Interactive simulation and comparative
visualisation of the bone-determined range of
motion of the human shoulder
Peter R. Krekel∗ Charl P. Botha∗ Edward R. Valstar†
Paul W. de Bruin† P.M. Rozing† Frits H. Post∗
Abstract
Pre-operative planning systems aid clinicians by giving insight into patient-specific
issues before surgery is performed. The ability to perform a virtual shoulder replace-
ment procedure enables the surgeon to explore the probable and plausible outcomes.
Pre-operative planning software assists the surgeon in this complex decision-making
process.
In our prototype pre-operative planning system for shoulder replacement, we create
patient-specific bone-determined range of motion (ROM) predictions based on colli-
sion detection using segmented CT-data. The gleno-humeral ROM is visualised with
motion envelopes, that indicate the maximum range of motion of the humerus in ev-
ery direction. The prosthesis placement parameters can be adjusted interactively in our
simulator, during which a novel visualisation technique depicts the differences between
the current and previous range of motion.
In this paper we present a fast and efficient method for highly interactive visual-
isation of collision detection based ROM for the gleno-humeral joint. We are able to
show in real-time the consequences of adjustments made to a planned shoulder prosthe-
sis alignment by using geometry clipping-based optimisation, as well as precalculation
and interpolation techniques.
1 Introduction
Osteoarthrosis and rheumatoid arthritis, the two most common forms of arthritis, can lead
to severe joint damage. The resulting pain and limited joint motion significantly restrict
the patient in performing daily activities. In such cases, a joint replacement, i.e. a surgical
procedure where parts of the joint are replaced with artificial components, may be indicated.
A successful joint replacement leads to pain relief and improved joint mobility.
Replacement operations have a high success rate in the case of the hip or the knee joint.
In the case of the shoulder, however, the procedure is often successful with regard to pain
relief, but far less successful with regards to post-operative joint mobility or the durability
of the implant. The extra complicating factors are the higher complexity of the shoulder
∗Data Visualisation Group, Delft University of Technology, The Netherlands, http://visualisation.tudelft.nl/
†Department of Orthopaedics, Leiden University Medical Centre, The Netherlands

Clavicula
Humerus prosthesis
Glenoid prosthesis
Scapula
Glenoid
Humerus
Figure 1: Illustration of a shoulder joint after total shoulder replacement.
joint and the limited field of view during surgery. Our primary motivation for developing
a pre-operative planning system is to assist surgeons in performing the difficult shoulder
replacement operation, and thereby helping to improve the success rate.
In a total shoulder replacement, the humeral head and the glenoid fossa are replaced with
artificial components, as shown in Figure 1. The standard technique for planning a shoulder
replacement is template-over-x-ray planning, which involves overlaying several transparent
templates of different prostheses on radiographs of the shoulder to determine an appropri-
ate prosthesis. However, the radiographs lack spatial information along the view direction,
leading to visual ambiguities that complicate the planning. Our prototype shoulder replace-
ment pre-operative planning system improves on this by allowing the surgeon to simulate
the surgery in 3-D. Patient-specific information is extracted from a pre-operative CT scan.
During the simulation, the system gives feedback on the surgeon’s virtual surgery with
regards to the predicted outcome of the operation.
An important aspect of this feedback is the interactive simulation and visualisation of the
post-operative bone-determined range of motion of the patient’s shoulder. This function-
ality allows the surgeon to experiment with different prosthesis implantation possibilities
and see, in real-time, what the effect of the changes would be on the post-operative bone-
determined ROM. The interactive patient-specific ROM simulation and visualisation is the
main subject and contribution of this paper.
The remainder of this paper is organized as follows: In section 2 we discuss existing work
in the area of pre-operative arthroplasty simulation. Section 3 describes the simulation of
bone-determined ROM for the gleno-humeral joint, followed by section 4 where visualisa-

