MRI-based Visualisation of Orbital Fat
Deformation During Eye Motion
Charl P. Botha1, Thijs de Graaf2, Sander Schutte2 Ronald Root2,
Piotr Wielopolski3, Frans C.T. van der Helm2, Huibert J. Simonsz4,
and Frits H. Post1
1 Data Visualisation, Delft University of Technology, Delft
2 Biomechanical Engineering, Delft University of Technology, Delft
3 Department of Radiology, Erasmus Medical Centre, Rotterdam
4 Department of Ophthalmology, Erasmus Medical Centre, Rotterdam
The Netherlands
Summary. Orbital fat, or the fat behind the eye, plays an important role in eye
movements. In order to gain a better understanding of orbital fat mobility during
eye motion, MRI datasets of the eyes of two healthy subjects were acquired respec-
tively in seven and fourteen different directions of gaze. After semi-automatic rigid
registration, the Demons deformable registration algorithm was used to derive time-
dependent three-dimensional deformation vector fields from these datasets. Visuali-
sation techniques were applied to these datasets in order to investigate fat mobility
in specific regions of interest in the first subject. A qualitative analysis of the first
subject showed that in two of the three regions of interest, fat moved half as much
as the embedded structures. In other words, when the muscles and the optic nerve
that are embedded in the fat move, the fat partly moves along with these structures
and partly flows around them. In the second subject, a quantitative analysis was
performed which showed a relation between the distance behind the sclera and the
extent to which fat moves along with the optic nerve.
1 Introduction
The human eye is able to rotate at up to 1000◦ per second and has an angular
range of 100◦ horizontally and 90◦ vertically. It is able to do all of this with
almost no translation of its centre. Eye movement is driven by six eye muscles.
The left image in Figure 1 shows the medial and lateral rectus muscles that
are responsible for horizontal motion. The right image shows the superior
and inferior rectus muscles that are responsible for vertical motion. The two
oblique eye muscles are able to perform torsionary eye motion, i.e. rotation
around the direction of gaze.
The exact nature and parameters of the mechanics supporting eye move-
ment is still not entirely clear. For example, as part of the “Active Pulley
,

222 C. P. Botha et al.
Fig. 1. The left image is of an axial slice of an MRI dataset of an eye showing the
medial and lateral rectus muscles and the optic nerve. The white material surround-
ing the eye-muscles is orbital fat. On the left of the image, part of the nose is visible.
The right image shows a slice orthogonal to that, intersecting at the diagonal line
shown on the axial slice. This orthogonal slice shows the superior and inferior rectus
muscles as well as the superior oblique muscle. The inferior oblique muscle is not
visible in this image, but is diagonally opposite to the superior oblique.
Hypothesis”, it was proposed that the connective tissue bands connecting the
horizontal rectus muscles to the inside wall of the orbit (eye socket), first de-
scribed by Tenon in 1816 and later called “pulleys” by Miller in 1989 [Mil89],
are responsible for the fact that these muscles show a specific inflection or
bending point during vertical eye motion [Dem02].
However, in recent work it was demonstrated with a finite element analysis
model of the eye as well as clinical observation that these muscles show this
inflection point without any connective tissue structures [SvdBK+03, Sch05].
It has also become clear that the orbital fat, i.e. the fat behind the eye, plays
an important role in the mechanics of eye movement. Currently, relatively
little is known about the mobility of this fat during eye movement.
This paper documents our initial efforts on studying the mobility of the
orbital fat during eye movements. Inspired by previous work in this re-
gard [AV02], we applied a deformable registration technique to derive 3-D
optical flow fields from two series of MRI datasets of two healthy subjects
in different directions of gaze. The resultant 3-D deformation vector fields
were used to visualise and measure the motion of orbital eye-fat during eye
movement.
Fields resulting from optical flow or deformable registration algorithms are
in actual fact displacement fields. However, in keeping with the registration
nomenclature we will also refer to them as deformation fields.
Our contribution lies in the fact that this study comes to relevant conclu-
sions about three-dimensional orbital fat mobility during eye motion. These
conclusions confirm previous work performed on two-dimensional data and
lead to interesting new questions. In addition, we demonstrate that using

