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Finite Element Study of Nerve Fibers around Retinal Arteries and Possible Risk Factors for Glaucoma

Permanent Link: http://ufdc.ufl.edu/UFE0045060/00001

Material Information

Title: Finite Element Study of Nerve Fibers around Retinal Arteries and Possible Risk Factors for Glaucoma
Physical Description: 1 online resource (73 p.)
Language: english
Creator: Chugh, Devesh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: glaucoma -- iop -- onh -- retina -- rnfl
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Glaucoma is an irreversible optic neuropathy that causesloss of peripheral and ultimately central vision. It is a pathologic conditionin which there is a progressive loss of retinal ganglion cells, specific visualfield deficit, and a characteristic excavative atrophy of the optic nerve.There are many forms and different subsets of this disease, but the exact causeand pathophysiology are still unknown. Intraocular pressure (IOP) has beenidentified as the most important factor. However, alone IOP is not able toexplain the cause of the disease. Other parameters, like blood flow, diameterof the retinal arteries, layer thickness and material properties of the tissuesneed to be studied. Many clinical observations have reported a change in thephysical structure of the retinal arteries and different layers of the retinain glaucoma. But there has been no study on the correlation between how variousfactors like retinal thickness, diameter of the artery and the materialproperties impact the retinal ganglion cells. A finite element eye model hasbeen created using commercially available software and the factors mentionedabove were studied. The simulations help characterize the stress-strain fieldaround the retinal arteries in the retinal layer. Within the literaturereported values of the parameters studied, the diameter of the retinal vesselsand the material properties have significant impact onto the stress-strainfield. We can conclusively say that in the nerve fibers near the retinalarteries there are extremely high stresses as compared to stresses producedonly by IOP.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Devesh Chugh.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Tran-Son-Tay, Roger.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0045060:00001

Permanent Link: http://ufdc.ufl.edu/UFE0045060/00001

Material Information

Title: Finite Element Study of Nerve Fibers around Retinal Arteries and Possible Risk Factors for Glaucoma
Physical Description: 1 online resource (73 p.)
Language: english
Creator: Chugh, Devesh
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2012

Subjects

Subjects / Keywords: glaucoma -- iop -- onh -- retina -- rnfl
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
Genre: Mechanical Engineering thesis, M.S.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Glaucoma is an irreversible optic neuropathy that causesloss of peripheral and ultimately central vision. It is a pathologic conditionin which there is a progressive loss of retinal ganglion cells, specific visualfield deficit, and a characteristic excavative atrophy of the optic nerve.There are many forms and different subsets of this disease, but the exact causeand pathophysiology are still unknown. Intraocular pressure (IOP) has beenidentified as the most important factor. However, alone IOP is not able toexplain the cause of the disease. Other parameters, like blood flow, diameterof the retinal arteries, layer thickness and material properties of the tissuesneed to be studied. Many clinical observations have reported a change in thephysical structure of the retinal arteries and different layers of the retinain glaucoma. But there has been no study on the correlation between how variousfactors like retinal thickness, diameter of the artery and the materialproperties impact the retinal ganglion cells. A finite element eye model hasbeen created using commercially available software and the factors mentionedabove were studied. The simulations help characterize the stress-strain fieldaround the retinal arteries in the retinal layer. Within the literaturereported values of the parameters studied, the diameter of the retinal vesselsand the material properties have significant impact onto the stress-strainfield. We can conclusively say that in the nerve fibers near the retinalarteries there are extremely high stresses as compared to stresses producedonly by IOP.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by Devesh Chugh.
Thesis: Thesis (M.S.)--University of Florida, 2012.
Local: Adviser: Tran-Son-Tay, Roger.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2012
System ID: UFE0045060:00001


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1 FINITE ELEMENT STUDY OF NERVE FIBERS AROUND RETINAL ARTERIES AND POSSIBLE RISK FACTORS FOR GLAUCOMA By DEVESH CHUGH A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQU IREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2012

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2 2012 Devesh Chugh

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3 T o my Parents

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4 ACKNOWLEDGMENTS It has been one of the toughest journeys of my life and I want to extend my sincere thanks to all the peop le who have helped me in getting across the line. I want to thank my advisor Dr Roger Tran Son Tay who guided me all these two years. With him, I have gained a research experience that is going to help me all my life. I also want to thank Dr Malisa Sarnt inoranont and Dr Nam Ho Kim for being on my committee and always extending time and help whenever I faced a problem in my project. I thank my friends in Gainesville who were like a family always supporting me away from my home I also want to thank my fr iends back home in India who have supported me throughout this time. I want to thank my father and mother who have been constant source of love, inspiration, motivation and guidance. I also want to thank for all the love, support and care that I received from my sisters, brother in laws and my girl friend Sakshi. My journey has contributio been possible with the patience, support and motivation that these people have extended to me.

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5 TABLE OF CONTENTS P age ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 LIST OF ABBREVIATIONS ................................ ................................ ........................... 10 ABSTRACT ................................ ................................ ................................ ................... 11 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 13 Glaucoma ................................ ................................ ................................ ............... 13 Objective ................................ ................................ ................................ ................. 14 Specific Aim ................................ ................................ ................................ ............ 15 2 BACK GROUND AND SIGNIFICANCE ................................ ................................ ... 17 Anatomy and Physiology of the Eye ................................ ................................ ....... 17 Structure ................................ ................................ ................................ ........... 17 The Fluid System of the Eye ................................ ................................ ............ 17 The Retina ................................ ................................ ................................ ........ 18 Optic Nerve Head (ONH) ................................ ................................ .................. 20 Blood Flow in the Eye ................................ ................................ ....................... 21 Mechanism of Glaucoma ................................ ................................ ........................ 21 Prevalence and Types of Glaucoma ................................ ................................ ....... 23 Present Analytical and Numerical Modeling for Glaucoma ................................ ..... 24 Significance ................................ ................................ ................................ ............ 25 3 MATERIALS AND METHODS ................................ ................................ ................ 27 Finite Element Model for the Retinal Nerve Fiber Layer ................................ ......... 27 Finite Element Model in ADINA ................................ ................................ .............. 33 Assumptions in this Model ................................ ................................ ................ 34 Boundary Conditions ................................ ................................ ........................ 35 Model Validation ................................ ................................ ................................ ..... 38 4 RESULTS ................................ ................................ ................................ ............... 44 Case 1: Effect of Variation of Diameter ................................ ................................ ... 44 Case 2: Effect of Thickness of Retina ................................ ................................ ..... 51 Case 3: Effect of Material Properties of Different Layers. ................................ ....... 55

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6 5 DISCUSSION ................................ ................................ ................................ ......... 59 Limitations of the Study ................................ ................................ ........................... 63 Conclusion ................................ ................................ ................................ .............. 63 Future Studies ................................ ................................ ................................ ........ 64 LIST OF REFERENCES ................................ ................................ ............................... 66 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 73

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7 LIST OF TABLES Table page 3 1 The va lues of the retinal artery diameter as reported in literature. ...................... 28 3 2 Thickness of choroid of the eye ................................ ................................ .......... 30 3 3 Thickness of retinal nerve fiber layer and retina as reported in literature ........... 31 3 4 Elastic properties of the different layers of the eye. ................................ ............ 32 3 5 Test c ase comparison of stress values of ADINA and analytical solution for a plate with a whole ................................ ................................ ............................... 40 3 6 Actual model comparison of stress values of ADINA and analytical solution ..... 42 4 1 Fixed parameters to study effect of diameter ................................ ..................... 44 4 2 Fixed parameters to study effect of retinal thickness ................................ .......... 52 4 3 Fixed parameters to study effect of material properties ................................ ...... 55 4 4 Conditions of IOP and BP. ................................ ................................ .................. 58

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8 LIST OF FIGURES Figure page 2 1 Formation and flow of the fluid in the eye ................................ ........................... 18 2 2 The system for outflow of aqueous humor from the eyeball into the conjunc tival veins ................................ ................................ ............................... 19 2 3 Retinal layers. Low p ower micrograph of human retina ................................ ...... 20 2 4 Nerve fiber fascicles fan out as they overlie a med ium sized blood vessel ........ 22 3 1 Plane stress model schematic used to analyze the retinal nerve fiber layer. ...... 34 3 2 OCT of a mouse ey e. Arrows pointing at the retinal vessels .............................. 35 3 3 Variation of IOP and BP with time. ................................ ................................ ..... 36 3 4 Representation of a 2D plane stress ele ment in ADINA ................................ ..... 37 3 5 Actual finite element model mesh from ADINA ................................ ................... 38 3 6 Test case schematic. ................................ ................................ .......................... 39 3 7 Superimposing plate with hole subject to tension and a thick cylinder pressurized from inside. ................................ ................................ ..................... 41 4 1 Representation of the radial lines where results were eval uated ........................ 45 4 2 Von Mises stress distribution for all time steps for vessel diameter=100 and WLR=0.4 along radial 1,2,3 and 7. ................................ ................................ ..... 46 4 3 Normalized variation of stress along radial1 for different diameters A) Maximum stress B) Minimum stress. ................................ ................................ .. 46 4 4 The retinal mesh with effective stress field for the model for two load combin ations. ................................ ................................ ................................ ..... 47 4 5 Maximum stress value across different radials(1,2,3 and 7) for different diameters. ................................ ................................ ................................ ........... 47 4 6 Pattern of strain yy for diameter=100 along radial 1,2,3 and 7, with WLR=0.4. .. 49 4 7 Normalized variation of strain yy along radial 2 for all diameters ........................ 49 4 8 Comparison of Maximum and minimum strain yy values in different radials for same diameter. ................................ ................................ ................................ ... 50

