Method and apparatus for determining differences in geometry of subject element using landmarks

Abstract

A method, performed by a computer, for measuring geometric length and offset differences of a subject element using landmarks obtained through, for example, analysis of medical data images. The method may include obtaining medical image data from a medical imaging device. The method includes measuring, by the computer, a first landmark vector between a femoral landmark and a second landmark at a first point in time from, for example, the medical data images. Further, the method includes measuring, by the computer, a second landmark vector between the femoral landmark and the second landmark at a second point in time which is later than the first point in time from, for example, the medical data images. Calculating an orthogonal projection of the first landmark vector into a sagittal plane and using the direction of the orthogonal projection of the first landmark vector into the sagittal plane as a length direction. Calculating a direction which is perpendicular to the sagittal plane and using this direction as an offset direction and calculating the length difference in the length direction and the offset difference in the offset direction from the first landmark vector and the second landmark vector.

Claims

1. A method for analysing images, performed by a computer, through analysis of medical image data, comprising the steps of: obtaining medical image data from a medical imaging device, the medical imaging device generating at least a CT or MR medical image data during a scan of a patient's femur connected to a patient's pelvis; measuring, by the computer, a first landmark vector between a femoral landmark and a second landmark at a first point in time from the medical image data; measuring, by the computer, a second landmark vector between the femoral landmark and the second landmark at a second point in time which is later than the first point in time from the medical image data; calculating, by the computer, an orthogonal projection of the first landmark vector into a sagittal plane and using the direction of the orthogonal projection of the first landmark vector into the sagittal plane as an element length direction; calculating, by the computer, a direction which is perpendicular to the sagittal plane and using the calculated direction perpendicular to the sagittal plane as an element offset direction; calculating, by the computer, the element length difference in the element length direction and the element offset difference in the element offset direction from the first landmark vector and the second landmark vector; preparing, by the computer, for presentation and output on a display unit of a medical navigation system the calculated element length difference and using the calculated element length difference in the medical navigation system.

2. A method, performed by a computer, for measuring a leg length difference and a leg offset difference of a patient's leg including a femur connected to a pelvis, comprising the steps of: measuring, by a registration tool operably connected to a computer, a first landmark vector between a femoral landmark and a second landmark at a first point in time; transmitting from the registration tool to an input unit of the computer in a medical navigation system, the measurement values of the first landmark vector; measuring by the registration tool operably connected to the computer, a second landmark vector between the femoral landmark and the second landmark at a second point in time which is later than the first point in time; transmitting from the registration tool to the input unit of the computer in the medical navigation system, the measurement values of the second landmark vector; calculating, by the computer, an orthogonal projection of the first landmark vector into a sagittal plane and using the direction of the orthogonal projection of the first landmark vector into the sagittal plane as a leg length direction; calculating, by the computer, a direction which is perpendicular to the sagittal plane and using this direction as a leg offset direction; and calculating, by the computer, the leg length difference in the leg length direction and the leg offset difference in the leg offset direction from the first landmark vector and the second landmark vector; preparing, by the computer, for presentation and output on a display device connected to the medical navigation computer the calculated leg length difference and using the calculated leg length difference in the medical navigation system.

3. The method according to claim 2, wherein an orientation of the sagittal plane is defined as being horizontal.

4. The method according to claim 2, wherein an orientation of the sagittal plane is determined as the orientation of a surface of an operating table on which the patient is located.

5. The method according to claim 2, wherein an orientation of the sagittal plane is determined from a plurality of inertial sensor data which are acquired from an inertial sensor attached to the tibia of the leg while the femur is locked in position and the tibia is flexed relative to the femur.

6. The method according to claim 4, wherein a first sagittal plane is determined for the first landmark vector, and a second sagittal plane is determined for the second landmark vector, and orthogonal projections of the landmark vectors into the corresponding sagittal plane are calculated.

7. The method according to claim 2, wherein calculating the leg length difference and the leg offset difference involves calculating a first orthogonal projection of the second landmark vector into the sagittal plane, calculating a second orthogonal projection of the first orthogonal projection onto the projection of the first landmark vector, determining the leg length difference as the difference in length between the projection of the first landmark vector and the second projection of the second landmark vector, and calculating the leg offset difference as the difference between the components of the first landmark vector and the second landmark vector in the leg offset direction.

