Elasticity, Viscosity, and Deformation of Orbital Fat
Ivo Schoemaker,
1,2
Pepijn P. W. Hoefnagel,
1,2
Tom J. Mastenbroek,
1
Cornelis F. Kolff,
1
Sander Schutte,
1
Frans C. T. van der Helm,
1
Stephen J. Picken,
3
Anton F. C. Gerritsen,
4
Piotr A. Wielopolski,
5
Henk Spekreijse,
6
and Huibert J. Simonsz
7
PURPOSE. For development of a finite element analysis model of
orbital mechanics, it was necessary to determine the material
properties of orbital fat and its degree of deformation in eye
rotation.
METHODS. Elasticity and viscosity of orbital fat of eight orbits of
four calves and two orbits of one rhesus monkey were mea-
sured with a parallel-plate rheometer. The degree of deforma-
tion of orbital fat was studied in two human subjects by
magnetic resonance imaging (MRI) through the optic nerve in
seven (first subject) or fourteen positions of gaze from left to
right. Bifurcations of veins in the fat were used as markers for
displacement of the fat.
RESULTS. The elastic shear modulus (G
) of calf orbital fat was
between 250 Pa and 500 Pa, and of monkey orbital fat it was
between 500 Pa and 900 Pa. The viscous shear modulus (G)of
calf orbital fat was between 80 Pa and 150 Pa, and for monkey
orbital fat it was between 300 Pa and 500 Pa. In the MRI scans,
it was found that markers in the fat, 1 to 5 mm posterior to the
sclera, rotated with the eye for 36% to 53% of eye rotation; the
remainder was accounted for by sliding of the eye within the
Tenon capsule and within the orbital fat.
CONCLUSIONS. Elastic and viscous shear moduli of orbital fat are
low. Little energy is dissipated in the fat. The required defor-
mation of the fat during eye rotation is limited because the eye
slides, to some extent, within the Tenon capsule. (Invest Oph-
thalmol Vis Sci. 2006;47:4819–4826) DOI:10.1167/iovs.05-
1497
L
ittle is known about the mechanical properties of orbital
fat. Although it has been the subject of detailed anatomic
studies, emphasis has been on the connective tissue septa
encompassing the fat
1
and on the vasculature.
2
The supporting
role of the fat has not been the subject of study, though the eye
slides in and is supported by the orbital fat. During the devel-
opment of a finite element analysis (FEA) model of the orbit,
3
the supporting role of the orbital fat proved to be very impor-
tant, for instance in stabilizing rectus muscle paths.
In this FEA model, the geometry of the structures in the
orbit, muscles, eye, fat, and bony orbit was determined, and
these structures were divided into a mesh of tetrahedra. Mate-
rial properties were assigned, and then deformations occurring
during eye rotation—such as those caused by a contracting eye
muscle—could be modeled. An FEA model of orbital mechan-
ics has the great advantage of few preliminary assumptions. In
a lumped model, the eye usually has three degrees of freedom
(i.e., the eye rotates about a fixed point of rotation). In the FEA
model of the orbit, the eye is supported by the orbital fat to
outbalance the force of eye muscles pulling the eye into the
orbit. Therefore, more accurate simulation of rotation in com-
bination with translation of the eye is possible. Some cases of
strabismus and orbital surgery can, hence, be modeled more
accurately. One of the simulations performed with the FEA
model was passive eye rotation about the line of sight,
3
imitat-
ing an experiment that had been performed previously in
vivo.
4
In this simulation of passive rotation of the eye about the
line of sight, the rectus muscle bellies remained in place,
presumably because of their containment within the orbital fat;
there were no explicit connections, such as pulley slings,
5
toward the orbital wall in the model. Stabilization of the muscle
bellies occurred even when the elasticity of the orbital fat in
the model was reduced to 200 Pa, a very low value. According
to the active pulley hypothesis,
5
the muscle bellies are kept in
place by pulleys. Pulley slings course toward the orbital wall
anteriorly and act like springs to stabilize the rectus muscle
paths in eye movements out of the plane of the muscle. The
active pulley hypothesis has been questioned recently by dem-
onstration of good eye motility in primates
6
and in a patient
with severe Crouzon syndrome,
7
each of whom lacked (part
of) the orbital wall. Recently, the functionality of the pulleys
was questioned further in a histology study by McClung.
8
In previous measurements of ocular mechanics, the stiff-
ness of the fat and connective tissue surrounding the eye was
measured indirectly by passive rotation of the eye itself, either
during strabismus surgery after detachment of the medial and
lateral rectus muscles or in awake volunteers without muscle
detachment. Robinson et al.
