The Knee 14 (2007) 133 – 137
A tibial-based coordinate system for three-dimensional data Clare Fitzpatrick a,⁎, David FitzPatrick a , Daniel Auger b , Jordan Lee b a
School of Electrical, Electronic and Mechanical Engineering, University College Dublin, Belfield, Dublin 4, Ireland b DePuy Orthopaedics Inc., Warsaw, Indiana, USA Received 22 June 2006; received in revised form 31 October 2006; accepted 3 November 2006
Abstract An accurate and repeatable tibial measurement system will aid in the definition of tibial geometry and improving tibial prosthesis design. Unlike in the femur, there is no standardized method for constructing a tibial coordinate frame. Most tibial measurements are given relative to femoral axes or the coordinate frame of the CT/MRI scanner or radiograph machine. The objective of this study was to establish an independent tibial coordinate frame. Data consisted of CT scans from 34 subjects. The tibial anatomical axis was chosen as the axial axis. The anteroposterior (AP) axis was selected to be parallel to the lateral surface of the tibial shaft and orthogonal to the anatomical axis and from this the mediolateral axis could be derived. The selected AP axis was compared with the surgical tibial AP axis by measuring their variability relative to a common axis, the posterior tibial condylar line (PTCL). The mean angle between the selected AP axis and the perpendicular to the PTCL was measured as −4.07°, standard deviation of 4.28°. The mean angle between the surgical AP axis and the perpendicular to the PTCL was measured as −18.56°, standard deviation of 4.66°. There was no significant difference in the variance of the two sets of measurements (p = 0.63). Variability of the selected AP axis was even smaller (standard deviation of 2.74°) when measured independently from the PTCL reference axis, by aligning virtual resection profiles. Anatomically, the selected AP axis was almost perpendicular to the posterior tibial condylar axis. This coordinate system can aid in gathering consistent and repeatable anthropometric data that can be used to improve tibial implant design and could also, in combination with CT/MR imaged-based computer assisted surgery, be used as a guideline for tibial component positioning in TKR. © 2006 Elsevier B.V. All rights reserved. Keywords: Tibial coordinate frame; 3D data; Axis variation
1. Introduction To draw any meaningful conclusions from measurements taken from multiple subjects the reference frame between subjects must be consistent. In the knee there are several well-defined femoral axes that can be used for this purpose [1] — anatomical axis [2,3], mechanical axis [4,5], Whiteside's line [6], femoral epicondylar axis [4–7], femoral posterior condylar axis [3,6,8]. The tibia, however, contains few easily identifiable landmark points. Current methods of registering or aligning the tibia are based on the radiograph set-up [9,10], CT/MRI
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scanner coordinate frame [11], femoral axes (epicondylar axis [12,13], posterior condylar line [14]) or the surgical tibial AP axis [13,15], which uses the position of the tibial tubercle, sometimes in conjunction with the second metatarsal bone. Measurements based on the scanner or femoral coordinate frame are subject to additional measurement variation as they are affected by the position of the patient, extension of the leg, axial tibial rotation, valgus/varus angle, flexion gap. Selection of the medial and lateral edges of the tibial tubercle tends to be subjective [16] and hence can lead to variability in the definition of the surgical AP axis. Using the second metatarsal bone as an alignment aid requires a scan of the foot, which involves additional scan time, cost and longer exposure to radiation. The purpose of this study was to develop a robust tibial coordinate frame, from which accurate anthropometric tibial data could be gathered, that
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was independent of the femur and required only proximal tibia data. 2. Methods Data consisted of 34 CT scans of normal Caucasian knees from 34 volunteer subjects with no history of disease, trauma, knee pain or patellar instability, which were obtained from a centre within the US under local ethical guidance and informed consent procedures. The CT scans included 19 scans of female subjects, comprised of nine left and 10 right knees, and 15 scans of male subjects, comprised of seven left and eight right knees. The mean age of the subjects was 58 years (range 40 to 76 years). Pixel size was 0.49 ×0.49 mm and slice thickness was 1.5 mm with an average of 54 slices per tibia (range 42 to 66 slices). CT scans were reconstructed and segmented using Mimics software (Materialize b.v., Leuven, Belgium) and imported as 3D stereolithography (STL) files, which describe solid models that can interact with most CAD packages, into a specifically developed analysis package. The anatomical axis is the best-defined axis in the tibia and hence was selected as the axial axis (z-axis) of