tion of ROM envelopes and comparative ROM visualisation is discussed. In section 5 we
explain the techniques we apply to enable fast updates of the comparative ROM visuali-
sation, which greatly improves the interactivity of our simulator. We present our results in
section 6, followed by our conclusions and discussion of future work in section 7.
2 Related Work
A wide range of pre-operative planning systems exist, for example Hip-Op [LPQ+02],
HipNav [SJB+97] and BrainLAB’s VectorVision1. However, to our knowledge no such
specific planning system for the shoulder joint is available at this time. Probable factors
here are the complexity and the relatively lower number of replacements of the shoulder
joint.
Some research has been done on pre-operative ROM estimation for the hip joint.
[JNSDG97] uses analytical modeling of the properties of implants to estimate both the
ROM and the chance of dislocation, with bony impingement hardly playing a part. The
approach of [RTE+98] resembles our approach more closely, by applying collision de-
tection to the 3D problem of bony impingement. Their system is designed for osteotomy
rather than joint replacement and only determines ROM for joint rotation along a single
user-defined axis.
The goal of the Comprehensive Human Animation Resource Model (CHARM) project
was “modelling a 3D solid human body part with its interior details and having physically
based simulation of movements and deformations” [MIR]. The emphasis of this project
was on animation, rather than patient-specific ROM prediction. For further reference, see
[Mau99].
Lastly, the Delft Shoulder and Elbow Model (DSEM) [vdH94] is a complete musculoskele-
tal model of the shoulder and elbow joint that mainly focusses on muscle function and the
involved forces and energy. However, the DSEM is not patient-specific and therefore not
yet usable for pre-operative planning.
3 ROM simulation
In order to calculate the ROM using a segmented CT dataset, we implemented a simplified
bio-mechanical model of the gleno-humeral joint. A generally accepted hypothesis is that
the gleno-humeral joint can be approximated by a ball-joint [MvdHRR98, vdGVBV02].
We combined this model with collision-detection on surface models of the skeletal struc-
tures in the patient’s shoulder.
The surface models are extracted from CT data using the segmentation techniques de-
scribed in chapter 4 of [Bot05]. With this approach, it is possible to extract accurate and
topologically correct surfaces describing the skeletal structures of the shoulder from CT
data. The techniques are also able to cope with arthritic shoulders where joint space nar-
rowing has occurred or the bone density has been affected. Conventional techniques, such
1http://www.brainlab.com/

A A
Medial Axis
Figure 2: A schematic representation of the humerus and its rotational axes. As can be seen
in this image, the additional range of motion as the result of endo/exorotation is related to
δ, the distance between the medial axis of the humerus and the vertical axis through the
center of rotation.
as double thresholding followed by region growing, do not work in such cases. Shoulder
replacement patients often suffer from both these symptoms.
During interactive simulation, we do not take into account rotation around the medial axis
of the humerus, i.e. endo/exorotation, thereby reducing the number of degrees of freedom
from three to two and greatly speeding up the simulation. This is a reasonable simplification
for the following reasons:
• For a healthy joint, the amount of ROM gained as a result of endorotation and exoro-
tation is only discernible in the upper extremes of the gleno-humeral joint. During
abductive arm movements, exorotation of the humerus is a common response to be
able to reach higher, though most of that particular ROM increase is coming from
the scapulo-thoracic joint.
• The maximum achievable ROM increase due to exorotation is relatively small. It is
related to the offset of the medial axis of the humerus in relation to the center of
rotation, as can be seen in Figure 2.
• Our simulation gives a conservative estimate of the shoulder ROM.
For testing purposes, we have included functionality in our simulator to determine and
visualise the extra range of motion gained by a single, adjustable exorotation angle. This
enabled us to confirm the above-stated assumptions.
The center of rotation of the gleno-humeral joint is defined by the diameter of the humeral
prosthesis, which has a spherical head. Therefore, adjustments made to the prosthesis also
affect the center of rotation. For initial placement of the humeral prosthesis, we have im-
plemented a sphere-fitting method. This entails that a sphere is fit over the humeral head to
approximate the ideal center of rotation, while continuously giving feedback on how much
of the sphere surface is near or touching the humerus surface.