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9 4 9 The pattern for strain zz for Radial1, 2, 3 and 7 for diameter =100 and WLR =0.4. ................................ ................................ ................................ ................... 50 4 10 The variation strain zz along different radials(1,2,3,7) for all diameter .............. 51 4 11 Normalized variation of strain zz for radial 1 for all diameters. ........................... 51 4 12 Normalized variation of stress along radial 3 for different retinal thickness. ....... 5 3 4 13 The variation of stress along different radials around the artery for different retinal thicknesses ................................ ................................ .............................. 53 4 14 Normalized variation of strain yy along radial 3 for different thicknesses. .......... 54 4 15 Variation of strain yy along different radials around t he artery for fixed thicknesses ................................ ................................ ................................ ......... 54 4 16 Normalized variation of stress for different retinal moduli at radial 2. ................. 56 4 17 The variation of stress for each radial and for different retinal moduli ................ 56 4 18 Normalized variation of strain yy for different retinal moduli at radial 2. .............. 57 4 19 Variation in strain zz for each radial and different retinal moduli ........................ 57 5 1 Estimation of the area of nerve fibers exposed to higher stresses. .................... 61

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10 LIST OF ABBREVIATION S ACG Angle Closure Glaucoma BP Blood Pressure FSI Fluid Structure Interaction GON Glaucomatous Optic Neuropathy IOP Intraoc ular Pressure LC Lamina Cribrosa OAG Open Angle Glaucoma OBF Ocular Blood Flow OCT Optical Coherence Tomography ONH Optic Nerve Head RNFL Retinal Nerve Fiber Layer RPE Retinal Pigment Epithelium

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11 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science FINITE ELEMENT STUDY OF NERVE FIBERS AROUND RETINAL ARTERIES AND POSSIBLE RISK FACTORS FOR GLAUCOMA By Devesh Chugh December 2012 C hair: Roger Tran Son Tay Major: Mechanical Engineering Glaucoma is an irreversible optic neuropathy that causes loss of peripheral and ultimately central vision. It is a pathologic condition in which there is a progressive loss of retinal ganglion cells, specific visual field deficit, and a characteristic excavative atrophy of the optic nerve There are many forms and different subsets of this disease, but the exact cause and pathophysiology are still unknown. Intraocular pressure (IOP) has been identifie d as the most important factor. However, alone IOP is not able to explain the cause of the disease. Other parameters, like blood flow, diameter of the retinal arteries, layer thickness and material properties of the tissues need to be studied. Many clinica l observations have reported a change in the physical structure of the retinal arteries and different layers of the retina in glaucoma. But there has been no study on the correlation between how various factors like retinal thickness, diameter of the arter y and the material properties impact the retinal ganglion cells. A finite element eye model has been created using commercially available software and the factors mentioned above were studied. The simulations help characterize the stress strain field aroun d the retinal arteries in the retinal layer. Within the literature reported values of the parameters

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12 studied, the diameter of the retinal vessels and the material properties have significant impact onto the stress strain field. We can conclusively say that in the nerve fibers near the retinal arteries there are extremely high stresses as compared to stresses produced only by IOP.

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13 CHAPTER 1 INTRODUCTION Glaucoma Glaucoma is an irreversible optic neuropathy that causes loss of peripheral and ultimately cent ral vision. It is a pathologic condition in which there is a progressive loss of retinal ganglion cells, specific visual field deficit, and a characteristic excavative atrophy of the optic nerve head In practice it has proven useful to speak about glaucom a patients if they present either with elevated Intraocular pressure (IOP), glaucomatous optic neuropathy (GON) or both 1 Whereas a number of indisputable risk factors, including elevated IOP, have been described, the pathogenesis leading to glaucomatous optic neuropathy remains poorly understood F or an eye w ith glaucoma, the reduction in visual sensitivity is a result of the loss of retinal ganglion cells and that retinal areas with greater losses of sensitivity have undergone greater glaucomatous losses of ganglion cells 2 4 Half of the people who suffer from the disease do not even know it until the disease has reached advanced stages 5 There are some clinica l measurable factors that are now being used to diagnose glaucoma l ike the retinal ne rve fiber layer (RNFL) thickness. S tudies have shown the overall RNFL thickness average to be the best diagnostic parameter for glaucoma 6 9 Other studies have shown the inferior 10 12 or superior 13 quadrant of the eye's RNFL thickness average to be the best, in agreement with clinical observation that glau comatous optic nerve damage seems to begin Also, the diameter of the retinal arteries of glaucoma patients has been observe d to vary from normal subjects Studies have shown that t he vessel diameters decreases significantly with increasing glaucoma

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14 stage independently of the patients' age 14 18 These factors when combined, affect the mechanical environment ( stress and strain distribution) of the retinal nerve fibers. Data available in literature shows how the ner ve fibers, in different parts of the human body, behave when subject to mechanical stresses and strains. F or example i n the peripheral n erves while 5% strain does not affect conduction, further elongation decrease s amplitude approximately linearly with str ain 19 T he pressure threshold at which the blood perfusion in sciatic nerves start s to decre ase in diabetic rats is 24.1 mm Hg and that in the normal controls is 47.1 mm Hg 20 T he blood perfusion of the sciatic nerve started to decrease at a mean pressure of 30.5mmHg and reached a stable lowe r level of 30% of pre compression value at 102.8 mmHg 21 In all the theories of the glaucoma the effect of IOP has been taken into account, but the effect of the retinal a rteries thickness of retinal layer and the material properties onto the stress strain field of the RNFL has not been explored. Objective The focus of this thesis was to develop a finite element model which can characterize the stress and strain field i n t he retinal nerve fiber layer, specifically around the retinal arteries. The retinal artery is embedded inside the retinal nerve fiber layer and exerts pressure on the nerve fibers all around it. To add to this, there is the intraocular pressure ( IOP) that acts on the inner limiting membrane of the retina. This study includes the variation of factors like IOP, arterial blood pressure, diameter of the retinal arteries, thickness of the retina and the material properties. Since g laucoma involves the loss of r etinal ganglion cells, we need to study the mechanical environment in the retinal nerve fiber layer. The objective of this study is to characterize the stress and strain distribution around the retinal nerve fiber layer and how some of

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15 the clinical measura ble parameters and material properties affect it. The variation of the input parameters thickness, diameter, material properties and the loading conditions will help us to establish in which area of the eye the retinal nerve fibers are exposed to higher st ress and strain values. This information can potentially help us to identify the risk for loss of ganglion cells withi n the retinal nerve fiber layer. Specific Aim To develop 2D Finite Elemen t Model for a cross section of retinal nerve fiber layer around t he retinal arteries under different pressure loading conditions We include the three load bearing layers i.e. retina, choroid and sclera, in the posterior portion of the eye. The arterial wall is embedded in the retinal layer and will be modeled as separa te within the retinal layer. The material properties considered in this model are purely elastic properties. Each layer wi ll have different material properties. We will cover the physiological range and use value s as reported in the literature Three value s are used, two extreme values and one in the middle. T he range for different layers is: Retina: Young's M odulus from 0.03MPa to 0.12MPa Choroid: Young's Modulus from 0.15 MPa to 0.25 MPa Sclera: Young's Modulus from 0.5 MPa to 4.0 MPa Arterial Wall: Young's M odulus from 0. 2 MPa to 0.5 MPa The geometrical properties i.e. the diameter of the retinal artery, t he thickness of each layer varies i n different regions of the eye We are concentrating on the physiological range. The values that will be used are 250 to 32 0 m for retinal layer, 280 to 370 for choroid, 900 to 1000 for sclera and 80 to 120 for the diameter. For all the range reported above we use two extreme values and one middle value.

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16 The pressure conditions inside the retinal artery ( BP) and press ure inside the eye ( IOP) are also incorporated with suitable pressure functions. They are varied to capture the different combinations of IOP and BP for the circadian variation in IOP and BP. The range for IOP is 1 3 mm Hg to 2 3 mm Hg and the range for BP is 80mm Hg to 120 mm Hg The mod el will be solved using commercially available software ADINA (ADINA R&D Inc., MA). The output from the model is the stress and strain fields around the retinal artery. The von mises stresses will be used to characterize the stress field and the strains will be analyzed in two directions to characterize the stre t ch and compression of the nerve fibers.

