U.S. patent application number 14/405427 was filed with the patent office on 2015-05-28 for determining a range of motion of an artificial knee joint.
This patent application is currently assigned to BRAINLAB AG. The applicant listed for this patent is Martin Bauer, Christian Brack, Oliver Fleig, Zohar Leder. Invention is credited to Martin Bauer, Christian Brack, Oliver Fleig, Zohar Leder.
Application Number | 20150148653 14/405427 |
Document ID | / |
Family ID | 46489181 |
Filed Date | 2015-05-28 |
United States Patent
Application |
20150148653 |
Kind Code |
A1 |
Fleig; Oliver ; et
al. |
May 28, 2015 |
DETERMINING A RANGE OF MOTION OF AN ARTIFICIAL KNEE JOINT
Abstract
A data processing method for determining a range of motion of an
artificial knee joint which connects a femur and a tibia via a
medial ligament and a lateral ligament, wherein at least the femur
comprises an implant which forms a medial condyle and a lateral
condyle, the method comprising the steps of: acquiring the maximum
lengths of the lateral ligament and the medial ligament for a
particular flexion angle of the knee joint; calculating a first
virtual position between the femur and the tibia in which the
lateral condyle of the femoral implant touches the tibia and the
medial ligament is stretched to its maximum length; calculating a
maximum valgus angle of the range of motion from the first virtual
position; calculating a second virtual position between the femur
and the tibia in which the medial condyle of the femoral implant
touches the tibia and the lateral ligament is stretched to its
maximum length; and calculating a maximum varus angle of the range
of motion from the second virtual position.
Inventors: |
Fleig; Oliver; (Baldham,
DE) ; Brack; Christian; (Neusass, DE) ; Leder;
Zohar; (Munich, DE) ; Bauer; Martin; (Munich,
DE) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Fleig; Oliver
Brack; Christian
Leder; Zohar
Bauer; Martin |
Baldham
Neusass
Munich
Munich |
|
DE
DE
DE
DE |
|
|
Assignee: |
BRAINLAB AG
|
Family ID: |
46489181 |
Appl. No.: |
14/405427 |
Filed: |
June 13, 2012 |
PCT Filed: |
June 13, 2012 |
PCT NO: |
PCT/EP2012/061188 |
371 Date: |
December 4, 2014 |
Current U.S.
Class: |
600/407 ;
600/595 |
Current CPC
Class: |
A61B 2034/2055 20160201;
A61B 90/361 20160201; A61B 5/1121 20130101; A61B 2034/104 20160201;
A61B 5/4585 20130101; A61B 34/10 20160201; A61B 2090/397 20160201;
A61B 5/1072 20130101; A61B 90/39 20160201; A61B 34/20 20160201 |
Class at
Publication: |
600/407 ;
600/595 |
International
Class: |
A61B 5/11 20060101
A61B005/11; A61B 19/00 20060101 A61B019/00 |
Claims
1. A data processing method for determining a range of motion of an
artificial knee joint which connects a femur and a tibia via a
medial ligament and a lateral ligament, wherein at least the femur
comprises an implant which forms a medial condyle and a lateral
condyle, the method comprising the steps of: acquiring the maximum
lengths of the lateral ligament and the medial ligament for a
particular flexion angle of the knee joint; calculating a first
virtual position between the femur and the tibia in which the
lateral condyle of the femoral implant touches the tibia and the
medial ligament is stretched to its maximum length; calculating a
maximum valgus angle of the range of motion from the first virtual
position; calculating a second virtual position between the femur
and the tibia in which the medial condyle of the femoral implant
touches the tibia and the lateral ligament is stretched to its
maximum length; and calculating a maximum varus angle of the range
of motion from the second virtual position.
2. The method according to claim 1, wherein the length of a
ligament is defined as the distance between the point on the femur
at which the ligament connects and a plane defined with respect to
the tibia.
3. The method according to claim 2, wherein the plane which is
defined with respect to the tibia is a tibial cutting plane.
4. The method according to claim 1, wherein calculating a virtual
position includes the steps of: calculating a virtual contact
position in which both the lateral condyle and the medial condyle
of the femur touch the tibia; and rotating the femur about the
contact point between one of the condyles and the tibia until the
opposing ligament is stretched to its maximum length.
5. The method according to claim 4, wherein calculating a virtual
contact position comprises the steps of: rotating the femur until
both condyles have the same distance from the tibia; and moving the
femur translationally relative to the tibia until both the condyles
of the femur touch the tibia.
6. The method according to claim 1, wherein calculating a virtual
position includes the steps of: determining a point on the femur at
which the ligament connects for a relative position between the
femur and the tibia in which the ligament is stretched to its
maximum length; and rotating the femur about said point until the
condyle opposite said ligament touches the tibia.
7. The method according to claim 1, wherein a surface model of the
femur is used for the calculating steps.
8. The method according to claim 1, wherein the condyles of the
femur are modelled as ellipses.
9. The method according to claim 4, wherein when the rotation is
performed, the axis of rotation is parallel to a cutting plane of
the tibia and lies within the sagittal plane of the tibia.
10. The method according to claim 1, wherein the maximum length of
a ligament is calculated from a transformation matrix which
represents a relative position between the femur and the tibia in
which the ligament is stretched to its maximum length.
