The role of eye size in its pressure and motility.

Abstract

A theoretical model demonstrates the influence of the globe's size on the effects of its intraocular pressure (IOP) and on its motility. Large globes seem more susceptible to the damaging consequences of elevated IOP, and move with greater difficulty than small ones. Routine measurement of axial length (AxL) may accordingly enhance precision in the diagnosis and management of glaucoma and strabismus.

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© 2007 Dove Medical Press Limited. All rights reserved
Clinical Ophthalmology 2007:1(2) 105–109
105
R E V I E W
The role of eye size in its pressure and motility
Harry H Mark
Yale-New Haven Hospital, New Haven,
CT, USA
Correspondence: Harry H Mark
Yale-New Haven Hospital, 20 York St,
New Haven, CT, USA
Tel +1 203 234 2212
Email iimd@aol.com
Abstract: A theoretical model demonstrates the influence of the globe’s size on the effects
of its intraocular pressure (IOP) and on its motility. Large globes seem more susceptible to
the damaging consequences of elevated IOP, and move with greater difficulty than small ones.
Routine measurement of axial length (AxL) may accordingly enhance precision in the diagnosis
and management of glaucoma and strabismus.
Keywords: axial length, glaucoma, intraocular pressure, motility, strabismus
Introduction
As instruments for estimating the globe’s size by measuring its axial length (AxL),
mostly by ultrasonography, have become more readily available and user friendly
(Kushner 2006), it seemed beneficial to briefly explore their utility in the diagnosis
and treatment of glaucoma and strabismus with the aim of promoting their routine
employment on the way to enhancing quality of care. Size being a geometrical entity,
and pressure and motility being physical ones, the following meta-analysis focuses
mainly on these disciplines as a starting point and foundation for ultimate clinical
application, recognizing full well the limitation of physical models representing
complex biological events.
Terms and definitions
Axial length denotes here the linear distance clinically measured from the anterior apex
of the cornea to the anterior surface of the opposite retina. Addition of the thickness of
the retina and sclera renders the actual geometrical distance about 1–1.5 mm longer,
but because of the higher curvature of the cornea the average external diameter of
the entire sphere is about 0.5 mm shorter than this. For purposes of physical analysis
we accept Duke-Elder (1973, p. 97–99): “On the whole it [the eye] is approximately
spherical except in the higher degrees of axial myopia when the sagittal diameter is
greatest.” Only the principal forces, and ocular movements in abstract horizontal and
vertical meridians, are here considered.
Acrophthalmos means here an abnormally long globe, similar to acrocephalos (long
head) or acromphalos (long navel). Brachomphalos is a short globe, similar to brachy-
cephalos and brachydont (short tooth). These terms, measured in millimeters, replace
here myopia and hyperopia which were often used to designate the globe’s size, because
the latter are measured in optical units of diopters, and do not always relate to size,
as Priestly Smith said (1891, p. 122): “Small eyes are not necessarily hypermetropic,
and hypermetropic eyes are not necessarily small.” For instance, the terms “Myopic
disc” or “Myopic degeneration with retinal detachment” actually referred to physically
long globes rather than near-sighted ones (Soheilian et al 2007), while Hyperopia as
a risk factor in angle closure (Lowe 1969), or in esodeviation, implied short globes.
Furthermore, studies that related glaucoma to “myopia” did not usually distinguish
between refractive myopia and axial myopia, an important determinant of the tonometric
pressure reading in these two forms (Mitchell et al 1999; Grodum et al 2001).