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17 CHAPTER 2 BACKGROUND AND SIGNI FICANCE Anatomy and Physiology of the Eye Structure The eye is a very complex organ that send s a huge amount of information to the brain. It has a very specific design to capture and analyze light The most important parts of the structure, relevant to this thesis are discussed in this section The outer shape of the eye is a non symmetric sphere flattened at the top and the bottom part and an outside bulge at the front part. The outer shell is called the sclera, which is visible to us as the white part Sclera is the site of attachment of the eye to external structures (muscles and connective ti ssues) and has portals for the passage of blood vessels and nerves in and out of the eye 22 It is light tight so that light can only e n ter through a small opening, called the cornea at the front, which is also the primary refractive element of the eye. The cornea and sclera limbus are thin elastic sheets and are made primarily of type I collagen fibrils 22, 23 The image of the object is formed at the retina which is at the back of the eye, and the light is focused by the cornea, lens, aqueous and vitreous humor. The lens contrib utes about one third of the eye's total dioptric power. The Fluid System of the Eye The fluid system ( Figure 2 1 ) that we discuss here is responsible for all the pressure that is exerted onto the retina, choroid and the sclera. To maintain the shape of th e eye formed by sclera and cornea it is necessary to provide pressure from the inside of the eye, therefore the eye is filled with intraocular fluid. It maintains sufficient pressure in the eyeball to keep it distended. This fluid in front of the lens is c alled the

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18 aqueous humor and vitreous humor is between the posterior surface of the lens and the retina. Total ocular volume is about 6.5ml of which 10% is aqueous humor The aqueous humor is a freely flowing fluid, whereas the vitreous humor, sometimes cal led the vitreous body, is a gelatinous mass held together by a fine fibrillar network composed primarily of greatly elongated proteoglycan molecules. Eighty percent of the interior volume of the eye is vitreous and the longest optical path from the cornea to the retina is through the vitreous 22 Aqueous humor is continually being formed in the ciliary process es at a rate of 2 to 3 microli ter s per minute 24, 25 The balance between formation and reabsorption of aqueous humor regulates the total volume and pre ssure of the intraocular fluid. Figure 2 1 Formation and flow of the fluid in the eye Rep rinted by permission from Elsevier Publications. Guyton & Hall: Textbook of medical Physiology 11 th Edition (Figure 49 19 Page 62 3 ) Elsevier, All copyrights with Elsevier Publications, Philadelphia The aqueous humor flows anterior to the lens and into t he angle between the cornea and the iris, then through a meshwork of trabeculae, finally entering the canal of

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19 Sclemm, which empties into extraocular veins (as shown in Figure 2 2 ). The average normal intraocular pressure is about 15 mm Hg, with a range of 12 to 20 mm Hg 24 The Retina The light is focused on to the retina and retina transforms the light energy into a signal to be communicated to the brain. Th e ph otoreceptors in the retina act as a group they transform the pattern of light and shade in the retinal image into a corresponding pattern of gradations in neural activity. The Figure 2 3 shows a typical histological section of the retina and a representati on of different cells along the thickness. After the light passes through the lens system of the eye and then through the vitreous humor, it enters the retina from the inside, that is it first passes through the ganglion cells, then through the plexiform a nd nuclear layers before it finally reaches the layer of rods and cones located all the way on the outer edge of the retina. This distance is a thickness of several hundred micrometer, which varies from one part of the eye to the other part of the eye 24 Figure 2 2 The system for outflow of aqueous humor from the eyeball into t he conjunctival veins. Reprinted by permission from Elsevier Publications. Guyton & Hall: Textbook of medical Physiology 11 th Edition ( Figure 49 21, Page 624 ) Elsevier All copyrights with Elsevier Publications, Philadelphia

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20 The layer beneath the retina is called the choroid. The choroid serves a double purpose: nourishment and absorpti on. The choroid carries blood to the retina and the humors, providing nourishment to the eye 24 Optic Nerve Head ( ONH) All ganglion cell axons and all branches of the central retinal artery and vein converge at the optic nerve head. Ganglion cell axons run in stereotypical pattern from their bodies to the ONH, which is their site of exit from the eye. The o ptic disc is a weak spot in the fundus of the eye because it is not reinforced by the sclera. It lacks photoreceptors and is therefore called the blind spot of the eye. In glaucoma there is characteristic atrophy of the optic nerve head and clinically optic disk damage is used to monitor the progress of glaucoma Figure 2 3 Retinal layers. ( Low power micrograph of human retina(wax histology): arrows, retinal vessels. Or i ginal magnification: x150. 26 ) Rep rinted by permission from Elsevier publications. The Eye: Basic Sciences in Practice by John V Forrester, 2002, Chapter 1, Figure 1.23, Page 3 7. All copyrights with Elsevier, Philadelphia.

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21 The nerve head can be divided into three structurally different par ts: the laminar portion, which is defined by scleral fibers that intersect the axons as they exit the eye (lamina cribrosa), the prelaminar portion lying between the lamina and vitreous; and the postlaminar portion, which is the first section of the optic nerve 22 The lamina cribrosa is considered as the primary damage site in the optic nerve head 27 28 Blood Fl ow in the Eye The blood supply to the eye arises primarily from the ophthalmic artery, which is the first branch of the internal carotid artery. At various points from the ophthalmic artery, different branches supply the eye and its associa ted structures. The centra l retinal artery branches off to penetrate the optic nerve approximately 10 to 15 mm behind the globe 29 Vasculature of the retina Retina has two separate sources of blood supply one from the central retinal arteries and the other from the bottom layered choroid. The retinal arteries and veins lie within the nerve fiber layer of the superficial retina 26, 29 The nerve fibers are observed to splay around the retinal arteries inside the retina. Figure 2 4 shows a nerve fiber fascicles fan out as they overlie a medium sized blood vessel. Mechanism of Glaucoma The pathogenesis leading to glaucoma is still not clearly understood. The primary causes of glaucomatous optic neuropathy are unknown. The disorder affects the individual axons of the optic nerve, which may die by apoptosis. Scientists have proposed two ma in theories, the Mechanical Theory and the Vascular Theory but none has been able to clearly define the path and cause of the disease. The research is proceeding in many different fronts: genetic, biochemical, cellular biological and

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22 mechanical to name a f ew 30 In this study we are concentrating on the mechanical factors that may affect the ganglion cells and its axons. Figure 2 4 Nerve fibe r fascicles fan out as they overlie a medium sized blood vessel (appearing as a black void) in the equatorial region of a cat retina. M agnification X 300 31 Reprinted by permission ARVO from Zhang X, Mitchell C, Wen R, Laties AM. Nerve fiber layer splaying at vascular crossings. Figure 3. IOVS, July 2002, Vol. 43, No. 7 Page 2064. All c opyright s with ARVO. Mechanical t heory 1 An increased intraocular pressure (IOP) leads to elongation, stretching and collapse of the laminar beams and their posterial displacement (bowing). The axons o f the retinal ganglion cells become damaged either directly, by increased pressure and pressure gradient, or indirectly, by tissue deformation. The axoplasmatic transport is impeded which may ultimately induce cell death, for example due to a lack of troph ic factors 1 Vascular t heory 1 The vascular theory of glaucoma considers glaucoma as a consequence of insuffi cient blood supply due to either an increased IOP or other risk

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23 factors reducing ocular blood flow (OBF). The main cause of this theory is the existence of glaucoma in patients with low IOP (called normal tension glaucoma). Prevalence and Types of Glaucom a In open angle glaucoma the angle between the cornea and the iris is open and while in angle closure glaucoma this angle is closed. Further, in some open glaucoma patients high IOP is observed which is called high tension glaucoma and in some patients low IOP is observed which is normal tension glaucoma (NTG) There were 60.5 million people with open angle glaucoma (OAG) and acute angle glaucoma (ACG) in 2010, which will increase to 79.6 million by 2020, and of these, 74% will have OAG. Women comprise 55% of OAG, 70% of ACG, and 59% of all glaucoma in 2010. Asians will represent 47% of those with glaucoma and 87% of those with ACG. Bilateral blindness will be present in 4.5 million people with OAG and 3.9 million people with ACG in 2010, rising to 5.9 and 5 .3 million people in 2020, respectively 32 In 2010 more than 2 million individuals in the United States were affected by o pen angle glaucoma Owing to the rapid aging of the US population, the total number of trea table OAG patients will increase to more than 3 million by 2020 32 and to 7.32 million by 2050 33 Studies consistently find that about half of those with glaucoma are unaware they have the disease 5 Given an estimated prevalence of glaucoma in the United States of 2.2 million people, this would represent a payer burden (largely Medicare and Medicaid) in excess of $300 million/year over and above the cost of providi ng routine care for glaucoma, such as intraocular pressure lowering medications and visual field testing 34

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24 Present Analytical and Numerical Modeling for Glaucoma The eye and its tissues are not easily accessible, therefore modeling is the most logical way to analyze the behavior of the tissue of eye and how they react to the different parameters of the environment they are in. A s imple model 35 use s the Laplace model to predict the stress onto the lamina cribrosa whereas there are others where ocu lar rigidity is defined to estimate the stresses 36 There are many other mathematical models 27, 37, 38 but the problem with these models is that the assumption s used make t he model are oversimplified These models do not depict the individual tissue behaviors and also they cannot individually vary the physiological parameters that the eye and its tissues are subject to. Therefore, these models cannot quantify the effects and the cause of glaucoma, which needs the understanding of the individual tissues that are subject to variable p arameters. A n umerical approach can incorporate more realistic conditions than analytical models can and has been widely used in engineering to de termine the mechanical response of complex biological tissues Previous numerical modeling has focused on modeling the optic nerve head ( ONH) and more specifically the lamina cribrosa (LC) which is considered as the primary site of the damage within the op tic nerve head Finite element m odels are made using the geometric and material property values from experimental data as listed in the literature and with 3D reconstruction of the eye 28, 39 49 These models studied the effects of the size and eccentricity of the scleral canal on the mechanical response of the ONH. They found that IOP related stresses within the connective tissues of the ONH could be substantial 41, 48 Eye sp ecific models were reconstr ucted by using images of histological sections from donor tissues of the human eyes obtained from the eye bank 40, 49 These models were then used to study the

