Abstract

Purpose: The physiological conditions and environment have vital roles in the heat transfer in the human tissues, such as the multilayered human-eye. In this paper, a mathematical model of the human eye subjected to an exponential laser beam concerning the change in blood perfusion, porosity, evaporation rate, and ambient temperatures has been constructed based on non-Fourier heat conduction law. Methods: The human eye has been divided into six layers. Appropriate boundary and interface conditions have been considered. A separable function has been assumed, and the twelve equations have been formulated in matrix form. The solutions have been calculated by using maple 17 software. Results: The results have been shown in figures with different cases. The absolute temperature distribution based on various values of the power density of laser irradiation and relaxation times parameters have been discussed first. The effect of the blood perfusion, porosity, evaporation rate, time, and ambient temperatures have also been discussed. Conclusions: The power density of laser irradiation, blood perfusion, porosity, evaporation rate, time, and ambient temperatures significantly affects the value of the temperature passing through the human eye layers.

References

1.
Cvetkovic
,
M.
,
Poljak
,
D.
, and
Peratta
,
A.
,
2008
, “Thermal Modelling of the Human Eye Exposed to Laser Radiation,”
16th International Conference on Software, Telecommunications and Computer Networks
16–20,
Split, Croatia
, Sept. 25–27.10.1109/SOFTCOM.2008.4669444
2.
Taflove
,
A.
, and
Brodwin
,
M. E.
,
1975
, “
Computation of the Electromagnetic Fields and Induced Temperatures Within a Model of the Microwave-Irradiated Human Eye
,”
IEEE Trans. Microwave Theory Tech.
,
23
(
11
), pp.
888
896
.10.1109/TMTT.1975.1128708
3.
Emery
,
A.
,
Kramar
,
P.
,
Guy
,
A.
, and
Lin
,
J.
,
1975
, “
Microwave Induced Temperature Rises in Rabbit Eyes in Cataract Research
,”
ASME J. Heat Transfer
,
97
(
1
), pp.
123
128
.10.1115/1.3450259
4.
Scott
,
J. A.
,
1988
, “
A Finite Element Model of Heat Transport in the Human Eye
,”
Phys. Med. Biol.
,
33
(
2
), pp.
227
242
.10.1088/0031-9155/33/2/003
5.
Scott
,
J. A.
,
1988
, “
The Computation of Temperature Rises in the Human Eye Induced by Infrared Radiation
,”
Phys. Med. Biol.
,
33
(
2
), pp.
243
257
.10.1088/0031-9155/33/2/004
6.
Lagendijk
,
J.
,
1982
, “
A Mathematical Model to Calculate Temperature Distributions in Human and Rabbit Eyes During Hyperthermic Treatment
,”
Phys. Med. Biol.
,
27
(
11
), pp.
1301
1311
.10.1088/0031-9155/27/11/001
7.
Mainster
,
M. A.
,
1979
, “
Ophthalmic Applications of Infrared Lasers–Thermal Considerations
,”
Investig. Ophthalmol. Visual Sci.
,
18
(
4
), pp.
414
420
. https://iovs.arvojournals.org/article.aspx?articleid=2175854
8.
Amara
,
E.
,
1995
, “
Numerical Investigations on Thermal Effects of Laser-Ocular Media Interaction
,”
Int. J. Heat Mass Transfer
,
38
(
13
), pp.
2479
2488
.10.1016/0017-9310(94)00353-W
9.
Sbirlea
,
G.
, and
L'Huillier
,
J.
,
1970
, “
A Powerful Finite Element for Analysis of Argon Laser Iridectomy: Influence of Natural Convection on the Human Eye
,”
WIT Trans. Biomed. Health
,
4
, pp.
67
79
.10.2495/BIO970071
10.
Chua
,
K.
,
Ho
,
J.
,
Chou
,
S.
, and
Islam
,
M.
,
2005
, “
On the Study of the Temperature Distribution Within a Human Eye Subjected to a Laser Source
,”
Int. Commun. Heat Mass Transfer
,
32
(
8
), pp.
1057
1065
.10.1016/j.icheatmasstransfer.2004.10.030
11.
Peratta
,
