Robotic alignment of femoral cutting mask during total knee

Robotic alignment of femoral cutting mask during total knee
Int J CARS
DOI 10.1007/s11548-008-0253-2
ORIGINAL ARTICLE
Robotic alignment of femoral cutting mask during total knee
arthroplasty
E. De Momi · P. Cerveri · E. Gambaretto ·
M. Marchente · O. Effretti · S. Barbariga ·
G. Gini · G. Ferrigno
Received: 10 January 2008 / Accepted: 18 June 2008
© CARS 2008
Abstract
Objective To investigate a new navigation system integrated
with a robotic arm for total knee replacement (TKR) procedures.
Materials and Methods The study here reported attempts
providing the surgeon with a robotic assistant handling the
surgical tools with superior stability removing tremors. The
system is equipped with an optical localization system, which
allows the real-time monitoring of the position and orientation of the surgical tools carried by the robot end-effector and
provides a feedback control to optimize the reaching of the
goal position.
Results Pilot experiments, performed aligning the femoral
cutting mask to the surgical position, together with the feasibility of the system, proved its accuracy and reliability.
Conclusion This paper shows the feasibility of a robotic
system for TKR, integrated with a navigation system, in order
to overcome limitations of both approaches.
Keywords Total knee replacement · Computer assisted
orthopedic surgery · Robotic surgery · Robot calibration ·
Closed-loop control
Introduction
Computer assistance of surgical intervention improves the
quality of total knee replacement (TKR) outcome in terms
E. De Momi (B) · P. Cerveri · E. Gambaretto · M. Marchente ·
O. Effretti · G. Ferrigno
Bioengineering Department, Politecnico di Milano,
Piazza Leonardo da Vinci 32, 20133 Milan, Italy
e-mail: elena.demomi@polimi.it
S. Barbariga · G. Gini
Electronics and Information Department, Politecnico di Milano,
Piazza Leonardo da Vinci, 32, 20133 Milan, Italy
of pain relief, joints range of motion, prostheses stability,
durability and lower limb mechanical alignment [7]. Navigation offers also improvements in the assessment of ligamentous stability [10], indicates proper components size and
pose and provides better placement, thus reducing implant
wear and loosening and consequently increasing prosthetic
lifespan [16]. The goal of computer assisted surgery (CAS)
is to reduce deviations from best practice and to eliminate
outliers in components alignment.
Before the surgical operation starts, reference frames built
with light-reflecting, light-emitting, or electromagnetic
markers (trackers) are fixed on the distal femur and on the
proximal tibia by self-cutting screws. Pivoting the femur
around the hip allows computing the hip joint centre, and
detecting bony landmarks with a tracked pointer allows computing the knee and the ankle centres. Such mechanical
centres define the limb mechanical axis and determine the
orientation of the distal cut of the femur (perpendicular to
the femoral mechanical axis). Traditional cutting guides are
equipped with trackers: the surgeon can thus drive cutting
guides, jigs, saw-blades and drills in real time while the
interactive user interface represents ideal and actual tools
position and orientation at the same time. When the desired
pose is reached, in case of TKR, cutting tools pose is maintained inserting cortical pins and self-cutting screws inside
the exposed bone surface. Data displayed on the visualization monitor (bone angle cuts and distance measurements)
informs the surgeon about alignment, implant size, orientation and relationship between bone and implant. In order to
accurately balance the ligaments, the surgeon can measure
residual laxities: anterior-posterior and medio-lateral at each
level of knee flexion. Finally, the surgeon can also control
the range of motion of the knee.
Jenny and Boeri [9] reported a significant improvement in
the femoral sagittal angle and in the tibial anterior posterior
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angles for navigated surgery. Mielke et al. [11] reported a tendency toward an optimal overall leg axis in computer assisted
interventions. Sparman et al. [17] reported a significant difference in favour of navigation concerning the mechanical
axes, the frontal and the sagittal femoral and the frontal tibial axes between 2 randomized patient groups. Although the
comparative studies on computer-navigation systems do not
show a definite trend in the outcome, all authors stated that
the use of the navigation results in a reduction of cases with a
high deviation from the desired alignment [5]. Notwithstanding the above cited advantages, CAS systems present some
drawbacks. The surgical cutting tools have to be manually
aligned by the surgeon, while he/she follows indications provided by the visualization interface. After alignment between
the desired cutting plane (or axis) and the current plane (or
axis), the surgical instrument has to be maintained in the
desired in pose during the cutting (or reaming) phase. Therefore the robot could act as a surgeon assistant holding firmly
the surgical tools.
