OPTIMIZING ALIGNMENT OF AN APPENDICULAR
Related Applications
This Application claims priority to U.S. Provisional Application No. 60/120,706, filed 16 February
1999, which is incorporated herein by reference.
Field of the Invention
The present invention concerns a process for determining the pivot center of proximal and
intermediary articulations, also known as joints, of an appendicular skeleton.
Background of the Invention
The appendicular skeleton comprises arms and legs and includes the proximal articulations
of those limbs (i.e., hips and shoulders) and the intermediary articulations (i.e., elbows or knees)
and distal articulations (wrists or ankles). The articulations are connected by proximal bone
segments (humerus for arms or femur for legs) and distal bone segments (radius for arms or tibia
for legs).
It is common for appendicular joints to be replaced with prosthetic devices. During such
replacements, it is very important that the joint be properly aligned - a misaligned bone can shorten
the lifespan of the replacement joint considerably, for example, as much as by 20% to 50% of the
time. Proper alignment using traditional methods requires a significant amount of skill and
experience.
During a surgery involving part of the appendicular skeleton, it is important for proper
alignment to know the pivot centers of the proximal and intermediary articulations of the skeleton.
In fact, when it is necessary to cut the proximal bone segment, for instance, it is important to make
the cut exactly at a right angle with respect to the plane connecting these two articulations, or pivot
centers. It is also useful to optimize pivot centers of articulations for physical therapy applications,
and for sports medicine applications. Determining the pivot point can also be used as a diagnostic
tool for tracking the progression of certain bone diseases.
In the case of the hip, for instance, the pivot center corresponds to the articulation center of
the hip, which is spherical. This is not the case with a non-spherical articulation, such as, for
example, the knee. The pivot center of the knee, for instance, corresponds to the average of a range
of points (the "cloud point") formed by the pivot centers of this non-spherical articulation during
the relative movement of the bone segments surrounding it.
Initially, articulations were positioned by observation. This method resulted in a relatively
high failure rate, leading to the development of mechanically assisted methods, such as those
reported in the prior art, such as, for instance, the method disclosed by F. Leitner, F. Picard, R.
Minfelde et al., Computer-Assisted Surgical Total Replacement of the Knee (published in the
Proceedings of the First Joint Conference, Computer Vision, Virtual Reality and Robotics in
Medicine, Medical Robotics and Computer Assisted Surgery (1997); and as published by S.L.
Delp, et al., Computer Assisted Knee Replacement, Clinical Orthopedics and Related Research,
354, 49-56 (1998). Throughout these methods, a set of data are generated which, when analyzed,
provides assistance in locating the ideal pivot point. Prior art techniques for generating data include
preoperative imagery, where the pivot point is determined prior to surgery. This method, however,
is somewhat complicated and requires sophisticated imaging equipment and technicians, and
sometimes engineers. In general, traditional techniques used to generate these data remain
somewhat rudimentary, and inaccuracies in these data generation techniques create inaccuracies in
the pivot points generated even by computer-assisted techniques.
One improvement to traditional pre-surgical determinations of the pivot point utilizes at
least four individual markers (optical-type, super-resonant, magnetic or inertial) which are
surgically screwed into the bones, and each of which each is associated to a means of detection,
such as a camera connected to a computer. This allows the medical staff to monitor the positioning
and orientation of each marker in real time during a surgical procedure. For purposes of this
invention, positioning is the x, y and z cartesian coordinates of the marker, and orientation is the
polar coordinates of this marker, expressed at the point of reference point.
When using this prior art method on a leg, for instance, the first two markers are affixed on
either side of the knee, at the extremities toward the tibia and the femur. Two additional markers
are affixed on the pelvis and a foot bone, respectively. The patient is placed horizontally, with his
femur raised and restrained from movement, and then the tibia is moved toward the motionless
femur. A computer is used during this movement to determine the maximal invariancy point,
which corresponds to the pivot center of the knee articulation. The pivot center of the hip
articulation may be determined in the same manner by moving the femur toward the trunk, and the
pivot center of the ankle articulation by moving the foot toward the tibia.
