Applied Mathematics, 2013, 4, 30-36
http://dx.doi.org/10.4236/am.2013.410A2003 Published Online October 2013 (http://www.scirp.org/journal/am)
Copyright © 2013 SciRes. AM
FEM Approach for Transient Heat Transfer in Human Eye
Gokul K. C.
*
, Dil Bahadur Gurung, Pushpa Raj Adhikary
Department of Natural Sciences (Mathematics), School of Science, Kathmandu University, Kavre, Nepal
Email:
*
gokulkc2@gmail.com
Received August 7, 2013; revised September 7, 2013; accepted September 14, 2013
Copyright © 2013 Gokul K. C. et al. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
In this paper, a bio-heat transfer model of temperature distribution in human eye is discussed using appropriate bound-
ary conditions for cornea and sclera. Variational finite element method with Crank-Nicolson scheme is used to calculate
the transient temperature distribution in normal human eye. The temperature with and without the effect of blood perfu-
sion and metabolism on retina is simulated and compared for various ambient temperatures, evaporation rates and lens
thermal conductivities. The obtained results are compared with experimental results and past results found in literatures.
The results show that the steady state corneal temperature is achieved in around 31 and 45 minute of exposure at ambi-
ent temperatures 10˚C and 50˚C respectively. Steady state eye temperature is achieved earlier at higher evaporation rate.
Similar result is achieved for higher lens thermal conductivity and also for lower ambient temperature.
Keywords: Human Eye; Bio-Heat Transfer; FEM; Numerical Simulations
1. Introduction
In a human body the internal body temperature almost
remains constant despite the fluctuation of environmental
temperatures up to certain limits. The main organ that
keeps core temperature constant is dermal part [1]. There
is no skin layer to keep the core temperature constant in
case of human eye. The skin layer (eyelid) covers eye
surface (cornea) for 3 seconds in a minute (in an average).
But for 57 seconds in a minute,ocular surface (cornea)
has to manage thermal stress of an environment. The hu-
man eye is relatively a small and complex organ, consists
of several sub domains with different material properties
and having complex geometry.
The calculation of the temperature distribution in hu-
man eye when it is heated or cooled is an important
aspect of the development of infrared and radiofrequency
safety guidelines and for hyperthermia and thermo-the-
rapy treatments of various ocular diseases [2]. The se-
verity of the physiological effect produced by small tem-
perature increases can cause eyesight to worsen. Actually,
a small temperature increase in the eye of 3˚C - 5˚C leads
to induce cataracts formation [3]. Some researchers be-
lieve that thermal effect can induce cataracts; other be-
lieves that it is the result of other biological and genetic
issues. One of the early theory suggested that heat ex-
changes within the anterior eye caused the cataract.
Verhoeff and Bell argued that cataract formed on the
posterior surface of the lens because the anterior surface
was cooled by circulation of the aqueous humor and so
the cornea was air cooled [4]. Investigation in Germany
showed that the cataracts were due to the raised tem-
perature induced indirectly through heat absorbed by the
iris, where a rich blood supply would be consistent with a
high degree of heating. At the same time Salil noticed the
rise in cataracts one year after a very hot, dry summer in
Iowa, highlighting likely environmental causes of catar-
acts [4].
Due to convective heat transport of the blood vessels;
the blood picks up energy from hot areas and deposits
this at cooler area or vice versa. The difficulty of mo-
deling in the eye is due to the impact of blood flow on
the heat transfer; however, incorporating the impact of
blood flow in heat transport calculation is very important
[2]. The temperature inside the human body depends on
the degree of temperature, duration of exposure and the
environmental conditions which cause heat gain/loss
from tissues [1]. Hence, blood flow and time are the main
factors that affect temperature distribution in human eye.
Lagendijk [5] used a finite difference method to cal-
culate the temperature distribution in human and rabbit
eyes during hyperthermia treatment. The heat transport
from the sclera to the surrounding anatomy is described
by a single heat transfer coefficient which includes the
impact of blood flow in choroid and sclera. Scott [6]
*
Corresponding author.