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25 relative influences of geome try and material properties of the ONH to changes in IOP 40, 41, 45 In the study by Segal et al. parameterized study of various geometr ic and material details of the ocular model to assess their impact on a host of outcome measures identified the five most important determinants of ONH biomechanics as: the modulus of the sclera, the globe radius of the eye, i ntraocular p ressure the modulus of the LC, and the thickness of the sclera 42 Basis of these m odels The hypothesis that Segal et al. have adopted is they want to cater to all types of glaucoma, as glaucoma occurs in eyes with high IOP and low IOP and therefore the hypothesis that even at normal levels of IOP, the con nective tissues of the ONH are constantly exposed to substantial levels of IOP related stress. The level of stress generated by normal levels of IOP is assumed to play a central role in the physiology and, in some eyes, the pathophysiology of all three ONH tissue types Therefore these models study the ONH tissue to analyze its behavior under IOP to ascertain the cause of glaucoma or what initiates the start of glaucoma. These models do not l ook into the impact of the IOP and the retinal arteries on to the retinal nerve fiber layer Significance It is still not clear how the pathop hy s iology of glaucoma is initiated. The models described above have given some insight about sclera and the ONH, but no study has been performed to study the retinal layer from a mechanical point of view. Glaucoma is essentially the loss of axons in the retinal nerve fiber layer and there are many mechanical factors that cause the stresses and strains on the axons in this layer. Studies have shown the overall RNFL thickness averag e to be the best diagnostic parameter 6 8 for glaucoma. Other studies have shown the inferior 10 12 or superior 13

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26 quadrant RNFL thickness average to be the best, in agreement with clinical observation that glaucomatous optic nerve damage seems to begin. However, its impact on the ganglion cells and its axons in the retinal artery has not been studied. Since the retina is essentially a plane with substantial area over which the blood vessels ramify, most retinal pathology is local in its early stages and cannot easily affect the entire area. The loss of the retinal ganglion cells can further affect the materia l properties of a substantial are a of retina. Also, predominantly only IOP is attributed as damag ing the axons in the nerve fibers, the stresses by the arteries and blood pressure are not considered In this study we characterize the se stresses in the RNFL that are caused by the retina l ar teries. The retinal blood vessels serve for nutrition of the retinal ganglion cells and their axons. The size of the artery plays a significant role as it is embedded inside the retinal nerve fiber layer and n arrowing of retinal arterial calibers in subj ects with glaucoma has been demonstrated 14, 15, 50 Through the modeling of various tissues and arteries inside the retinal never fiber layer and simulating realistic eye conditions, like varying the IOP and blood pressure over time, we can gain an insight of how mechanical stresses affects the retinal nerve fiber layer. Such a model could serve as a potential tool to help us to identify the risk for loss of ganglion cells within the reti nal nerve fiber layer.

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27 CHA PTER 3 MATERIALS AND METHODS Finite Element Model for the Retinal Nerve Fiber Layer The eye is one of the most complex organs of the human body. The conditions inside the eye vary from one point to the other. Therefore, to analyze the retinal nerve fiber l ayer from a mechanical point of view we need to make simplifying assumptions and consider the most important parameters. W e can point out the following parameters that can affect the nerve fibers around the retinal arteries Geometrical factors The geom etrical factors go into defining the physical parameters of the environment in our model. These are listed as follows. Diameter of the retinal artery Radius of the eye (Curvature/change of direction of flow) Length of the artery Thickness of the different layers of the eye: Retina, Choroid, Sclera Artery Wall Branching of the arteries Mechanical properties of different layers. The material properties define how material behaves to the applied load. These are listed as follows Retina Choroid Sclera Arter y wall Flow properties. The flow properties determine the pressures and are listed as follows. Pressure outside the artery( IOP ) Pressure inside the artery( arterial pressure ) Viscosity of the b lood Blood f low rate Diameter of the retinal artery. The ret inal arterial diameters which have a major influence on the arterial blood pressure owing to Hagen and are

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28 therefore of major clinical interest. The retinal artery diameter varies from the point of bifurcation to the very end of these art eries. The vasculature of each and every human being is different and there are some mean values for the retinal diameters that are based upon population surveys. These population based data suggest that generalized retinal arteriolar narrowing, an indicat or of localized vascular change, is significantly associated with optic nerve damage caused by OAG 17 T here is variation in the value reported in literature for a specific region of the eye Diameter s from some of t he major population studies and some experimental studies are listed in Table 3 1. Table 3 1. The values of the retinal artery diameter as reported in literature. Reference Region of the Eye Diameter( m) Normal GON Eye Eye Comments 14 S uper o temporal 106 18 89 17 For Age <65: Caliber measured 105 18 88.8 16 For Age >65 Infer ortemporal 113 20 88.6 14 For Age <65: Caliber measured 107 14 92.4 18 For Age >65 17 Not Specified 183 2.6 194 0.4 Measurements 0.5 to 1.0 disk dia meter from ONH. They used a formula given in 51 this formula gives higher values and was later corrected in 52 18 Superotemporal 115 18 87.3 18 Measurements just outside the margin of optic disk Vi supac software used. Inferotemporal 110 16 87 21 Superonasal 96 14 72 17 Infer onasal 89 16 71 18 16 Super o temporal 111 16 112 16 Measurement at optic d isk border. Caliber measured Measurement of the temporal superior and inferior vessels 53 Infer otemporal Super ornasal Infer otemporal Not specified 117 17 97 15 94 14 101 15 117 86 95 12 91 12 100 8

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29 Radius of the eye globe. The eye is not exactly spherical in shape. The end to end distance varies from one point to other. I t is maximum from anterior to the posterior section and minimum from the top to bottom section. The anterior to posterior distance is higher because of the bulge out of the cornea, the distance is usually between 22mm to 23.5mm 22 Since the retina is essentially a plane with substantial area over which the blood vessels ramify we can ignore the effect of the blood vessel curvature. Thic kness of the different layers of the e ye T he properties of the different layers of the eye are not spatially uniform and they vary from poin t to point. This applies to all the layers of the eye. This impacts the load distribution in the nerve fiber layer and the blood arteries. The thicknesses of the different layers involved in t his analysis are tabulated in Table 3 2 The difference in thickness also arises in these values because different approaches/algorithms are used to analyze the image data. For e xample in some studies 54 retinal thickness is defined from internal limiting membrane and retinal pigment epithelium, and in a different study 55 it is defined as between the vitreoretinal interface and the inner and outer segments of the photo receptors. Table 3 2 and 3 3 list all the reported values of thickness of the choroid and the retina respectively. The sclera is thickest at the posterior pole (996 181 ), thinnest at the equator (491 91 ) and the thickness is in between at the corneoscleral limbus (588 63 ) 56 Similar results were reported in another study where the range of thickness was reported between 10 00 to 900 near the optic nerve to 250 at the equator and 390 at limbus 57 There has been more convergence on the thickness of sclera as compared to other layers because of its high rigidity.

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30 Table 3 2. Thickness of choroid of the eye Mechanical properties of the different layers The material properties of the most of the eyes soft tissues are anisotropic, viscoelastic and nonlinear. However, it is usually assumed that soft tissues behave as isotropic, e lastic, linear materials in order to simplify the analysis. These assumptions are likely to be reasonable for small strains, due to static load application and a spatial scale that is large compared to the relative correlation length of elastic variability in the tissue sample. Reference Region of the Eye Thickness ( m) Normal Affected Eye s Eye s Comments 58 Choroid Anterior 80 -In vivo measurement s gave 0.42mm. 59 Superior 241.5 62.0 172.377.9 In vivo measurements. Normal control eyes were highly myopic Affected ey es: Secondary closure glaucoma Superotemporal Temporal Inferotemporal Inferior Fovea 244.8 61.0 161.5 45.0 159.9 41.0 162.1 47.6 276.1 74.1 161.1 71.9 110.9 40.1 115.4 36.1 123.4 44.3 166.7 40.9 54 60 61 Central Subfield Nasal Inner Macula Nasal Outer Macula Superior Inner Macula Superior Outer Macula Temporal Inner Macula Temporal Outer Macula Inferior Inner Ma cula Inferior Outer Macula Peripapillary Not specified 355 73 343 72 316 71 360 67 362 61 359 71 357 63 356 78 355 75 16313 307 70.1 332 60 322 58 297 57 345 58 356 53 337 60 340 56 334 67 338 73 --Normal eye: Axial length<25.0mm Affected eye: Axial length>25.0mm --

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31 Table 3 3 Thickness of retinal nerve fiber layer and retina as reported in literature Reference Region of the Eye Normal Affected Eyes Eyes Comments 62 Temporal quadran t Superior quadrant Nasal quadrant Inferior quadrant 170 58 240 57 220 70 266 64 ----RNFL defined from inner limiting membrane to Bruch's Membrane 63 Temporal Superior Nasal Inferior 89.9 15.6 134.6 23.3 91 .9 28.9 138.1 23.2 49.4 23.9 77.9 31.2 53.0 36.0 76.3 31.2 Affected eye: Advanced glaucoma 64 Perifoveal avg. 211.4 16.8 185.7 16.8 55 Center Fovea Mean Fovea Temporal Inner Macula Superior Inner Macula Nasal Inner Macula Inferior Inner Macula Temporal Outer Macula Superior Outer Macula Nasal Outer Macula Inferior Outer Macula 157.8 3.2 191.6 2.7 255.6 1.9 272.2 2.1 269.3 2.0 266.8 2.0 221.0 1.8 240.7 2.1 257.6 2.2 230.3 1.9 ----------Retina defined as between vitreoretinal interface to inner and outer segments of photoreceptors 54 Central Subfield Nasal Inner Macula Nasal Outer Macula Superior Inner Macula Superior Outer Macula Temporal Inner Macula Temporal Outer Macula Inferior Inner Macula 256 13 321 14 297 20 315 15 28 1 13 310 14 267 13 315 14 --------retinal thickness is defined from internal limiting membrane and retinal pigment epithelium 65 Superior Inferior Temporal Nasal Mean 146.6 32.2 143.5 32.9 66.9 34.6 117.2 33.1 119.7 28.1 ----Only Nerve fiber layer thickness 500 from the ONH 65 Superior Inferior Temporal Nasal Mean 133.5 34.7 128.7 42.0 91.5 35.8 89.2 31.0 110.7 30.9 -----Only Nerve fiber layer thickness 750 from the ONH