9
and Collins et al.
10
found 0.48
g/deg eye rotation when the eye was rotated horizontally after
detachment of the medial and lateral recti. In 29 awake volun-
teers, Collins et al.
11
found 1.05 g/deg, on average, when the
eye was pulled nasally and 0.94 when the eye was pulled
temporally, whereas the other eye fixated a target ahead and
without muscle detachment. Barmack,
12
Garcı´a et al.,
13
and
Igarashi et al.
14
found similar values. In all these measurements,
force was applied on a single point on the sclera, causing
displacement of the center of the globe.
3
In analyses of these previous measurements, no distinction
has been made between elasticity of the fat and its encapsu-
lating connective tissue, elasticity of the optic nerve, and slid-
ing of the sclera within Tenon capsule. The latter component
is important because less deformation of the orbital fat occurs
during eye rotation if the sclera slides within Tenon capsule.
The elasticity and the viscosity of the orbital fat, together
with its degree of deformation during eye rotation, constitute
important parameters for the FEA model of the orbit but have
not been measured previously. Therefore, we measured the
From the Departments of
1
Biomechanical Engineering and
3
Poly-
mer Materials and Engineering, Delft University of Technology, Delft,
The Netherlands; the Departments of
4
Public Health,
5
Radiology, and
7
Ophthalmology, Erasmus Medical Centre, Rotterdam, The Nether-
lands; and
6
The Netherlands Institute for Neuroscience, Amsterdam,
The Netherlands.
2
These authors contributed equally to the work presented here
and should therefore be regarded as equivalent authors.
Submitted for publication November 23, 2005; revised April 12,
2006; accepted August 28, 2006.
Disclosure: I. Schoemaker, None; P.P.W. Hoefnagel, None; T.J.
Mastenbroek, None; C.F. Kolff, None; S. Schutte, None; F.C.T. van
der Helm, None; S.J. Picken, None; A.F.C. Gerritsen, None; P.
Wielopolski, None; H. Spekreijse, None; H.J. Simonsz, None
The publication costs of this article were defrayed in part by page
charge payment. This article must therefore be marked “advertise-
ment” in accordance with 18 U.S.C. §1734 solely to indicate this fact.
Corresponding author: Huibert J. Simonsz, Department of Oph-
thalmology, Erasmus Medical Centre, Molewaterplein 40, NL 3015 GD
Rotterdam, The Netherlands; simonsz@compuserve.com.
Investigative Ophthalmology & Visual Science, November 2006, Vol. 47, No. 11
Copyright © Association for Research in Vision and Ophthalmology 4819

material properties of calf and monkey orbital fat and quanti-
fied the degree of deformation in two human subjects with
MRI.
METHODS
We measured the elasticity and viscosity of orbital fat of both orbits of
four calves and one rhesus monkey. We needed ample orbital fat to be
able to perform the measurement with sufficient accuracy. Calf orbital
fat was a convenient option. Calf orbit contains much fat, and a meat
processing facility was close to the laboratory housing the appropriate
measurement apparatus (this was important because the mechanical
properties of fat change rapidly postmortem). The rhesus monkey was
killed elsewhere for another study concerning the visual cortex. We
also measured the elasticity and viscosity of kidney fat of the same
animals for comparison: kidney fat has a dampening function and is not
subjected to torsional deformation. All procedures were performed in
compliance with the ARVO Statement for the Use of Animals in Oph-
thalmic and Vision Research.
Samples consisted of fat and its encapsulating connective tissue.
These two components are inseparable. Measurement of the fat within
the fat cells or its encapsulating connective tissue in isolation cannot
be performed without destroying its structure and thereby its overall
material properties. Moreover, these overall material properties pro-
vide the most useful data for the FEA model. The specimens of the
orbital fat seemed homogeneous on macroscopic inspection.
Dynamic mechanical measurements were performed with a rheo-
meter (ARES; TA Instruments, New Castle, DE) equipped with
100FRTN1 force transducer with a range of 0.004100 g
cm torque
and 0.1100 g normal force, parallel-plate geometry. In the parallel-
plate rheometer, the top plate is stationary and the bottom plate
rotates in an oscillatory fashion at various frequencies. The torque
generated during the oscillation is recorded, whereas the oscillation
rate or frequency is decreased in stages. Rheological parameters of the
tested material can be calculated using simple equations applied to the
torque measured at the various frequencies. Because of the simple
geometry of the shearing area, it is possible to express the results in
fundamental units—Pa for elasticity and Pa
s for viscosity.