A.
,
2007
, “
Electromagnetic Modelling of Human Eye Exposed to Conductive Keratoplasty
,”
WIT Trans. Biomed. Health
,
12
, pp.
223
229
.10.2495/BIO070221
12.
Dodig
,
H.
,
2005
, “Hybrid BEM/FEM Calculation of Thermal Rise in the Human Eye Exposed to Time Harmonic EM Waves,” 18th International Conference on Applied Electromagnetics and Communications,
Dubrovnik
, Croatia, Oct. 12–14.10.1109/ICECOM.2005.204933
13.
Rafiq
,
A.
, and
Khanday
,
M.
,
2016
, “
Thermal Behavior of Human Eye in Relation With Change in Blood Perfusion, Porosity, Evaporation and Ambient Temperature
,”
J. Thermal Biol.
,
62
, pp.
138
142
.10.1016/j.jtherbio.2016.06.024
14.
Khanafer
,
T. K.
, and
Vafai
,
K.
, in
2009
,
Advances in Numerical Heat Transfer
, Vol.
3
,
CRC Press
, Boca Raton, pp.
13
40
.
15.
Pennes
,
H. H.
,
1948
, “
Analysis of Tissue and Arterial Blood Temperatures in the Resting Human Forearm
,”
J. Appl. Physiol.
,
1
(
2
), pp.
93
122
.10.1152/jappl.1948.1.2.93
16.
Tullius
,
T. K.
, and
Bayazitoglu
,
Y.
,
2012
, “Relaxation Time Effect on the Human Head Using the Thermal Wave Model,”
ASME
Paper No. IMECE2012-89980.10.1115/IMECE2012-89980
17.
Tullius
,
T. K.
, and
Bayazitoglu
,
Y.
,
2013
, “
Analysis of Relaxation Times on the Human Head Using the Thermal Wave Model
,”
Int. J. Heat Mass Transfer
,
67
, pp.
1007
1013
.10.1016/j.ijheatmasstransfer.2013.08.097
18.
El-Bary
,
A. A.
,
Youssef
,
H. M.
,
Omar
,
M.
, and
Ramadan
,
K. T.
,
2019
, “
Influence of Thermal Wave Emitted by the Cellular Devices on the Human Head
,”
Microsyst. Technol.
,
25
(
2
), pp.
413
422
.10.1007/s00542-018-4012-1
19.
Dehghani
,
A.
,
Moradi
,
A.
, and
Jafari
,
R.
,
2011
, “Modelling of Transient Heat Transfer in Human Eye With a Tumour Using 3D Finite Element Method,”
Fifth International Conference on Bioinformatics and Biomedical Engineering
,
Wuhan, China
, May 10–12, pp.
1
4
.10.1109/icbbe.2011.5780465
20.
Dodig
,
H.
,
Poljak
,
D.
, and
Peratta
,
A.
,
2012
, “Hybrid BEM/FEM Edge Element Computation of the Thermal Rise in the 3D Model of the Human Eye Induced by High Frequency EM Waves,”
20th International Conference on Software, Telecommunications and Computer Networks 1–5 (SoftCOM 2012)
,
Split, Croatia
, Sept. 11–13. https://ieeexplore.ieee.org/document/6347605
21.
Liu
,
K.-C.
,
2015
, “
Analysis for High-Order Effects in Thermal Lagging to Thermal Responses in Biological Tissue
,”
Int. J. Heat Mass Transfer
,
81
, pp.
347
354
.10.1016/j.ijheatmasstransfer.2014.10.035
22.
Tzou
,
D. Y.
,
2014
,
Macro-to Microscale Heat Transfer: The Lagging Behavior
,
Wiley
,
Pondicherry, India
.
23.
Nakayama
,
A.
, and
Kuwahara
,
F.
,
2008
, “
A General Bioheat Transfer Model Based on the Theory of Porous Media
,”
Int. J. Heat Mass Transfer
,
51
(
11–12
), pp.
3190
3199
.10.1016/j.ijheatmasstransfer.2007.05.030
24.
He
,
Y.
,
Shirazaki
,
M.
,
Liu
,
H.
,
Himeno
,
R.
, and
Sun
,
Z.
,
2006
, “
A Numerical Coupling Model to Analyze the Blood Flow, Temperature, and Oxygen Transport in Human Breast Tumor Under Laser Irradiation
,”
Comput. Biol. Med.
,
36
(
12
), pp.
1336
1350
.10.1016/j.compbiomed.2005.08.004
25.
Deepika
,
B.
,
Ramya
,
V.
,
Yamuna
,
T.
, and
Kalpana
,
R.
,
2015
, “A Numerical Analysis of Temperature Distribution in Human Eye When Exposed to Electromagnetic Radiation,” IEEE International Conference on Electronics, Computing and Communication Technologies (
CONECCT
) 1–5,
Bangalore, India
, July 10–11.10.1109/CONECCT.2015.7383942
You do not currently have access to this content.