Introducing The Shape Of Globe

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Introducing the shape of globe as a predisposing factor 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

KEYWORDS Glaucoma; Predisposing factor; Shape of globe; Spatial configuration; Biomechanics; Stress; Strain

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

Introduction

* Corresponding author. Tel.: þ98 9177075754; fax: þ98 7118421834. E-mail address: [email protected] (A. Hoseinzadeh).

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

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A. Mehdizadeh et al.

a number of risk factors such as intraocular pressure (IOP), myopia, gender, race, genetic predisposition and hyperopia [2]. Two principal theories for the pathogenesis of glaucoma have been described: a mechanical and an ischemic theory [3]. We introduced a new theory for glaucoma [4], in which mechanical stress is the main responsible factor for glaucomatous damage. According to the stress theory, stress develops glaucomatous damage by two ways: 1. Stress generates strain (tissue deformation) within tissues that experience load. Strain can deform and interrupt the retinal layers, which end in glaucoma. The magnitude of strain is based on the material properties of the tissues, including how well the tissues are able to resist deformations induced by the applied stress [5]. 2. Also, stress pressurizes vessels, which leads to obstruction of retinal vessels and decreased perfusion of the optic nerve cells and finally cell death [5].

The biomechanical model for the eye From a geometrical standpoint, a sphere is the set of all points in three-dimensional (3D) space which is at distance of ‘‘r’’ from a fixed point of that space, where ‘‘r’’ is a positive real number called the radius of the sphere. The sphere is the only complete symmetrical spatial configuration while a spheroid is a quadric surface obtained by rotating an ellipse about one of its principal axes and in spite of sphere; it is not completely symmetric [6]. Stress (s) is an applied force and strain is the deformation in the material to which stress has been applied [7]. Analysis of the eye as an idealized spherical shell is considered. Within the wall of any pressurized spherical shell, the two principal stresses reside within the plane of the sphere wall (the third stress is radial in direction and minimal in magnitude; Fig. 1). In the eyeball, linear elasticity theory predicts that the planar wall stresses are equal and orthogonal, and that each stress can be approximated by the equation:

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

sZPR=2t

ð1Þ

where P is the inner pressure (IOP), R is the inner radius of the sphere (approximately one half of the axial length), and t is the thickness of the sphere wall (scleral thickness) [8]. Today, the Goldmann applanation tonometer provides the gold standard for the clinical measurement of IOP [9]. Axial length and scleral thickness were measured ultrasonically using A-scan ultrasonography and ultrasound biomicroscopy (UBM), respectively [10].

The hypothesis IOP-related force has a predictable distribution and leads to predictable levels of IOP-related stress [11]. Stress distribution is homogenous in all points of a sphere. In a nonsphere configuration for example a spheroid, there is not complete symmetry (3D); then stress distribution is not homogenous and stress is less at some points and more at the others. If the eyeball is a sphere, then the stress distribution is homogenous in all its points. Here we assume the eyeball as a non-sphere. So, the distribution of IOP-related stress won’t be homogenous and stress magnitude would be less at some points and more at the others. Different individuals have different eyeball’s shapes and different patterns of stress distribution in their eyes. So based on the eyeball’s shape deviation from a sphere, they will have more or less stress load in the site of glaucoma injury. In other words, distribution and magnitude of IOP-related stress within the site of glaucoma injury for a given level of IOP are primarily determined by the 3D shape of the eye. There are other examples of the effect of geometry and shape 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, we introduce eyeball’s shape as a predisposing factor for glaucoma.

Discussion Like all other events in nature, glaucomatous damage has specific causes and glaucoma presents with specific patterns and does not occur at random [2]. Recognizing glaucoma predisposing factors helps us understand the mechanism of disease and guides screening and treatment toward specific populations and subpopulations. The eyeball is routinely considered as a sphere, but there are some evidences show that the globe is not a sphere. One of them obtained from eyeball imaging shows that the contours and the plane sections of the globe are not definite circle (Fig. 2). Two empirical observations are consistent with the hypothesis. The first is that ethnicity and sex are established risk factors for glaucoma. For example, the prevalence of glaucoma is 20e40 times higher in Eskimos than in Caucasians [13]. Congdon et al. [13] and the Rotterdam study [14] in their studies found different prevalence of glaucoma between men and women. There are several morphological differences in the body structure among individuals. The false pelvis is shallow in the female and

Author's personal copy Introducing shape of the globe as a predisposing factor for glaucoma

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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) and through the axial section (b) of the eye. Length measures (millimeters) were taken from both the axial and sagittal sections, height from 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.)

deep in the male. The pelvis inlet is transversely oval in the female but hurt shaped in the male. The pelvis cavity is roomier in the female than in the male, and the distance between the inlet and the outlet is much shorter. The pelvic outlet is larger, the sacrum is shorter, wider and flatter and the pubic arch is more rounded and wider in the female than in the male [15]. The angle of the elbow is more valgus in the female than in the male [16]. Tallness varies among different races. Pelvic inlet shape is different among women of different races and is classified into four groups: gynecoid, android, anthropoid and platypelloid according to its shape [15]. In the eye we can see structural differences among different ethnicities and sexes; for example axial length and optic disc area are bigger in blacks than whites [17]. Anterior chamber depth and eye size are smaller in women than men [18]. According to these anatomical differences that exist in body structure, variation in shape of the eyeball is also possible. Secondly, there are some conditions such as myopia and hyperopia in which, the shape of the globe, for example its axial length has been changed. These conditions are considered as risk factors for glaucoma [2] and the current explanation of this relationship is that anatomical alterations of the eyeball’s shape in such conditions may involve trabecular meshwork [19] but in our theory this anatomical alteration directly leads to increasing the risk of glaucoma by changing the distribution of IOP-related stress load. Since glaucoma has no clinical manifestation until the last stages and is one of leading causes of irreversible blindness throughout the world [20], glaucoma screening program for early detection of high-risk individuals and their management is very important. Current glaucoma screening methods include IOP measurement, optic nerve head and peripapillary retinal evaluation and visual function tests [21]. Current diagnostic procedures of glaucoma do not take the shape of eyeball or oculometric measurements into account.

We suggest using eyeball’s shape for early detection of glaucoma. There are three other factors in addition to eyeball’s shape, including thickness of the globe’s wall which was shown previously by authors to be related with central corneal thickness (CCT) [22], pressure (IOP), and inner radius that should be measured together for each individual and stress load should be calculated in different points of the globe. Then eyes with more stress load in the site of glaucoma injury are more prone to glaucoma.

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