# Steady State Heat Analysis of the Eye Using Finite Element Method

**Roya Heydari Forushani**

^{1}, Kamran Hassani^{1*}, Farhad Izadi^{2}^{1}Department of Biomechanics, Science and Research Branch, Islamic Azad University, Tehran, Iran.

^{2}Mechanical Engineering Department, Islamic Azad University of Najafabad, Iran.

- *Corresponding Author:
- Kamran Hassani

Department of Biomechanics

Science and Research Branch

Islamic Azad University

Golzare 1, Tehran, Iran

**Accepted date:** September 30, 2011

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## Abstract

Invasive methods in measuring eye temperature are normally dangerous. Therefore, computational models can be used as a useful tool to study the heat transfer in human eye. The previous two-dimensions (2D) models were not able to describe the heat analysis of the eye precisely. This study presents a 3D finite element eye model which simulates the eye temperature distribution in steady state condition. Our results show a discrepancy of 3.61%, maximum, when compared to the experimental ones. We calculated a maximum temperature of 36.966°C and minimum of 34.606°C which are in reasonable agreement with literatures.

## Keywords

Eye, FEM, modeling, Heat transfer

## Introduction

The rate of eye diseases has been increased in developing countries since last decades. The main reason is associated with the food diets and the life style in these societies. The mathematical and computational models are the tools for studying of the biological systems and maybe be used for early diagnosis of the eye diseases. This is very important for treatment of the diseases because the optometrist enables to perform related clinical treatments.

In the early of 1950s, non-invasive techniques were used to obtain temperature of a cornea surface . Erfon et al [1] obtained results of the ocular surface temperature using infrared imaging approach to have a mean of 34.3 C while Purslor et al [2] reported a variation of 33.9 to 36.1°C. E.Y.K.Ng et al [3] presented a 2D model and simulated the eye structure using finite element method. They later obtained ocular surface temperature using a bioheat equation [4]. Ean-Hin Ooi et al [5] simulated the aqueous humor hydrodynamics in the eye heat transfer. Sharon et al [6] modeled the heat exposure and damage to the eye lens in 2007. Eric Li et al [7] studied the bioheat transfer in the eye using the 3D alpha finite element method in 2010. Shafahi et al [8] studied the eye response to thermal disturbances and analyzed the role of primary thermal transport mechanisms on the eye subject to different conditions. In this study, we have developed a threedimensional finite element model of the human eye and investigated the heat transfer the heat transfer in the eye structure. We have calculated the temperature distribution and heat flow inside the eye. We have picked six points in the structure and studied the effects of convection coefficient, blood temperature, ambient temperature and evaporation rate in the model. We do not claim that the model is perfect due to lack of experimental data on human eye but believe that computational modeling can help the researchers to understand the thermal mechanisms in the eye much better.

## Materials and Methods

Using the literature anatomical data [3] for 2D model of
the eye, we have constructed the 3D model by CATIA
software.The complete 3D structure has been shown in **Figure 1**. The model is discretized using triangular elements.
The number of elements is found to be 56335.The
generated mesh for the eye structure has been shown in **Figure 2**. We have considered the value of blood convection
coefficient at sclera equal to 65 w/m^{2}k [9]. Blood
temperature entering the eye is taken as 37°C [9]. The
ambient convection coefficient was assumed to be 10
w/m^{2}.k [10] while the ambient temperature is 25 °C.
Emissivity of the cornea was considered as 0.975 [11]
and the evaporation rate of the normal eye was assumed
to be 40 w/m^{2}. he properties of the human eye for different
domains were extracted from the literature [3] . Based
on the above values, we have considered appropriate
boundary conditions for the model. Thereafter, using finite
element method, a steady state analysis for a normal eye was analyzed and various simulations were carried
out using ANSYS software. W have considered the steady
state thermal condition and applied the convection, radiation
and heat to simulate the heat transfer in the eye structure.
The convection was applied for cornea and sclera.
The temperature of cornea is the same as the ambient but
it is the same as blood temperature for sclera. The heat is
radiated from cornea as well; therefore emissivity value is
applied for it. It should be noted that heat flux normally
occurs in cornea. The simulation was run for six defined
points O,A,B,C,D and E which relate to the corneal surface,
anterior of aqueous humor, anterior of lens, anterior
vitreous, posterior of vitreous and the sclera as presented
in **Figure 3**.