This solution has certain drawbacks. It requires a large number of markers, and since each
marker must be attached to the corresponding bone, it is necessary to affix with screws at least
some of these markers to the bone in question. These affixing procedures are time-consuming and
can be rather traumatizing for the patient. Also, many methods of moving the body to collect data
points for determining the pivot point are used, with differing outcomes. Lastly, differences in
bone structure between patients make standardization of traditional techniques for locating optimal
pivot points difficult.
Thus, it would be useful to have an optimized positioning method for use with computer
assisted orthopedic surgery, which would provide accurately and reliably provide data for
generating an optimal articulation pivot point, and which would be faster and less traumatizing for
the patient than traditional methods of determining an optimal pivot point. It would also be
advantageous to develop a standard technique which could be used for any bone structure and
which could account for a wide variety of bone deformities.
The present invention overcomes these drawbacks, in that it provides a means for
determining the pivot center of an articulation using only a single marker.
Summary of the Invention
It is an object of the present invention to provide a method for optimizing the alignment of
orthopedic prosthetic devices.
It is a further object of the invention to provide a method of generating data points from
physical movements for use in determining the optimal pivot point of a bone articulation that is
more accurate and reproduceable than prior art methods.
It is yet another object of the invention to provide a method for determining an optimal
pivot point that is fast and less traumatic to the patient as compared to prior art methods.
It is another object of the invention to provide an optimal movement sequence for
generating data points which can be used to reliably and accurately locate optimal pivot points of
articulations.
It is also an object of the invention to locate an optimal pivot point using a single marker.
In this regard, the invention is a method for determining pivot centers for the proximal and
intermediary articulations of an appendicular skeleton, for use during computer-assisted orthopedic
surgery or other diagnostic or rehabilitative treatments. The novel method of the invention requires
the affixation of a single marker to the bone, which may be affixed by screws or by less traumatic
methods such as but not limited to external affixation devices such as elastic bands. Pivot centers
for proximal and intermediary articulations may be determined through the use of at least one
marker placed between intermediary and distal joints, and pivot centers for intermediary and distal
articulations may be determined through the use of at least one marker placed over or at least near
the distal joint.
Once the marker is affixed to the bone, the pivot center is determined using rotational
movements of the appendicular skeleton in accordance with the sequence of the invention. The
sequence of the invention utilizes at least the first and second rotations of the proximal bone
segment around the proximal articulation in accordance with the first and second axes, sensibly
orthogonal to each other, and at least the third and fourth rotations of the distal bone segment
around the intermediary articulation, along the third and fourth axes, sensibly orthogonal to each
other.
During the movement sequence, data points on the position and orientation of the marker
are collected on a continuous basis from a predetermined point of reference, the localizer. Next,
from among the resulting data collected on a continuous basis, a minimal number of distinct
postures of the skeleton during the movement sequence are selected, and to each posture is ascribed
a value representing the position and orientation of the marker in the predetermined point of
reference. Next, from all of the values the coordinates of the optimal pivot point (also called
rotational center) of the proximal and intermediary articulations is determined. Once the optimal
pivot points are determined, the optimal alignment of the articulations are possible. "Patient" as
used herein denotes legged mammals, most particularly people although it is contemplated and
within the scope of the present invention that the methods disclosed herein would work with other
legged mammals as well.
Brief Description of the Drawings
The invention shall be described below with reference to the attached drawings, provided
solely as non-limited examples, in which:
Figure 1 is a perspective view diagram of a patient in a supine position, showing three
planes and three physiological axes connected to the patient;
Figure 2 is a side perspective view showing a patient whose appendicular skeleton is
undergoing a first movement from a sequence of the procedure in accordance with the invention;
Figures 3 is a side perspective view of the appendicular skeleton of a patient that is
undergoing a first movement from a sequence of the procedure in accordance with the invention;
Figure 4 is a top perspective view of the appendicular skeleton of a patient that is
undergoing a first movement from a sequence of the procedure in accordance with the invention;
and
Figure 5 is a side perspective view showing a patient whose appendicular skeleton is
undergoing a second movement from a sequence of the procedure in accordance with the invention.