8. The method according to claim 2, wherein calculating the leg length difference and the leg offset difference involves calculating an orthogonal projection of the second landmark vector into the sagittal plane, rotating the orthogonal projection of the second landmark vector within the sagittal plane such that its direction matches the direction of the projection of the first landmark vector, determining the leg length difference as the difference in length between the projection of the first landmark vector and the rotated second landmark vector, and calculating the leg offset difference as the difference between the components of the first landmark vector and the second landmark vector in the leg offset direction.

9. The method according to claim 2, wherein calculating the leg length difference and the leg offset difference involves calculating a difference vector between the first landmark vector and the second landmark vector and decomposing the difference vector into its components in the leg length direction and the leg offset direction.

10. The method according to claim 2, comprising the steps of obtaining neutral position data which define a neutral position of the leg at the first point in time and obtaining second position data which define a position of the leg at the second point in time, wherein the second landmark vector is only determined if the second position data match the neutral position data.

11. The method according to claim 10, wherein the position data are acquired from an inertial sensor.

12. The method according to claim 2, wherein the first and second landmark vectors are calculated from two landmark reference vectors, wherein each landmark reference vector represents a vector between the respective landmark and the reference point common to the femoral and second landmarks and at least one of the landmark reference vectors is determined using a light beam which is emitted from a light beam source and pointed at an offset point, the light beam source having a known distance from the landmark and a known orientation relative to the direct line from the light source to the landmark, determining the first and second landmark vectors, including acquiring the direction of the light beam and the distance between the light beam source and the offset point, and calculating the landmark reference vector from the known distance between the light source and the landmark, the known orientation of the light source relative to the direct line from the light source to the landmark, the direction of the light beam, the distance between the light beam source and the offset point and the reference offset between the offset point and the reference point.

13. The method according to claim 12, wherein the second landmark is a virtual landmark, being the center of rotation of the acetabulum; one of the landmark reference vectors is a virtual landmark reference vector for the virtual landmark and is determined as the average of two auxiliary reference vectors, wherein each auxiliary reference vector represents a vector between an auxiliary landmark and the common reference point and comprising the steps of obtaining neutral position data which define a neutral position of the leg at the first point in time and obtaining second position data which define a position of the leg at the second point in time, wherein the second landmark vector is only determined if the second position data match the neutral position data, wherein the position data are acquired from an interior sensor, and wherein the respective auxiliary landmark is used as the landmark.

14. A non-transitory computer-readable storage medium storing a program which, when running on a computer, causes the computer to perform the steps of determining by a registration tool connected to a computer, a first landmark vector between a femoral landmark and a second landmark at a first point in time; receiving from the registration tool to an input unit of the computer of a medical navigation system, the measurement values of the first landmark vector; determining a second landmark vector between the femoral landmark and the second landmark at a second point in time which is later than the first point in time; receiving from the registration tool to the input unit of the computer on the medical navigation system, the measurement values of the second landmark vector; calculating, by the computer, an orthogonal projection of the first landmark vector into a sagittal plane and using the direction of the orthogonal projection of the first landmark vector into the sagittal plane as a leg length direction; calculating, by the computer, a direction which is perpendicular to the sagittal plane and using this direction as a leg offset direction; and calculating, by the computer, the leg length difference in the leg length direction and the leg offset difference in the leg offset direction from the first landmark vector and the second landmark vector; preparing, by the computer, for presentation and output on a display device connected to the computer the calculated leg length difference and using the calculated leg length difference in the medical navigation system.

15. A device for determining a leg length difference and a leg offset difference of a patient's leg including a femur connected to a pelvis, comprising a computer that executes a program that causes the computer to obtain medical image data from a medical imaging device, the medical imaging device generating at least CT or MR medical image data during a scan of a patient's femur connected to a patient's pelvis; determine, by the computer, a first landmark vector between a femoral landmark and a second landmark at a first point in time; determine, by the computer, a second landmark vector between the femoral landmark and the second landmark at a second point in time which is later than the first point in time; calculate, by the computer, an orthogonal projection of the first landmark vector into a sagittal plane and use the direction of the orthogonal projection of the first landmark vector into the sagittal plane as a leg length direction; calculate, by the computer, a direction which is perpendicular to the sagittal plane and use this direction as a leg offset direction; and calculate, by the computer, the leg length difference in the leg length direction and the leg offset difference in the leg offset direction from the first landmark vector and the second landmark vector; transmit, by the computer, for presentation to an output unit of a medical navigation system the calculated leg length difference and using the calculated leg length difference in the medical navigation system.