11. A computer program embodied on a non-transitory computer
readable medium which, when running on a computer or when loaded
onto a computer, causes the computer to determine a range of motion
of an artificial knee joint which connects a femur and a tibia via
a medical ligament and a lateral ligament, wherein at least the
femur comprises an implant which forms a medial condyle and a
lateral condyle, by performing the steps of: acquiring the maximum
lengths of the lateral ligament and the medial ligament for a
particular flexion angle of the knee joint; calculating a first
virtual position between the femur and the tibia in which the
lateral condyle of the femoral implant touches the tibia and the
medial ligament is stretched to its maximum length; calculating a
maximum valgus angle of the range of motion from the first virtual
position; calculating a second virtual position between the femur
and the tibia in which the medial condyle of the femoral implant
touches the tibia and the lateral ligament is stretched to its
maximum length; and calculating a maximum varus angle of the range
of motion from the second virtual position.
12. A computer on which the computer program according to claim 11
is running or into the memory of which the computer program is
loaded.
13. A medical navigation system comprising a computer according to
claim 12 and at least one of a stereoscopic camera and an
electromagnetic receiver, wherein the stereoscopic camera and the
electromagnetic receiver are operatively coupled to the computer.
Description
[0001] The present invention relates to a data processing method, a
computer program, a computer and a medical navigation system for
determining a range of motion of an artificial knee joint.
[0002] A knee joint connects a femur and a tibia. One
characteristic for describing the knee joint is its range of
motion. In this document, "range of motion" means the range between
the maximum varus angle and the maximum valgus angle for a
particular flexion angle between the femur and the tibia. In other
words, the range of motion describes the maximum tilt between the
femur and the tibia in the coronal plane. The range of motion can
optionally be given for a plurality of flexion angles, thus
resulting in an envelope which describes the maximum varus/valgus
angle over the range of flexion angles.
[0003] The range of motion is of particular interest in the case of
an artificial knee joint, where the range of motion refers to the
post-operative range of motion. In an artificial knee joint, at
least the femur comprises an implant at its distal end. The implant
forms a medial and a lateral condyle, thus recreating the original
bone. Typically, the proximal end of the tibia is cut off. This cut
is defined by a cutting plane. A tibial implant is typically,
though not necessarily, placed onto the tibial cut.
[0004] Where a "bone" is mentioned in this document, this may refer
to the bone itself or any implant attached (or to be attached) to
the bone. The expression "femur" therefore relates to the femur
alone or to a combination of the femur and a femoral implant, and
the expression "tibia" may refer to the tibia alone or to a
combination of the tibia and a tibial implant.
[0005] The aim of a total knee arthroplasty is to achieve a proper
functionality of the artificial knee joint. This is assessed on the
basis of the post-operative range of motion. It is therefore an
object of the present invention to determine the range of motion
before the arthroplasty is actually performed. "Determining" thus
has the meaning here of "simulating" or "predicting". From this
(predicted) post-operative range of motion, it is possible to
determine whether or not the parameters, such as the selected
implant(s) or the position or positions, are correct and will lead
to a desired result.
[0006] The present invention relates to a method for determining a
range of motion of an artificial knee joint which connects a femur
and a tibia via a medial ligament and a lateral ligament, wherein
at least the femur comprises an implant which forms a medial
condyle and a lateral condyle. The method comprises the step of
acquiring the maximum lengths of the lateral ligament and the
medial ligament for a particular flexion angle of the knee joint.
The maximum length of a ligament is the maximum length to which the
ligament can be stretched, in particular without causing damage to
the ligament.
[0007] The method also comprises the step of calculating a first
virtual position between the femur and the tibia in which the
lateral condyle of the femoral implant touches the tibia and the
medial ligament is stretched to its full length. This first virtual
position depends on the structure of the femoral implant, the
position of the femoral implant on the femur, the maximum length of
the medial ligament and the shape of the tibia (including, where
applicable, a tibial implant). The next step then relates to
calculating a maximum valgus angle of the range of motion from the
first virtual position.
[0008] The method also comprises the step of calculating a second
virtual position between the femur and the tibia in which the
medial condyle of the femoral implant touches the tibia and the
lateral ligament is stretched to its maximum length and the step of
calculating a maximum varus angle of the range of motion from the
second virtual position. These two steps are analogous to the steps
of calculating the first virtual position and the maximum valgus
angle, but relate to the knee joint being bent outwards rather than
inwards.
[0009] Preferably, the internal/external rotation, the
anterior/posterior location and the lateral location are identical
for the first and second virtual positions. The flexion angle is
necessarily identical for the first and second virtual positions.
Within this document, the term "position" means the spatial
location in up to three translational dimensions and/or the
rotational alignment in up to three rotational dimensions.
[0010] Given the maximum varus and valgus angles, the range of
motion of the artificial knee joint for the particular flexion
angle is known. The process of determining the range of motion, or
at least one of the maximum varus angle and maximum valgus angle,
of the artificial knee joint can be repeated for a plurality of
flexion angles in order to obtain an envelope of the range of
motion over a range of flexion angles.
[0011] Within the scope of the present invention, the acquiring
step does not involve manipulating a body in any way but rather
merely receiving data, in particular maximum length datasets which
represent the maximum length of the lateral ligament and the medial
ligament. The present invention can however also comprise
non-surgical procedures for measuring the maximum length.