Examples of active medical robotic devices are the CASPAR system (OrtoMaquet, Rastatt/Germany) [12], whose
clinical application include hip arthroplasty and knee surgeries (TKR—and anterior cruciate ligament—ACL) and
Robodoc system (Integrated Surgical Systems, USA), which
is used for total hip replacement. Semi-active robotic assistive system were developed for orthopaedic surgery [4,14]
starting from 1990s. In the ACROBOT system the surgeon
guides the robot using a handle with a force sensor servoing fixed to the robot tip. The robot provides a 3D motion
constraint that prevents milling outside a predefined safe
region.
Robotic systems (both active and semi-active systems)
make use of CT scans and information input during a preoperative planning session to create a sequence of instructions
to the robot defining where the bone is to be prepared or
removed. Also, the bone has to be rigidly fixed on the operating table and registered with respect to the robot, with an
invasive approach.
Recently, minimally invasive approach has lead to the
development of a mini bone-attached robotic system based
on parallel kinematics (MBARS) for joint arthroplasty and
for patellofemoral replacement in particular [20]. Despite the
reduced dimensions of the 6 degrees of freedom (DoF) robot
footprint, the attachment of the robot to the bone exposed surface requires invasive fixation and the robot working volume
is rather limited. A current drawback to most bone-mounted
robotic TKA systems, however, is that they require substantial incision of the quadriceps muscle and reflection of the
patella in order to fix the robot. With a similar approach,
Praxiteles [13] is a miniature robot with 2 motorized DoF,
precisely aligned to the cutting planes with a 2 DoF adjustment device. In mini-invasive approach, Praxiteles is laterally
fixed on the femur, if the bone is resistant enough. Since the
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robot proximity to the knee, the actuation unit has to be sterilized and replaced after a while. While the robot is moving
towards the desired pose, there is no control on the current
robot pose and no further correction, in case of misalignment,
is possible.
In order to overcome previously listed limitation, the
approach presented herein integrates a navigation system
with a robotic arm, as proposed by [1]. The study here reported
attempts providing the surgeon with a robotic assistant handling the surgical tools, removing tremor or unintentional
slipping of the tool. Pilot experiments, performed aligning
the femoral cutting mask to the goal position on sawbones
lower limb models, together with the feasibility of the system, proved its accuracy and reliability.
Materials and methods
The proposed system integrates a prototypical navigation
system (KNEELAB) [2], which uses an Hybrid Polaris (NDI,
Canada) optical localization system (sampling rate 20 Hz),
with a 6 DoFs serial robot FS-03N with D70 controller
(Kawasaki Heavy Industries) (see Table 1 for characteristics).
In order to rigidly connect the surgical instrument (femoral
distal cutting mask, Lima-Lto, Udine, Italy) to the robot
end-effector, a modular surgical tool device was designed
and developed.
Table 1 FS-03N Kawasaki robot characteristics
Type
Articulated robot
JT
Degrees of freedom
Motion
range
Maximum
speed
1
320◦
250◦ /s
2
210◦
180◦ /s
3
480◦
180◦ /s
4
720◦
600◦ /s
5
270◦
300◦ /s
6
720◦
600◦ /s
JT
Torque
Moment
of inertia
4
4.0 Nm
0.078 Kg m2
5
4.0 Nm
0.078 Kg m2
6
2.0 Nm
0.020 Kgm2
6
Working envelope and maximum speed
Wrist load capacity
Repeatability
0.03 mm
Maximum payload
2 Kg
Driving motors
Brushless AC servomotors
Mass
∼20 Kg
Int J CARS
Fig. 1 a Robot calibration scheme: A is the known transformation
matrix between C M (coordinate system of the femur mask) and C B
(coordinate system of the robot base measured by the localization system); B is the known transformation matrix between C E (coordinate
system of the robot end-effector) and C R (internal coordinate system
of the robot base); X is the unknown transformation matrix between
C M and C E ; Y is the unknown transformation matrix between C B and
C R . b Picture of the system developed. On the left the graphical user
interface is shown
Robot calibration
Rotational and translational parameters are both determined
in each minimization step, combining the metric for translation and rotation errors and bringing them to the same order
of magnitude [18].