MRI-based Visualisation of Orbital Fat Deformation During Eye Motion 223
interactive advection volumes is an effective way of investigating orbital fat
mobility based on 3-D optical flow vector fields derived from MRI.
The rest of this paper is structured as follows: section 2 contains a brief
summary of work related to this study. Section 3 explains the methods and
tools we used for our study. In section 4 we show the results of our analysis
and in section 5 we summarise our findings and indicate avenues for future
work.
2 Related Work
There are numerous examples of estimating 3-D motion given a set of volumes.
For example, in [dLvL02], block matching is used to derive motion vectors.
We have chosen the Demons deformable registration algorithm [Thi96] due to
its straight-forward implementation and the fact that it is a proven choice for
the non-rigid registration of MRI datasets. However, we do plan to test more
optical flow approaches in the future.
In [AV02], the 2-D Lucas and Kanade optical flow algorithm [LK81] is
extended to three dimensions and applied to various test datasets as well as
an MRI dataset of an eye in different directions of gaze. For reasons men-
tioned previously, we selected the Demons algorithm. In addition, we make
use of advection to quantify the fat motion. Another important difference is
that [AV02] focuses more on the validation of the actual technique rather than
on the investigation of actual fat mobility. It does come to the conclusion that
the orbital fat “deforms like a liquid and less like a solid”. It also describes
how the fat fills the area behind the moving optic nerve from above and below
during horizontal motion. This is described as “this tissue [the fat], thus, fills
the vacuum left by the nerve, as behind a spoon moving through syrup”.
In a previous two-dimensional study based on MRI data, it was determined
that the orbital fat surrounding the optic nerve moves horizontally only 54%
as much as the optic nerve itself during horizontal eye motion [SHM+06].
3 Methods
3.1 Acquisition
MRI volume datasets were acquired of the eyes of two healthy subjects in
respectively seven and fourteen different directions of gaze.
For the first subject, T1-weighted scans were acquired on a 1.5 Tesla Gen-
eral Electric MRI scanner. We made use of a mobile transceiver surface coil
for higher resolution. This resulted in seven 512×512×84 MRI datasets with
resolution 0.273 × 0.273 × 0.5mm. For the deformation analysis, four of the
datasets were used: the central direction of gaze, and three directions of gaze
to the left.

224 C. P. Botha et al.
Fig. 2. The acquisition setup. The subject’s head has been fixed to the scanning
table. The mobile transceiver is visible over the subject’s right eye.
For the second subject, T1-weighted scans were acquired on a 3 Tesla
General Electric MRI scanner. This resulted in fourteen 512× 512× 128 MRI
datasets with resolution 0.312× 0.58× 0.4mm. For the deformation analysis,
thirteen of these datasets were used: the central direction of gaze, six directions
to the left and six to the right.
Figure 2 shows the acquisition setup. The inside of the MRI tube was
marked with fixation points at the desired directions of gaze for the subject
to focus on during the acquisition.
3.2 Software Tools
The Delft Visualisation and Image processing Development Environment, or
DeVIDE, is a software environment for the rapid prototyping and applica-
tion of visualisation and image processing techniques [Bot04]. It makes use
of the VTK [SML99] and ITK [ISNC03] software toolkits. Its primary user
interface is a graphical canvas where boxes, representing functional modules
or algorithms, can be placed. These boxes can be connected together to form
function networks. This is similar to other packages such as OpenDX [AT95]
and AVS [UFK+89]. What distinguishes DeVIDE is its focus on medical visu-
alisation and image processing, and the extensive interaction facilities made
possible by the use of Python [vR01], a very high level dynamically typed lan-
guage, in the program main loop. All processing and visualisation described
in this paper was performed using the DeVIDE software.
3.3 Pre-processing
During image acquisition, the subject’s head was fixed to the MRI patient ta-
ble with surgical tape in order to minimise head motion during the relatively