[0012] The expression "acquiring data" encompasses in particular
the scenario (within the framework of a data processing method) in
which the data are determined by the data processing method or
program. Determining data in particular encompasses measuring
physical quantities and transforming the measured values into data,
in particular digital data, and/or computing the data by means of a
computer, in particular by computing the data within the method of
the invention. The meaning of "acquiring data" in particular also
encompasses the scenario in which the data are received or
retrieved by the data processing method or program, for example
from another program, a previous method step or a data storage
medium, in particular for further processing by the data processing
method or program. Thus, "acquiring data" can also for example mean
waiting to receive data and/or receiving the data. The received
data can for example be inputted via an interface. "Acquiring data"
can also mean that the data processing method or program performs
steps in order to (actively) receive or retrieve the data from a
data source, for instance a data storage medium (such as for
example a ROM, RAM, database, hard disc, etc.), or via the
interface (for instance, from another computer or a network). The
data can be made "ready for use" by performing an additional step
before the acquiring step. In accordance with this additional step,
the data are generated in order to be acquired. The data are in
particular detected or captured (for example, by an analytical
device). Alternatively or additionally, the data are inputted in
accordance with the additional step, for instance via interfaces.
The data generated can in particular be inputted (for instance,
into the computer). In accordance with the additional step (which
precedes the acquiring step), the data can also be provided by
performing the additional step of storing the data in a data
storage medium (such as for example a ROM, RAM, CD and/or hard
drive), such that they are ready for use within the framework of
the method or program in accordance with the invention. Thus,
"acquiring data" can also involve commanding a device to obtain
and/or provide the data to be acquired. The acquiring step in
particular does not involve an invasive step which would represent
a substantial physical interference with the body requiring
professional medical expertise to be carried out and entailing a
substantial health risk even when carried out with the required
professional care and expertise. Acquiring, in particular
determining, data in particular does not involve a surgical step
and in particular does not involve a step of treating a human or
animal body using surgery or therapy. This also applies in
particular to any steps directed to determining data. In order to
distinguish the different data used by the present method, the data
are denoted (i.e. referred to) as "XY data" and the like and are
defined by the information which they describe which is preferably
referred to as "XY information".
[0013] Within the anatomy of a knee joint, a ligament connects to
the femur at a defined point and to the tibia at a defined point.
Due to the shape of the bones, in particular the tibia, a ligament
might not be straight. It can therefore be advantageous to not
consider the actual length of the ligament, but to instead define
the length of a ligament as the distance between the point on the
femur at which the ligament connects to the femur and a plane
defined with respect to the tibia. This plane which is defined with
respect to the tibia is preferably the tibial cutting plane. This
tibial cutting plane is either a planned (virtual) cutting plane or
the plane of a cut which has been performed before the method
according to the present invention is carried out and which does
not form part of the present invention. A tibial cutting plane is
typically, though not necessarily, perpendicular to the mechanical
axis of the tibia and therefore a transverse plane.
[0014] In one embodiment of the invention, calculating a virtual
position includes the step of calculating a virtual contact
position in which both the lateral condyle and the medial condyle
of the femur touch the tibia and the step of rotating the femur
about the contact point between one of the condyles and the tibia
until the opposing ligament is stretched to its maximum length. The
opposing ligament with respect to the lateral condyle is the medial
ligament, and the opposing ligament with respect to the medial
condyle is the lateral ligament. This approach starts from a stable
virtual contact position in which both condyles are in contact with
the tibia without penetrating into the tibia. The femur is then
rotated about one of the contact points as far as the opposing
ligament permits, thus resulting in the maximum possible varus or
valgus angle.
[0015] In one embodiment, calculating the virtual contact position
comprises the step of rotating the femur until its condyles have
the same distance from the tibia (or, preferably, from the tibial
cutting plane) and the step of moving the femur translationally
relative to the tibia until both the condyles of the femur touch
the tibia, i.e. the femur and the tibia are first aligned and then
brought into contact.
[0016] As outlined above, the maximum length of a ligament is
determined from a relative position between the femur and the tibia
in which the ligament is stretched to its maximum length. Since the
feature point on the femur at which the ligament connects is known,
the position of this point, in particular relative to the tibia, is
also known or can be determined. In another embodiment of the
invention, a (first or second) virtual position is calculated by
rotating the femur about said point until the condyle opposite the
stretched ligament touches the tibia. This approach is
complementary to the previously described approach in which a
contact point is first determined and a rotation is then performed
until a ligament is fully stretched.
[0017] In one embodiment of the present invention, a surface model
of the femur and preferably also of the tibia is used for the
calculating steps. The calculating steps comprise calculating a
virtual position or a virtual contact position. A surface model of
a bone represents the three-dimensional structure of the surface of
the bone, for example as a grid model or a three-dimensional image
dataset. Within this approach, collision techniques can be used in
order to determine whether or not the femur and the tibia are in
contact. A surface model of the tibia (or the tibial implant) or a
plane defined in relation to the tibia can be used in the
calculating steps.
[0018] As an alternative to using a surface model of the femur, the
femur can also be described mathematically. The condyles of the
femur in particular can be described mathematically because they
are in contact with the tibia. The condyles of the femur are
preferably modelled by a mathematical function and preferably as
ellipses. Within this approach, geometrical methods can be used to
calculate the contact position in which at least one condyle of the
femur touches the tibia.