Two Dynamic Reference Bases (DRBs), rigid bodies composed by three or more light-reflecting markers, are attached
to the robot base and to the robot end-effector. During robot
calibration transformation matrices X (transformation
between the surgical tool and the end-effector) and Y (transformation between the DRB fixed on the robot base and the
robot base internal reference frame), as shown in Fig. 1, are
computed. Transformation matrices A and B, represented in
Fig. 1 as well, are provided given by the localization system and by the direct kinematic chain from the joint-angle
readings of the robot, respectively. For N different poses of
the robot, the so called “sensor-actuator” calibration procedure (or “hand-eye calibration”, [19]) is then performed in
order to solve the system of equations, expressed by means
of homogeneous transformation matrices:
Ai−1 · X = Y · Bi i = 1, . . . , N
(1)
where 6 independent parameters for transformation matrix
X and 6 independent parameters for transformation matrix
Y are needed.
Two methods were applied to compute X and Y and their
performances were compared: the closed form solution of
the system of equation, as proposed by [3], and an iterative
approach we developed. The latter proved to be more robust
to noise, confirming the hypothesis of [6], who stated that
iterative approaches behave better than closed form solution
in presence of noise. In our approach, transformation matrices are expressed as exponential maps and the following cost
function F is minimized with respect to the 12 unknown parameters (6 DoFs for X and 6 DoFs for Y ), with Levenberg
Marquardt optimization algorithm:
(2)
F = Ai−1 · X − Y Bi i = 1, . . . , N
Patient calibration
The patient femur positions and orientations are firstly computed in order to perform anatomy calibration. A DRB is
rigidly attached to the bone (femoral reference frame). Joint
centres of rotation are automatically computed via kinematic
passive movements (hip centre) or via manual point digitisation (knee centre) in order to compute the femoral mechanical axis and the epicondylar line (in the femoral coordinate
systems). The navigation software automatically computes
the optimal distal cutting plane, perpendicular to the femoral
mechanical axis, in terms of varus/valgus, internal/external
rotation and posterior/anterior slope and cutting resection
level. Automatic tracking of possible movements of the
anatomical structure to be operated upon eliminates the need
for rigid patient fixation.
Robotic alignment and feedback correction
Given the calibration matrices X and Y , the end effector
pose in the robot internal reference frame (robot input) for
achieving the desired mask alignment is therefore computed,
with reference to the femoral DRB (Fig. 2):
Brobot = Y · C · M · X
(3)
where X and Y were determined during the calibration procedure already described, M is the current position of the limb,
expressed in the robot base DRB fixed to the robot base, and
C is the transformation matrix of the desired cutting plane
expressed in the femoral DRB.
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Calibration repeatability was also tested, repeating the
unknown transformation matrices computation in different
experimental conditions, without either perturbing the pose
of the surgical tool with respect the end-effector or displacing
the DRB on the robot base.
Experimental protocol: robot accuracy and performances
Fig. 2 Robot command determination (B) in order to reach the desired
position and orientation with the surgical tool, given current M transformation (position and orientation of the femur)
In order to further correct the alignment of the femoral
cutting mask (reducing the difference between the current
and the desired position and orientation), the transformation
matrix C is consequently updated, as shown in Fig. 3. Whenever the localization system detects a difference between the
desired position of the mask (in the femoral DRB), Ĉ, and
the current one, C, matrix Ĉ is updated in Ĉcorrected and the
robot input (B) consequently computed.
Experimental protocol: robot calibration
The robot calibration was performed 7 times moving the endeffector in 20 approximately equispaced positions in a 3D
grid within the defined working volume (0.75 m × 0.75 m ×
0.5 m). Both the end-effector position in the robot reference frame (B), read by the robot encoders, and the surgical tool DRB expressed in the robot base DRB (A), detected
by the localization system, were collected. Both the algorithm (closed form solution and iterative approach) were then
applied to the collected data (leaving one acquisition out from
each calibration session for validation purposes) and residual
errors were computed, using the metrics introduced by [19],
for each one of the acquisitions left out from the calibration.