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Mark
Intraocular pressure (IOP) is here given in ‘units’ instead
of the wishful ‘mm Hg’ because the clinical tonometric
measurements are not direct manometric ones but merely
estimates which vary according to the instrument used and
to the globe’s physical structure. Precise language is of
relevance when communicating clinical or other precise
data (Crooke 1981).
Intraocular pressure
The newborn’s globe is soft and small, growing larger as its
IOP increases with the begining of aqueous humor produc-
tion (Kinsey 1945). Some have therefore seen the IOP as
the impetus to the globe’s growth (similar to an inflating
balloon) or to its excessive growth that leads to axial myopia
(Barraquer 1971; Graul et al 2002). With increased volume
the globe’s coats also become thinner.
By definition, pressure (P) is directly proportional to its
generating force (F) and inversely proportional to the surface
area (A) to which it is applied perpendicularly: P = F/A.
Goldmann chose for his tonometer a constant area of applana-
tion where resistance of the average cornea to the applanating
force was conteracted by the attractive force of the average
tear film. Nevertheless, the force needed to applanate the
flatter area of a large globe is smaller than the one needed
for the steeper cornea of a small globe, where the volume
displaced is also relatively larger (Figure 1), (Mark 1973).
Laplace’s equation applies these circumstances specifically
to elastic spheres, such as the growing globe: P = 2T/r, where
T denotes the tangential (not perpendicular) shearing stress
on the surface, and r stands for the radius, that is, the size of
the sphere (Szczudlowski 1979; Cahane and Bartov 1992).
It follows that for a given pressure P, its effect on stretching
the sclera or retina is greater in a large globe [2T = Pr] than
a small one, whereas at the same time the perpendicularly
applied counter-pressure diminishes.
When Jonas Friedenwald (1937) began researching cali-
bration of impression tonometers (Schiotz) he introduced an
equation for ‘scleral rigidity’ where the tonometric reading
was inversely proportional to ocular volume, the larger the
globe the lower the reading on the tonometer for the same
intra-ocular force (Weekers and Grieten 1964). The value of
the coefficient itself was found to be considerably reduced
in high axial myopia (acrophthalmia) (Draeger 1966).
Lower tonometric readings in high volume globes were then
discovered also with the applanation method (Leighton 1974).
In 513 adult eyes we found a 0.29 unit (“mmHg”) decrease
in tonometric reading for every one millimeter increase in
axial length, and the 30 longest eyes were over 1 unit softer
than the 30 shortest ones (Mark et al 2002).
When pressure in a container of any shape is increased, it
assumes the form of a sphere because a sphere contains the
maximum volume under the minimum surface area. There-
fore, as the IOP in en elongated ellipsoid globe is directed
towards forming it into a sphere, it is more effective on the
lateral walls than on the anterior-posterior axis (Figure 2);
F
A
R
r
••••
•••••
Figure 1 A smaller force (F) is needed to applanate the same area (A) in a larger
globe (R) than a smaller one (r).
Figure 2 Intraocular forces in an elongated globe act further back and are
directed more sideways.

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Role of eye size in its pressure and motility
it thus stretches the retina in the fundus, as manifested by the
myopic (acrophthalmic) cup and crescent (Curtin and Karlin
1971) and distorted brightness distribution (Westheimer
1968). For the same reason it is also easier to indent or appla-
nate an ellipsoid shape, where there is room for expansion,
than an already spherical one (Mark 2002). Acrophthalmic
globes are in this manner exposed to triple jeopardy of
damage due to increased IOP: 1.) According to Laplace the
force of stretch on the surface is higher in larger globes.
2.) It is also higher in elongated globes. 3.) The tonometric
reading is deceptively low. All this, not counting the as yet
in vivo unmeasurable malleability or elasticity of the ocu-
lar coats. The fact that increased IOP was the cause of the
glaucomatous visual-field defect was convincingly shown
experimentally (Gafner and Goldmann 1955).
On the other hand, smaller and shorter globes are at risk
for angle-closure and acute glaucoma (Lowe 1969). Our study
confirmed that the globes of women were over one millimeter
shorter than those of men, and women are well known to be
affected by acute angle-closure more often than men.
Knowledge of AxL may thus clinically alert us to the
potential for angle closure, suggesting provocative tests or
peripheral iridotomy in short globes. Their higher tonometic
record may partially explain “ocular hypertension”. Large
globes caution us to be vigilant to visual-field loss caused
by deceptively low tonometric readings (“low/normal ten-
sion glaucoma”). Additional in vivo data of scleral thickness
promises to further our knowledge on the effect of IOP and
its measurement.
Ocular motility
“Near-sighted eyes often have limited motility”, said
Helmholtz, who gave his own horizontal range of motion as
100° and vertically 90°. Having mentioned earlier that myo-
pic eyes are longer, he must have meant acrophthalmic eyes
rather than refractive “myopes” (Helmholtz 1896). Southall
called them “sluggish” (Southall 1937). This motility deficit
is somewhat ameliorated by the enlarged visual-field due to
the prismatic effect of corrective concave glasses (but not
contact-lenses).
In order for a large globe to rotate a certain angle β
(Figure 3, top) its surface at A is moved a certain distance
AB (The small amounts under consideration here minimize
the difference between arc and chord values). However, an
equally large displacement on a smaller globe (CD = AB)
results in a larger angle α of rotation (α > β). Conversely,
when both globes need rotate an equal angle (say β) the
surface of the larger one moves a longer distance than the
smaller (AB > CE). The angle of rotation is proportional to
the distance that the end-point A or C is moved and to the
length of the radius OA or OC, where AB/OA = tangent β.
That is, in order to rotate a globe a given angle, its surface
must move the farther the longer its radius (AxL, size).
We deal here with basic kinematics rather than the more
complex dynamics. There, Archimedes’ principle of the lever
would also apply, where for equal displacements a stronger
force is required at the end of a shorter lever OC than a
longer one OA. The effect of the rotational force depends
therefore not only on the force of the muscle’s contraction
and its length but also on the length of the rotated arm – the
globe’s size (Gillies 1984).
A numeric example may illustrate the theoretical
principle. In order to focus at a normal reading distance
(d) of say 13” (330 mm), each eye separated by a normal
papillary distance of 60 mm (2a) must rotate inward at an
angle α of about 5° (Figure 4): a/d = 30/330 = 0.09; tan
0.09 = 5°. In order for small globes with a radius of say
11 mm (AxL about ∼22 mm) to converge this amount, their
medial surfaces at C must move backwards almost 1 mm
A
A
B
C
C
D
E
α
O
R
S
β
Figure 3 Schematic representation of moving forces acting on the surface of globes
of different size.

