, we wish to point out that our protocol prescribes using the same yellow wavelength laser as in the clinical trials reported in [5]. However, there the power used was $167mW$ with an exposure time of $87msec$, thus yielding a much higher radiant exposure. Hence, with our protocol, we expect the same coagulation efficiency but with much less risk of damaging neighboring tissues. This, of course, should be further tested with a clinical study.

## Disclosures

The authors declare that there are no conflicts of interest related to this article.

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