[0019] Not only the pivotal point but also an axis of rotation is
required in order to define a rotation. Preferably, the axis of
rotation is parallel to a cutting plane of the tibia (either a
planned cutting plane or an actual cutting plane) and lies within
the sagittal plane of the tibia. The axis of rotation is also
deemed to be parallel to the cutting plane if the axis of rotation
lies within the cutting plane. With such an axis of rotation, the
rotation does not change the internal/external angle or the flexion
angle.
[0020] In one embodiment, the maximum length of a ligament is
calculated from a transformation matrix which represents a relative
position between the femur and the tibia in which the ligament is
stretched to its maximum length. This transformation matrix
represents all the degrees of freedom (up to three rotational
and/or up to three translational degrees of freedom) of the
relative position and is for example a homogeneous 4.times.4
matrix. Homogeneous matrices are used to unify the calculations of
three-dimensional rotations and translations in a four-dimensional
space. This matrix can be determined by observing marker devices
which are attached to at least one of the bones, preferably with
one marker device attached to each bone, wherein a bone is
registered to the marker device attached to it. It should be noted
that the process of attaching a marker device to a bone or of
registering a bone to a marker device, for example using a pointer,
is not part of the present invention, but is performed before the
range of motion is determined.
[0021] It is the function of a marker to be detected by a marker
detection device (for example, a camera or an ultrasound receiver
or analytical devices such as CTs or MRIs), such that its spatial
position (i.e. its spatial location and/or alignment) can be
ascertained. The detection device is in particular part of a
navigation system. The markers can be active markers. An active
marker can for example emit electromagnetic radiation and/or waves,
wherein said radiation can be in the infrared, visible and/or
ultraviolet spectral range. The marker can also however be passive,
i.e. can for example reflect electromagnetic radiation in the
infrared, visible and/or ultraviolet spectral range or can block
x-ray radiation. To this end, the marker can be provided with a
surface which has corresponding reflective properties or can be
made of metal in order to block x-ray radiation. It is also
possible for a marker to reflect and/or emit electromagnetic
radiation and/or waves in the radio frequency range or at
ultrasound wavelengths. A marker preferably has a spherical and/or
spheroid shape and can therefore be referred to as a marker sphere;
markers can also, however, exhibit a cornered--for example,
cubic--shape.
[0022] A marker device can for example be a reference star or a
pointer or one marker or a plurality of (individual) markers which
are preferably in a predetermined spatial relationship. A marker
device comprises one, two, three or more markers, wherein if there
are two or more markers, these are in a predetermined spatial
relationship. This predetermined spatial relationship is in
particular known to a navigation system and for example stored in a
computer of the navigation system.
[0023] Merely for informational purposes, two possible approaches
for ensuring that a ligament is stretched to its maximum length are
described here. In the first approach, a varus or valgus stress is
applied to the knee joint, for example by exerting an external
lateral force on the knee, such that the ligament is fully
stretched. This is performed once with a varus stress for acquiring
a transformation matrix which represents a fully stretched lateral
ligament and once with a valgus stress for acquiring a
transformation matrix which represents a fully stretched medial
ligament. If the range of motion is to be determined for a
plurality of flexion angles, it is preferable to sample a plurality
of transformation matrices by applying a lateral (varus or valgus)
stress to the knee joint and bending the knee over a range of
flexion angles while taking the transformation matrix samples.
[0024] In a second approach, a spreading device is inserted into
the knee joint and adjusted such that both ligaments are fully
stretched. In this case, a single transformation matrix is
sufficient to calculate the maximum length of both the medial and
the lateral ligament. As in the first approach, the knee can be
bent over a range of flexion angles in order to determine a
plurality of transformation matrix samples and so obtain an
envelope of the range of motion.
[0025] The invention also relates to a program which, when running
on a computer or when loaded onto a computer, causes the computer
to perform one or more or all of the method steps described herein
and/or to a program storage medium on which the program is stored
(in particular in a non-transitory form) and/or to a computer on
which the program is running or into the memory of which the
program is loaded and/or to a signal wave, in particular a digital
signal wave, carrying information which represents the program, in
particular the aforementioned program, which in particular
comprises code means which are adapted to perform any or all of the
method steps described herein.
[0026] Within the framework of the invention, computer program
elements can be embodied by hardware and/or software (this includes
firmware, resident software, micro-code, etc.). Within the
framework of the invention, computer program elements can take the
form of a computer program product which can be embodied by a
computer-usable, in particular computer-readable data storage
medium comprising computer-usable, in particular computer-readable
program instructions, "code" or a "computer program" embodied in
said data storage medium for use on or in connection with the
instruction-executing system. Such a system can be a computer; a
computer can be a data processing device comprising means for
executing the computer program elements and/or the program in
accordance with the invention, in particular a data processing
device comprising a digital processor (central processing unit or
CPU) which executes the computer program elements and optionally a
volatile memory (in particular, a random access memory or RAM) for
storing data used for and/or produced by executing the computer
program elements. Within the framework of the present invention, a
computer-usable, in particular computer-readable data storage
medium can be any data storage medium which can include, store,
communicate, propagate or transport the program for use on or in
connection with the instruction-executing system, apparatus or
device. The computer-usable, in particular computer-readable data
storage medium can for example be, but is not limited to, an
electronic, magnetic, optical, electromagnetic, infrared or
semiconductor system, apparatus or device or a medium of
propagation such as for example the internet. The computer-usable
or computer-readable data storage medium could even for example be
paper or another suitable medium onto which the program is printed,
since the program could be electronically captured, for example by
optically scanning the paper or other suitable medium, and then
compiled, interpreted or otherwise processed in a suitable manner.