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Clinical Ophthalmology 2007:1(2)
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Mark
(CE, Figure 3) [CE = 11 × tan 5° = 1]. This surface of larger
globes, with a radius of say 16 mm (AxL ∼ 32), must recede
approximately 1.5 mm to achieve the same result [AB = 16 ×
tan 5° = 1.5], an increase of almost 50%. The opposite side
of the globes (at S) must of course advance in the opposite
(forward) direction.
When converging to a given near point, a pair of large
globes must move farther than smaller ones, or, the stimulus
for their convergence must be stronger (assuming equally
strong muscles). With equal stimuli, the large eyes (often
myopic) will show convergence insufficiency, a common
clinical occurrence. For the same reason, small globes (often
hyperopic) may exhibit excessive convergence at near, or eso-
phoria. In cases of significant disparity in size of the same pair
(“anisometropia”) the smaller eye may overshoot its target, or
the larger one will be deficient, solely by dint of their different
sizes, no matter what their refractive or accommodative status.
Recognizing at the same time that the accuracy of focusing
at near depends on a number of other hard to measure and
complex psychophysical factors of space perception, aside
from simple mechanical and optical ones (Mark 1962).
The clinical applicability of these principles to surgery,
which is more an art than science, has been well covered in the
literature (Gillies 1982; Kushner and Vrabec 1987; Kushner
1993). It is limited by the complex anatomical circumstances
and functional variations (Miller 1989). Furthermore, in
pediatric patients Axl measurements are difficult and the
globe grows with age. Therefore “Experienced surgeons
will establish their own ‘tables’ for the amount they will
recess or resect a muscle for a certain measured deviation”
(Wagner 2005). Nevertheless, “We agree with Kushner et al
that despite the approximation involved, the use of A scan
is superior to other methods of estimating the amount
of extraocular muscle surgery required” (Gillies 1991).
“A statistically highly significant negative correlation was
found between the axial length and the response to strabis-
mus surgery” (Krzizok 1994), that is, the larger the globe
the smaller the response to the same surgery.
Suppose one wished to straighten an eye diagnosed with
esotropia of 20 prism diopters (∼10°). If its AxL were about
22 mm, the medial rectus ought to be theoretically recessed
2 mm, and the lateral advanced (or shortened) 2 mm. If,
however, AxL was 32 mm, the displacement of the insertions
must measure almost 3 mm in order to achieve the same
effect, for 2 mm of surgery will result in under correction.
In conclusion, I have tried to impress upon the reader
the significant influence of globe size, measured by its axial
length, on the effects and measurement of its intraocular
pressure and on its motility. The geometrical and physical
models serve as simplified skeletons upon which the com-
plex biological components of anatomy, neurology, and
biochemistry may then be fleshed. Future statistical data on
the relation of AxL to eso and exo deviation, in addition to the
customary refractive data, will be helpful. So may be in vivo
data on scleral thickness. At present, the routine addition to
our clinical armamentarium of measurable Axl data promises
to enhance the quality of our diagnosis and management of
glaucoma and of strabismus.
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