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Introducing the shape of globe as a predisposingfactor for glaucoma

Alireza Mehdizadeh, Amin Hoseinzadeh*, Afsoon Fazelzadeh

School of Medicine, Mashad University of Medical Sciences, Mashad, Iran

Received 29 January 2008; accepted 30 January 2008

KEYWORDSGlaucoma;Predisposing factor;Shape of globe;Spatial configuration;Biomechanics;Stress;Strain

Abstract Glaucoma is a common blinding disease worldwide with a number of risk factorssuch as intraocular pressure, myopia, gender, race and hyperopia. Here we introduce eyeball’sshape as a predisposing factor for glaucoma. If the eyeball is a sphere, the stress distribution ishomogenous. We assume the eyeball as a non sphere. Then, the distribution of stress will notbe homogenous. Different individuals have different eyeball’s shapes and different patterns ofstress distribution in their eyes. So based on the eyeball’s shape deviation from a sphere theywill have different risks for glaucoma. The eyeball is routinely considered as a sphere, butsome evidences show that the globe is not a sphere. Two empirical observations are consistentwith the hypothesis. The first is that ethnicity and sex are established risk factors for glau-coma. On the other hand there are several morphological differences in the body structureamong individuals. According to these anatomical differences, eye’s shape is different amongdifferent races and between two sexes. Secondly, there are some conditions such as myopiaand hyperopia in them the shape of the globe has been changed. These conditions are risk fac-tors for glaucoma too. Glaucoma screening program for early detection of high risk individualsis very important. Current diagnostic procedures of glaucoma do not take the shape of eyeballinto account. We suggest using eyeball’s shape for early glaucoma detection. There are threeother factors in addition to eyeball’s shape, including thickness of the globe’s wall, intraocularpressure, and inner radius that should be measured together for each individual and stress loadshould be calculated in different points of the globe. Then eyes with more stress load in site ofinjury are more prone for glaucoma. More accurate measurements of the factors which arecontributing in stress value for each case, lead us toward better glaucoma screening.ª 2008 Elsevier Ltd. All rights reserved.

Introduction

The term glaucoma refers to a group of diseases that have incommon a characteristic optic neuropathy with associatedvisual field loss [1]. Glaucoma is a complex disease with

* Corresponding author. Tel.:þ98 9177075754; fax:þ98 7118421834.E-mail address: hoseinzadeha831@mums.ac.ir (A. Hoseinzadeh).

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anumberof risk factors suchas intraocularpressure (IOP),my-opia, gender, race, genetic predisposition and hyperopia [2].

Two principal theories for the pathogenesis of glaucomahave been described: a mechanical and an ischemic theory[3]. We introduced a new theory for glaucoma [4], in whichmechanical stress is the main responsible factor for glau-comatous damage. According to the stress theory, stressdevelops glaucomatous damage by two ways:

1. Stress generates strain (tissue deformation) within tis-sues that experience load. Strain can deform and inter-rupt the retinal layers, which end in glaucoma. Themagnitude of strain is based on the material propertiesof the tissues, including how well the tissues are able toresist deformations induced by the applied stress [5].

2. Also, stress pressurizes vessels, which leads to obstruc-tion of retinal vessels and decreased perfusion of theoptic nerve cells and finally cell death [5].

The biomechanical model for the eye

From a geometrical standpoint, a sphere is the set of allpoints in three-dimensional (3D) space which is at distanceof ‘‘r’’ from a fixed point of that space, where ‘‘r’’ is a pos-itive real number called the radius of the sphere. Thesphere is the only complete symmetrical spatial configura-tion while a spheroid is a quadric surface obtained by rotat-ing an ellipse about one of its principal axes and in spite ofsphere; it is not completely symmetric [6].

Stress (s) is an applied force and strain is the deforma-tion in the material to which stress has been applied [7].

Analysis of the eye as an idealized spherical shell isconsidered. Within the wall of any pressurized sphericalshell, the two principal stresses reside within the plane ofthe sphere wall (the third stress is radial in direction andminimal in magnitude; Fig. 1).

In the eyeball, linear elasticity theory predicts that theplanar wall stresses are equal and orthogonal, and thateach stress can be approximated by the equation:

sZPR=2t ð1Þ

where P is the inner pressure (IOP), R is the inner radius ofthe sphere (approximately one half of the axial length), andt is the thickness of the sphere wall (scleral thickness) [8].

Today, the Goldmann applanation tonometer providesthe gold standard for the clinical measurement of IOP [9].Axial length and scleral thickness were measured ultrason-ically using A-scan ultrasonography and ultrasound biomi-croscopy (UBM), respectively [10].

The hypothesis

IOP-related force has a predictable distribution and leadsto predictable levels of IOP-related stress [11]. Stress distri-bution is homogenous in all points of a sphere. In a non-sphere configuration for example a spheroid, there is notcomplete symmetry (3D); then stress distribution is not ho-mogenous and stress is less at some points and more at theothers.

If the eyeball is a sphere, then the stress distribution ishomogenous in all its points. Here we assume the eyeball asa non-sphere. So, the distribution of IOP-related stresswon’t be homogenous and stress magnitude would be lessat some points and more at the others.

Different individuals have different eyeball’s shapes anddifferent patternsof stressdistribution in their eyes. So basedon the eyeball’s shape deviation from a sphere, they will havemore or less stress load in the site of glaucoma injury.

In other words, distribution and magnitude of IOP-relatedstress within the site of glaucoma injury for a given level ofIOP are primarily determined by the 3D shape of the eye.There are other examples of the effect of geometry andshape on the magnitude and distribution of wall stress [12].

