1. 1 Copyright © 2016 University of Nottingham
M.Eng. Mechanical Engineering
MM4MPR Individual Research Paper 2015/16
Adhesively Fixed Reference Points for Surgical Navigation and Robotic Surgery
H.P.F Müller-Jones, D. McNally
Faculty of Engineering,
University of Nottingham, UK
ABSTRACT
Although surgical navigation and robotic surgery have increased in use, they remain limited by the accuracy of sensors and registration, reliance on
surgeon expertise and radiation exposure. By assessing the accuracy of adhesively fixed reference points both as a direct reference for a robotic arm
and as a drill guide, their use in replacing current methods can be quantified. Three fixed reference marker models were created from an initial
computed tomography (CT) scan of an L4 vertebra through additive manufacturing for comparison; the optimal case (res 134µm, threshold 50%
wrap 0.3mm), intermediary case (res 278µm, threshold 60%, wrap 0.9mm) and reasonable worst case (res 500µm, threshold 70%, wrap 1.3mm). A
best fit scan and registration method could then determine the translational and axial accuracies of the markers via their 3D point clouds.
The mean accuracy of each marker in relation to its own optimal placement was found to range between 0.18mm for the optimal marker and
0.54mm for the worst case. A noticeable difference of 0.12mm was seen in the accuracy of the optimal marker when printed on the Robotix and
Makerbot, indicating an additional printer error. Slippage down the bone from the initial placement was also evident in the comparisons, an error
caused by the lack of an appropriate adhesive when testing. Despite these errors, the accuracy of the intermediary and worst markers in relation to
the desired optimal placement averaged to 0.45mm and 0.64mm respectively. When compared to the current accepted error in spine surgery of
<2mm [1] and the theoretical best accuracy of <1mm [2] these markers increase accuracy between 18-91%. Axially, the results were evenly
spread with all values within the tube of danger and ¾ within the tube of fit. Compared to the 2.9% and 55%[3, 4] misalignment of other studies,
the 0% misalignment of results demonstrated that even the combined movements showed an improvement on current methods.
Even without an adhesive, these fixed reference points have shown accuracies consistently better than those currently seen in surgical navigation.
The use of an adhesive and a more precise 3D printer would improve accuracies even further. These markers open up a new area of surgery
whereby a reduction in reliance on surgeon expertise, radiation exposure, cluttered surgeries, surgery time and improvement in accuracy not only
makes surgery simpler, but helps prevent complications and potentially save lives.
INTRODUCTION
Surgical navigation has been used increasingly since its
conception in the 90’s however its use is limited by the
accuracy of sensors and registration, reliance on surgeon’s
expertise and radiation exposure. Inaccuracies found
within surgical navigation are produced from a range of
errors appearing in registration and positioning of the
reference points, whether this be due to skin shifting or
difficulty of placement. Current methods depend on
surgeon skill and an imaging C-arm or O-arm which has a
large physical presence, shown in Figure 1, and
significant radiation exposure.
Figure 1: Layout of navigation with robotic surgery in
current methods
The theoretical accuracy of spinal surgery is ≤1mm [2],
however current methods using sensors rarely achieve
this. The use of bone anchored screws as opposed to skin
markers has been shown to avoid skin shifting to improve
accuracy [1], however this is more commonly used
elsewhere in surgery. By attaching directly to the jaw in
dental surgery [5], teeth mounted sensors have produced
an accuracy of 0.5mm [1]. This accuracy has been
reproduced in a pinless method of using ceramic bones on
the femur and pelvis, with an additional pre-operation
registration accuracy 1.2mm.
Navigation in surgery has been widely discussed [6-11]
and although accuracy through use of surgical navigation
is better than free hand techniques [12], there is still a
dependence on the expertise of the surgeon [3, 13]. For
pedicle screw insertion, the assistance of some form of
intraoperative imaging reduces misplacement from 5-55%
[3, 14] to 3.7%-38.9% [15]. Comparative studies tend to
find both percentages lower, with misplaced screws for
free hand at 7%-13.4% [12] and assisted at 2.9%-4.6%
[4]. The range of these results largely depends on surgeon
skill as shown by Hu et al [16] whereby the placement of
screws improves with experience. The remaining error is
a combination of surgeon expertise and registration error.