The data storage medium is preferably a non-volatile data storage
medium. The computer program product and any software and/or
hardware described here form the various means for performing the
functions of the invention in the example embodiments. The computer
and/or data processing device can in particular include a guidance
information device which includes means for outputting guidance
information. The guidance information can be outputted, for example
to a user, visually by a visual indicating means (for example, a
monitor and/or a lamp) and/or acoustically by an acoustic
indicating means (for example, a loudspeaker and/or a digital
speech output device) and/or tactilely by a tactile indicating
means (for example, a vibrating element or vibration element
incorporated into an instrument).
[0027] The method in accordance with the invention is in particular
a data processing method. The data processing method is preferably
performed using technical means, in particular a computer. The data
processing method is in particular executed by or on the computer.
The computer in particular comprises a processor and a memory in
order to process the data, in particular electronically and/or
optically. The calculating steps described are in particular
performed by a computer. Determining steps or calculating steps are
in particular steps of determining data within the framework of the
technical data processing method, in particular within the
framework of a program. A computer is in particular any kind of
data processing device, in particular electronic data processing
device. A computer can be a device which is generally thought of as
such, for example desktop PCs, notebooks, netbooks, etc., but can
also be any programmable apparatus, such as for example a mobile
phone or an embedded processor. A computer can in particular
comprise a system (network) of "sub-computers", wherein each
sub-computer represents a computer in its own right. The term
"computer" includes a cloud computer, in particular a cloud server.
The term "cloud computer" includes a cloud computer system which in
particular comprises a system of at least one cloud computer and in
particular a plurality of operatively interconnected cloud
computers such as a server farm. Such a cloud computer is
preferably connected to a wide area network such as the world wide
web (WWW) and located in a so-called cloud of computers which are
all connected to the world wide web. Such an infrastructure is used
for "cloud computing" which describes computation, software, data
access and storage services which do not require the end user to
know the physical location and/or configuration of the computer
delivering a specific service. In particular, the term "cloud" is
used as a metaphor for the internet (world wide web). In
particular, the cloud provides computing infrastructure as a
service (IaaS). The cloud computer can function as a virtual host
for an operating system and/or data processing application which is
used to execute the method of the invention. The cloud computer is
for example an elastic compute cloud (EC2) such as is provided by
Amazon Web Services.TM.. A computer in particular comprises
interfaces in order to receive or output data and/or perform an
analogue-to-digital conversion. The data are in particular data
which represent physical properties and/or are generated from
technical signals. The technical signals are in particular
generated by means of (technical) detection devices (such as for
example devices for detecting marker devices) and/or (technical)
analytical devices (such as for example devices for performing
imaging methods), wherein the technical signals are in particular
electrical or optical signals. The technical signals in particular
represent the data received or outputted by the computer.
[0028] The present invention also relates to a medical navigation
system comprising a computer as described above and at least one of
a stereoscopic camera and an electromagnetic receiver. The
stereoscopic camera or the electromagnetic receiver is used to
ascertain the position of a marker device attached to a bone. A
stereoscopic camera captures a three-dimensional image from which
the position of the marker relative to the camera can be
calculated. An electromagnetic receiver receives electromagnetic
radiation emitted from a marker device attached to a bone. The
position of the marker device relative to the electromagnetic
receiver can be calculated from the received electromagnetic
signal.
[0029] It is within the scope of the present invention to combine
one or more features of two or more embodiments, where technically
feasible, to form another embodiment. It is also within the scope
of the present invention to omit features which are not essential
to implementing the inventive concept or to replace such a feature
with another feature, in particular a feature exhibiting a similar
function.
[0030] The invention shall now be explained in more detail with
reference to the accompanying figures, which show:
[0031] FIG. 1 a medical navigation system for carrying out the
invention;
[0032] FIG. 2 a pre-operative knee joint, with the medial ligament
stretched;
[0033] FIG. 3 the knee joint of FIG. 2, with the lateral ligament
stretched;
[0034] FIG. 4 an envelope of the pre-operative range of motion;
[0035] FIG. 5 a knee joint for explaining a ligament model;
[0036] FIG. 6 the knee joint of FIG. 1 after a tibial cut, together
with a spreading device;
[0037] FIG. 7 a knee joint comprising a femoral and a tibial
implant;
[0038] FIG. 8 the knee joint of FIG. 7 with a varus stress applied
to it;
[0039] FIG. 9 the knee joint of FIG. 7 with a valgus stress applied
to it;
[0040] FIG. 10 an ellipse which is used as a model for the femoral
implant;
[0041] FIG. 11 a model for calculating the maximum varus angle;
[0042] FIG. 12 a surface model of a femoral implant; and
[0043] FIG. 13 a screenshot showing a calculated envelope of the
range of motion.