The Root Mean Square Error (RMSE)
error
in the rotation
unit quaternion were computed as q − q̂ andthe
RMS of
the relative errors in the translation as t − t̂ / t̂, where q
and t are the quaternion and the translation parameters representing the estimated calibration matrices and q̂ and tˆ the
parameters computed with the acquisition left out.
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In order to check the overall system performances, we carried
out several tests in our laboratories using sawbones lower
limb models. After DRB fixation on the sawbone femoral
and tibial models, desired cutting plane were computed using
the navigator software developed (KNEELAB).
The overall system accuracy was tested transforming the
desired femoral cutting mask position, expressed in the
anatomical reference frame, to the robot reference frame,
giving such a command to the robot end effector, and recording the automatically reached pose. The test was performed
40 times, changing the position of the bone in the optical
localization device working volume for three experimental sessions (re-calibrating the system before each session).
Bone motions were detected and actuation signals for the
robot were generated in order to align the femoral mask in
the desired pose with respect to the femoral reference frame.
The reached pose was acquired for 10 s at 20 Hz. For each
trial, the difference between the desired surgical tool position
and the actual one was computed in terms of varus/valgus,
internal/external angles and anterior/posterior slope and
resection level RMSEs:
2
M i=1 v̂i − vi
(4)
RMSE =
M
where M = 10 s · 20 Hz = 200 samples, v̂ is the obtained
value (for positions and orientations) and v the desired one.
In order to assess robot performances in terms of alignment stability with respect to manual positioning, 4 orthopedic surgeons (not expert in navigation; subjects 1–4) were
asked to manually align the femoral cutting mask as indicated
by the navigation software and to maintain the goal position
for 10 s. Each trial was repeated 10 times, allowing the subject
to rest between trials. The same alignment was performed by
the robot 10 times and the reached position was registered
for 10 s. Errors were computed as RMSEs between the target position and orientation and the actual ones during the
registration phase. A non parametric tests (Kruskar–Wallis
p < 0.05) was then performed in order to validate the robot
alignment performances against the manual positioning.
The robot is provided with a basic control scheme which
allows it to further correct the reached position, once the
localization system detects a difference between the desired
position and the actual one. The robot transformation matrix
describing the robot end effector pose respect to the robot
Int J CARS
Fig. 3 Update of matrix C if an
error between the desired mask
position and orientation and the
actual ones, with reference to
the anatomical DRB, is detected
by the localization system
internal reference base is therefore updated in order to minimize the error between the desired position and the actual
one.
The stability provided by the robotic alignment, with
respect to the manual positioning, was also computed in terms
of data dispersion (evaluated as the difference between the
95◦ and the 5◦ percentile of the acquired data distribution),
grouping together the ten trials for each subject, resembling
a single trial lasting 100 s.
Results
Experimental protocol: robot calibration
As shown in Fig. 4, residual errors of the iterative method are
lower than those of the closed form solution (Danilidis) in all
the calibration sessions (relative translation errors less than
0.005 and norm of the differences of the quaternions less than
0.015). Danilidis performances appeared to be unacceptable
in 2 calibration sessions (#3 and #7).
Fig. 4 Residual errors (median values ±25◦ percentile 75◦ percentile)
in the robot calibration for both translation (a) and rotation (b)
Experimental protocol: robot accuracy and performances
The errors of the robot are below 0.7◦ in varus/valgus alignment (with currently accepted clinical threshold of 3◦ ), below
1.3◦ in internal/external alignment and below 2◦ in case of
anterior/posterior slope. The errors are almost uniformly distributed in the working volume considered and in the different
experimental sessions performed.
Figure 5 shows the comparison between the performances
of the manual positioning performed by the four subjects and
the robotic automatic alignment. Even if there is a residual
error always present in the actual position and orientation
of the cutting mask with respect to the desired position,
the robot behaves better with a statistically significant difference both in the translation (resection level) and in the
rotation (varus/valgus, internal/external, anterior/posterior).
The better behaviour is particularly evident as far as the internal/external and the varus/valgus values are concerned.
The feedback control allows further correction of the surgical cutting tool towards the desired position, as reflected
by Fig. 6. One can see how the adjustment of the robot endeffector transformation allows for error reduction in each
alignment parameter, except from the internal/external value
which was already low.