Additionally, our simulator is capable of handling hemi-protheses, which is a prosthesis
without a glenoid component, and reversed prostheses, where the spherical component is
placed at the glenoid. For the latter, the center of rotation is situated more inward.
For all prostheses, the ROM envelopes are constructed in the following way. The humerus
is aligned with an initial orientation, which will be the starting alignment for all iterations.
The simulation consists of two nested iterations. During the outer iteration, the humerus is
rotated around the axis marked with Ai in figure 2. Note that axis Aj rotates along with
Ai. At each rotation, the maximum possible orientation of the humerus around axis Aj is
found by making use of a binary search. By repeatedly dividing the search interval in half,
our ROM determination executes in O(log n), where n relates to the effective resolution of
the end result of the binary search. Whenever colliding polygons are detected, we reverse
the search direction. After an evaluation of available collision detection libraries [Kre05],
we selected the Optimized Collision Detection library, or OPCODE [Ter01]. OPCODE is a
fast and accurate collision detection library based on memory-optimised bounding-volume
hierarchies and most suitable for our particular problem domain. The pseudo-code version
of the ROM determination procedure can be seen in Algorithm 1. The algorithm is also
explained in Figure 3. For every change in the planning, the complete ROM has to be
recalculated.
For hemi-protheses an extra step is required. The humeral head should make contact with
the glenoid at all times. Therefore, the humerus has an additional binary search iterator for
a translational component as well, rather than just for the rotational extremes. This is not
necessary for total shoulder prostheses, as we are targeting conformal prostheses, where
the diameters of the glenoid and humerus components are equal. However, using the hemi-
prosthesis modelling functionality, our system should be able to simulate non-conformal
prostheses as well.
4 Visualisation
Once all directions of our ROM envelope have been probed for their maximum angles, we
can begin constructing the ROM visualisation. We draw lines between the center of rotation
and an arbitrary point within the end of the shaft of the humerus, and then transform these
lines according to their respective maximum angles. The resulting envelope is shown in
Figure 4.
For each change made to the virtual prosthesis placement by the surgeon, a new ROM en-
velope is calculated. This enables the surgeon to visualise directly the complete shoulder
range of motion for a particular set of operational parameters. Being able to see the enve-
lope update in real-time as changes are being made, helps the surgeon to investigate the
effect of even small changes to the planned operation.
Several parameters that define the placement of the humerus prosthesis can be adjusted
during the interaction. First of all, the cutting plane at the humeral head can be translated
along its normal, as well as rotated around two axes perpendicular to the normal. Also, the
position of the humerus prosthesis relative to the humerus can have a small offset in any
direction within the cutting plane. These adjustments are also illustrated in figure 6.

Algorithm 1 The ROM determination algorithm.
function DetermineROM(resolution, angle, angle increment)
i← 0
while i < 360 do
t angle← angle
t angle increment← angle increment
while (abs(t angle increment)> e) do // e is a threshold for t angle increment
SetOrientation(0,0,0) // Set the humerus to an initial orientation
RotateZ((i/resolution) * 360)
RotateY(t angle)
RotateZ(-(i/resolution) * 360)
if CDQuery()> 0 then // There are colliding polygons
t angle increment← -abs(t angle increment) // Make the increment negative
else
t angle increment← abs(t angle increment) // Make the increment positive
end if
t angle increment← t angle increment ×0.5 // Cut increment in half
t angle← t angle+t angle increment // Add the increment to the previous angle
end while
AddToArray(t angle)
i← i + 360/resolution // Proceed to the next direction
end while
The ROM determination algorithm. The auxiliary function CDQuery returns the number of colliding
polygons. The parameters resolution, angle and angle increment are adjustable and define the
number of envelope lines, the initial angle we use for our simulation and the increment we add
to the previous angle at each iteration, respectively. Also, the search range depends on these three
parameters.

(a) (b) (c)
(d) (e) (f)
Figure 3: Binary search algorithm for one line of the ROM envelope. The blue humerus (a)
represents the initial orientation. At each iteration, the increment is added to the previous
angle (a, d, e) and halved. If colliding polygons are detected, the increment is preceded by
a negation (b, c). If the increment is smaller than a certain threshold, the line is added to
the envelope (f).
Figure 4: The visualisation of ROM by means of envelopes.

Figure 5: Comparative visualisation of two ROM envelopes. The first envelope is a pre-
viously determined ROM which was set as a reference envelope by the user. The second
envelope is continuously updated for every adjustment applied to the prosthesis placement
parameters.
Placement of the glenoid prosthesis is performed according to a method described in section
3.1 of [Bot05]. It is quite strictly constrained by the quality and the geometry of the scapula.
Therefore, we focused on the alignment of the humeral prosthesis.
In order to facilitate this important investigation of the increase or decrease in range of
motion that results from a particular change in the planning, we have implemented com-
parative visualisation functionality whereby the difference between two ROM envelopes
can be explicitly visualised. The comparative visualisation is also updated in real-time as
the surgeon interacts with the planning.
For two consecutive envelopes we depict improvements and deteriorations by connecting
the lines with colored polygons. A red polygon denotes that the most recent envelope has
a more limited ROM in that particular direction than the reference envelope, while a green
polygon states the opposite. Additionally, the end points of the lines are connected with
arrows, pointing towards the most recent envelope. The resulting visualisation is shown in
Figure 5. The reference envelope can be set to the current or any previously determined
ROM envelope at all times.
5 Optimisation
To support the interactive usage of our system, we focussed on decreasing the time required
to display consecutive ROM envelopes during prosthesis placement adjustments. We have

