Simulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach

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dc.contributor.affiliationУнiверситет Кадi Айяд, Лабораторiя прикладної математики та обчислювальної технiки,Факультет науки i технiки
dc.contributor.affiliationUniversit´e Cadi Ayyad, Laboratoire de Math´ematiques Appliqu´ees et Informatique, Facult´e des Sciences et Techniques
dc.contributor.authorАхмедоу Бамба С.
dc.contributor.authorЕллабиб, А.
dc.contributor.authorЕл Мадкоури А.
dc.contributor.authorAhmedou, B. S.
dc.contributor.authorEllabib, A.
dc.contributor.authorEl Madkouri A.
dc.date.accessioned2023-03-06T12:28:11Z
dc.date.available2023-03-06T12:28:11Z
dc.date.created2020-01-01
dc.date.issued2020-01-01
dc.description.abstractУ цiй роботi дослiджено чисельне двовимiрне моделювання розподiлу тепла в людському оцi. Для отримання розподiлу тепла в людському оцi застосовується дуальний метод граничних елементiв (DRBEM). Метод Дiрiхле–Ноймана для областей без перекриття в поєднаннi з DRBEM використовується для пошуку бiльш точного зображення розподiлу тепла в людському оцi, яке подається як двi, три та чотири пiдобластi. Отриманi результати порiвнюються з лiтературними експериментальними та чисельними дослiдженнями. Моделювання запропонованих алгоритмiв з достатньою точнiстю описує розподiл тепла в людському оцi.
dc.description.abstractIn this work, a numerical bi-dimensional simulation of heat distribution in the human eye is investigated. A dual reciprocity boundary element method (DRBEM) is applied to obtain the heat distribution in the human eye. The non-overlapping Dirichlet–Neumann domain decomposition method combined with DRBEM is used to find a more accurate representation of heat distribution in the human eye presented for two, three and four subdomains. The result obtained are compared with literature experimental and numerical studies. The simulations of proposed algorithms describe with sufficient accuracy the heat distribution in the human eye.
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dc.format.pages13
dc.identifier.citationAhmedou B. S. Simulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach / Ahmedou B. S., Ellabib A., El Madkouri A. // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2020. — Vol 7. — No 1. — P. 1–13.
dc.identifier.citationenAhmedou B. S., Ellabib A., El Madkouri A. (2020) Simulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach. Mathematical Modeling and Computing (Lviv), vol. 7, no 1, pp. 1-13.
dc.identifier.doiDOI: 10.23939/mmc2020.01.001
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/57503
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofMathematical Modeling and Computing, 1 (7), 2020
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dc.relation.references[6] Fielder A. R., Winder A. F., Sheridaidah G. A. K., Cooke E. D. Problems with corneal arcus. Transactions of the Ophtalmological Societies of the United Kingdom. 101 (1), 22–26 (1981).
dc.relation.references[7] Fontana S. T., Brubaker R. F. Volume and DOF the anterior chamber of the normal aging human eye. Arch. Ophthalmol. 98 (10), 1803–1808 (1980).
dc.relation.references[8] Gokul K., Dil Bahadur G., Pushpa R. FEM approach for transient heat transfer in human eye. Appl. Math.4 (10B), 30–36 (2013).
dc.relation.references[9] Horven I., Larsen C. T. Contact probe for corneal temperature measurements. Acta Ophthalmologica. 53(6), 856–862 (1975).
dc.relation.references[10] Lagendijk J. J. A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. Physics in Medicine and Biology. 27, 1301–1311 (1982).
dc.relation.references[11] Mapstone R. Measurement of corneal temperature. Experimental Eye Research. 7, 237–243 (1968).
dc.relation.references[12] Martin D. K., Fatt I. The presence of a contact lens induces a very small increase in the anterior corneal surface temperature. Acta Ophthalmologica. 64 (5), 512–518 (1986).
dc.relation.references[13] Ng E. Y. K., Ooi E. H. FEM simulation of the eye structure with bioheat analysis. Computer Methods and Programs in Biomedicine. 82 (3), 268–276 (2006).
dc.relation.references[14] Ooi E. H., Ang W. T., Ng E. Y. K. Bioheat transfer in the human eye: A boundary element approach. Engineering Analysis with Boundary Elements. 31 (6), 494–500 (2007).
dc.relation.references[15] Pennes H. H. Analysis of tissue and arterial blood temperatures in the resting foream. J. Appl. Physiol. 1(2), 93–122 (1948).
dc.relation.references[16] Purslow C., Wolffsohn J. S., Santodomingo–Rubido J. The effect of contact lens wear on dynamic ocular surface temperature, Contact Lens and Anterior Eye. Contact Lens & Anterior Eye. The Journal of The British Contact Lens Association. 28 (1), 29–36 (2005).