[0044] FIG. 1 shows the basic structure of a medical navigation
system 1. The medical navigation system 1 comprises a computer 2
which is connected to a display device 5, to an input device 6 and
to a stereoscopic camera 7. The display device 5 is configured to
display information acquired or calculated by the computer 2. The
input device 6, such as a keyboard, a mouse, a trackball, a touch
screen or a combination of these, is configured to receive
information and provide data corresponding to the information to
the computer 2. The computer 2 comprises a central processing unit
(CPU) 3 and a memory 4. The CPU 3 performs the method of the
present invention by processing data. The memory 4 comprises data
to be processed by the central processing unit 3 and/or program
code to be executed by the CPU 3. The stereoscopic camera 7
captures a three-dimensional image from which the position of a
marker device, and therefore the position of an object to which the
marker device is attached, can be calculated. This calculation can
be performed in the camera 7, in the CPU 3 or by both in
combination.
[0045] FIG. 2 shows a pre-operative knee joint between a femur 8
and a tibia 9. The femur 8 comprises a medial condyle 8a and a
lateral condyle 8b. When the knee joint is bent, the femoral
condyles 8a and 8b roll and/or glide on the corresponding surface
of the tibia 9. The femur 8 and the tibia 9 are connected by a
medial ligament 10 which connects to a feature point F.sub.m of the
femur 8, namely the medial epicondyle. A lateral ligament 11 which
connects the femur 8 and the tibia 9 is correspondingly connected
to another feature point F.sub.l of the femur 8, namely the lateral
epicondyle.
[0046] A marker device 12 is rigidly attached to the femur 8, and a
marker device 13 is rigidly attached to the tibia 9. The femur 8
and tibia 9 are each registered with reference to the corresponding
marker device 12 or 13, respectively, for example using a pointer
(not shown). The registration data are stored in the memory 4 of
the medical navigation system 1. Attaching a marker device to a
bone or registering a bone to a marker device is not however part
of the present invention.
[0047] In FIG. 2, the lateral condyle 8b of the femur 8 touches the
surface of the tibia 9, while the medial ligament 10 is stretched
to its maximum length. This relative position between the femur 8
and the tibia 9 represents a maximum valgus angle.
[0048] FIG. 3 shows the knee joint of FIG. 2, but with a varus
stress applied to it. The medial condyle 8a of the femur 8 is in
contact with the surface of the tibia 9, while the lateral ligament
11 is stretched to its maximum length. This relative position
between the femur 8 and the tibia 9 represents the maximum varus
angle. The difference between the maximum valgus angle and the
maximum varus angle, with all other parameters such as
internal/external rotation and flexion angle remaining unchanged,
represents the range of motion of the knee joint.
[0049] The range of motion of the knee joint is preferably
determined over a range of flexion angles. The envelope describing
the range of motion over such a range of flexion angles can be
interpolated from the maximum varus and/or valgus angles for the
individual flexion angles sampled. For example, a varus stress is
applied to the knee and the knee is bent over the range of flexion
angles. Over this range, the medical navigation system samples the
position of the marker devices 12 and 13 in order to calculate the
relative position between these marker devices and therefore also
between the femur 8 and the tibia 9. The maximum varus angle can be
calculated for each sample, which corresponds to a particular
flexion angle. A valgus stress is then correspondingly applied to
the knee and the knee is bent over the range of flexion angles. A
plurality of maximum valgus angles are calculated, which correspond
to the plurality of flexion angles. The maximum varus and valgus
angles over the range of flexion angles result in an envelope of
the range of motion of the knee joint. An example of such an
envelope is shown in FIG. 4. The horizontal axis represents the
flexion angle, while the vertical axis represents the varus
(upward) and valgus (downward) angle.
[0050] Due to the shape of the femur and the tibia, even a fully
stretched ligament (a ligament stretched to its maximum length) is
not completely straight but rather may comprise curved sections. In
order to reduce computational complexity, the ligaments 10 and 11
are preferably considered to be straight. In addition, the maximum
length of a ligament need not necessarily be defined as the maximum
distance between the points at which the ligament is connected to
the femur 8 and tibia 9, respectively. In this example embodiment,
the length of a ligament is instead defined as the distance between
the point F.sub.m or F.sub.l, respectively, and a plane P which
defines a tibial cut. The tibial cut can be an actual tibial cut
which has been made prior to performing the present invention and
which is therefore not part of the present invention, or a planned
tibial cut. The ligaments 10 and 11 are considered to be
perpendicular to the surface of the tibial cutting plane P. This is
shown in FIGS. 5a and 5b which represent a frontal view and a side
view of the knee joint, respectively.
[0051] In FIG. 5a, the maximum length of the medial ligament 10 is
denoted as D.sub.m and the maximum length of the lateral ligament
is denoted as D.sub.l. Since the ligaments are connected to the
femur and may twist for different flexion angles, the maximum
length of a ligament may depend on the flexion angle. The maximum
ligament lengths D.sub.m and D.sub.l are therefore also related to
the index i, resulting in maximum ligament lengths D.sub.m,i and
D.sub.l,i.
[0052] In this process, a plurality of relative positions between
the femur 8 and the tibia 9 are sampled. Each relative position is
represented by a transformation matrix T.sub.i, wherein 0<i<N
is used as an index for identifying the individual samples within
the plurality of samples and wherein the matrix is preferably a
4.times.4 matrix. Since the femur 8 and the tibia 9 are registered
to their respective marker devices 12 and 13, the positions of the
points F.sub.m and F.sub.l relative to the tibia 9 are also known
or can be calculated.