Description

(1) The invention and potential alternatives shall now be explained in more detail with reference to the accompanying drawings, which show:

(2) FIG. 1 a femur at two different points in time;

(3) FIG. 2 a geometry of two landmarks and a reference point;

(4) FIG. 3 a system for determining a landmark vector, including a registration tool;

(5) FIG. 4 a geometry for determining a landmark vector;

(6) FIG. 5 a first example of determining the leg length difference and the leg offset difference;

(7) FIG. 6 a geometry for determining the leg length difference;

(8) FIG. 7 an example of determining the orientation of a sagittal plane;

(9) FIG. 8 a second example of determining the leg length difference and the leg offset difference; and

(10) FIG. 9 an example of determining a virtual landmark.

(11) FIG. 1 shows a femur 1 at two different points in time. The femur 1 comprises a femoral shaft and a femoral head 1a which are connected by a femoral neck. The femoral head 1a rests in a socket, the acetabulum, of the pelvis 2. The femoral head 1a is located at the proximal end of the femur 1. At its distal end, the femur 1 comprises a medial condyle, a lateral condyle and an intercondylar notch between them. The distal end of the femur 1 is connected to a tibia (not shown) via the knee joint.

(12) FIG. 1 also shows a sagittal plane 3 which is perpendicular to the plane of the drawing. The sagittal plane extends in an up-down (superior-inferior or cranial-caudal) direction and in a front-back (anterior-posterior or ventral-dorsal) direction relative to the patient's body. The mechanical axis of the femur 1, which runs through the centre of the femoral head 1a and the centre of the intercondylar notch, lies approximately within the sagittal plane 3.

(13) FIG. 1 also shows a global co-ordinate system GCS which is an earth-fixed co-ordinate system. Orientations (also referred to as directions) of lines or vectors are determined or measured in this global co-ordinate system.

(14) The structure of the femur 1 has changed between the first and second points in timein particular, the femoral neck has become longer. The structural change in the femur 1 is illustrated in an exaggerated manner in order to emphasise it in the drawings.

(15) FIG. 1 also shows two landmarks LM1 and LM2. The landmark LM1 is a point on the greater trochanter of the femur 1, and the landmark LM2 is a point on the acetabular rim of the socket of the pelvis 2. The landmark LM1 is also referred to as the femoral landmark, and the landmark LM2 is an example of a second landmark.

(16) A vector between the two landmarks LM1 and LM2 is referred to as a landmark vector. The position of the landmark LM1 relative to the landmark LM2 changes between the first point in time and the second point in time, because the structure of the femur 1 and/or pelvis 2 has changed, hence the landmark vector also changes between the first point in time and the second point in time. The landmark vector at the first point in time is referred to as LMV1, and the landmark vector at the second point in time is referred to as LMV2.

(17) In the present invention, a landmark vector is not determined by acquiring the exact locations of the landmarks in the global co-ordinate system and determining the landmark vector from the difference between the locations. Only the directions and the lengths of the landmark vectors LMV1 and LMV2 are used in order to calculate the leg length difference and the leg offset difference. Methods for determining the landmark vectors include a direct measurement or a determination from medical image data, such as CT or MR image data.

(18) As an option, a landmark vector can be determined from two landmark reference vectors between the respective landmark and a common reference point. The principle of this approach is shown in FIG. 2.

(19) As shown in FIG. 2, the two landmarks LM1 and LM2 and the common reference point P.sub.R constitute the corners of a triangle. The landmark vector LMV is represented by the side of the triangle between the landmarks LM1 and LM2. The landmark reference vector between the landmark LM1 and the common reference point P.sub.R is referred to as RLV1, and the landmark reference vector between the landmark LM2 and the common reference point P.sub.R is referred to as RLV2. Once the two landmark reference vectors RLV1 and RLV2 are known, for example by being measured, then the landmark vector LMV can be calculated.

(20) In an exceptional case, the two landmarks LM1 and LM2 and the common reference point P.sub.R may all lie on one line. In this case, the three points do not constitute a triangle. However, the landmark vector LMV can still be calculated from the two landmark reference vectors RLV1 and RLV2.