MRI-based Visualisation of Orbital Fat Deformation During Eye Motion 225
long total scan duration. Acquisition takes approximately one minute per
direction of gaze, but significant time is spent on setup actions between di-
rections of gaze. In spite of the head fixation, slight subject head motion did
occur. In order to eliminate this rigid head motion in the acquired data, cor-
responding sets of six bony landmarks each were defined in all datasets. The
datasets representing the central direction of gaze was chosen as the reference.
Rigid transformations, optimal in a least squares sense, were derived to map
the three other landmark sets onto the reference set [Hor87]. These transfor-
mations were used to resample the data volumes with cubic interpolation, thus
eliminating most of the rigid motion. All registrations were visually inspected
and improved if not satisfactory by re-adjusting the selected landmarks.
As explained in section 3.1, the inside of the MRI tube was marked with
fixation points at the desired directions of gaze. However, the desired direc-
tions of gaze and the final actual directions of gaze were obviously not equal,
as the subjects could focus with either one of their eyes. In order to deter-
mine the actual directions of gaze, we started by segmenting the lenses in all
datasets and determining the centroids of these segmentations. Segmentation
was based on a thresholding and 3-D region growing starting from a user se-
lected marker in the lens. Subsequently a sphere was fitted to the eye in order
to find its centre. Figure 3 illustrates this procedure. The vector between the
centre of the lens and the centre of the eye determines the direction of gaze.
For each of the subjects, one of the datasets was chosen as the reference, or
centre direction of gaze.
Fig. 3. Procedure for determining the actual directions of gaze. The lens is auto-
matically segmented and its centroid is determined. The actual direction of gaze is
determined by this centroid and the centre of the sphere that has been fitted to the
eye.

226 C. P. Botha et al.
For the first subject we determined the three directions to the left of the
centre direction to be respectively 33◦, 24◦ and 14◦. For the second subject,
the actual directions of gaze were 37.5◦, 30.1◦, 26.0◦, 18.8◦, 12.4◦, 4.6◦ to the
left of the centre direction, and 7.0◦, 12.8◦, 18.9◦, 25.5◦, 32.3◦ and 38.6◦ to
the right.
3.4 Deformable Registration
The Demons deformable registration algorithm [Thi96] was used to determine
the 3-D vector datasets describing the orbital fat deformation from the central
direction of gaze through all directions of gaze to its left and to its right. In
the case of the first subject, deformation fields were determined from 0◦ to
14◦, from 14◦ to 24◦ and from 24◦ to 33◦. For the second subject, fields were
determined starting from the central direction to all directions to the left and
to the right. The Demons algorithm was chosen due to its straight-forward
implementation, and the fact that it is often used for this kind of deformable
registration problem. We have also implemented the 3-D version of the Lukas
and Kanade optical flow algorithm and as part of our future work plan to
compare it with the Demons approach.
Because the Demons algorithm is based on the assumption that corre-
sponding points in the source and target datasets have the same intensity, the
intensity values of each pair of datasets were normalised by using a histogram
matching implementation from ITK [ISNC03].
3.5 Visualisation and Measurement
The resulting vector fields can be visualised with traditional flow visualisation
techniques such as glyphs or streamlines, but these techniques all suffer from
the problems plaguing most three-dimensional flow visualisation techniques:
occlusion, lack of directional cues, lack of depth cues and visual complexity.
To compound matters, we are dealing with time-varying data. In spite of all
this, existing techniques are a great help in localising regions of interest that
can be examined in more depth with other techniques.
In our case, we were interested in the fat deformation in specific areas. We
chose to apply user-guided advection volumes. Small sub-volumes are placed
in regions of interest. Each sub-volume is defined by a containing polygonal
surface. Points are placed within the interior of this sub-volume at a user-
definable density. Each of these points, as well as the vertices defining the
containing surface, can then be displaced by the interpolated deformation
vectors at their various positions, for that time-step. Figure 4 shows this
process for a single time-step and a single spherical volume. The deformed
volume, shown on the top right, is used as the initial volume for the next
vector field. In this way we can keep on deforming the volume as many times
as we have vector datasets.

MRI-based Visualisation of Orbital Fat Deformation During Eye Motion 227
Fig. 4. The sub-volume advection, shown for a single spherical region of interest
and for a single time-step. The sphere on the left is the original as selected by the
user. The object on the right has been deformed by the current vector field. The
vector field associated with the next time step will subsequently be applied to the
vertices of the deformed region of interest.
The DeVIDE software allows one to place any number of these volumes
in an MRI dataset. As soon as a volume is placed, it is advected through all
loaded vector fields and the initial volume as well as all deformed volumes for
that point are visualised. An already placed volume can also be moved. This
allows for the interactive exploration of a time-varying deformation vector
field. Figure 5 shows an example of such an interactive visualisation with four
initial volumes advected over 12 vector datasets.
Another important reason to select specific regions of interest is the fact
that the deformation field has the highest quality on textured structures em-
bedded in the orbital fat. Similar to the previous 2-D study [SHM+06], we
experimented by placing advection volumes on vascular structures, preferably
on bifurcations.
Results can be visually studied. In addition, similar to the actual direc-
tion of gaze determination discussed in section 3.3, the relative direction of
a specific advected volume can be determined with regards to the centre of
the eye.
4 Results
The two subjects were studied using different methods. The first subject was
part of a pilot study, and we qualitatively inspected specific anatomical regions
with advection volumes. In the second subject, we quantitatively tracked a
number of fat regions chosen specifically on vascular structures in the orbital
fat, also using advection volumes.