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32 Table 3 3 Continued Reference Region of the Eye Normal Affected Eyes Eyes Comments 65 Superior Inferior Temporal Nasal Mean 316.9 48.1 286.1 50.4 223.5 23.9 271.3 3 0.6 277.6 33.4 -----Retina: from vitreoretinal interface to RPE 65 Superior Inferior Temporal Nasal Mean 285.0 32.7 269.2 35.2 253.5 36.3 239.0 30.6 262.2 30.3 -----Retina: from vitreoretinal interface to RPE 75 H Table 3 4. Elastic properties of the different layers of the eye. Reference Layer (Region) Elastic modulus (E) kPa Model Comment 66 Retina 20 Bovine Invitro experiment and mathematical model 67 Retina 1.0 to 2.09 Porcine Spatial mapping of E. E defined at steps from ONH 68 Retina 100 to 110 Porcine Different strain rates used. 6 9 Retina 19.512.2 to 107.858 Porcine Tension test 70 Retina Choroid Combined 15.6 34.25 Human In vivo measurements 58 Choroid Anterior Posterior 2.21.5x10 2 7.57x10 2 Human In vitro te sting. Tension test. 69 Choroid 18421221 to 37392638 Porcine Tension test in different environmental conditions. 71 Peripappillary Sclera 2930 to 6150 Human Tension test in different environmental conditions. 72 Sclera 1.10.8 to 1.470.33 3.87.57 to 4.360.60 Human Porcine Drained Secant Modulus for both cases. 73 58 Sclera Sclera 33.378 200 to 2600 Human Human Average of several values Posterior Sclera 74 Sclera 49401220 to 71461580 Monkey

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33 Again as for the thickness, the material properties of the sclera are mostly studied and well documented in the literature. Other layers like the choroid, retina have had v ery little focus from this point of view, but recently there have been few studies to determine the material properties of the other layers. There is no convergence in the reported values when compared to other studies 66 70, 74, 75 Table 3 4 lists the elastic modulus for the different layers being studied in this study. There are few reported studies on the viscoelastic properties of the sclera, and this has been limited to monkey and rabbit models 74, 75 Finite Element Model in ADINA We use a simplified model to analyze the effect of the various geometrical and material properties that have been listed in the previous section. To focus on the how the stress strain field in n erve fiber layer is affected all around the retinal arteries, we take a cross se ction of the retinal artery and the different layers around it as shown in the Figure 3 1. Computational domain. The domain is shown in the Figure 3 1. There are three differe nt tissue layers, retina, choroid and sclera. The artery is embedded in the retinal layer. Since the arteries are not fixed at the ends inside the eye, we can reduce the problem to a 2D plane stress model. The nodes at the interface between different layer s are shared to ensure contact between the layers. For example, the artery is free to expand and it deforms the retinal layer around it and therefore causes the stress and strain in retinal layer Similarly, the nodes between retina and choroid are shared and nodes between choroid and sclera are shared. The retina is loaded from top with the IOP and the artery has internal pressure acting on the inside surface. The outside vertical edges, for all the three layers, are constrained to move only in Z direction

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34 (edges L1 to L6 as shown in Figure 3 1). The width of the model is 700 m The bottom edge is fixed as this is the point where eye is attached to the body (edge L7 in the Figure 3 1) The tissue layers retina, choroid, sclera and the artery wall layer are attributed linear elastic material properties with different elastic modulus as reported in the literature. Figure 3 1. P lane stress model schematic used to analyze the retinal nerve fiber layer. Assumptions in this Model Isotropic elastic material pr operties for each layer. The reason for this was there were no visco elastic properties reported in the literature for retina and choroid. P lane stress model. Since the arteries are not fixed in the retinal layer, a plane stress assumption is assumed. Ret inal artery in the model is geometrically centered in the retinal layer.

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35 We assume this cross section of the retina is near the optic nerve head and far away from the retina edge (i.e. within the white circular border area as shown in Figure 3 2 left imag e, the radius of the circle being 5 times the radius of optic disk). The reason for this is that we want to analyze the effect of large arteries, the artery diameter is highest near the optic nerve head and it decreases as we move away from optic nerve hea d. Fig ure 3 2. OCT of a mouse eye. Arrows pointing at the retinal vessels A) Front view of the mouse eye in OCT. B) A cross section, showing the artery and different layers of the eye. No thermal effects, temperature does n ot affect the output i.e. stress and strain. The shear traction by the vitreous humor onto top layer of the retina is negligible and not accounted in the study. Viscous effects between different layers are also neglected. We have also neglected the shear g radient by the blood flow on the walls of the retinal vessels. No fluid flux due to pressure gradient across tissues. Boundary Conditions Degrees of freedom x translation, y rotation, x rotation and z rotation are constrained. Only free degrees of freedom are y translation, z translation. These follow from plane stress condition. artery. This leads us to a width of L4 one retinal artery. Retina Edge X Y Y Z Cross section of the retina with artery Cross section of the retina with artery A B X C

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36 I OP is applied to the top edge. T he vertical edges (L1 L6 in Figure 3 1) are constrained to move only in the vertical ( Z ) direction. Figure 3 2 which shows an OCT of an eye of a mouse. In the image on the left, we can see the artery and vein network and in the right image we can see a cross section (C at one location. The vertical edges of the model will have negligible expansion in the Y direction (see Figure 3 2). The lateral expansion will only be pronounced near the retina edge in outward direction(X direction) away from optic nerve head of the retina. If we observe in vertical cross section of the OCT ( right image of Figure 3 2), its vertical edge ( pointed with arrow) will be forced from both side ( in Y direction) of the material and hence expansion in Y direction inside the circular region will be minimal. Hence the boundary condition of vertical edges to move in vertical direction (Z direction) can be applied. Since it is a plane stress model, we do have non zero strain in X direction. The bottom ed ge (L7 in Figure 3 1) is the outer layer of the sclera, where sclera is connected to the rest of the body and therefore constrained to not to move in all directions. The top layer is exposed to IOP, a pressure function is used to include the variation of the IOP (refer Figure 3 3 ) Arterial inner surface of the blood vessel is subject to the blood pressure. Another pressure function is used to descri be to capture this variation. Figure 3 3. Variation of IOP and BP with time. (Please note: this is not a t ime dependent problem, IOP and BP are varied to capture different load combinations that occur within the eye due to circadian rhythms. In ADINA, for soft tissues due to convergence issues we cannot jump from one load to other load in one step, we need to go in small load steps)

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37 Figure 3 4. Representation of a 2D plane stress element in ADINA (ADINA Inc MA) Details a bout the model in ADINA A plane stress element in ADINA is as show n in the Figure 3 4. Equation 3 1 represents the equation which is sol ved and for the calculation of all element matrices and vectors, numerical Gauss integration is used. In linear analysis using ADINA, the finite element system equilibrium equations to be solved are (3 1) Where K is the stiffness matrix, U is the displacement vector and R is the load vector. The two material constants used to define the constitutive relation are = Young's modulus, = Poisson's ratio. Mesh s ize and sensitivity Two dimensional nine node elements were used throughout the m odel. The mesh sensitivity was checked in the preliminary stages with three different mesh sizes. The number of elements varied in the thre e cases were 4879, 10943, 43467 For example, for a retinal thickness of 280, choroidal thickness of 330, sclera thic kness of 960 and retinal diameter of 100 the total number of elements were 10943. Error for this specific case was then checked and found to be ~0.4% for the retinal layer and ~1% for the arterial wall. For choroid and sclera it was O ( ~10 4 ). With a mesh size of 5 units (total elements = 43647, for the same example mentioned above) the results were within 0.5% with respect to mesh size of 10 and with mesh size

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38 15 units ( total elements = 4879 for the same example mentioned above ) the dif ference in results were within 2.2%. Mesh size of 10 was then used to do all the simulations. Actual finite element model is shown in Figure 3 5. Figure 3 5. Actual finite element model mesh from ADINA Model Validation Test Case To check the ADINA modeling and s olutions, we compared results with a benchmark problem of an infinite plate with a hole in tension ( Figure 3 6). There

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39 is an analytical solution for the stress on the horizontal line of symmetry which is given by Equation 3 2 76 This an alytical solution is valid for linear elastic properties and for the hole dimension being very small compared to the length of the plate. ADINA was then used to solve same problem, to simulate infinite plate the width and height of the plate were kept very large as compared to the hole dimension. The hole dimension was 5mm and the tensile stress was 25MPa on the top edge of the plate. Results of analytical solution ( Equation 3 2) and ADINA are compared in Table 3 5. (3 2) Figure 3 6. Test case schematic.