Within spinal surgery, registration of image to patient has
an accepted error of <2mm [1] with additional errors in
navigation equipment and a varying time cost. The
commonly used method of optoelectric markers on
surgical tools incurs a registration time of 9.67 minutes
[17] to 12.8 minutes [1] to operations. This method
requires complex coordinate manipulations and the use of
the fluoroscope at different viewing angles, with further
corrections required to counter the distortions caused by
Robot Arm
O-Arm
Sensors

2. 2 Copyright © 2016 University of Nottingham
Spinous
process
Superior
articular
process
Nerve
root
Facet joint
Transverse
process
Marker
Placement
Ligamentum
flavum
the spherical shape of the image intensifier. This
combined with the error found in the C-arm, whereby the
weight of the frame is variably stressed dependent on
position causing deformation, has been found to limit the
accuracy of the system to 0.55mm [18].
Improvements in accuracy to current methods often come
at a cost of increased radiation exposure, with navigation
equipment taking up space in an already crowded surgery,
as seen in Figure 1. The use of X-ray fluoroscopy to
automate digital x-ray image registration as opposed to a
CT vertebral based registration system is equivalent to 30
C-arm exposures [19]. An O-arm can achieve better
alignment and resolution [13], with increased radiation
equivalent to 38 C-arm exposures [19]. The single patient
radiation average exposure for a C-arm is 1.1mSv
(average annual exposure in the UK is 2.7mSv) and
exposure can increase 10- 12 fold or more for more
complex surgeries [3]. This combined with the general
agreement that fluoroscopy remains cumbersome due to
having to maneuver around the C-arm in an already
crowded surgery[3, 20] has led to alternative methods;
electromagnetic navigation via a special field generator
placed below the patient does not interfere with the
surgical site or line of site in conventional optical systems
and creates better visualization than a fluoroscopic data
set [21]. This method reduces the radiation exposure
however it limited by its high cost.
As the adhesively fixed markers of this paper are
modelled directly from the initial CT scan of the patient,
the need for registration is removed, with the ability to be
used as a reference point or drill guide removing the
reliance on surgeon expertise. This fixed reference point
can be directly attached to by the robot arm, removing the
need for a C-arm or other navigation equipment, freeing
up space in a busy surgery. A reduction in radiation
exposure is also provided as both guided and unguided
surgeries take a minimum additional 3 images after the
initial CT scan, whereas the proposed method requires
only the initial CT scan. As these benefits are
supplementary, the accuracy of these new adhesively
fixed reference points (markers) will be compared to the
accepted error of <2mm for spinal surgery and the
theoretical error of <1mm in order to assess their
usefulness in the improvement of surgical navigation and
robotic surgery.
METHODOLOGY
The reference markers were modelled by performing a
Boolean subtraction of a generic baseline marker model
and various bone models. This imprints the surface of the
bone onto the inner surface of the marker, ensuring
complete congruence between the bone and marker
surfaces whilst allowing the exterior of the markers to
remain identical. The bone models were all created from
the same initial data set to again act as a control.
This initial data set was obtained for an L4 vertebra from
the lumbar spine using a CT scan at resolution 134µm and
manipulated using Mimics software. The resolution of the
scan was chosen as an optimum to correspond with the
best possible clinical scan resolution of 128µm [22, 23].
Mimics software was then used for segmentation due to
the partial volume effects of the 3-dimensional scan. A
threshold was initially set at 15,000; 50% of the average
bone density as found from an average of mean filter
results. This was then eroded to remove lone anomalies
and dilated to return the edges before exporting to 3Matic
software as a 3D model.
Due to the nature of bones in vitro and the quality of
bones produced from cadavers, gaps in cortical bone are
common and as such the 3D model was wrapped to make
a solid model of the bone. As additive manufacture is
used in this study to create physical models for testing,
the smallest resolution of 3D printer available determined
the initial wrap of 0.3mm.
The completed bone model was used to create the generic
baseline marker from which future different bone models
could be subtracted from. The position of this marker on
the L4 bone in the body is limited by the ligamentum
flavum and other joints within the body. Because of this,
the only plausible location is on the lamina of the
posterior, as highlighted in Figure 2. This location further
allows access to the pedicle for pedicle screw insertion
and the use of the curved edges as natural locators.