(21) FIG. 3 schematically shows a system for determining a landmark vector. The system comprises a registration tool 4 and a medical navigation system 10.

(22) The registration tool 4 comprises a body 5 featuring a landmark point 6 which is to be held against a landmark, such as for example the landmark LM1 as shown in FIG. 3. A light beam source 7 which is capable of emitting a light beam 9 is rigidly attached to the body 5. The location and orientation of the light beam source 7 on the body 5 is known, such that the distance between the light beam source 7 and the landmark point 6 and the direction of the light beam 9 relative to the body 5 is known. An orientation sensor 8 for determining the orientation of the registration tool 4 in the global co-ordinate system is rigidly attached to the registration tool 4. If the global co-ordinate system is an earth-fixed co-ordinate system, then the orientation sensor 8 can for example be an inertial sensor such as a three-axis gyroscope. The orientation sensor 8 is capable of transmitting the determined orientation to the medical navigation system 10.

(23) The medical navigation system 10 comprises a receiving unit 11 for receiving the orientation of the registration tool 4 from the orientation sensor 8, and a central processing unit 12 which is adapted to run a program which implements the method described herein and is connected to the receiving unit 11 in order to receive the orientation of the registration tool 4 from the receiving unit 11. The central processing unit 12 is also connected to a memory device 13 in which the program and/or data for performing the method is/are stored.

(24) The navigation system 10 also comprises an input unit 14 for receiving information and an output unit 15 for displaying information.

(25) The principle of determining a landmark direction shall now be explained with reference to FIG. 4. As shown in this figure, the landmark point 6 of the registration tool 4 is held at the landmark LM1, and a reference device 16 is provided in such a way that it is static in the global co-ordinate system GCS. The orientation of the reference device 16 is either known and provided to or stored in the medical navigation system 10 or is determined using an orientation sensor (not shown) and sent to the medical navigation system 10. The reference point P.sub.R is defined on the reference device 16.

(26) In the present example, the light beam source 7 is a laser range finder which is capable of determining the distance between the laser range finder 7 and a point at which the laser beam 9 is reflected. It is also capable of transmitting the determined distance to the medical navigation system 10 via the receiving unit 11.

(27) The registration tool 4 is held such that the light beam 9 hits the reference device 16. The point at which the light beam 9 hits the reference device 16 and is reflected back to the registration tool 4 is referred to as the offset point P.sub.O. Since the orientation of the light beam source 7 can be measured using the orientation sensor 8, and the distance between the offset point P.sub.O and the light beam source 7 can be measured, the medical navigation system 10 can calculate the vector d.sub.1 from the light beam source 7 to the offset point P.sub.O. The light beam source 7, the landmark LM1, the offset point Po and the reference point P.sub.R constitute a quadrilateral, as can be seen from FIG. 4. The vector RLV1 from the landmark LM1 to the reference point P.sub.R is the landmark reference vector which is associated with the landmark LM1. This vector can be calculated if enough information about the quadrilateral is available.

(28) The vector d.sub.LS from the landmark LM1 to the light source 7 can be calculated from the known relative position between the light source 7 and the landmark point 6 in combination with the orientation of the registration tool 4 as determined using the orientation sensor 8. The offset vector d.sub.O can be calculated from the orientation of the reference device 16 and the location of the offset point P.sub.O on the reference device 16. This location can be determined automatically, for example by a camera which captures an image of the reference device 16 and calculates the location by identifying the offset point P.sub.O in the image, or manually by an operator who identifies the location of the offset point P.sub.O on the reference device 16 and inputs this information into the medical navigation system 10 using the input unit 14.

(29) Once the vectors d.sub.LS, d.sub.1 and d.sub.O are known, the vector RLV1 representing the landmark reference vector of the first landmark LM1 can be calculated.

(30) As compared to the illustration in FIG. 1, the two landmark vectors LMV1 and LMV2 in FIG. 5 have the landmark LM1 in common (as a start or end point) instead of the landmark LM2. These two illustrations are equivalent because both correctly represent the shift between the landmarks LM1 and LM2 from the first point in time to the second point in time.