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40 The percentage error was acceptable considering the limitation that the numerical model was not actually infinite. A second validation check was then performed for the actual model. Tab le 3 5. Test case comparison of stress values of ADINA and analytical solution for a plate with a whole Distance from center Ratio Analytical Plate Stress ADINA Stress Percentage error R(mm) A/R (MPa) (MPa) 5.00 1.000 75.000 74.709 0.39 5.65 0.885 57.746 59.827 3.48 6.30 0.793 47.700 48.477 1.60 6.96 0.719 41.465 41.038 1.04 7.61 0.657 37.391 37.357 0.09 8.26 0.605 34.612 34.570 0.12 8.91 0.561 32.647 32.209 1.36 9.57 0.523 31.215 30.816 1.30 10.22 0.489 30.144 29.774 1.24 10.87 0.460 29.324 28.922 1.39 11.52 0.434 28.684 28.365 1.13 12.17 0.411 28.176 27.875 1.08 12.83 0.390 27.766 27.482 1.03 13.48 0.371 27.430 27.208 0.82 14.13 0.354 27.153 26.962 0.71 14.78 0.338 26.921 26.755 0.62 15.43 0.324 26.725 26.6 22 0.38 16.09 0.311 26.557 26.468 0.34 16.74 0.299 26.414 26.328 0.33 17.39 0.288 26.289 26.215 0.28 18.04 0.277 26.181 26.111 0.27 18.70 0.267 26.086 26.010 0.29 19.35 0.258 26.002 25.929 0.28 20.00 0.250 25.928 25.854 0.28 Actual m odel v alidation A second check was performed to validate the actual model. By superimposing the stress fields ( Figure 3 7) of an infinite plate with a hole subject to tension and a very thick cylinder subject to internal pressure were used to

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41 compare the resul ts obtained from ADINA. Our particular problem does not match the exact analytical solution of the problem mentioned as in our case the plate is finite and the pressurized hole is being approximated as a very thick cylinder, therefore the analytical result s will give reasonable values only near the artery wall, the deviation will increase as we move away from the artery wall. Figure 3 7. Superimposing plate with hole subject to tension and a thick cylinder pressurized from inside. Analytical solution fo r stress for a thic k cylinder problem is given by Equation 3 3 76 (3 3) 76 K and C are constants and are determined based on boundary condition of the cylinder. Since we are approximating the cylinder to be infinitely large, the boundary condition for the cylinder analytical soluti on become

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42 Where p is the blood pressure inside the artery ( ) and A being the internal radius (45 m in this specific case). U sing above boundary conditions E quation 3 4 reduces to (3 4) Analytical solution for the plate with =0.00227MPa and A=45 m were calculated using E quation 3 3. This solution will only hold good for stress near the hole. ADINA results from a model with exact conditions of pressure and h ole dimension (with artery radius=45 m, IO P =0.00227MPa and BP=0.01295MPa) were compared with the resultant analytical stress. Sigma 1(in Table 3 6) is calculated from E quation 3 2 and sigma 2 is the stress for cylinder which is given by E quation 3 4. The t wo stresses sigma 1 and sigma 2 are then added and compared with ADINA stress. Comparison is presented in Table 3 6. Table 3 6. Actual model comparison of stress values of ADINA and analytical solution Distance from hole center Relative distance from ho le Approximate Plate Stress (Equation 3 2) Approximate Hole Stress (Equation 3 4) Total Stress ADINA STRESS Percentage error R(mm) A/R sigma1 (MPa) sigma2 (MPa) (MPa) (MPa) 45.00 1.0000 0.00680 0.01295 0.01975 0.01979 0.2302 46.02 0.97 78 0.00646 0.01238 0.01884 0.01886 0.1028 47.04 0.9566 0.00615 0.01185 0.01800 0.01792 0.4302 48.06 0.9363 0.00587 0.01135 0.01722 0.01749 1.5045 49.08 0.9169 0.00562 0.01089 0.01651 0.01705 3.2044 50.10 0.8982 0.00539 0.01045 0.01584 0.01569 0.9489 51.12 0.8803 0.00519 0.01003 0.01522 0.01538 1.0406 52.14 0.8631 0.00500 0.00965 0.01464 0.01507 2.8311

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43 Percentage error in stress values very near the hole (for the A/R values less than 0.86), was always less than 3.3%. Since these are only approximat e analytical solution that we are comparing with, we can conclude that the results obtained from ADINA are acceptable and hence same scheme of modeling was used throughout the study.

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44 C HAPTER 4 RESULTS C ase 1: Effect of Variation of Diameter Table 4 1. F ixed parameters to study effect of diameter Layer Thickness Elastic modulus ratio Retina 280 70kPa 0.49 Choroid 330 187kPa 0.49 Sclera 960 3000kpa 0.48 Vessel Wall WLR*=0.4 300kPa 0.4 Material properties: Linear Elastic properties iso tropic Varying parameter: Vessel m. WLR= Wall to lumen ratio Physiological relevance The diameter would cover all the major regions of the eye. WLR is average value. All the values used are i n the tables which summarized the geometric properties in C hapter 3. To better quantify the r esults we have evaluated stress and strain fields at different radial lines as shown in Figure 4 1 Stres s Maximum stress is near the wall and then the stress decreases as we go away from the wall. The pattern for varia tion of stress as we move away from the artery wall is similar for all the diameters ( 80 120). To show specific patterns, we have plotted data along different angular radials, this is as shown in Figure 4 2. As this is a symmetric problem, other radial plo ts are omitted in this Figure The pattern for radial 3 and 7 is a little different than for the others, because of the small length of the radial over which the stress is observed. For other diameters, there is a change in the magnitude of the maximum and minimum values for the stress. Figure 4 3 a and b depict this pattern of variation of maximum and minimum stress. For normalization the value corresponding to the lowest parameter i.e. 80 m diameter are used, this practice is followed for all the normaliz ed curves in this thesis. Contours of the stress distribution for two load combinations is shown in Figure 4 4

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45 Figure 4 1. Representation of the radial lines where results were evaluated With increase in the vessel diameter it is expected that the max imum stress will increase for all the other parameters being fixed. For the variation of minimum stress, which occurs at the away from the wall and is affected only by the IOP the observed pattern is because the dimensions of the retina are fixed and the same point is now closer to the vessel wall (fo r higher diameter), therefore the minimum stress value increases. To depict the effect of variation of stress values for one diameter at different radial position we have included Figure 4 5 The stress value s peak for radials 3 and 7. Similarly the minimum value varies across all the radials. Strain yy. The strain yy(in the horizontal direction) changes nature as we move around the artery wall.

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46 Fig ure 4 2 Von Mises s tress distribution for all time steps for vessel dia meter =10 0 and WLR =0.4 along radial 1,2,3 and 7 The pattern is same for all other diameters as well. However the magnitude of stress change for different diameters Figure 4 3 Normalized variation of stress along radial1 for differen t diameters A) Maximum stress B) Minimum stress The variation of minimum and maximum value is same for all other radials as well. Base stress values correspond to the specific case of 80 m diameter. A B

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47 Figure 4 4 The retinal mesh with effective stres s field for the model for two load combinations For the above image the IOP=21.1 and BP=116.5 and for the bottom image th e IOP=21.3 and BP=77.7(All pressures in mmHg) The case parameters are diameter=100, retinal thickness =280, E=0.07MPa(retina) Figur e 4 5. Maximum stress value across different radials (1,2,3 and 7) for different diameters.

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48 But as have symmetry, the strain patterns are same for radials 1 and 5 and 2,4,6 and 8 and 3 and 7. The strain values along these radial pairs are very close. The v ariation of t he strain yy along radial 1, 2, 3 and 7 is as shown in Figure 4 6 Along radial 1, t he nerve fibers are compressed along this direction The value is maximum compressive near the wall and strain reduces as we move away. A s observed for the str ess the value of the maximum compressive strain in y y direction is maximum near the vessel wall and this value increases a s the diameter increases Figure 4 7 a and b show the minimum and maximum value pattern across different diameters. The pattern is simi lar to the variation of the stress values along the same radial line. The minimum and maximum stress and strain yy occur at the same positions as for the stresses. The variation of maximum and minimum strain yy for all diameter s along different radials is shown in Figure 4 8 Along radial 2 t he nerve fibers are compressed The value is maximum compressive near the wall and strain reduces as we move away. The pattern of variation of maximum and mini mum values across radial 1 3 6 and 8 is same as for radial 2 as shown in Figure 4 7 The minimum and maximum stress and strain yy occur at the same positions as for the stresses. Along radial 3 t he big difference is that in this case the nerve fibers are stretched and are in tension. The value is maximum tensil e near the wall and strain reduces as we move away. The pattern of variation of maximum and minimum values across others radials is same as for radial 2 as shown in Figure 4 7 Strain zz As we clubbed the strains along yy direction, we observe similar grouping for s train zz ( Radial 1 and 5, radial 2, 4 6 and 8 3 and 7).