228 C. P. Botha et al.
Fig. 5. A visualisation with four advection volumes over 12 time-varying vector
fields. The volumes have been chosen in the same plane as the optic nerve, on
venous landmarks in order to verify the findings of a previous 2-D study. In each
of the four cases, the green sphere in the middle is placed in the centre direction of
gaze, and is advected both to the left and to the right.
In the first subject, three regions were selected for closer qualitative in-
spection:
1. The region between the medial rectus and the eye. As the eye turns anti-
clockwise, this muscle “rolls up” onto the eye.
2. Around the optic nerve right behind the eye.
3. The region at the apex where the eye-muscles and optic nerve meet, about
25mm behind the eye.
In all of these regions a number of spherical volumes were placed and
advected with the three deformation vector fields. In the first case, i.e. be-
tween the medial rectus and the eye, the resolution of the datasets and of the
resultant vector fields was too low to make any kind of judgement.
In the second case, seven small spherical volumes were placed directly
behind the eye: six surrounding the optic nerve at regular angles and one in
the optic nerve itself. As the left eye turns anti-clockwise, the optic nerve
moves medially, i.e. in the direction of the nose. The fat surrounding the optic
nerve moved in the same direction and primarily transversally. What was
significant, is that the fat moved only half as much as the optic nerve.

MRI-based Visualisation of Orbital Fat Deformation During Eye Motion 229
In the third case, advected volumes indicated that the fat moved primarily
in the same direction as the muscles. Once again, the fat moved half as much
as the muscles.
In the second subject data, we selected a number of advection volumes
specifically on vascular features in the orbital fat. In the first case, four markers
were chosen in the same axial plane as the optic nerve in order to confirm the
findings of [SHM+06]. In that 2-D analysis, a single MRI slice containing the
optic nerve was selected for the analysis and markers were manually tracked
for all acquired datasets.
In our case, the relative direction of a specific advection volume in any
vector field can be determined similarly to the way in which the directions
of gaze were determined. Figure 6 shows the relative rotations for each of
the four selected volumes over all vector fields. For each advection volume,
the linear regression with derived coefficients a and b is shown as well. Our
findings, although based on optical flow advection, concur with their manually
tracked results. In our case, fat rotation is between 0.35 times and 0.07 times
as much as eye rotation for markers with a distance between 3.3mm and
14.0mm behind the eye. In [SHM+06], fat rotation at 4mm was 0.36 times as
much and at 14.5mm 0.07 times as much as the eye rotation.
We also selected four markers in a plane completely above the optic nerve.
Although not as pronounced, there is a clear relation between the distance
direction of gaze (degrees)
5
0
-5
-10
-15
-40 -30 -20 -10 0 10 20 30 40
10
15
re
la
tiv
e
ro
ta
tio
n
of
m
ar
ke
r (
de
gr
ee
s)
d = 3.3
a = 0.35, b = -0.22
a = 0.16, b = -0.49
a = 0.12, b = -0.22
d = 14.0
a = 0.07, b = -0.38
d = 6.3
d = 9.9
Fig. 6. Relative angles of four advection volumes in an axial slice containing the
optic nerve over relative direction of gaze. d refers to the distance behind the eye
for that specific advection volume. Also shown is the linear regression derived from
this data with coefficients a and b.