the new coordinate frame. It was noted that the lateral surface of the tibial shaft could be reasonably well represented by a plane. Using specifically developed software (in Visualization Toolkit (VTK, Kitware Inc., New York, USA) visualization software; and Tcl, a programming language), the anatomical axis (axis 1) of each tibial model was determined (Fig. 1). Several points (15–25 points per model) were picked on the lateral surface of the shaft, the best-fitting plane to these points was calculated [17], and the normal vector (axis 2) to this plane was noted (Fig. 2). An axis orthogonal to axes 1 and 2 was calculated (axis 3). From this, an axis orthogonal to axis 1 and axis 3 was determined (axis 4). The model was then transformed from its original CT coordinate frame such that axes 4, 3 and 1 were the x-, y- and z-axes, respectively, of the new coordinate system, with the y-axis representing the newly defined AP axis (Fig. 3). All measurements were made in this coordinate frame. The posterior tibial condylar line (PTCL) was used as a reference to assess the variability of the selected AP axis. The most posterior point on each condyle was selected. A plane parallel to the anatomical axis was passed through both points. The normal vector (axis 5) to this plane was perpendicular to the PTCL (Fig. 4). The angle between axis 5 and the y-axis was measured (angle 1). The variability of angle 1 was then compared, using Student's t-test, with the variability of the angle between the surgical AP axis and the perpendicular to the PTCL (angle 2) (Fig. 5). PAST (University
Fig. 1. 3D CT reconstruction of the proximal tibia showing the tibial anatomical axis (axis 1).
Fig. 2. 3D CT reconstruction of the proximal tibia showing the axis normal to the lateral surface of the tibial shaft (axis 2). of Oslo, Norway) was the statistical analysis package used, with p b 0.05 assumed to be significant. The surgical AP axis was defined by a plane parallel to the anatomical axis which passed through the medial third of the tibial tubercle and the centre of the tibial eminences. The mid-point between the tibial spines was calculated (point 1). An axial slice at the position of the tibial tubercle was examined. Points were picked at the medial (point 2) and lateral (point 3) edges of the tibial tubercle and a point through the centre of the medial third was calculated (point 4 = (point 2) ⁎ 5/6 + (point 3) ⁎ 1/6). A plane parallel to the anatomical axis was passed through point 1 and point 4. The normal vector (axis 6) to this plane was
Fig. 3. 3D CT reconstruction of the proximal tibia showing the AP axis of the new coordinate system.
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Fig. 4. 3D CT reconstruction of the proximal tibia showing the most posterior points on the tibial condyles. A plane is passed through these points, parallel to the anatomical axis. Axis 5 is the normal vector to this plane. Axis 5 is perpendicular to both the anatomical axis and the posterior tibial condylar line (PTCL). perpendicular to the surgical tibial axis (Fig. 6). The angle between the surgical tibial axis and axis 5 was measured (angle 2). For both the y-axis and the surgical tibial axis, if, relative to axis 5, it was internally rotated the angle was defined as positive, if it was externally rotated the angle was defined as negative. The second toe can be used as a guide for the surgical AP axis, and without it this axis may be subject to increased variability. In addition, the variability of both the surgical and the selected AP axes is dependent on the posterior tibial condylar axis, which itself has some degree of variance. This allows a comparison between the surgical AP axis and the selected AP axis
Fig. 5. 3D CT reconstruction of the proximal tibia showing the mean y-axis 4.1° externally rotated (angle 1), and mean surgical AP axis 18.6° externally rotated (angle 2), from the reference axis (axis 5). Axis 5 is perpendicular to the PTCL.
Fig. 6. 3D CT reconstruction of the proximal tibia showing point 1, the centre of the tibial eminences, and point 4, the medial 1/3 of the tibial tubercle. A plane is passed through these points, parallel to the anatomical axis. Axis 6 is the normal vector to this plane. Axis 6 is perpendicular to both the anatomical axis and the surgical AP axis. but does not provide an independent measurement of the variability of the new coordinate frame. Hence, a second method was used to quantify the variability of the new reference frame. For each subject, the profile at a depth of 5 mm below the articular surface was examined. The profiles were then aligned with one another and the rotation needed to achieve best fit was noted. 40–50 points were picked on the articular surface of the tibia, with equal numbers of points selected from each condyle. The best-fitting plane to these points was calculated (Fig. 7). A plane parallel to, and 5 mm below,
Fig. 7. 3D CT reconstruction of the proximal tibia showing 20 points on each condyle which were used to calculate the best-fitting plane.