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49 Figure 4 6 Patte rn of strain yy for diameter=100 along radial 1 2, 3 and 7 with WLR=0.4. Figure 4 7 N ormalized variation of strain yy along radial 2 for all diameters A ) Minimum strain yy B) Maximum strain yy. Base strain values correspond to specific case of 80 m diameter. Along radial 1 and 2, the strain zz changes its nature as we move away from the artery walls. Since radial 1 and 5 are along the horizontal axis, due to the expansion of the artery the nerve fibers along these radials are in stretched condition, but as we move away this effect reduces and due to IOP they get compressed. A B

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50 Figure 4 8 Comparison strain yy values in different radials for same diamete r. A) Minimum strain yy. B) Max imum strain yy Figure 4 9 T he pattern for strain zz for Radial1 2, 3 and 7 for diameter =100 and WLR =0.4. (This strain is for the maximum strain zz configuration) The distance from the vessel wall where this transition occurs increases with increase in the diameter. Figure 4 9 show the pattern for radial1, 2, 3 and 7. The variation of strain zz along different radials, for one diameter is as shown in Figure 4 10 The variation of maximum and minimum values for radial 1 a cross all diameters is as shown in Figure 4 1 1 Along radial 3 and 7 the nerve fibers remain in compression only. A B

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51 The nerve fibers above and below the artery are subject to constant compression from the IOP and the expanding arteries. Figure 4 10 Th e variation st rain zz along different radials ( 1, 2, 3, 7 ) for all diameters A) Minimum strain zz B) Maximum strain zz Figure 4 1 1 N ormalized variation of strain zz for radial 1 for all diameters. A) Minimum strain zz B) Maximum strain zz. Base stra in values correspond to 80 m diameter case. Case 2: Effect of Thickness of Retina Among the three layers studied, the retinal thickness is observed to have some impact on the stress distribution Therefore, results for only the retinal thickness are presen ted. Same model is used for this analysis. The summary of all the properties is listed in Table 4 2. A B A B

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52 Table 4 2. Fixed parameters to study effect of retinal thickness Layer Thickness/ Diameter Elastic modulus r atio Retina -70kPa 0.49 Choroid 3 30 187kPa 0.49 Sclera 960 3000kPa 0.48 Vessel Wall Dia=90 WLR*=0.4 300kPa 0.4 Material properties: Linear Elastic isotropic properties only. Varying parameter: Physiological relevance The retinal thickness would cover all the major regions of the eye. WLR is average value. This is all referenced in the tables which summarized the geometric properties in Chapter 3. Stre ss The stress variation pattern is same as in the case 1. Here we will describe the variation in stress magnitude across the different thicknesses of retina. As we increase the thickness of retina, stress decreases for most of the locations around the ar tery, except radial 1 and 5 where the stress increases (by 0.1%) when we first increase the thickness from 250 to 280 (12%) and then it decreases (0.5%) Figure 4 1 2 shows the variation of maximum and minimum value of stress along radial 3 P attern for maxi mum stress in radial s 1 to 8 is same and decreases continuously except radial 1 and 5, for which there is slight increase in first thickness increase from 250 to 280 However, i f we talk of percentages the change in stress values are most significant alon g radial 3. There is almost 7% in crease in the maximum stress value as we decrease the thickness from 320 to 2 5 0 (21% decrease) For radial 7 its about 5 %. The variation of minimum and maximum along different radials around the artery for fixed thi cknesses is shown in Figure 4 1 3

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53 Figure 4 1 2 N ormalized variation of stress along radial 3 for different reti nal thickness. A) Minimum stress. B) Maximum stress Base stress values are f or specific case of Retina thickness 250 m Figure 4 1 3 The variation of stress along different rad ials around the artery for different retinal thicknesses A) Minimum stress B) Maximum stress Strain yy Figure 4 1 4 show s the change s in the values of maximum and minimum strain yy with different retinal thicknesses. The pattern of variation along a particular radial is same as discussed in section 1 of this C hapter. T he m ax imu m value of strain yy change at radial 2 is approximately 15 % and minimum strain yy which occurs far away from artery wall it is 40 % as we decrease the t hickness from 320 to 250 A B A B

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54 Figure 4 1 4 N ormalized variation of strain yy along radial 3 for dif ferent thicknesses. A) Minimum strain yy B) Maximum strain yy Base stress values are for specific case of Retina thickness 250 m Figure 4 1 5 V ariation of str ain yy along different radials around the artery for fixed thicknesses. A) Minimum strain y y B) Maximum strain yy Strain zz The pattern is same as shown in Figure 4 1 5 show s the changes in the va lues of maximum and minimum strain yy with different retinal thicknesses along different radials The pattern of variation along a particular radial is same as for the different diameter (case 1) section of this C hapter. However, there is change in magnitude of the value and these are depicted in the Figure 4 1 5 Again, the A B A B

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5 5 percentage change in the maximum values is along radial 3 and 7 when we decreas e the thickness from 320 to 250. Case 3: Effect of Material Properties o f Different Layers With a standard geometry we varied the material properties of the different tissue layers, to see the impact on stress and strain of the nerve fibers around the art ery wall. Ho wever the impact of the choroid and the sclera was very small and the variation in stress ificantly presented. Same model was used to study the impact Table 4 3 Fixed parameters to study effect of material properties Layer Thickness/ Diameter Elastic modulus r atio -Stress. The pattern of variation of stress is same as in the case 1. However, the change in stress values with repo rted elastic moduli is very high. T he value of stress increase to almost 60% as we increase the elastic moduli of retinal layer in the given physiological range as reported in literature Please note that we only varied the modulus of the retinal l ayer. If we increase of all the different layers with same factor, we do not observe any change in the stress values, which should be expected. But when we change only material property of one layer we observe change in the stress values. T he variation of the maximum and the minimum values of stress are shown in Figure 4 1 6

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56 The variation of stresses along different radials for different moduli is shown in Figure 4 1 7 Again, the gap between stress values for different elastic moduli is sign ificant F igure 4 1 6 N ormalized variation of stress for different retinal moduli at radial 2 A) Maximum stress B) Minimum stress. Base values correspond to stress for moduli of 0.03MPa Figure 4 1 7 The variation of stress for each radial and for d ifferent retinal moduli A) Maximum stress B) Minimum stress Strain zz : The patterns for strain zz are very similar to the strain yy. To show how the elastic moduli affects the strain zz in the nerve fiber, see the Figure 4 19 A B A B

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57 Figure 4 1 8 N orm alized variation of s train yy for different retinal moduli at radial 2 A) Minimum strain yy. B) Maximum strain yy. Base values correspond to the case of E=0.03MPa. Figure 4 1 9 Variation in strain zz for each radial and different retinal moduli A) Minimum strain zz B) Maxuimum strain zz Effect of BP and sensitivity to IOP The pressure conditions in the eye keep varying with time. To study the impact of change in stress values with different IOP conditions we calculated the percentage change in th e stress with given IOP conditions and varying BP. The various IOP and BP conditions are listed in Table 4 3 Basically this helps to understand the variation in RNFL stresses in the eye of patients with different IOP conditions (high tension and low tensi on glaucoma). The variation for the first set of IOP condition(Average to high IOP) was approximately equal for all the A B A B

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58 thicknesses ~ 2 2 4 %, 1 1 4 % and 4.7 % for a jump from minimum to average BP, average to high BP and finally from high to maximum BP(49% in crease). These variations were within 1 % for all the different radials. For high and low IOP the variation from minimum BP to average BP (25% increase) and from average to maximum(19% increase) was ~2 3 % and ~ 15 % which is similar to the previous case. Si nce we have linear elastic properties, we do not observe any significant effect of BP on RNFL stress with the changing IOP conditions, therefore this analysis is limited to this case only. But these results highlight the importance of the impact of BP onto the nerve fibers adjoining the retinal arteries. Table 4 4 Conditions of IOP and BP. Time IOP BP IOP condition BP condition Increase in Stress 6.88E 01 19.842 80.062 Avg to High IOP Min BP -4.00E 03 17.586 101.997 Avg IOP Avg BP 22.43 % 2.80E 02 1 8.103 112.884 Avg to High IOP High BP 11.41 % 6.40E 02 18.868 119.991 Avg to High IOP Max BP 4.71 % 1.88E 01 21.202 80.001 High IOP Min BP -2.52E 01 22.097 100.336 High IOP Avg BP 23.73 % 3.16E 01 22.703 119.978 High IOP Max BP 15.39 % 9.44E 01 14.55 3 80.014 Low to Avg IOP Min BP -8.80E 01 15.801 99.822 Low to Avg IOP Avg BP 16.10 % 8.16E 01 17.155 119.995 Low to Avg IOP Max BP 26.34 %

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59 CHAPTER 5 DISCUSSION Th ere are many models for the eye to study glaucoma but most of these have concentrat ed on modeling the lamina cribrosa and the ONH which is considered as the primary site of injury in glaucoma This is the first model which studies the nerve fiber layer from a mechanical point of view. The 2D model allows us to study the impact of the re tinal arteries and IOP on the nerve fibers In addition, we have quantified stress strain field in the retinal nerve fiber layer behavior with varying material properties and geometric properties. Mechanical stretching of nerve fibers is known to cause mor phologic and functional changes S ome data is available on how the nerve fibers in different parts of the human body behave when subject to mech anical stresses and strains. There is variability and inconsi stency in the liter ature in this data for exampl e it is reported that in t he pressure threshold that blood perfusion in sciatic nerves started to decreas e in diabetic rats at 24.1 mm Hg and that in the normal controls was 47.1 mm Hg 20 and t he blood perfusion of the nerve started to decrease at a mean pressure of 30.5mmHg and reached a stable lower level of 30% of pre compression value at 102.8 mmHg 21 I n peripheral ner ves while 5% strain does not affect conducti on, further elongation decreases amplitude approximately linearly with strain 19 In our study, for the given range of properties studie d, we did encounter stresses and strains of that level. But we have to keep in mind that the values are very sensitive to material proper ties, the se vary a lot than that used in our study 19 21 Also, a direct comparison cannot be made as these results are reported for test s over a comparatively large group of nerves than that studied in our study. F or example the nerves where 10 1 2 mm long in the experiments