Some demands must be met when measuring with a parallel-plate
rheometer. The measurements must be performed in the linear vis-
coelastic regime of the sample, the fat specimen should consist of one
piece, and the entire surfaces of the upper and lower plates of the
rheometer should be in good contact with the specimen. During our
measurements we made sure these conditions were met as much as
possible while taking into account the experimental constraints im-
posed by sample origin. The temperature of the plates was 37°C 
1°C. The pressure exerted by the upper plate on the specimens during
the measurements was approximately 500 Pa, which is near the esti-
mated
15
and measured
16
orbital pressures of approximately 500 to
1000 Pa.
To determine the linear viscoelastic regime of the samples, a strain
sweep at fixed frequency was performed before the actual measure-
ments in a separate specimen. This showed that the viscoelasticity of
orbital fat of calves and rhesus monkeys was linear from 0% to almost
130% deformation. Therefore, we chose to measure only at a deforma-
tion of 5% (ratio between excursion and height), thereby avoiding
irreversible damage to the specimen caused by excessive deformation.
Because we had first demonstrated that the viscoelasticity was linear
up to 130% deformation, this was permissible. The strain sweep was
made at one specific angular velocity; strain sweeps at different angular
velocities gave no additional information.
During subsequent frequency sweeps, the lower plate was rotated
sinusoidally at different angular velocities (
), at fixed strain amplitude,
in the linear regime. The experiments started with a maximal angular
velocity of 100 rad/s, and this decreased stepwise to 0.1 rad/s over a
period of 5.5 minutes. In a dynamic mechanical measurement, oscilla-
tory shear strain () was applied to the sample where  
0
sin(
t).
17
The resultant stress was analyzed in terms of the elastic stress and the
viscous dissipation using a storage modulus G
, and a loss modulus G,
by: /
0
 G
sin(
t)  G cos(
t).
17
Here,  was the measured
dynamic stress. The first term in this expression was in phase with the
applied strain and represented the elastic response of the material, as
expressed by the elastic shear modulus G
(storage modulus). The
second term was out of phase and attributed to viscous dissipation. It
was related to the viscosity via G
,
17
where  was the viscosity.
Because it was related to the viscous dissipation of energy, G was
called the viscous shear modulus (loss modulus) of the material and
depended on the viscosity and the speed of deformation.
The first series of measurements, in two sessions, were done on
eight specimens of orbital fat derived from eight orbits of four calves.
Calf heads were obtained immediately after slaughtering at a meat
processing facility and were transported within half an hour to the
laboratory in thermally insulated containers. Immediately before mea-
surement, the orbital contents were removed by exenteration,
whereby the skin was incised in a circular fashion down to the orbital
rim and the periorbita was lifted from the walls of the bony orbit. The
root of the resultant sac, deep in the orbit, was subsequently cut off,
enabling the removal of the orbital contents in one piece. Each exen-
teration took approximately 5 minutes. From the orbital fat we took a
large section, leaving its inner structure intact. This section was placed
onto the lower circular plate (d  50 mm) of the high-precision
parallel-plate rheometer, and a second circular plate was lowered onto
the specimen. Four measurements (first session) were performed with
a circular top plate of d  50 mm. The other four measurements
(second session) were performed with a circular top plate of d  25
mm because it was not always possible to cut a single piece of fat of 50
mm. The time between the end of the exenteration and the start of the
measurement was less than 1 minute. Measurements were taken be-
tween 65 and 213 minutes postmortem.
The second series of measurements was performed on two speci-
mens of orbital fat derived from the orbits from one rhesus monkey
(Macaca mulatta, male, 8 years old). The orbital contents of the
rhesus monkey were removed by exenteration approximately 10 min-
utes after death. After the exenteration, the orbital fat was put into a
FIGURE 1. To assess the rotation of a
marker in the orbital fat relative to
the head in 7 (first subject) or 14
horizontal positions of gaze, the di-
rection of gaze ( 
1
 
0
) relative
to a head-fixed reference frame and
the angle between the direction of
the marker (
1
) and the head-fixed
reference frame were used. The di-
rection of the marker in approximate
gaze ahead was taken as 
0
. These two
frames form part of Movie 1 (http://
www.iovs.org/cgi/content/full/47/
11/4819/DC1).
4820 Schoemaker et al. IOVS, November 2006, Vol. 47, No. 11