Figure 2: Marker placement relative to the spine [24]
This natural location is created from the three surfaces
available in this area, as show in Figure 3, and is integral
to the design of the baseline marker. This marker was
created from a rough surface drawn in this area which was
wrapped to create a 3D model. Wrapping was using
instead of extrusion to allow curved edges and the
reduction of stress in sharp corners. A cylinder was added
via Boolean addition to represent either the robot
attachment or drill guide hole and the cylinder wrapped to
avoid sharp corners at this connection. Future bone
models were subtracted from this completed baseline
marker to allow the exterior surface of each marker to
remain identical.
Figure 3: The baseline marker’s use of natural
location
Surface
Location
Point Cylinder

3. 3 Copyright © 2016 University of Nottingham
A: Fringe Projection B: Real Bone
C: Scan Image D: Point Cloud
Impact of Variables
In order to assess the error caused by the three variables,
resolution, threshold and wrap, these were individually
changed and compared to the optimal marker. This
optimal marker was modeled at the best resolution
134µm, threshold 50% and wrap 0.3mm and as one
variable was changed, the others remained at these
optimal values. The resolution was varied between
134 µm and the reasonable worst case resolution for a CT
scan of 500 µm and the threshold between 30%-70% as
reasonable upper and lower bounds for thresholding. The
wrap was varied 0.3mm-1.3mm as the minimum was set
by the precision of the 3D printer increased by 1mm to
find its effect. These variations are shown in Table 1,
where the optimal marker values are highlighted in blue.
Table 1: Variable values (optimal marker highlighted)
Resolution (µm) 134 204 278 352 400 500
Threshold (%) 30 40 50 60 70
Wrap (mm) 0.3 0.5 0.7 0.9 1.1 1.3
Each variation of marker model was compared to the
optimal marker within Cloud Compare software which
converts models to point clouds in order to find distances
between them. As the variable markers were only
modelled and not manufactured, the use of the same axis
meant registration was not necessary. Although not
manufactured, the point cloud comparison was set to
include 99% of points for continuality. This 99% excludes
anomalies, especially those which are caused by rough
edges on the outer surface of the marker where supports
had been for 3D printing. This selection of points to
include is shown in Figure 4 below.
Figure 4: Inclusion of 99% points to exclude anomalies
Translational Accuracy
The translational accuracy of the markers was found by
3D printing the models and using a best fit scan and
registration method to compare their point clouds. The
optimal marker was initially manufactured in ABS plastic
on the Robotix printer, chosen for its low cost of filament
and precision of 0.3mm. This marker was then placed in
its optimal position on the real bone, figure 5B, and a
technical fringe pattern projected onto the surface, 5A. As
this warps due to form, 5C, the image is 3D, thus creating
a 3D point cloud in Cloud Compare, shown in figure 5D.
As it is 3D, when comparing point clouds the movement
of the marker in all directions is measured, indicating a
level of congruence between the marker and the bone.
Figure 5: Fringe Projection creation of point cloud
When used in surgery, the use of an adhesive will need to
be compensated for within the wrap; however for the
purpose of the tests in this study no adhesive was used.
Any form of permeant attachment would allow no repeat
readings and any removable adhesive would have had a
large effect on the congruence of the marker to the bone.
For this reason, readings were taken with the bone upside
down in order to use a combination of gravity and the
natural 3-surface location of the bone.
Once the initial reading in the optimal place was taken,
the optimal marker was removed, replaced and rescanned
five times to determine the spread of accuracies. Within
Cloud Compare, the point clouds produced were
registered to compensate for movement of the bone,
shown in Figure 6. Using 99% inclusion of points, the
translational distances between the two point clouds were
found.
Figure 6: Before and after registration of point clouds
Two additional variations of marker were also
manufactured and tested, a reasonable worst case and an
intermediary marker. These are abbreviated for the
remainder of the paper as W.M (worst marker), I.M
(Intermediary marker) and O.M (optimal marker). As per
Table 1, W.M had the reasonable worst variable values,
resolution 500µm threshold 70% wrap 1.3mm, and I.M
had median values resolution 278µm threshold 60% wrap
0.9mm.
Due to technical issues with the Robotix printer, these
additional markers, alongside a copy of O.M for
consistency, were printed on the Makerbot printer which
claims the same precision. The first test of finding the
Anomalies

4. 4 Copyright © 2016 University of Nottingham
individual marker accuracy used the aforementioned
method of comparing replacements of each marker to its
own optimal placement for each of the O.M, I.M and
W.M.