dc.relation.references[17] Rysa P., Sarvaranta J. Thermography of the eye during cold stress. Acta Ophthalmologica. 123, 234–239(1973).
dc.relation.references[18] Scott J. A. A finite element model of heat transport in the human eye. Physics in Medicine and Biology.33 (2), 227–241 (1988).
dc.relation.referencesen1] Amara E. H. Numerical investigations on thermal effects of laser ocular media interaction. International Journal of Heat and Mass Transfer. 38 (13), 2479–2488 (1995).
dc.relation.referencesen[2] Danumjaya P., Pani A. K. A block monotone domain decomposition algorithm for nonlinear singularly perturbed parabolic problem. International Journal of numerical analysis and modeling. 3 (2), 211–231(2006).
dc.relation.referencesen[3] Charles M.W., Brown N. Dimensions of the human eye relevant to radiation protection (dosimetry). Phys. Med. Biol. 20 (2), 202–218 (1975).
dc.relation.referencesen[4] Cicekli U. Computational model for heat transfer in the human eye using the finite element method. M. Sc. Thesis, Department of Civil and Environmental Engineering, Louisiana State University (2003).
dc.relation.referencesen[5] Efron N., Young G., Brennan N. A. Ocular surface temperature. Current Eye Research. 8 (9), 901–906(1989).
dc.relation.referencesen[6] Fielder A. R., Winder A. F., Sheridaidah G. A. K., Cooke E. D. Problems with corneal arcus. Transactions of the Ophtalmological Societies of the United Kingdom. 101 (1), 22–26 (1981).
dc.relation.referencesen[7] Fontana S. T., Brubaker R. F. Volume and DOF the anterior chamber of the normal aging human eye. Arch. Ophthalmol. 98 (10), 1803–1808 (1980).
dc.relation.referencesen[8] Gokul K., Dil Bahadur G., Pushpa R. FEM approach for transient heat transfer in human eye. Appl. Math.4 (10B), 30–36 (2013).
dc.relation.referencesen[9] Horven I., Larsen C. T. Contact probe for corneal temperature measurements. Acta Ophthalmologica. 53(6), 856–862 (1975).
dc.relation.referencesen[10] Lagendijk J. J. A mathematical model to calculate temperature distributions in human and rabbit eyes during hyperthermic treatment. Physics in Medicine and Biology. 27, 1301–1311 (1982).
dc.relation.referencesen[11] Mapstone R. Measurement of corneal temperature. Experimental Eye Research. 7, 237–243 (1968).
dc.relation.referencesen[12] Martin D. K., Fatt I. The presence of a contact lens induces a very small increase in the anterior corneal surface temperature. Acta Ophthalmologica. 64 (5), 512–518 (1986).
dc.relation.referencesen[13] Ng E. Y. K., Ooi E. H. FEM simulation of the eye structure with bioheat analysis. Computer Methods and Programs in Biomedicine. 82 (3), 268–276 (2006).
dc.relation.referencesen[14] Ooi E. H., Ang W. T., Ng E. Y. K. Bioheat transfer in the human eye: A boundary element approach. Engineering Analysis with Boundary Elements. 31 (6), 494–500 (2007).
dc.relation.referencesen[15] Pennes H. H. Analysis of tissue and arterial blood temperatures in the resting foream. J. Appl. Physiol. 1(2), 93–122 (1948).
dc.relation.referencesen[16] Purslow C., Wolffsohn J. S., Santodomingo–Rubido J. The effect of contact lens wear on dynamic ocular surface temperature, Contact Lens and Anterior Eye. Contact Lens & Anterior Eye. The Journal of The British Contact Lens Association. 28 (1), 29–36 (2005).
dc.relation.referencesen[17] Rysa P., Sarvaranta J. Thermography of the eye during cold stress. Acta Ophthalmologica. 123, 234–239(1973).
dc.relation.referencesen[18] Scott J. A. A finite element model of heat transport in the human eye. Physics in Medicine and Biology.33 (2), 227–241 (1988).
dc.rights.holder©2020 Lviv Polytechnic National University CMM IAPMM NASU
dc.subjectрозподiл тепла
dc.subjectлюдське око
dc.subjectдуальний метод
dc.subjectметод граничних елементiв
dc.subjectheat distribution
dc.subjecthuman eye
dc.subjectdual reciprocity method
dc.subjectboundary element method
dc.subject.udc65N38
dc.subject.udc92C50
dc.titleSimulation of heat distribution in the human eye using discontinuous dual reciprocity boundary element method and non-overlapping domain decomposition approach
dc.title.alternativeМоделювання розподілу тепла в людському оці за допомогою дуального розривного методу граничних елементів та методу декомпозиції для областей без перекриття
dc.typeArticle

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Mathematical Modeling And Computing. – 2020. – Vol. 7, No. 1