## Results

The results of the simulation can be analyzed and discussed
by different variations and parameters. **Figure 4** shows the temperature distribution in the eye structure.
The minimum obtained temperature is 34.606 °C. When
the heat moves from the cornea towards the optic nerves
the temperature increases by the maximum of 36.966 °C.

Effects of blood and ambient convection coefficient shall
be considered as the most important factor for study of
heat flow in the eye. The increase of the ambient convection leads to decreasing of corneal surface temperature.
The reason is that heat transfer increases from the surface. **Figure 5** and **figure 6** show the effects of blood and ambient
convection coefficient on different picked points
along the eye structure. **Figure 7 **represents the effect of
the ambient temperature on the structure. An increase of
the temperature causes the increase of different parts of
the eye. The effect of increasing the blood temperature
has been shown in **Figure (8)**. Obviously, the eye temperature
increases due to increase of blood temperature.
The cornea surface contains a layer of lipid that is produced
by the meibomian glands [12]. When the layer is
damaged, the rate of evaporation increases to 320
w/m2[13]. We have shown the effects of the evaporation
rate in **Figure (9)**. The temperature of the eye has increased
with the increasing of the evaporation rate.

## Discussions

Scott [14] and E.Y.K.Ng [3] showed that the main parameters
affecting the eye temperature are blood temperature,
ambient temperature and evaporation rate. We have
tried to simulate the effects of theses parameters on the
different parts of the eye. We have calculated the minimum
and maximum eye temperature using the temperature
contour which was shown in **Figure(4)** where the
minimum temperature was 34.64°C . The temperature has
been compared to the others results in accordance with
the literature [15,16,17,18]. The rate of discrepancy between
our result and the literature varies from 0.9% to
4.07%. It should be noted that the minimum temperature
belongs to point O which is the most sensitive part of the
eye structure [14]. We have compared obtained temperatures
to E.Y.K.Ng’s results [3] and found out a mean rate
of discrepancy equal to 2.7%. The rate of discrepancy
between our other results and the literature is less than 3%
but we have not included the comparison of the data any more. The important point is to see whether the results of
the modeling are reliable. The ambient temperature has
been considered 25°C in our model however the temperature
was different from 20 to 25°C in the previous simulations.
Therefore the effects of ambient temperature on the
eye were different in the simulations. On the other hand,
the thermal conductivity and material properties which
were applied in the previous simulations are quite different
therefore, the results are different. However, the rate
of discrepancy is the best factor for comparison of the
modeling results to the literature. One reason for lacking
of experimental results is that invasive methods are required
for collection of clinical data however these methods
can only performed on animals. Therefore, the detailed
verification of the simulations is limited. We believe
these types of simulations, including our model,
represent a good understanding of the temperature distribution
in the eye structure and could be a useful tool for
the students to be familiar with the effects of heat flux
inside the eye.

## Conclusions

We introduced a finite element model of heat flow in the eye structure under steady state condition. Due to lack of experimental data and clinical observation, the verification of the results was only performed using available literatures including previous simulations. However, we have presented a 3D model which can calculate the eye temperature more suitable than a 2D model. The next step could be the study of heat flux in the eye using non steady condition and blood flow inside the eye arteries. By the way, we believe the model can help the biomedical engineering students to be familiar with the stream of heat in the eye structure although we require better mathematical and computational models.

## Acknowledgements

Authors of the manuscript hereby declare that have not any conflict of interests.

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