(a) (b) (c)
Cutting plane
(d)
Figure 6: These are the possible placement adjustments, that are also systematically mod-
ified during precalculation. In (a) we see the humerus, which can be translated along the
cutting plane. In (b) it is translated along the normal of the cutting plane. In (c) and (d) we
see the two axes used for orientation changes. Note that all adjustments are applied to the
humerus only, thereby changing its position relative to the prosthesis.
implemented two kinds of optimisations. Only one optimisation should be picked, depend-
ing on the intentions of the user. The first optimisation is based on precalculation and aims
at a thorough exploration of the ROM for a single prosthesis. The second optimisation is
based on geometry clipping and more suitable for comparison of the ROM of different
prosthesis types. When no time is available for precalculation, this optimisation should be
selected.
We describe both these optimisation methods in the following two subsections. In section
6, we show the results of performance and accuracy measurements on our simulator with
and without optimisation.
5.1 Precalculation and interpolation
To ensure a satisfactory frame-rate, we optimised the simulation through precalculation
and interpolation techniques. During the initialization phase, a variable number of ROM
envelopes are precalculated. Depending on the resolution and ranges, this number can vary
from 400 to as much as 2000. For a single orientation of the humerus prosthesis, we start
by precalculating envelopes for translational adjustments along the cutting plane (see Fig-
ure 6a). This is then repeated for translational adjustments along the normal of the cutting
plane (Figure 6b). Finally, the previous two steps are repeated for variations of the prosthe-
sis orientation (Figure 6c and d).
Now that we have completed the precalculation step we can interpolate the ROM predic-
tions at a high frame-rate, with only little accuracy loss. When the CPU is idle, the accurate
ROM envelope can be calculated and replace the interpolated envelope with a smooth tran-
sition.
The drawback of this approach is that the precalculations only hold for a single type and
size of a prosthesis. When the surgeon wants to compare the ROM of various prostheses
for a particular dataset, precalculation will have to be done for each of those prostheses.

5.2 Collision Clipping
For the concept of collision clipping, we differentiate between placement adjustments that
require geometry adaptation (GA) and those that do not. Geometry adaptation is necessary
for prosthesis placement adjustments that redefine the cutting plane, relative to the humerus
(see Figure 6b, c & d).
A problem with geometry adaptation is that the bounding boxes hierarchy, which is used
by the collision detection library, becomes outdated and needs to be rebuilt. This can take
up to 3 seconds for high-density models, slowing down the simulation unacceptably.
Instead of performing collision detection queries on the clipped model of the humerus,
we use the unclipped model. Thus, our collision detection queries may return collisions
of polygons that would normally have been clipped. By adding an additional query to the
algorithm, we can find out on which side of the cutting plane the colliding polygons are
located. If they are on the same side of the cutting plane as the prosthesis, the collisions
are ignored. Otherwise, the algorithm can terminate, since we only need one admissible
collision to identify an unacceptable humerus alignment.
Another slow down is caused by the clipping of the humerus model itself. Because we
have now separated the graphical representation from the collision detection algorithm, the
humerus model does not necessarily have to be clipped, other than for graphical represen-
tation purposes. Therefore, we use a much faster graphics hardware geometry cutting plane
instead of an accurate clipping algorithm.
6 Results
So far, the prototype system we developed has been tested on two in-vivo shoulder CT
datasets of patients requiring total shoulder replacements, with more tests being planned.
However, due to the consistent results generated by the specialised segmentation tech-
niques, we do not expect much deviation from these results for other datasets.
An orthopaedic surgeon used our simulator and these datasets for prosthesis placement
analysis and stated that the presented ROM estimations correlated with anticipated be-
haviour. We received positive feedback on the interactively updated comparative visualisa-
tions, which was experienced as both fast and intuitive.
The accuracy of the interpolation is dependent on the variable density of precalculated
ROM envelopes. For this specific benchmark, we calculated the deviation between various
different ROM envelopes that were calculated with and without optimisation. In total, the
deviation was measured for 5000 ROM angles. The median deviation was 0◦, the inter-
quartile range (IQR) was 0.15◦ (0◦ − 0.15◦) and the maximum absolute deviation was
2.67◦. This deviation is small enough to be justified by the significant interactive speed-
increase gained through the optimisation.
We benchmarked the precalculation process as well as the interactive performance of our
simulator on a Pentium 4 running at 2.66 GHz with 512 MB of RAM. The humerus model
consisted of 50.000 polygons, while the scapula consisted of 155.000 polygons. Precalcu-
lation of 1782 complete ROM envelopes took 22 minutes. This has to be performed once
per patient shoulder and can be integrated with the CT acquisition workflow.