[0053] FIG. 6 shows an alternative approach for determining the
maximum ligament lengths D.sub.m and D.sub.l. After the tibial cut
has been performed, a spreading device 14 is inserted between the
femur 8 and the tibia 9 and adjusted to fully stretch both the
medial ligament 10 and the lateral ligament 11 at the same time.
The maximum lengths can then be calculated from the relative
position between the femur 8 and the tibia 9. This process can
likewise be performed for a particular flexion angle or also over a
range of flexion angles.
[0054] FIG. 7 shows a post-operative knee joint between the femur
8, which comprises a femoral implant 8c, and the tibia 9 which
comprises a tibial implant 9a. The tibial implant 9a is also
referred to as an insert or tray and can have the shape of a disc.
The femoral implant 8c forms the medial condyle 8a and the lateral
condyle 8b. In order to reduce computational complexity, the
surface of the tibial implant 9a facing the femur 8 is considered
to be planar. It should be noted that this post-operative knee
joint is a virtual knee joint which is simulated before
arthroplasty is actually completed.
[0055] The post-operative situation assumes a particular choice for
the femoral implant 8c and tibial implant 9a and a particular
position of the femoral implant 8c on the femur 8 and the tibial
implant 9a on the tibia 9. The purpose of the present invention is
to calculate the range of motion of the post-operative artificial
knee joint if these assumptions were actually implemented. In view
of the calculated range of motion, it is possible to amend one or
more of these assumptions until a desired range of motion
results.
[0056] For each sample, the distances D.sub.m,i and D.sub.l,i are
calculated using the following equations:
d.sub.m,i=|T.sub.i.times.F.sub.m,i-P|
d.sub.l,i=|T.sub.i.times.F.sub.l,i-P|
The product of the transformation matrix T.sub.i and the position
F.sub.m,i or F.sub.l,i of the feature points F.sub.m and F.sub.l,
respectively, transforms the corresponding point into the
co-ordinate system of the tibia 9. The length of a ligament is then
the shortest signed distance between this transformed point and the
plane P of the tibial cut.
[0057] FIG. 8 shows a calculated relative position between the
femur 8 and the tibia 9 for a virtual post-operative artificial
knee joint in which the medial condyle 8a of the femur 8 (more
specifically, the femoral implant 8c which is not explicitly
designated in FIGS. 8 and 9) is in contact with the tibial implant
9a, and the lateral ligament 11 is stretched to its maximum length
which has previously been calculated as D.sub.l. This relative
position represents the maximum varus angle for the given femoral
and tibial implants and the particular flexion angle. FIG. 9
correspondingly shows a relative position between the femur 8 and
the tibia 9 in which the lateral condyle 11 of the femur 8 touches
the tibia 9, and the medial ligament 10 is stretched to its maximum
length D.sub.m for the particular flexion angle. The other
parameters of the relative position, in particular the
internal/external rotation, the anterior/posterior position and the
lateral position are the same as those indicated by the
corresponding transformation matrix T.sub.i which is used to
determine both the maximum varus and maximum valgus angles.
[0058] The maximum varus and/or valgus angles are calculated for
each recorded transformation matrix T.sub.i. This results in a
calculated, predicted post-operative envelope for the range of
motion, as shown in the screenshot in FIG. 13 which is from a
computer program which is running on the computer 2 and
implementing the present invention. If the envelope of the range of
motion is satisfactory, then the implants and the implant positions
used to predict this range of motion can be implemented in actual
arthroplasty, which again is not itself part of the present
invention. As can be seen from the screenshot in FIG. 13, the
parameters of the implants can be amended in order to predict the
range of motion for different sets of parameters.
[0059] The relative positions shown in FIGS. 8 and 9 can be
calculated in a number of ways. Two examples of possible approaches
shall be described in more detail in the following.
[0060] In the first approach, the condyles of the femoral implant
8c are modelled as ellipses, as shown in FIGS. 10 and 11. The two
ellipses representing the condyles are spaced apart by a distance
d.sub.c. The sizes of the ellipses and the distance d.sub.c depend
on the femoral implant 8c selected.
[0061] In this first approach, the two ellipses representing the
condyles 8a, 8b are first brought into contact with the surface of
the tibia 9. For this purpose, the minimum distances between the
two ellipses and the cutting plane P of the tibia (or the surface
of the tibia in general) are calculated, as shown in the side view
in FIG. 10. These two distances are then used to calculate the
angle by which the femur 8, including the implant 8c, has to be
rotated and the distance by which the femur 8 and the tibia 9 have
to be moved translationally relative to each other in order for the
two ellipses to touch the surface of the tibia 9. For this purpose,
the axis of rotation and the translational direction have to be
known. In one implementation example, they are calculated as
follows.