Figure 6 is a schematic representation of the hardware required for determining the optimal
pivot point of an articulation in accordance with the method of the invention.
Description of the Invention
Figure 1 represents, in a simplified drawing, a patient lying down, with a complete
designation in reference 2. This patient has a trunk 4, two upper appendicular skeletons 6 and two
lower appendicular skeletons 8.
The position of a patient is defined by three physiological planes, with three corresponding
physiological axes. The frontal plane, designated by reference 10, is associated a beam of frontal
axes 12 which are perpendicular to the frontal plane 10 and which therefore extend from the rear to
the front of the patient.
The sagittal plane 14 is the median plane of the patient, extending from the medial axis to
the lateral side of the patient. A beam of sagittal axes 16, perpendicular to sagittal plane 14, are
associated with the sagittal plane.
Axial plane 18 is the horizontal plane perpendicular to the frontal plane 12 as well as the
sagittal plane 14, that is going through the cranium of the patient. A beam of axes, called axial 20,
is associated with the axial plane 18, and perpendicular to it.
Figures 2 to 4 show the patient in Figure 1 undergoing a first movement in the
determination procedure described herein, in accordance with the methods of the invention.
The lower appendicular skeleton 8 of the patient 2 includes a proximal articulation 22, i.e.
the articulation of the hip connecting skeleton 8 to trunk 4, a proximal bone segment 24, i.e. femur,
and intermediary articulation 26, i.e. the knee and a distal bone segment 28, i.e. tibia, articulated on
the femur 24, by the knee 26. The distal segment 28 ends with a distal articulation 30, i.e. the ankle
to which the foot 32 is connected.
The procedure in accordance with the invention simultaneously determines the pivot center
of multiple articulations in an appendicular skeleton, such as, for instance, the hip 22 and knee 26
articulations. The preferred embodiment illustrated here will be the hip and knee, although the
principles of the invention apply similarly to any set of articulations within the appendicular
skeleton, such as but not limited to the articulations of the arm, and the knee-shoulder articulations.
Each of these other articulations are also embodiments of the invention, and the same principles are
used to describe these embodiments as set forth below.
In the illustrated preferred embodiment, hip and knee articulations, an optical marker 34 is
placed preferably on the patient's tibia 28. In all embodiments, it is preferable that the marker be
placed between an intermediary articulation and a distal articulation. The invention provides an
advantage over the prior art in that markers may be affixed without the use of screws, although
traditional methods of using screws to affix markers to the bone may be used. Using the method of
the invention, markers may be affixed to a bone, such as a tibia, with glue or an elastic band, or any
other suitable means that now exists or may be developed. The marker can be affixed anywhere
along the bone, in the case of the illustrated embodiment, the tibia 28, and is most optimally located
where the bone is very near to the skin of the limb.
The marker 34 includes transmitters 40, in this embodiment most optimally at least three
transmitters, connected to a receiver, or locator 42 (such as but not limited to a camera), in contact
with a processing device 44 such as but not limited to a computer, as shown in Figure 6. The
transmitters 40 may be infrared diodes, for example, or any other marker material suitable for use
with the invention, including but not limited to ultrasound or accelerometer markers, and the
receivers 42 are adapted to receive signals from the transmitters 40. The marker 34, locator 42, and
processing device 44 may be any commercially available system, such as that marketed by the
company NORTHERN DIGITAL under the trademark OPTOTRAK, as illustrated in Figure 6.
The receiver insures the locating, on a continuous basis, of the position and orientation of the
marker at the point of reference of this receiver. The computer connected to the locator allows
measurement and data collection of distinct values indicative of the positions and orientations of the
marker.
