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.

Claims

1-18. (canceled)

19. A method to assist in knee arthroplasty, the method comprising: determining for one or more flexion angles of a knee joint of a patient: a first relative position of a tibia and a femur of the patient when the knee joint is under varus stress; and a second relative position of the tibia and the femur when the knee joint is under valgus stress; determining a range of motion including the first and second relative positions; and outputting to a user the range of motion for each of the one or more flexion angles.

20. The method of claim 19, wherein the first and second relative positions are determined subsequent to a cut of a proximal end of the tibia and an insertion of a spreading device between the femur and the tibia.

21. The method of claim 19, wherein the first relative position represents a maximum varus angle and the second relative position represents a maximum valgus angle.

22. The method of claim 19, further comprising: generating, for each of the one or more flexion angles, a first length of a lateral ligament and a second length of a medial ligament based on the first and second relative positions; generating, for each of the one or more flexion angles, a maximum varus angle and a maximum valgus angle for an implant based on the first and second lengths; and determining a range of motion envelope from the maximum varus and valgus angles.

23. The method of claim 22, further comprising measuring the first and second lengths perpendicular to a tibial cutting plane.

24. The method of claim 22, further comprising determining at least one of the first length or the second length based on a distance between a point on the femur and a tibial cutting plane.

25. The method of claim 19, further comprising generating one or more transformation matrices representing one or more of the first or second relative positions.

26. The method of claim 19, further comprising: receiving at least one position or size parameter for an implant; and modifying the range of motion based on the position or size parameter.

27. A non-transitory computer readable medium on which is stored software which, when implemented by a processor, causes the processor to perform steps of: determining for one or more flexion angles of a knee joint of a patient: a first relative position of a tibia and a femur of the patient when the knee joint is under varus stress; and a second relative position of the tibia and the femur when the knee joint is under valgus stress; determining a range of motion including the first and second relative positions; and outputting to a user the range of motion for each of the one or more flexion angles.

28. The non-transitory computer readable medium of claim 27, wherein the first and second relative positions are further determined when lateral and medial ligaments of the knee joint are stretched to their maximum lengths, respectively.

29. The non-transitory computer readable medium of claim 27, wherein the first and second relative positions represent maximum varus and valgus angles, respectively, and wherein the software, when executed by the processor, further causes the processor to perform a step of determining the maximum varus and valgus angles using a surface model of the femur in which at least one of a lateral condyle or a medial condyle of the femur is modelled.

30. The non-transitory computer readable medium of claim 27, wherein the software, when executed by the processor, further causes the processor to perform a step of generating a first length of the lateral ligament or a second length of the medial ligament from one or more transformation matrices.

31. The non-transitory computer readable medium of claim 30, wherein the software, when executed by the processor, further causes the processor to perform a step of generating the first and second lengths in relation to a plane through a resected surface of the tibia.

32. The non-transitory computer readable medium of claim 27, wherein the software, when executed by the processor, further causes the processor to perform steps of: receiving input to amend a position or size parameter for an implant based on the range of motion; and outputting to the user a modified range of motion determined based upon the input.

33. The non-transitory computer readable medium of claim 27, wherein the software, when executed by the processor, further causes the processor to perform a step of determining the range of motion further based upon at least one of a position or a size of at least one of a femoral implant or a tibial implant.

34. The non-transitory computer readable medium of claim 27, wherein the first and second relative positions are determined after an insertion of a spreading device between the femur and a resected surface of the tibia.

35. A system to assist in knee arthroplasty, the system comprising: a device that determines for one or more flexion angles of a knee joint of a patient: a first relative position of a tibia and a femur of the patient when the knee joint is under varus stress; and a second relative position of the tibia and the femur when the knee joint is under valgus stress; a processor that determines a range of motion including the first and second relative positions; and a display which displays the range of motion for each of the one or more flexion angles.

36. The system of claim 35, wherein the device further determines the first and second relative positions when lateral and medial ligaments of the knee joint are stretched to their maximum lengths, respectively.

37. The system of claim 35, wherein the device further determines first and second maximum lengths of lateral and medial ligaments, respectively, perpendicular to a tibial cutting plane.

38. The system of claim 35, wherein the processor further determines the range of motion based on a difference between the first and second relative positions.

39. The system of claim 35, wherein the device determines the first and second relative positions after an insertion of a spreading device between the femur and a resected surface of a cutting plane of the tibia.

40. The system of claim 35, wherein the one or more flexion angles comprise a plurality of flexion angles and the processor further determines a range of motion envelope.

41. The system of claim 40, wherein the processor further determines the range of motion envelope based on one or more of a first position of a femoral implant relative to the femur or a second position of a tibial implant relative to the tibia.

42. The system of claim 35, wherein the display further displays the range of motion over the one or more flexion angles along an axis.

Description

[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. 5A a frontal view of a knee joint for explaining a ligament model;

[0036] FIG. 5B a side view of a knee joint of FIG. 5A;

[0037] FIG. 6 the knee joint of FIG. 1 after a tibial cut, together with a spreading device;

[0038] FIG. 7 a knee joint comprising a femoral and a tibial implant;

[0039] FIG. 8 the knee joint of FIG. 7 with a varus stress applied to it;

[0040] FIG. 9 the knee joint of FIG. 7 with a valgus stress applied to it;

[0041] FIG. 10 an ellipse which is used as a model for the femoral implant;

[0042] FIG. 11 a model for calculating the maximum varus angle;

[0043] FIG. 12 a surface model of a femoral implant; and

[0044] FIG. 13 a screenshot showing a calculated envelope of the range of motion.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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.

[0049] 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.

[0050] 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.

[0051] 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 511 which represent a frontal view and a side view of the knee joint, respectively.

[0052] 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.

[0053] 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 4×4 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.

[0054] 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.

[0055] 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.

[0056] 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.

[0057] 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×F.sub.m,i−P|

d.sub.l,i=|T.sub.i×F.sub.l,i−P|

[0058] 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.

[0059] 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.

[0060] 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.

[0061] 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.

[0062] 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.e. The sizes of the ellipses and the distance d.sub.e depend on the femoral implant 8c selected.

[0063] 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.

[0064] 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×({right arrow over (t)}.sub.cut_ant×{right arrow over (n)}.sub.sp)

where t.sub.cut_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×{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.

[0065] The vector

{right arrow over (f)}.sub.up={right arrow over (f)}.sub.impl_right×{right arrow over (r)}.sub.impl

is then used together with the vector

{right arrow over (f)}.sub.impl_right=M.Math.{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

[00001]$\beta ={\cos }^{-1}\left(\frac{\stackrel{.fwdarw.}{f_{\mathrm{up}}}•\stackrel{.fwdarw.}{n_{\text{?}}}}{.Math.f_{\mathrm{up}}.Math..Math.n_{\text{?}}.Math.}\right).\text{?}\text{indicates text missing or illegible when filed}$

[0066] The index i has been omitted from the vectors in order to improve the legibility of the formulae. The vector f.sub.impl_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_cut represents the normal vector to the tibial cutting plane P. A rotation matrix R.sub.i can be defined in terms of β.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.

[0067] 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.

[0068] 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 α, 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.

[0069] 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).

[0070] 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.

[0071] 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).