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Fig. 5 Accuracy (median values ± 25◦ percentile 75◦ percentile) in
the cutting mask alignment in terms of orientation (a) and position (b).
The stars indicate the statistical difference
Fig. 7 Stability in the orienting (a) and in the positioning (b) of the
cutting mask
Discussion and conclusion
Fig. 6 Residual errors median values ±25◦ percentile 75◦ percentile)
before and after the feedback correction in terms of orientation (a)
position (b) of the cutting mask
Robot stability, along the whole trial duration, was greater
with respect to each subject stability in terms of lower data
dispersion for both the position and the orientation of the
cutting mask and was less than 30% with respect to the best
performing subject. Figure 7b shows the great difficulty of all
the subjects to hold the mask in the desired anterior/posterior
alignment with respect to the varus/valgus orientation.
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This paper shows the feasibility of a robotic system for TKR,
integrated with a navigation system, in order to overcome
limitations of both these approaches. In current navigation
system, the surgeon faces some difficulties when fixing the
cutting masks to the bones with cortical pins and screws. On
the contrary, all robotic systems currently on the market or
reported in literature require the rigid fixation of the patient
limbs [8] or the rigid fixation of the robot directly on the
patient exposed bone surfaces [13,15]. Our approach, allowing the real time tracking of the bone pose with respect to the
robot, avoids any rigid fixation of the bone, thus allowing a
mini-invasive intervention. At the same time, it overcomes
the limitations of the navigation systems and offers the surgeon help in holding firmly the surgical instrument.
Our robotic system does not require any pre-operative
image since the operative plan is based on biomechanical
information acquired during the navigated surgical procedure
(image-less procedure). Also, since the robot is not directly
in contact with the patient, sterilization of robotic parts is not
required since the robotic arm could be easily draped and the
sterile surgical tool easily attached to the robot end effector.
The robot end effector was modified in order to host a wide
range of surgical instrument since the carrier depth can be
easily adapted to host different shapes.
Since the medical procedures require maximum precision
and accuracy, the robot calibration method has to be robust
to noise sources, which can occur in the operating room,
and repeatable if performed in different operation conditions.
For this reason, we chose an iterative approach to compute
the two unknown transformation matrices X (transformation
Int J CARS
from the robot end effector to DRB of the surgical tool) and Y
(from the robot internal reference frame to DRB fixed on the
robot base). Residual errors have the same order of magnitude of the tracking RMSE reported in the optical localization
system datasheet (0.35 mm). Further investigation will concern the metric for the rotation and translation errors, since
residuals are not frame invariant [18] and preconditioning is
crucial for minimization convergence.
Robots performances, tested with several alignment repetitions within the operating working volume, assessed the
robotic system reliability for different limb positions and
orientations, even if the robot operates with an open-loop
control modality. Biggest residual errors regards the anterior/posterior orientation with respect to the femoral mechanical coordinate system and are due to the non-perfectly fixed
femur sawbone blockage system. It was therefore necessary
to keep into account the update of the matrix describing the
transformation (M) of the limb in real time.
When compared with the accuracy reached by the manual
alignment, robots performances are significantly better with
regards to all the performances indices evaluated. Robotic
alignment is further improved by the feedback correction
which consider both the displacements due to the limb motion
and possible errors in the kinematic chain and updates the
robot command accordingly. Stability of the feedback control loop must be improved by properly design a controller. At
now, the real time control has not yet been implemented, but
the Kawasaki robot control provides the possibility to be programmed in real time, compensating any unwanted patient
movements. The patient limb could therefore be maintained
fixed by a non invasive cast. Localizing both the robot and
the patient positions in real time allows increasing the safety
of the surgical procedure, since unwanted collisions with the
system could be avoided.
Another crucial issue the robotic alignment tries to solve
is to assure mask stability during pins insertion in the bone
while fixating the mask for cutting. It is clearly visible that, in
order to align the femoral cutting mask to the desired position
and orientation, the subjects took advantage of the physiological anatomy of the used sawbones, in fact varus/valgus
values are more stable than the other measured parameters.
This trick would not be possible in the real operating room,
since the patients present arthritic knees where the condylar
symmetry has been compromised.
Acknowledgments Authors are thankful to Lima-Lto (Udine, Italy)
for supporting this work and to TIESSE ROBOT Spa (BS-Italy) for
providing the Robot FS-03N.
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