The starting position of the first movement to which patient 2 is subjected to determines the
pivot center of the hip 22 and knee 26 articulations, as illustrated in Figures 3 and 4. In this
position, seen from the side (Figure 3), the patient's trunk 4 is horizontal, the femur is raised at an
angle α of about 60° from the axial axis 20a going from the articulation of the hip 22. The main
axis 36 of the tibia 28 is inclined with regard to the main axis 38 of the femur 24, at an angle β of
about 90° in that resting position. Moreover, given the above (figure 4), the femur 24 forms an
angle γ with regard to axis 20a of about -10°.
The first movement of the sequence in accordance with the invention requires a moving,
such as but not limited to a pedaling, of the appendicular skeleton 8 combined with a rotation of the
skeleton around the axial axis and plane 20a going through the articulation of the hip 22. The
articulation of the ankle 30, therefore, is subjected to a movement in the shape of an H helix.
During the pedaling movement, angle α varies alternatingly between around 40° and 60°,
angle β varies alternately between around 20° and 120°, while angle γ increases continuously
from about -10° to 20°. The diameter D of the helix along which the ankle 30 moves is about 30
cm. During this movement, the number of revolutions of the helix is between about 5 and 50,
although fewer or more revolutions may be used.
This first movement described with references in figures 2 to 4 prompts three rotations, i.e.
a rotation of the femur 24 around the frontal axis and plane 12a going through the hip 22, a rotation
of this femur around the sagittal axis and plane 16a going through the hip 22, as well as a rotation
of the tibia around the sagittal axis and plane 16b going through the articulation of the knee 26.
During this movement, the locator enables finding the position and orientation of the
marker. We select distinct postures through the computer, i.e. 150 in the example in question. This
selection is run at regular time periods during this movement. Six values are designated for each
posture, i.e. three cartesian coordinates and three polar coordinates of the marker for the point of
reference determined by the locator. This first movement, therefore, results in 900 data points
obtained.
The sequence in accordance with the invention includes a second movement shown in
figure 5. To carry out this second movement we first place the patient in the position shown with
full lines in figures 3 and 4, i.e. femur raised at an angle of 60° from the horizontal plane, and the
tibia at a right angle to this femur. Then, while keeping the femur stationary, we pivot the tibia 28
around its main axis and plane 36, at the dimension of angle γ of about 15°. This rotation
movement of the tibia around its axis and plane is done by exercising a continuous pressure on the
extremity of the foot 32, next to the ankle 30, in the direction of the knee 26. This second
movement is most optimally practiced for 5 to 50 repetitions, back and forth, although more
repetitions may be performed.
During this second movement, we select 50 successive positions of the appendicular
skeleton, and use the transmitter, receiver and the processor to collect approximately 300 data
points for the position and orientation of the marker 34, although more or fewer values may be
obtained and function with the invention. For the embodiment described here, the entire sequence,
including the first and second movements, results in approximately 1,200 known data points, or
values, collected which correspond to three cartesian coordinates and three polar coordinates of the
marker at the reference point of the locator.
During the sequence, the trunk of the patient must remain relatively immobile within the
point of reference of the locator. Light movements of less than 2 mm and rotations of less than 1°
are, however, acceptable as long as their occurrences can be deemed as random.
Seven unknowns are consistent for the 200 samples taken throughout the sequence. These
are, first of all, the three cartesian coordinates of the pivot center of the hip, at the reference point of
the locator of the three cartesian coordinates of the pivot center of the knee articulation, at the actual
reference point of the marker, as well as distance D separating these two pivot centers.
For j varying from 1 to 200, corresponding to the number of sample positions, we note T,d
(j) of the homogeneous matrix known to have been taken from the three cartesian coordinates and
the three polar coordinates of the distal marker (d) measured for each sampling at the point of
reference of the localizer (1).
We also note the P^ position, i.e. the three cartesian coordinates at the distal point of
reference (d) of the intermediary articulation (i).
We also note the P,p position, i.e. the three cartesian coordinates at the point of reference of
the locator (1) of the pivot center of the proximal articulation (p).