A second test found the accuracies of the I.M and W.M
relative to the O.M. This second test re-registered each
point cloud of I.M and W.M placements to that of the
optimal placement of the O.M. From this, their distances
were found to find a relationship between the different
qualities of markers.
Axial Accuracy
In order to determine axial accuracy, the cylinder was
treated as a drill guide hole and the axial displacement of
its center line for each placement compared. For the point
clouds obtained using the method for individual marker
accuracy as outlined above, a cylinder was best fit to the
point cloud cylinder within Cloud Compare. Any results
which could not clearly fit a clear cylinder were excluded.
Within 3Matic, the co-ordinates of the center lines of
these cylinder models were found.
Through use of a transitional matrix, Eq. (1) below, to
align the vectors of these center lines, the X, Y, Z
displacements at a certain depth of hole were found. This
comparison of a center line of a placement to the optimal
center line is shown in Figure 7.
𝐷𝑖𝑓𝑓 = [
(𝑥1 − 𝑥2) + 𝐷(𝑥1̂ − 𝑥2̂)
(𝑦1 − 𝑦2) + 𝐷(𝑦1̂ − 𝑦2̂)
(𝑧1 − 𝑧2) + 𝐷(𝑧1̂ − 𝑧2̂ )
] (1)
Table 2: Definition of variables
(𝑥1, 𝑦1, 𝑧1) Base co-ordinates of the optimal line
(𝑥2, 𝑦2, 𝑧2)
Base co-ordinates of the line being
compared
𝐷𝑖𝑓𝑓
Difference between the lines being
compared
𝐷 Depth of hole
𝑥1̂ The unit vector of the optimal line
Figure 7: Axial method for comparing displacements
For comparison to literature, the drill guide used the
measurements for pedicle screw surgery. For such
surgery, a screw of ∅6mm is inserted with a tolerance
tube of fit of ∅8mm and a tube of danger of ∅10mm,
outside of which the screw will breach the cortical bone,
shown in Figure 8. The pedicle screw itself was assumed
50mm long, with the tubes both with depth 15mm.
Figure 8: Pedicle screw insertion[25]
RESULTS
Impact of Variables
The three variables were found to have a maximum
combined error of 0.19mm for the W.M, with the
resolution having the largest error and wrap the smallest.
The resolution was limited by the 0.3mm wrap, hence
large distances for resolutions <300µm, as shown in
Figure 9. After 300µm, the distance increases as the
resolution is made worse as would be expected. The
resolution is the only uncontrollable variable and as such
error will be kept minimal by appropriate selection of
wrap and threshold.
Figure 9: Resolution Error
The threshold error increases exponentially as it is
increased or decreased from 50%, indicating the
importance of threshold selection as a 10% change in
threshold can cause an error of ~0.06mm. This is shown
in Figure 10 below.
Figure 10: Threshold Error
The error in wrap acts as expected; it exponentially
increases as the larger the wrap, the less detail kept and
0
0.05
0.1
0.15
200 300 400 500
Distance(mm)
Resolution(µm)
Resolution Error
0
0.02
0.04
0.06
0.08
0.1
25 35 45 55 65 75
Distance(mm)
Threshold (%)
Threshold Error
Depth 15mm
Pedicle
screw ∅6mm
Tube of fit
∅8mm
Tube of danger
∅10mm
(𝑥2, 𝑦2, 𝑧3)
Comparison
line
(𝑥1, 𝑦1, 𝑧1)
Optimal line
D

5. 5 Copyright © 2016 University of Nottingham
the greater the displacement from the original model. This
can be seen in Figure 11. This is the smallest of the three
errors with maximum 0.04mm at a 1.3mm wrap however
indicated that the wrap should be kept as small as the
precision of printer will allow.
Figure 11: Wrap Error
Threshold and resolution are tied in that a worse
resolution will require a lower threshold to ensure only
bone is accepted. Although resolution may not be
controllable in a real situation, by ensuring the wrap is
kept as small as possible and an appropriate threshold is
selected, the errors in variables can be kept to a minimum.
Translational Accuracy: Individual Markers
The accuracies of the markers compared to their
individual optimal placements ranged from 0.09-0.78mm.