With rendering Without rendering
no GA GA no GA GA
no-opt 1.79 0.27 1.93 0.30
coll-clip 2.38 (× 1.33) 2.22 (× 8.22) 2.70 (× 1.40) 2.69 (× 8.97)
interp 19.23 (× 10.74) 10.81 (× 40.04) 388.7 (× 201.4) 374.4 (× 1248)
Table 1: Speed of simulation and rendering in updates per second. no-opt, coll-clip and
interp are short for “no optimisation”, “collision clipping” and “interpolation” respectively.
Collision clipping refers to the measure documented in section 5.2. Interpolation refers to
the measure documented in section 5.1. GA refers to “geometric adaptation” (see section
5.2). All performance figures are specified as updates per second, figures in parentheses
refer to speedups relative to “no optimisation” performance.
Performance figures for the interactive ROM simulation are listed in Table 1. As can be
seen, the speed increase due to collision clipping varies from a factor of 1.33 to 8.22 for
normal usage of the simulator. The speed increase due to interpolation varies from a fac-
tor of 10.74 to 40.04. If we discard the graphical representation, the speed increase by
interpolation gets as high as a factor of 1248. From these results we draw the following
conclusions:
First, when no optimisation takes place, adjustments that require the geometry to be modi-
fied have a much lower update rate than other adjustments. This originates in the problem
of geometry adaptation (described in section 5.2) and results in an update rate of 0.27 up-
dates/s.
Second, the frame-rates of the aforementioned adjustments are substantially higher when
we apply the collision clipping optimisation. This optimisation enables interactive usage of
our simulator without any form of precalculation. Consequently, we can use this technique
to explore and compare the ROM estimations for multiple types and sizes of prostheses.
Third, the speed increase for interpolated ROM envelopes without graphical feedback is
extremely large. This can be ascribed to the interpolation process, which is far less compu-
tationally expensive than the accurate determination of a single ROM envelope. For unop-
timised ROM calculations and collision clipping, hardly anything of the routine is changed
when graphical feedback is disabled, explaining the poor speed increase for these cate-
gories.
We conclude from these results that both optimisations are very effective. Compared to
interpolated ROM estimations, the frame-rate for real-time exploration with collision clip-
ping is on the low side. Perhaps additional speed increase is possible if we use heavily
decimated models or limit the search range to areas where problems are likely to occur.
Nevertheless, the fact that collision clipping does not require precalculation steps, makes it
a good alternative for precalculated ROM predictions.

7 Conclusions and Future Work
In this paper we presented a practical technique for the calculation and visualisation of
shoulder range of motion envelopes. We designed an extensive precalculation and interpo-
lation scheme that enables the exploration of a shoulder replacement planning in real-time.
For every change made by the surgeon during the pre-operative planning, the resulting
range of motion can be interactively visualised. We also employ the graphics hardware
clipping plane to achieve interactivity at a lower frame-rate, without the requirement of
precalculation.
Because comparing different ROM envelopes is crucial for the evaluation of different pre-
operative choices, we implemented a comparative visualisation for ROM envelopes. The
comparative visualisation can also be updated interactively and explicitly shows differences
in mobility that result from the surgeon’s actions during the pre-operative planning.
We performed measurements to show that the difference between interpolated and calcu-
lated ROM envelopes is relatively small. Speed measurements showed that the simulator is
highly interactive when we apply precalculation and interpolation techniques.
The system we describe in this paper concerns bone-determined ROM, which provides
feedback on the risk of impingement. We plan to extend this with information on the pres-
ence of muscle tissue, ligaments and cartilage. Alternatively, a model of these aspects could
be used, such as the DSEM, described in section 2. While the model would greatly com-
plement our impingement-based ROM system, it is not yet patient-specific [vdHVP+92].
Still, integration of the DSEM is under consideration for future work.
Our simulator is an important component of a pre-operative arthroplasty planning system
for the shoulder joint [Bot05]. However, the presented techniques are generic and applica-
ble to other joints as well, such as the hip and knee joint. With regard to the simulator, we
will continue to add new functionality and refine existing features to better fit clinical prac-
tice, for example expansion of the prostheses database and improvement of user interface
elements.
Finally, we plan to perform a validation study on cadaver shoulders, where motion limita-
tion should correspond to the ROM estimations of our simulator.
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