Finally, we note the P,, position, i.e. the three cartesian coordinates at the point of reference
of the locator (1) of the pivot center of the intermediary articulation (i).
By definition, the distance D separating the two pivot centers, proximal and intermediary,
respectively, corresponds to the standard of the vector shaped by these centers. We can, therefore,
note:
D = ... P„ - P,p -
Pip is an unknown constant during the 200 samples, which is not the case of P,,. But, by definition,
we have Ph = Tld . Pdl. However, T,d is known, and Pd, does not vary for each of the 200 positions.
We therefore have, for 1 = 1 to 200
This leads to obtaining a system of 200 equations with 7 unknowns, which is highly linear
and, therefore, does not allow, a priori, solution to be obtained. We, therefore, reformulate this
system of equations by adding, for each one of them, either a j included between 1 and 200, or a
secondary unknown called εj corresponding to an error term. We then obtain a system of 200
equations with 207 unknowns.
This system allows for an infinite number of solutions; the invention uses the one for which
the sum of the squares of the εj error values is minimal. This solution is obtained, for example, by
means of a classical-type minimizing algorithm for the smallest squares. We can, for example, use
the commonly known LEVENBERG-MARQUARDT algorithm as well as an algorithm applying
a gradient descent at a regular pace, or any other suitable algorithm now known or developed in the
future.
For the embodiment described here, the use of such a least squares algorithm is preferable.
However, it is also possible to solve the system of 200 equations with 7 unknowns without using an
error value. In this case, we cut these 200 equations into as many sub-systems with 7 equations, so
as to form a partition of 7-equation sub-systems with 7 unknowns, each one allowing a partial
solution. We then obtain a number of partial solutions corresponding to the number of the partition
sub-system. We then keep a final calculated solution, i.e. by arithmetic averages of the partial
solutions. It is anticipated that the method of the invention will generate data which may be
analyzed by any suitable commercially available program.
Once the cartesian coordinates of the pivot centers of the hip and knee articulations are
established, the computer determines the axis connecting these pivot centers. The surgeon then
proceeds with cutting the femur at a 90° angle from this axis.
The invention has been described as a sequence which prompts a first movement generating
three different rotations, then a second movement generating a unique rotation, for a total of four
rotations. Each of the 150 positions sampled thus allows to obtain data regarding the three different
rotations.
It is also possible to prompt a single movement during which the four rotations mentioned
above are activated simultaneously. In this case, a smaller number of sampled positions shall be
required, given that each position reveals the four simultaneous positions.
It is also possible to move the patient's appendicular skeleton in a sequence prompting three,
even four successive movements, each involving one or two rotations of either bone segment
around the corresponding articulation. In this case, if we wish to reach the same degree of precision
as in the example described above, it is necessary to proceed with a higher number of samples than
in that example.
In the described embodiment, for example, we use an optical-type marker. However, we
can use any other marker, such as a magnetic or inertial marker combined with a tracking device
which reports the position and orientation of this marker at a determined point of reference.
It is also possible to determine the pivot centers of the elbow and shoulder articulations, by
moving the upper appendicular skeleton in accordance with a sequence involving at least two
rotations of the humerus. and at least two rotations of the radius.
The procedure in accordance with the invention is preferable to traditional techniques, as it
involves just one marker. Moreover, given the nature of the distal bone segment to which the
marker is attached, it is not necessary to use screws. Gluing or attaching the marker on this bone
segment by means of an elastic band has been found to be sufficient.
The sequence making use of two successive movements involving three different rotations,
respectively, and then a sole rotation, is preferable as long as it is simple to undertaken and provides
sufficient data to avoid a high number of samples.
It is understood that for example purposes a single representative embodiment is described
above, although the invention may be used with many other embodiments, including all
appendicular articulations. It should be understood that various changes and modifications to the
embodiment described herein will be apparent to those skilled in the art. Such changes and
modifications can be made without departing from the spirit and scope of the present invention and
without diminishing its attendant advantages. It is therefore intended that such changes and
modifications be within the scope of the claims.