The results for the marker printed on the Robotix printer
(O.MR) had the greatest accuracy, with an average
0.18mm compared to the average accuracy of the same
marker printed on the Makerbot of 0.3mm. As the
standard deviations of the two data sets are identical, both
0.12, it can be deduced that this shift in mean is likely due
to printer error over human error, assumed at ~0.12mm.
Table 3: Translational results for individual markers
O.MR O.M I.M W.M
Distance(mm)
0.36 0.23 0.19 0.78
0.13 0.20 0.19 0.44
0.15 0.44 0.31 0.49
0.09 0.22 0.36 0.49
0.41 0.16 0.49
X̄ 0.18 0.30 0.25 0.54
σ 0.12 0.12 0.09 0.14
All three of the markers printed on the Makerbot have two
distinctive groups of distances; for example I.M ~0.2mm
and ~0.35mm. These distinct groups could indicate that
the marker is roughly in the same place, but either side of
a ridge of printed plastic at 0.3mm.
With regards to the individual patterns, the variation in
accuracy of the O.M as seen in Table 3 is shown in
Figures 12 and 13 below, where the matching blue of
bone and marker in Figure 10, 0.20mm, shows little
movement and green in Figure 11, 0.44mm, shows larger
movement. It can be seen that the marker moved as a
whole, demonstrated by the large proportion of green,
which shows that it was human error as opposed to errors
in the surface of the marker which caused the
displacements.
Figure 12: O.M best accuracy 0.20mm
Figure 13: O.M worst accuracy 0.44mm
The I.M has a 0.06mm lower average than the O.M which
coupled with the lowest standard deviation of 0.09mm
demonstrates that the marker was consistently in roughly
the same place. This is due to the reduced level of detail
on the surface as demonstrated in Figure 14 below, where
the largest displacements can be seen on the edges of the
marker where the more intricate holes and raises have lost
detail and expanded due to the threshold and wrap.
Figure 14: I.M worst accuracy 0.36mm
0
0.01
0.02
0.03
0.04
0.05
0.3 0.8 1.3
Distance(mm)
Wrap (mm)
Wrap Error
0mm
20mm
40mm
60mm
80mm
0mm
20mm
40mm
60mm
80mm
0mm
20mm
40mm
60mm
80mm

6. 6 Copyright © 2016 University of Nottingham
W.M has the worst accuracy as would be expected.
Similarly to the I.M, the largest displacements occur on
the edges of the marker, most notably the lower edge as
shown in Figure 15. This larger displacement is caused by
reduced detail and slipping of the marker due to gravity.
Figure 15: W.M worst accuracy 0.78mm
This slippage combined with human error makes up the
remainder of the error. All three of the markers display
this area of largest displacement which is a combination
of the circular feature on the surface of the marker
resultant from a hole in the bone and this slippage due to
gravity. It should also be noted that apart from an
anomaly in the first measurement of the W.M, the
standard deviations are decreasing. As the tests were
performed in order of best to worst, this indicates that
although they may be consistently in the wrong place, the
markers are placed closer together each time indicating
that repeatability is improving with placement. This
evidence of other error is summarised in Table 4 below.
Table 4: Other error
X̄ (mm) Other error (mm) Percent of X̄
O.M 0.300 0.180 59.9
I.M 0.245 0.004 1.4
W.M 0.537 0.231 43.0
For the W.M, printer error ~0.12mm, resolution, threshold
and wrap error 0.19mm. For the average 0.54mm, this
leaves ~0.23mm for human error, slippage and modelling
error. Interestingly the other error for the intermediary
marker was negligible, demonstrating that it was the
marker closest placed in the same as its optimal position
over the average placements.
Translational Accuracy: Comparisons
When compared to the optimal placement of the O.M, the
average I.M accuracy is 0.45mm and W.M 0.64mm. If
considering the average internal translational accuracy of
O.M (0.3mm), the average I.M accuracy is 50% worse
and W.M 113% worse. The results are summarised in
Table 5 below.
Table 5: Comparisons of I.M and W.M to O.M
I.M W.M
Distance(mm)
0.57 0.67
0.59 0.63
0.38 0.67
0.40 0.64
0.36 0.50
0.39 0.74
X̄ 0.45 0.64
σ 0.10 0.08
The standard deviation decrease from O.M to W.M, as
shown in the spread of data in Figure 16, is due to the less
detailed marker being able to be placed in consistently the
wrong place due to lack of locators. The increased
average of the I.M and W.M show that the translational
accuracy decreases with reduced detail, however only by
a maximum of ~0.35mm.