(31) As in FIG. 1, so also FIG. 5 shows the femur 1 with its femoral head 1a in the socket of the pelvis 2. FIG. 5 also shows the mechanical axis 18 of the femur 1. This mechanical axis 18 runs through the centre of rotation of the femoral head 1a and the intercondylar notch. The leg length difference is defined in the direction of the mechanical axis 18, while the direction of the leg offset, i.e. a lateral shift of the femoral shaft between the first and second points in time, is defined in a lateral direction which is perpendicular to the mechanical axis 18 and runs through the femoral landmark LM1.

(32) In order to determine the leg length difference and the leg offset difference, the relative shift between the landmark LM1 and the landmark LM2 from the first point in time to the second point in time has to be separated or decomposed into a component in the leg length direction and a component in the leg offset direction. In FIG. 5, this shift is represented by a difference vector DV. In the example shown in FIG. 5, the difference vector DV is decomposed into the leg length difference d1 and the leg offset difference d2.

(33) As outlined above, some embodiments assume that the leg offset direction is perpendicular to the sagittal plane 3. It is then necessary to determine the orientation of the sagittal plane 3. Two different approaches for determining the orientation of the sagittal plane are given below. In addition, it is apparent from FIG. 5 that the relative shift between the landmark LM1 on the femur and the landmark LM2 on the pelvis depends not only on the structural change in the femur 1 but also on a changed rotational alignment between the femur 1 and the pelvis 2. In order to correctly determine the leg length difference and the leg offset difference from the two landmark vectors LMV1 and LMV2, it is necessary to ensure that there is no such change in the rotational alignment or that any change in the rotational alignment is compensated for. Both approaches are described below.

(34) A detailed description of how the leg length difference d1 is determined according to the present invention, that is using a sagittal plane 3 as shown in FIG. 1, shall now be given with reference to FIG. 6. In this figure, the sagittal plane 3 is equivalent to the plane of the drawing. The line P1 is the orthogonal projection of the first landmark vector LMV1 into the sagittal plane 3, while the line P21 is the first orthogonal projection of the second landmark vector LMV2 into the sagittal plane 3. If the change in the structure of the femur 1 also shifts the femoral shaft in the anterior-posterior direction, then the directions of the lines P1 and P21 are not identical. The anterior-posterior difference between the first landmark vector LMV1 and the second landmark vector LMV2 is irrelevant for calculating the leg length difference. A second line P22 is then calculated as an orthogonal projection of the first projection (line P21) of the second landmark vector LMV2 into the sagittal plane 3 and onto the line P1. In an alternative, the line P21 is rotated onto the line P1 instead. The directions of the lines P1 and P22 are then identical, and the leg length difference d1 is calculated as the difference in length between the lines P1 and P22.

(35) A first approach for determining the orientation of the sagittal plane 3 assumes that the patient is in a lateral recumbent position at both the first and second points in time. It is then assumed that the sagittal plane 3 is a horizontal plane. In a second approach, an orientation sensor is used to determine the orientation of the surface on which the patient lies, such as for example the surface of an operating table. This orientation is determined in the global co-ordinate system GCS and provided to the medical navigation system 10.

(36) Another approach for determining the orientation of the sagittal plane 3 is illustrated in FIG. 7. FIG. 7 shows the femur 1 connected to the tibia 19 via a knee joint. The femur 1 is locked in position, preferably in its neutral position, relative to the pelvis 2. The tibia 19 is then flexed and/or extended relative to the femur 1, as indicated by the arrow in FIG. 7. An orientation sensor 20 attached to the tibia 19 then samples a plurality of orientation datasets for different alignments between the femur 1 and the tibia 19. The plane in which the orientation sensor 20, and therefore the tibia 19, moves can be calculated from these orientation datasets. The orientation of this plane is then used as the orientation of the sagittal plane 3.

(37) One approach for ensuring that the relative orientation, i.e. the rotational alignment, between the femur 1 and the pelvis 2 is identical at the first and second points in time uses an orientation sensor 17 attached to the patient's leg, as indicated in FIG. 5. In the example illustrated in FIG. 5, the orientation sensor 17 is attached to the soft tissue of the patient, for example using adhesive tape or bandaging. The orientation sensor 17 determines its orientation within the global co-ordinate system GCS at the first point in time and transmits this to the medical navigation system 10.