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60 reported, whereas our model the nerve fiber layer was 700 m long (the maximum length for a nerve fiber running across the artery) So comparative to these experimental studies we are studying the micro environment of the nerve fibers inside the retina. Therefore we cannot draw direct comparison to these studies and more experimental studies are called for. Putting the results in physiological perspective, near the ONH which is considered as the primary site of injury in glaucom a two effects are prominent, the high vessel diameter (as the retinal vessels exit the ONH) and the retinal thickness ( as all the nerve fibers converge at this point) From our simulations we observe that around the retinal arteries, the stresses increase by ~ 10 % when diameter increases by 12.5%( from ) and only by ~ 6 % observe that increasing retinal thickness by 28% ( ) reduces stress only by 2%. The retinal vessels produce more stress on adjacen t nerve fibers than these are relaxed by increase in thickness With these results in mind we can say that near the ONH t he axons of the ganglion cells are exposed to comparatively very high stress es caused by the retinal arteries If we now observe in th e different quadrants of the eye, in superior temporal region ha makes the nerve fibers in this quadrant to be exposed highest level of stresses, as compa red to other regions of the eye. As pointed out earlier, studies have shown the overall RNFL thickness average to be the best diagnostic parameter 6 8 for glaucoma. Other studies have shown the inferior 10 12 or superior 13 quadrant RNFL thickness

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61 average to be the best, in agreement with clinical observation that glaucomatous optic nerve damage seems to begin. The cause for this is still no t known. From our simulations we can conclude that this region has the highest volume of nerve fibers that are exposed to higher stresses. There might be a possibility high stresses caused by retinal vessels might trigger loss of RNFL cells, thereby decrea sing its thickness of retinal layer in this region. As mentioned above the nerve fibers around the retinal arteries are exposed to almost double the stresses than that on the nerve fibers away from the artery walls. To approximately quantify t his region we have included Figure 5 1. We can estimate the volume per unit length of the retinal vessels of the retinal nerve fiber layers that are in the shaded gray area. It comes out to be approximately 38% of the cross sectional area (considered in this study) of the retina is exposed to higher stresses ( outside the shaded area the stress are below 10% of the maximum stress value) Figure 5 1 Estimation of the area of nerve fibers exposed to higher stresses. This clearly shows the impact of the retinal vess els on to the retinal nerve fibers. Shaded area ~38% of the retinal cross section.

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62 Another observation can be made about the nerve fibers on top and bottom of the vessel being subject to maximum stresses and strains. So nerve fiber splaying can affect the stresses onto the nerve fibers at the vascular crossing. The material property of the retinal nerve fiber layer is one of the important factors that determine how the nerve fibers bear the load. There is 6 0% increase in stress values and 30 % de crease in st rain values when we double the elastic modulus of the retina from 0.03MPa.The increase is ~ 5 0% and ~20% in stress and strain values respectively when we increase the modulus further by 70% ( from 0.07 to 0.12MPa ) The material properties of individual neuro ns in the human retina and of the whole retinal nerve fiber layer have been studied 77 In glaucoma there is considerable loss of axons of the ganglion cells, this can change the mechanical properties of retinal ner ve fiber layer. We can have variable properties across the whole retina, if we can map the material property of a volume of retinal layer to cell density in that region, we can have better understanding of the behavior of retinal layer in terms of its mate rial properties and stress distribution Another important aspect is the viscoelastic properties of the different tissues studied in this study. T here is a reported change in viscoelastic properties of the sclera for a monkey with glaucoma 74 The va lues reported were not adequate to be incorporated in the model and there was no viscoelastic properties reported anywhere for choroid. Also for cells in the r etinal layers the elastic behavior dominates over the viscous behavior 77 However, we feel that viscoelastic properties will play an important role in glaucoma, because these properties are time dependent and the ch ances of glaucoma increases with age 32, 78

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63 This study highlights the role of the high diameter, the role of retinal thickness and material properties on the environment of the nerve fibers around the retinal arter ies Limitations of the Study All the data that has been used in this study has been derived from the literature. Different researchers use different techniques to measure various properties. For example, for the diameter of the retinal artery there are ma ny different equipment that were used, each equipment manufacturer have their own algorithms to analyze the images obtained. They cannot produce same results. To add, the there is al so var iation in nature of study as different studies target different regi ons of the eye. The material properties of the soft tissues like retina and choroid are inconsistent T here is big difference in the reported material property values as compared to other properties like diameter and thicknesses. We have tried to cover mo st of t he range of the reported values and predict how it affects the retinal nerve fiber layer. We could not find any reported viscoelastic property for the tissue concerned (except sclera for monkey model). We strongly feel that viscoelastic properties w ill play very important role in glaucoma and the mechanical environment of the retinal ganglion cells. Conclusion We have studied the mechanical parameters that affect the stresses and strains on the nerve fiber layer. This is the first study to characteri ze the effect of retinal vessel diameter, retinal material properties and the thickness of the retinal layer on to the nerve fibers. We observe that with increasing diameter the stresses increase significantly. The thickness of the retina does not affect t he nerve fibers significantly. From the point of glaucoma, around the retinal arteries the retinal ganglion cells are exposed to extremely

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64 high stresses as compared to stresses induced only by the IOP This stress increases with increase in retinal vessel diameter. The simulations also show that near ONH because the diameter of the retinal vessels and the retinal thickness are maximum, the nerve fibers are exposed to higher stresses near the ONH which is clinically observed to assess glaucoma damage and p rogress Within the reported values for all the parameters t he material properties are most significant However, the material properties reported in the literature lacks consistency, which needs further experimental investigation. Future Studies To most accurat ely determine the effect of the parameters studie d we need convergence on the material properties and the geometrical properties of these layers. With more accurate modeling data, a 3D fluid structure interaction ( FSI ) model would best describe the stres s es and strain in the nerve fiber layer. The decrease in the retinal thickness leads to lesser blood flow requirement and that over a long period of time can lead to remodeling of the retinal arteries to decrease in caliber. This effect can be capture d in 3D FSI models with viscoelastic material properties and accurate geometry. We already have some good OCT techniques which have high repeatability and confidence for measuring the thickness of the retina. We still need good techniques to measure the th ickness of choroid and sclera non invasively. Also techniques should be developed for measuring the material properties of different layers non invasively. The ultimate goal should be to be able to predict the stresses and strain in the nerve fiber layer of a patient with some image scans for the geometry and non invasive material testing for material properties Glaucoma is a multifactorial pathology, with the impact of each parameter being clear, the next step should be to look at interactions of these

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65 p arameters like IOP with BP, thicknesses of retina, artery diameter on how they affect the retinal nerve fiber layer.

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71 64. Tanito M, Itai N, Ohira A, Chihara E. Reduction of po sterior pole retinal thickness in glaucoma detected using the retinal thickness analyzer. Ophthalmology 2004;111:265 275. 65. Schuman J, Hee M, Puliafito C, Et Al. Quantification of nerve fiber layer thickness in normal and glaucomatous eyes using optical coherence tomography A P ilot S tudy Archives of Ophthalmology 1995;113:586 596. 66. Jones I, Warner M, Stevens J. Mathematical modeling of the elastic properties of retina A determination of young modulus Eye 1992;6:556 559. 67. Franze K, Francke M, G unter K, et al. Spatial mapping of the mechanical properties of the living retina using scanning force microscopy. Soft Matter 2011;7:3147 3154. 68. Wollensak G, Spoerl E. Biomechanical characteristics of retina. Retina the Journal of Retinal and Vitreous Diseases 2004;24:967 970. 69. Chen K, Rowley A, Weiland J. Elastic properties of porcine ocular posterior soft tissues. Journal of Biomedical Materials Research Part a 2010;93A:634 645. 70. Shahbazi S, Mokhtari Dizaji M, Mansori M. Noninvasive estimation o f the ocular elastic modulus for age related macular degeneration in the human eye using sequential ultrasound imaging. Ultrasonics 2012;52:208 214. 71. Spoerl E, Boehm A, Pillunat L. The influence of various substances on the biomechanical behavior of lam ina cribrosa and peripapillary sclera. Investigative Ophthalmology & Visual Science 2005;46:1286 1290. 72. Mortazavi A, Simon B, Stamer W, Geest J. Drained secant modulus for human and porcine peripapillary sclera using unconfined compression testing. Expe rimental Eye Research 2009;89:892 897. 73. Battaglioli J, Kamm R. Measurements of the compressive properties of scleral tissue Investigative Ophthalmology & Visual Science 1984;25:59 65. 74. Downs J, Suh J, Thomas K, Bellezza A, Hart R, Burgoyne C. Viscoe lastic material properties of the peripapillary sclera in normal and early glaucoma monkey eyes. Investigative Ophthalmology & Visual Science 2005;46:540 546. 75. Downs J, Suh J, Thomas K, Bellezza A, Burgoyne C, Hart R. Viscoelastic characterization of pe ripapillary sclera: Material properties by quadrant in rabbit and monkey eyes. Journal of Biomechanical Engineering Transactions of the Asme 2003;125:124 131. 76. Lai WM, Knovel, Krempl E, Rubin D. Introduction to continuum mechanics 4th ed. ed. Amsterdam ; Boston: Butterworth Heinemann/Elsevier; 2010.

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72 77. Lu Y, Franze K, Seifert G, et al. Viscoelastic properties of individual glial cells and neurons in the CNS. Proceedings of the National Academy of Sciences of the United States of America 2006;103:17759 17764. 78. McCarty C, Stanislavsky Y, Livingston P, Taylor H. Prevalence of and risk factors for primary open angle glaucoma in The Melbourne Visual Impairment Project. Investigative Ophthalmology & Visual Science 1997;38:3358 3358.

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73 BIOGRAPHICAL SKETCH Devesh Chugh completed his schooling in New Delhi, India. He also completed After his degree, Devesh worked for three years in Engineers India Limited, one of the top EPC Company in India. Devesh joined UF in fall 2010 and is going to join PhD program in mechanical engineering at UF in spring 2013.