Since stress is the main responsible factor for glaucoma,risk of glaucoma varies among different populations. So, weintroduce eyeball’s shape as a predisposing factor forglaucoma.

Discussion

Like all other events in nature, glaucomatous damage hasspecific causes and glaucoma presents with specific pat-terns and does not occur at random [2]. Recognizing glau-coma predisposing factors helps us understand themechanism of disease and guides screening and treatmenttoward specific populations and subpopulations.

The eyeball is routinely considered as a sphere, butthere are some evidences show that the globe is nota sphere. One of them obtained from eyeball imagingshows that the contours and the plane sections of theglobe are not definite circle (Fig. 2).

Two empirical observations are consistent with thehypothesis. The first is that ethnicity and sex are estab-lished risk factors for glaucoma. For example, the preva-lence of glaucoma is 20e40 times higher in Eskimos than inCaucasians [13]. Congdon et al. [13] and the Rotterdamstudy [14] in their studies found different prevalence ofglaucoma between men and women. There are severalmorphological differences in the body structure among in-dividuals. The false pelvis is shallow in the female and

Figure 1 Depiction of principal stresses within a thin-walledspherical pressure vessel of radius R. The two largest principalstresses, s1 and s2, are equal, at right angles to each other, andreside within the plane of the wall. The third principal stress,sr, is minimal in magnitude and directed toward the center ofthe sphere [8].

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deep in the male. The pelvis inlet is transversely oval in thefemale but hurt shaped in the male. The pelvis cavity isroomier in the female than in the male, and the distancebetween the inlet and the outlet is much shorter. The pel-vic outlet is larger, the sacrum is shorter, wider and flatterand the pubic arch is more rounded and wider in the fe-male than in the male [15]. The angle of the elbow ismore valgus in the female than in the male [16].

Tallness varies among different races. Pelvic inlet shapeis different among women of different races and isclassified into four groups: gynecoid, android, anthropoidand platypelloid according to its shape [15].

In the eye we can see structural differences amongdifferent ethnicities and sexes; for example axial lengthand optic disc area are bigger in blacks than whites [17].Anterior chamber depth and eye size are smaller in womenthan men [18].

According to these anatomical differences that exist inbody structure, variation in shape of the eyeball is alsopossible.

Secondly, there are some conditions such as myopiaand hyperopia in which, the shape of the globe, forexample its axial length has been changed. These condi-tions are considered as risk factors for glaucoma [2] andthe current explanation of this relationship is that ana-tomical alterations of the eyeball’s shape in such condi-tions may involve trabecular meshwork [19] but in ourtheory this anatomical alteration directly leads to increas-ing the risk of glaucoma by changing the distribution ofIOP-related stress load.

Since glaucoma has no clinical manifestation until the laststages and is one of leading causes of irreversible blindnessthroughout the world [20], glaucoma screening program forearly detection of high-risk individuals and their managementis very important. Current glaucoma screening methods in-clude IOP measurement, optic nerve head and peripapillaryretinal evaluation and visual function tests [21].

Current diagnostic procedures of glaucoma do not takethe shape of eyeball or oculometric measurements intoaccount.

We suggest using eyeball’s shape for early detection ofglaucoma. There are three other factors in addition toeyeball’s shape, including thickness of the globe’s wallwhich was shown previously by authors to be related withcentral corneal thickness (CCT) [22], pressure (IOP), and in-ner radius that should be measured together for each indi-vidual and stress load should be calculated in differentpoints of the globe. Then eyes with more stress load inthe site of glaucoma injury are more prone to glaucoma.

References

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[3] Flammer J, Orgul S, Costab VP, Orzalesic N, Krieglsteind GK,Serrae LM. The impact of ocular blood flow in glaucoma.Prog Retin Eye Res 2002;21:359e93.

[4] Mehdizadeh AR, Hoseinzadeh A, Fazelzadeh A. What is thereal cause of glaucoma? Med Hypotheses 2007;69:459e60.

[5] Hoseinzadeh A, Movahedi MM, Mehdizadeh AR. A novelmechanism for the pathogenesis of glaucoma based onbiomechanical properties of the eye. Iran J Med Phys 2007;4:10e6.

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Figure 2 MRI slices of the eye. The images are of a female participant’s eye. Scans were taken in the sagittal plane (a) andthrough the axial section (b) of the eye. Length measures (millimeters) were taken from both the axial and sagittal sections, heightfrom the sagittal image, and width from the axial image. A, anterior; P, posterior; N, nasal; T, temporal; S, superior; I, inferior.(From: Atchison DA, Jones CE, Schmid KL, Pritchard N, Pope JM, Strugnell WE, Riley RA. Eye shape in emmetropia and myopia.Investig Ophthalmol Vis Sci 2004;45:3380e6.)

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[17] Oliveira C, Harizman N, Girkin CA, Xie A, Tello C,Liebmann JM, et al. Axial length and optic disc size in normaleyes. BJO 2007;91:37e9.

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[19] Harris A, Rechtman E, Siesky B, Jonescu-Cuypers C,McCranor L, Garzozi H. The role of optic nerve blood flow inthe pathogenesis of glaucoma. Ophthalmol Clin N Am 2005;18:345e53.

[20] Epidemiology. In: Gupta D, editor. Glaucoma: diagnosis andmanagement. Philadelphia: Lippincott Williams & Wilkins;2005. p. 3.

[21] Glaucoma screening. In: Shields MB, editor. Textbook of glau-coma. 4th ed. Baltimore: Williams & Wilkins; 1998. p. 137e41.

[22] Mehdizadeh AR, Hoseinzadeh A, Fazelzadeh A. Centralcorneal thickness as a risk factor for glaucoma. Med Hypothe-ses 2007;69:1205e7.

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