(38) Before the second point in time, the orientation sensor 17 intermittently or continuously determines its orientation in the global co-ordinate system GCS and transmits this to the medical navigation system 10, where it is displayed on the display unit 15. The orientation of the femur 1 relative to the pelvis 2 can then be adjusted until the orientation of the orientation sensor 17 in the global co-ordinate system GCS matches its orientation at the first point in time, wherein a match can be deemed to have been achieved if the difference with respect to the orientation at the first point in time is below a predetermined threshold. The medical navigation system 10 can optionally indicate on the display unit 15 whether or not the orientations of the orientation sensor 17 match.

(39) Additionally or alternatively, the medical navigation system 10 can sample the data from the registration tool 4 at the second point in time only, if the orientations of the orientation sensor 17 match.

(40) The orientation sensor 17 can be any orientation sensor, such as for example a gyro sensor, which is capable of transmitting the raw sensor output data or the orientation in the global co-ordinate system to the medical navigation system 10. One example of a device which contains such an orientation sensor is an iPod such as is produced by Apple, Inc.

(41) One approach for compensating for a change in the rotational alignment between the femur 1 and the pelvis 2 between the first and second points in time is illustrated in FIG. 8. The position of the femur 1 at the first point in time is shown by the complete representation of the femur 1 exhibiting the mechanical axis 18a. The position of the femur 1 relative to the pelvis 2 at the second point in time is indicated by the partial representation of the femur 1 exhibiting the mechanical axis 18b. The landmark, vector LMV1 is determined at the first point in time, and the landmark vector LMV2a is determined at the second point in time.

(42) The mechanical axes 18a and 18b are determined from the landmark LM3 and the landmark LM4. The landmark LM3 is the centre of rotation of the femoral head 1a, which coincides with the centre of rotation of the acetabulum, and is thus a virtual landmark which cannot be accessed directly. The landmark LM4 is a point on the intercondylar notch or on the patella and can therefore be referred to as the patellar landmark. The landmark vectors representing the mechanical axes 18a and 18b can be determined using landmark reference vectors between the landmark LM3 or LM4, respectively, and a common reference point such as for example the common reference point P.sub.R, in the same way as has already been described above. A rotational transformation T is then calculated which transforms the direction of the mechanical axis 18b into the direction of the mechanical axis 18a, in particular about the landmark LM3, i.e. the centre of rotation of the acetabulum. This rotational transformation T is then applied to the second landmark vector LMV2a, resulting in a transformed second landmark vector LMV2. The leg length difference and the leg offset can then be calculated from the two landmark vectors LMV1 and LMV2, as described above.

(43) As outlined above, the virtual landmark LM3 cannot be accessed directly using the registration tool 4. An indirect approach to determining a reference landmark vector for a virtual landmark shall accordingly now be described with reference to FIG. 9.

(44) This approach uses two auxiliary landmarks AL1 and AL2 on the acetabular rim of the pelvis 2. The centre of rotation of the acetabulum, and therefore the virtual landmark LM3, is considered to be halfway between the two auxiliary landmarks AL1 and AL2. In order to determine the landmark reference vector RLV3 between the virtual landmark LM3 and the common reference point P.sub.R, a first auxiliary landmark reference vector ARV1 between the auxiliary landmark AL1 and the common reference point P.sub.R and a second auxiliary landmark reference vector ARV2 between the second auxiliary landmark AL2 and the common reference point P.sub.R are determined. The reference landmark vector RLV3 is then calculated as the average of the first auxiliary landmark reference vector ARV1 and the second auxiliary landmark reference vector ARV2.

(45) As an alternative, the mechanical axes 18a and 18b can be determined by acquiring the vectors, or at least the directions of the vectors, between the landmark LM4 and the two auxiliary landmarks AL1 and AL2, respectively, and then calculating the direction of a mechanical axis as the average of the two directions of said vectors.

(46) As an alternative to the approach of using projections of the landmark vectors into a sagittal plane for determining the leg length direction, the directions of the mechanical axes 18a and 18b can be used as the leg length directions at the first and second point in time, respectively. In one embodiment, the transformation is applied to the second landmark vector LMV2 as described above, such that the leg length directions for the first landmark vector LMV1 and the transformed second landmark vector LMV2 are identical. The two landmark vectors thus become directly comparable.

(47) In another embodiment, the first landmark vector LMV1 is decomposed into components in the leg length direction and the leg offset direction based on the direction of the mechanical axis 18a and the second landmark LMV2 is decomposed based on the direction of the mechanical axis 18b. The corresponding components of the two landmark vectors are then compared to calculate the leg length difference and the leg offset difference.