Figure 16: Translational distances from optimal
placement of O.M
Axial Accuracy
At a tube depth of 15mm, all results were within the tube
of danger, with ¾ within the tube of fit, as shown in Table
6 below. The spread of results across all three markers is
fairly uniform when axial and translational accuracies are
considered together, with the O.M having the largest
average combined displacement of 1.05mm.
Table 6: Combined axial and translational results
Distance(mm)
O.M I.M W.M
0.97 1.43 0.91
0.79 0.37 0.66
1.13 0.25 0.64
1.33 0.99 0.69
X̄ 1.05 0.76 0.72
The furthest XYZ co-ordinates of comparative centre
lines at 15mm depth are shown graphically in Figure 17.
These co-ordinates are plotted with a 1mm diameter tube
so as to demonstrate breech in any direction of the ∅8mm
tube of fit. The ∅10mm tube of danger is also plotted in
the same way as a 2mm tube.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
TranslationalDistance(mm)
Translational Distance from Optimal
Placement of O.M
O.M I.M
W.M O.M Average
I.M Average W.M Average
0mm
20mm
40mm
60mm
80mm

7. 7 Copyright © 2016 University of Nottingham
This graph demonstrates the spread and shows it is
limited to ~1mm diameter. The points for each marker are
bunched together, due to the translational element
whereby the markers are consistently in the same but
incorrect place.
Figure 17: Plot of axial results with 1 and 2mm tube
Although the Z direction is not as important, due to the
base of the tube entering the anterior where there is more
room, the Z direction is shown in Figure 18 below for
clarity. From this it can be seen that nearly half of the
points exceed the base of the tube, meaning for the full
pedicle length ~1mm depth tolerance is required.
Figure 18: Z plot of axial results with 1mm tube
These results show that the rotation of the marker is
negatively correlated to detail of the marker. This is
clearer when only axial displacement is considered, as
shown in Table 7 below. As the detail decreases from O.M
to W.M, the marker is less able to rotate axially and as
such the axial displacement decreases.
Table 7: Axial tube exit error
O.M I.M W.M
Distance(mm)
0.59 0.18 0.22
0.69 0.00 0.15
1.11 0.63 0.20
0.58 0.42 0.17
X̄ 0.74 0.31 0.19
DISCUSSION
Although surgical navigation is being increasingly used, it
remains limited by its accuracy, reliance on expertise and
radiation exposure. As the decrease in radiation, surgery
time, registration and machinery physical presence are all
supplementary, the assessment of accuracy in relation to
current methods determines the use of these adhesively
fixed reference points for surgical navigation and robotic
surgery.
The use of these markers reduces, but is still limited by,
human error. Firstly, within initial modelling a level of
competence is required in interpreting the resolution of
the scan and therefore selecting the correct threshold. An
incorrectly selected threshold by 10% on even the best
scan can cause a ~0.06mm error. A second error could
occur in the drawing of the curve for the baseline marker
as if the natural locators of the bone are not utilised, the
accuracy is likely to decrease. Most importantly, for the
measurement of accuracy for this paper, it was assumed
that the optimal initial placement of each marker was
indeed perfect, however in reality it is unlikely that the
marker was placed exactly perfectly.
This error in placement is also due to slippage, an error
caused by the lack of an adhesive in the tests. Due to the
lack of suitable adhesive with which to replicate these
tests, the actual effect of slippage is unknown however
can be assumed to have a significant effect on the final
accuracies.
The accuracies are also largely affected by the method of
manufacture. The markers are limited by the 0.3mm
precision and as such the matching wrap, although
smoothing problem areas for ease of printing, removes
much of the intricate congruence a higher precision
printer would achieve. The further issue with the printers
used is the need for supports and the rough edges created.
Although the use of 1% exclusion does remove some of
these anomalies when cloud comparing, some of these
edges alter the accuracy results.
Comparison with current methods
The results in this paper show that the translational
accuracy of these markers is much better than current
accepted error of <2mm for spinal surgery [1]and the
theoretical error of <1mm [2]. Further to this, even the
best accuracy of 0.5mm [1] seen in other surgery is
exceeded by all but the W.M. As shown in Table 8, the
percentage improvements are significant, even with the
limitations defined above.
