Validation of a Model to Predict
Temperature Increase in the
Human Eye When Subjected to a
Laser Source
Corinna Sue Thompson, Antonio Campo, PhD., University
of Vermont, Undergraduate Research Endeavors
Competitive Awards
September 2006
Abstract:
Heat transmission and cooling of the human eye has many important scientific and medical applications. From surgery to workplace and laboratory safety, eye protection is key. Mathematical models for the human eye exist with certain limitations on boundary conditions (Campo, Ridouane). Models of and experiments done on other mammals have been shown inadequate in describing the complex mechanisms of the human eye.
Progress was made in the 1970’s and 80’s with animal eye experimentation (Lagendijk). Since then, finite volume methods to determine temperature changes and material properties numerically have been implemented to support
experimental findings. Information from experimental data is still necessary to utilize and evaluate the results of finite volume analysis. Some variations in
temperature due to thermal conductivity and convective coefficient are presented. A thorough understanding of the fundamental physics of the heat transfer is also imperative.
The tools available to researchers doing finite volume analysis today are more accurate and faster than those used over the past three decades when similar methods were employed. It is important to reexamine the problem of heat transfer within the eye again using more sophisticated technology. Recent work has focused mainly on developing a sensitivity analysis for the finite volume method so that data presented can be well understood in the context of known uncertainties.
Introduction:
Current work concerning human eye tissue degeneration in response to heat and light exposure is preliminary. Finite element analysis and variation in temperature calculations have been done assuming the eye is unexposed. In these studies a very simple 2 dimensional geometry representing the eye was used. The tissue in the eye was assumed homogenous and with properties similar to water1.
We plan to continue work that was started by addressing issues of eye exposure and cooling with tears. A similar finite volume method will be used in simulations with varying boundary conditions. Changes will be made addressing the asymmetry of the eye with the optic nerve located just below the hemisphere. Because heating and cooling of the unexposed eye is predominately achieved with blood flow, we will spend some time examining heat transfer with the capillaries adjacent to the eye itself.
Our more comprehensive work will have applications in the growing fields of laser eye surgery and new IC chip implantations for the blind. Awareness of heating and cooling mechanisms in the eye aid the materials science and optics industries when formulating eye protection devices.
Background:
The eye is subject to heat in many ways, but the most harmful heat sources are thought to be infrared radiation (IR) sources, i.e. molten glass and metal, lasers3. Infrared
radiation is divided up into three subgroups: IR-A, IR-B, and IR-C. Each type of radiation corresponds to a to a different range of wavelengths1.
• IR-B is 1400-3000 nm
• IR-C, far infrared is 3000-10000 nm
Figure 1: The different classifications of infrared radiation are absorbed by
different tissues within the eye1.
Not all parts of the eye exposed to radiation will absorb the same wavelengths. Tissues within the eye vary in terms of absorption capabilities and resistance to damage. When one type of tissue absorbs the energy, the surrounding tissues are heated by conduction. Under normal conditions, the eye is constantly cooled by convection with blood flow throughout the vasculature and exposure to air and tears at the anterior surface.
Figure 2: The anatomy of the human eye5. Corneal damage is concerning
because it absorbs most forms of IR to protect the retina6.
Hypothesis:
Many pathologies of the human eye are related to the cellular changes that occur as a result of heat damage3. Extended exposure to radiation will cause overall
temperatures in the eye to increase and affect tissue that does not absorb the radiation2.
Currently, the regulation for exposure may not be strict enough for some purposes and too limiting for others.
Figure 3: The electromagnetic spectrum. As wavelengths increase, the energy of
the photons decreases4.
Methods:
Finite element modeling will be used to impose appropriate boundary conditions on the subject. These boundary conditions can then be varied to model different
conditions in the eye1.
The bio-heat transfer equation follows for this model: (1)
The mesh size chosen for this model varies as the different tissue and infrared radiation absorbance changes. The model has three boundaries on which to apply conditions, and four points of general interest along the visual axis.
H
T
k
t
T
c
=
∇
⋅
∇
+
∂
∂
)
.
(
ρ
The data presented here are for the assumption that the eye is unexposed eter is changed in the simulation, all others are maintained. This is with the purpose of first understanding how these parameters effect temperatur
1
. When one param
e variations within the human eye.
Data: Table 3: ugh D e Table 1: Table 2:
Tables 1, 2, and 3 show the change in the temperature distribution at points A thro under different boundary and material conditions. They come from work done using th computational program FLUENT by Ridouane and Campo.
Discussion:
Environmental temperature changes affect temperatures in the different regions of the eye, as seen in table 1. A radiation source in the ambient environment would mos likely increase these temperatures even more. Table 2 shows the effect of thermal conductivity on the temperature at the four points. An increased thermal conductivity leads to more heat transferred from an area of high temperature. Table 3 outlines temperature variation due to the change in the convective heat transfer coefficient hs,
from the sclera to the center of the eye. A similar table could be generated for the convective heat transfer coefficient hc. When tabulating this data, all other properties of
the eye were taken to be the “base” values found in literature3.
t
Figure 4: The finite volume mesh used in simulations1. Assumptions about the
symmetry of the system allow for this simplification in geometry.
2 Γ 3 Γ 1 Γ
C
B
A
D
Conclusions
It is essential to have a safe and reliable way to determine these limits. A better understanding of heat transfer in the human eye will lead to improved standards and regulations in industry. This topic will also have an impact on the conditions under which and the details of various laser related eye surgeries7.
Figure 5 corresponds to the base case heating by conduction. The data presented represents a sensitivity study formulated to justify this finite volume analysis.
Figure 5: Predicted finite volume results for the steady-state isothermal contours
eye1. Here the temperature shown is in Kelvin. for the healthy human
Future work still needs to be done in the area of heat transfer and the tissue of th eye. Ideally, experimental work would be done along side computational and th
modeling. Another program, FemLab for ex
e eoretical ample or even a Solid Works add on Flo orks, could be used to validate the above results found using FLUENT. A different rogram may afford the user more freedom in both geometry and boundary conditions.
cknowledgements:
I would like to thank Prof. Antonio Campo for his interest in this project and ontinued encouragement. El Hassan Ridouane, as well as other members of Dr.
ampo’s graduate research team, have been valuable and appreciated consults on this pic. We are thankful for the generous support of the Undergraduate Research ndeavors Competitive Award.
W p A c C to E
References
1. Ridouane, E.H., A. Campo, Model for the Heat Transmission in the Human Eye.
. Lagendijk, J.J.W., A mathematical model to calculate temperature distributions in -311.
ion. Phys. Med. Biol., 1988, 33, 243-257. Proc. of ASME-IMECE, 2005.
2
human and rabbit eyes during hyperthermic treatment. Phys. Med. Biol., 1982, 27,1301 1
3. Scott, J.A., The computation of temperature rises in the human eye induced by infrared radiat
4. Electromagnetic spectrum, March 27, 2006.
http://www.bcm.edu/bodycomplab/Images/emspect.jpg
5. Sagital section of the adult human eye, April 5, 2006. http://webvision.med.utah.edu
6. McCally, R.L., C.B. Bargeron, Corneal Epithelial Injusry Thresholds for Multiple-Pulse Exposures to TM:YAG Laser Radiation at 2.02 um. Health Physics, 2003, 85,420-427.
7. Cosalia, K., j. Weiland, M. Humayun, G. Lazzi, Thermal Elevation in the Human Eye and Head Due to the Operation of a Retinal Prosthesis. IEEE Trans. On Biomedical Engr., 2004, 51, 1469-1477.