[0062] The axis of rotation is defined by a vector r.sub.impl which
is calculated as
{right arrow over (r.sub.impl)}={right arrow over
(n.sub.sp)}.times.({right arrow over
(t.sub.cut.sub.--.sub.ant)}.times.{right arrow over
(n.sub.sp)})
where t.sub.cut.sub.--.sub.ant is a vector pointing in the anterior
direction of the tibia 9 and lying in the cutting plane P and
n.sub.sp is a vector pointing to the right-hand side of the femur
8. The vector n.sub.sp is calculated as
{right arrow over (n.sub.sp)}={right arrow over
(f.sub.ant)}.times.{right arrow over (f.sub.mech)}
where f.sub.ant is a vector pointing in the anterior direction of
the femur and f.sub.mech is a vector corresponding to the
mechanical axis of the femur. The vector r.sub.impl thus represents
the line forming the intersection between the femoral sagittal
plane and the tibial cutting plane P.
[0063] The vector
{right arrow over (f.sub.up)}={right arrow over
(f.sub.impl.sub.--.sub.right)}.times.{right arrow over
(r.sub.impl)}
is then used together with the vector
{right arrow over (f.sub.impl.sub.--.sub.right)}=M{right arrow over
(f.sub.right)}
to calculate the angle by which the femoral implant has to be
rotated about the line defined by r.sub.impl as
.beta. = cos - 1 ( f up .fwdarw. n tibia _ cut .fwdarw. f up
.fwdarw. n tibia _ cut .fwdarw. ) . ##EQU00001##
[0064] The index i has been omitted from the vectors in order to
improve the legibility of the formulae. The vector
f.sub.impl.sub.--.sub.right points to the right-hand side of the
femoral implant 8c and is calculated from the vector f.sub.right
which points to the right-hand side of the femur 8 and the
transformation matrix M which represents the position of the
femoral implant 8c relative to the femur 8. The vector
n.sub.tibia.sub.--.sub.cut represents the normal vector to the
tibial cutting plane P. A rotation matrix R.sub.i can be defined in
terms of .beta..sub.i and r.sub.impl,i and represents the rotation
needed in order to move the femur 8 into a position relative to the
tibia 9 in which its condyles 8a and 8b are equally distant from
the surface of the tibia 9.
[0065] The distance g by which the femur 8 has to be moved
translationally relative to the tibia 9 is given by the shortest
distance between the ellipse which represents the condyle and the
surface of the tibia 9, as shown in FIG. 10. This is a merely
two-dimensional problem. The point E on the ellipse which is
nearest to the tibia 9 must have a tangent which is parallel to the
surface of the tibia 9 (which is modelled as being planar). Reduced
to two dimensions, this plane which defines the tibial surface
becomes a line. The desired distance g is the distance between this
line and the tangent to the ellipse, which is parallel to said
line. The tangent can be calculated from the standard equation for
an ellipse.
[0066] As can be seen from the schematic drawing in FIG. 11, the
contact point of one ellipse--in this case, the medial ellipse--is
fixed and used as the centre of rotation. The lateral ligament 11
and two ellipses representing the femoral implant 8c are indicated
in their starting position by continuous lines. In its starting
position, the lateral ligament 11 is not fully stretched. The femur
8 is then rotated about its contact point with the tibia 9 such
that the opposing ligament--in FIG. 11, the lateral ligament 11--is
stretched to its maximum length. The lateral ligament 11 and the
two ellipses are indicated in this position by dotted lines. The
rotation is indicated by a curved arrow. The rotation moves the
feature point F.sub.l upwards and to the left. The angle .alpha.,
which represents the maximum varus angle, is then calculated using
simple trigonometric functions. This process is then repeated, with
the other ellipse remaining in contact with the tibia 9 while the
femur 8 is rotated until the opposing medial ligament 10 is fully
stretched.
[0067] Alternatively, the condyles are not modelled as ellipses but
are rather represented by the actual shape of the femoral implant,
as shown in FIG. 12. In this case, a suitable mathematical
description of the implant surface will most likely not be
available. Instead of calculating the extent of the relative
rotational and translational movement between the femur 8 and the
tibia 9, an iterative approach can be applied. The relative
position between the femur 8 and the tibia 9 is first altered by a
translational movement along n.sub.sp until one of the condyles
touches the surface of the tibia 9. The femur 8 is then rotated
about the contact point and the vector r.sub.impl until the other
condyle touches the tibia. This process can be repeated if the
first condyle is no longer touching the surface of the tibia after
the rotation. Collision detecting techniques are preferably applied
in order to detect whether or not a condyle of the femoral implant
8c is in contact with the tibia 9 (or tibial implant 9a).
[0068] In a second general approach, the two condyles of the femur
8 are not initially brought into contact with the tibia 9, as in
the first approach. Instead, the feature point F.sub.m or F.sub.l
at which a ligament connects to the femur 8 is used as the centre
of rotation for the femur 8. The position of the point F.sub.m
relative to the tibia 9 as shown in FIG. 2 is for example fixed as
the centre of rotation, because the post-operative position of the
point F.sub.m relative to the tibia 9 is assumed to be equal to the
pre-operative relative position. The femur is then rotated about
this point, about the vector r.sub.impl which is calculated as in
the first approach, until the opposite condyle is in contact with
the tibia 9. Thus, if the point F.sub.m is for example fixed as the
centre of rotation, then the femur 8 is rotated about this point
until the lateral condyle 8b touches the tibia 9. Whether or not
the femur and the tibia are touching can be determined using known
collision detecting techniques.
[0069] It should again be noted that the present invention does not
comprise any surgical steps but rather merely relates to simulating
the predicted outcome of an arthroplasty performed using the
assumed parameters for the implant(s).
* * * * *