These improvements are likely to increase with use of
adhesive and improved additive manufacture methods,
however demonstrate the ability of the markers to
improve accuracy in comparison to current methods.
Table 8: Improvements on current methods
O.MR O.M I.M W.M
Mean(mm) 0.18 0.30 0.45 0.64
% improvement on
accepted error 2mm
91 85 78 68
% improvement on
theoretical error 1mm
41 35 28 18
% improvement on
other surgery 0.5mm
16 10 3 -7
 O.M
 I.M
 W.M
 O.M
 I.M
 W.M

8. 8 Copyright © 2016 University of Nottingham
For axial accuracy, misalignment of previous studies refer
to perforation of the pedicle whereby this study shows 0%
outside the tube of danger where perforation occurs. With
previous studies finding misalignment between 2.9% and
55% [3,4], it is obvious that the axial accuracy of these
markers is better than previous studies. When considering
that these results combine both translational and rotational
movement, the axial accuracy is likely to improve with
adhesive and additive manufacture methods to the same
degree as translational accuracy.
This improvement through use of an adhesive may be
limited by its effect on the congruence of the marker and
bone; however the use of a thin film is likely to show
negligible negative impact. A further improvement may
be found by exploring the relationship between axial
rotation and detail as the reduced rotation with reduced
detail may mean that a greater detail may not actually be
optimal. Despite this, the accuracy results obtained
remain promising.
This accuracy shows more than an improvement on
current methods; they further demonstrate the reduced
reliance on surgeon expertise due to the drill guide
reducing misalignment. The translational results also
demonstrate this, due to the ability of anyone to put the
marker in place without skill and still obtain favourable
results. Again when adhesives are used, this task is likely
to become even easier.
This simplification of surgery also applies to further
benefits, with the need for a C-arm in an already busy
surgery eliminated and reducing both the time cost of
registration and the extra 1.1mSv in radiation. Monetary
costs are also reduced through the method of manufacture
and even if a more expensive 3D printer [26] was used for
better precision, this would cost £980 for a precision of
0.02mm and <£5 per print as opposed to the imaging cost
of ~£500 for a C-arm[27].
CONCLUSION
Even without an improvement in accuracy, the benefits of
removing the C-arm, registration and reliance on surgeon
expertise would arguably justify these markers use for
surgical navigation and robotic surgery. The best average
translational accuracy of 0.18mm for the optimal marker
(printed on the Robotix printer) demonstrates the high
accuracies possible. The 18-91% improvements on
current methods for spinal surgery indicate that even the
reasonable worst case model of marker is an improvement
on current methods. The resulting 0% misalignment
compared to the 2.9-55% of current methods when
considering pedicle screw insertion using these markers
as a drill guide further demonstrates this improvement.
Although further work is needed in optimizing the
selection of parameters and adhesive used, these results
clearly demonstrate the benefits of using these markers
with regards to improving accuracy in surgery. By having
a direct reference point, navigation is made simpler and
registration is no longer required.
This improvement in accuracy and additional
simplification of surgery and navigation could not only
make surgery easier and cheaper, but reduce misalignment
and complications; potentially saving lives.
Future Work
With regards to the models themselves, future work
would require the optimisation of the parameters used
when modelling the markers. Although the current results
are promising, the investigation of other bone models and
finding of a guideline set of parameters for which to aim
for would make the modelling of future markers simpler,
and also increase the accuracies found here.
An appropriate material for the markers would also need
to be found. This would depend on whether the markers
are left in the body, in which case a bio inert or
degradable material would have to be used. The recent
improvements in the 3D printing of organic material may
be a future consideration for material.
These considerations also apply to the use of adhesive
within the body. Again this relies on whether the marker
is removed from the body. The adhesive choice would
also have to consider thickness of adhesive, so as not to
affect the congruence of surfaces, and also setting time.
ACKNOWLEDGEMENTS
Thank you to the staff of the biomechanics lab at the
University of Nottingham who donated their time to help
me better understand the field, with special thanks to Alan
Parish who provided Mimics and 3-Matic tutoring. Also
to Jason Young for his continued help with additive
manufacture and finally Petros Stavroulakis for all his
support on imaging and measuring of accuracy.
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