230 C. P. Botha et al.
2
-2
-4
-6
-8
-40 -30 -20 -10 0 10
0
4
6
8
re
la
ti
ve
r
ot
at
io
n
of
m
ar
ke
r
(d
eg
re
es
)
direction of gaze (degrees)
d = 3.4
a = 0.19, b = 0.09
d = 6.1
d = 8.2
d = 14.3
a = 0.13, b = -0.12
a = 0.09, b = -0.50
a = 0.17, b = -0.43
20 30 40
Fig. 7. Relative angles of four advection volumes in an axial slice above the optic
nerve over relative direction of gaze. d refers to the distance behind the eye for that
specific advection volume. Also shown is the linear regression derived from this data
with coefficients a and b.
behind the eye and the ratio of fat rotation to eye rotation. Figure 7 shows
the measurements and linear regression for the markers in this plane.
In the third case, we chose a number of vascular markers in random posi-
tions around the optic nerve. The relation between distance and rotation ratio
is still apparent although far less pronounced. See Figure 8 for the measure-
ments and linear regression results.
5 Conclusions and Future Work
In this paper we have documented an initial study of 3-D orbital fat dynamics
based on multiple MRI datasets acquired of a two healthy subjects’ eyes during
different directions of gaze. Time-varying three-dimensional vector fields were
generated by applying the Demons deformable registration technique to pairs
of MRI datasets of sequential directions of gaze. These vector fields were
visualised with the DeVIDE software system and analysed by making use of
advection volumes.
In the first subject it was qualitatively determined that directly behind the
eye and at the apex where the muscles and the optic nerve meet, fat moves
50% less than respectively the optic nerve and the muscles embedded in it. In
other words, orbital fat moves partly along with these moving structures, but
it partly deforms around them as well.

MRI-based Visualisation of Orbital Fat Deformation During Eye Motion 231
2
0
-2
-4
-6
-8
-10
-40 -30 -20 -10 0 10 20 30 40
4
6
8
re
la
tiv
e
ro
ta
tio
n
of
m
ar
ke
r (
de
gr
ee
s)
direction of gaze (degrees)
d = 2.8
d = 4.5
d = 5.8
d = 6.8
d = 10.3
d = 13.5
d = 13.6
a = 0.20, b = -0.24
a = 0.16, b = -0.37
a = 0.19, b = -0.63
a = 0.16, b = -0.22
a = 0.09, b = -0.04
a = 0.05, b = -0.35
a = 0.05, b = -0.14
Fig. 8. Relative angles of seven advection volumes randomly selected in vascular
features around the optic nerve over relative direction of gaze. d refers to the distance
behind the eye for that specific advection volume. Also shown is the linear regression
derived from this data with coefficients a and b.
In the second subject, the rotation angles of specific vascular markers were
tracked over all thirteen vector fields. For markers in the same plane as the
optic nerve, our findings correlated well with the findings of a previous 2-D
study of the same data where markers were manually tracked from frame to
frame. For markers in a plane above the optic nerve, there was still an apparent
inverse relation between the distance from the eye and the ratio between the
deformation of the fat and the rotation of the eye itself. For vascular markers
randomly chosen all around the optic nerve, the relation was weaker. This is
to be expected, as markers further above and below the optic nerve will be
less affected by the motion of the optic nerve itself through the fat.
In all cases, motion of the vascular structures, calculated according to the
Demons optical flow, was a fraction of the eye rotation. This implies that the
optic nerve moves through the fat. In other words, orbital fat has to deform
less, which would probably require less energy.
With the Demons algorithm, we could only reliably track textured fea-
tures, such as the vascular structures, in the fat. We plan to implement more
robust 3-D optical flow techniques in order to be able to track a large part of
the orbital fat reliably. Subsequently, we will measure advection for a dense
sampling of complete orbital fat regions of interest in order to see if our find-
ings still hold.

232 C. P. Botha et al.
The interactive advection volumes constitute an effective method to visu-
alise and quantify local fat deformation. However, a more global visualisation
technique would be useful to help understand the complex orbital fat defor-
mation fields. One interesting idea is the development of a realistic fluid flow
simulation and visualisation that uses the derived vector fields as basis, so
that the fat deformation can be studied in pseudo real-time. We will also con-
tinue our investigation of alternative techniques for the visualisation of local
deformation.
The fixation of the subject’s head during scanning has to be improved.
The rigid motion can be eliminated as explained in this paper, but it is desir-
able to minimise head motion during the acquisition phase. For the residual
motion that still might occur, it is important to localise easily identifiable
rigid landmarks during acquisition. We are currently investigating techniques
to improve head fixation and landmark localisation.
Importantly, the approach documented in this paper is based on the acquis-
tion of a series of static scenes. During the acquisition of a particular direction
of gaze, the eye is in a state of equilibrium. Due to this, the dynamic behav-
iour of orbital fat during eye movements, e.g. the viscous or inertial effects,
is not captured. In spite of its limitations, our approach still yields valuable
information about the 3-D deformation of orbital fat, especially since it is cur-
rently not possible to acquire real-time 3-D MRI data of the eye in motion. In
future, we will make use of 2-D tagged MRI to study the dynamic behaviour
in more detail and integrate these effects into our 3-D model.
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