Mathematical model for temperature distribution in human eye

Abstract

As a bike rider, I always compelled to think about my eye health, when riding in high speed and in extreme cold. I frequently visit to ophthalmologists not only for the treatment but to get scienti_c and satisfactory causes, prevention and control measures of my eye problems. My curiosity raised several queries, however, hardly answered. I heartily thank Dr. Dil Bahadur Gurung, my re- search supervisor, to make me able to answer my queries by myself. Two wheeler users are increasing day by day and proportionally eye prob- lem holders in our country. According to di_erent medical theories, the main factors behind dry eye, eye irritation, refractive errors, excess tearing, cataract etc. are the environmental temperature uctuations, wind, pollution, ultravio- let(UV)/infrared(IR) rays, electromagnetic waves etc. In the sense of thermoreg- ulation all these factors either increase or decrease eye tissue temperature, which indirectly induce such abnormalities. In this thesis, study have been carried out for the temperature variation in human eye tissues due to several internal and external factors. Internal factors include blood perfusion, metabolism, blinking, tearing, thermal conductivities. External factors include di_erent ambient temperatures, evaporation rates, and air speeds. Some medical therapies or treatments like laser surgeries, hyperther- mia, cryosurgery are used to treat several eye abnormalities like refractive errors, glaucoma, cataract, diabetic retinopathy, eyelid carcinoma etc. The treatment procedure is either heating or cooling eye tissues by external means. We end up the thesis by presenting the impact of two laser refractive error treatment proce- dures: laser in situ keratomileusis (LASIK) and laser thermal keratoplasty (LTK) in temperature distribution of cornea. The thesis is divided into six chapters. Chapter-wise cameo description of the present study is as follows. Chapter 1 deals with the general introduction on human eye anatomy and physiology. It covers the general heat transfer mechanisms in human eye namely conduction, convection, metabolism, perfusion and evaporation. The derivation of Pennes bio-heat equation and the signi_cance of using it in human eye has been discussed. At the end, we present the review of literature. Chapter 2 deals with the mathematical theory of _nite elements. It cov- ers the basic theory of _nite elements, calculus of variations, weak formulations, _nite element solution procedure of elliptic boundary value problems and heat equation. The solution procedure of bio-heat equation in one and two dimensions in human eye discretization has been discussed. In thermoregulation of human body, about 50-80% of heat ow in the tissue is carried in or out by blood ow. In human eye only few layers retina, choroid, iris, and ciliary body, constitutes only 5% of entire volume, having blood ow. Chapter 3 deals with comparative study of temperature distribution in human eye with and without taking the e_ects of blood ow in these tissues. Nu- merical calculations are carried out using di_erent tear evaporation rates, blood temperatures, ambient temperatures and lens thermal conductivities. Both one and two dimensional steady and transient state cases are included. Convergence of temperature values by varying the mesh size has been carried out. The numer- ical results are compared with past experimental and similar simulation results. Eyelids are the thin fold of skin that cover and protect the anterior surface of the eye globe from local injury. Blinking is regarded as the continuous inter- rupted eyelid closure or opening and it's thermal e_ect will compromise between these two. During blinking heat loss via convection, radiation, and tear evapo- ration from cornea is prevented, warm tear is layered across corneal surface and the vessels of palpebral conjunctiva provide heat to anterior eye. Chapter 4 deals with the steady and transient temperature distribution of human eye in case of eyelid closure, opening and blinking. Eyelid is considered as a heating/cooling source of anterior cornea and model as a part of ocular component. Besides the various functions of eyelid blinking, heating and cooling mechanism play impor- tant role in maintaining anterior eye temperature. The eye temperature using di_erent values of evaporation rates, blood temperatures, ambient temperatures, lens thermal conductivities, blinking rates, blood perfusion rates and their im- pact on eye diseases like presbyopia, cataract etc. are investigated. The results so obtained are compared with past results. High air speed makes thinner the thermal boundary layer between cornea and environment. This accelerates evaporation and heat transfer. Eyelid blinking increases with increased airow speed into the eye. Increased blinking increases corneal temperature when drops below normal level. In cold climatic condition, high speed wind causes rapid temperature drop. Most often eye injuries caused by cold exposure occur in individuals who try to force their eyes open in cold weather in combination with wind such as two wheeler rider. Chapter 5 investi- gates the temperature changes in two wheeler rider's cornea in his/her di_erent speed and their impact on eye health. The numerical calculations are carried out during eyelid opening, closure and blinking with appropriate forced convection coe_cient at di_erent air speeds and ambient temperatures. Refractive errors are some of the most common ophthalmic abnormalities worldwide. Refractive surgeries were developed so that people could enjoy good vision with no or reduced dependence on glasses or contact lenses. Two types of laser surgical techniques: lamellar and thermal are available to reshape the corneal curvature. Ultraviolet (UV) emitting argon uoride (ArF) excimer laser is used to sculpt cornea in lamellar procedure, whereas, infrared (IR) emitting holmium yttrium aluminum garnet (Ho:YAG) laser is used to shrink cornea in thermal procedure. Tissue heating is common in all types of laser surgical tech- niques. Chapter 6 deals with the temperature distribution of cornea in di_erent laser refractive surgeries. Characteristics of optical and thermal processes and inuence of radiation and tissue parameters on the results of laser action are in- vestigated. The results of mathematical modeling in di_erent surgical techniques are discussed, compared and validated with experimental results.