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this plane was used to define a typical resection profile. 180 points taken at equiangular intervals about the centroid of the profile were used to define the profile. Using these points, the Iterative Closest Point algorithm [18] was used to align the profiles. The first profile was set as the reference profile (selected AP axis set at 0°), each subsequent profile was matched to the reference, and the rotation required to give the best match was recorded. This technique gives a measure of variability that is independent of another axis.
3. Results The angle between the y-axis and axis 5 (perpendicular to PTCL) was −4.07°, standard deviation of 4.28° (range: −14.27° to 5.31°). The angle between the surgical AP axis and axis 5 (perpendicular to PTCL) was −18.56°, standard deviation of 4.66° (range: −29.20° to −11.14°) (Fig. 5). There was no significant difference in the variance of the two sets of measurements (p = 0.63). The selected AP axis was almost perpendicular to the tibial posterior condylar line. When each profile was matched to the first profile, the mean rotation required was 0.61°, standard deviation of 2.74° (range: −3.78° to 7.92°).
4. Discussion When constructing a tibial coordinate frame, the variability of the axes should be as small as possible. The AP axis selected in this study was less variable than the surgical AP axis when referenced against the posterior condylar line (standard deviations of 4.07° and 4.66°, respectively). The variability of the selected AP axis was also measured independently of the PTCL, by aligning resection profiles. Small rotations only were needed to optimally match the profiles (mean rotation of 0.61°, standard deviation of 2.74°), validating the consistency of the new tibial coordinate frame. There have been several studies which have compared tibial geometry or tibial component orientation between multiple subjects and hence have required a consistent reference frame. Many of these studies have taken measurements based on the radiograph set-up or CT/MRI scanner [9–11]. While precautions can be taken to limit the amount of influence that this will have on measurements (restraining the limbs, controlling quadriceps contraction, etc.) anatomic variation makes it susceptible to alignment error. Others have based their reference frame on femoral axes [12–14] and so tibial measurements will include variation due to axial rotation and varus/valgus alignment. There have been some studies which have used a purely tibial coordinate frame. Unfortunately, most of these do not give a rigorous description of how they established their coordinate frame [19–22] and of those that do [23,24] most have not attempted to quantify the variability of these axes. The variability of our chosen AP axis (std 2.74°) is similar to that measured by Akagi et al. [12,16] who defined a tibial AP axis and measured it with reference to the femoral epicondylar axis (std 2.88°). To our knowledge this is the first study which has established and quantified the variability of a standardized coordinate frame based purely on the proximal tibia. This technique has relevance for researchers. When getting the
mean and modes of variation for a group of data, be it for ligament insertion sites, cartilage position, articular surface geometries or resection profiles, inconsistence in the choice of reference frame will result in a distorted representation of the mean geometry, and incorrect positioning of mean insertion sites and cartilage. Our method can aid in producing accurate mean geometries and ligament and cartilage positions. It does not require information about the distal tibia (shorter scan times, less ionising radiation), nor is it derived from femoral orientation and is therefore independent of tibial internal/external rotation. It quantifies the variability of the selected AP axis independently of another axis. It does not involve articular surface reference points and hence is equally applicable to osteoarthritic knees. Surgically, this coordinate system can be applied to CT/ MR imaged-based computer assisted surgery to establish a consistent reference frame for tibial component positioning. This would be particularly useful in revision surgery where articular surface landmarks have been removed and also in osteoarthritic knees where degeneration and osteophytic growth can make PTCL identification more difficult. This method can help to improve accuracy of tibial measurements, which will aid in gathering consistent and repeatable anthropometric data that can be used to improve tibial implant design and could also, in combination with CAS, be used as a guideline for tibial component positioning in TKR. Acknowledgements This study had been supported by a research grant from DePuy Orthopaedics Inc. References [1] Luo C-F. Reference axes for reconstruction of the knee. Knee 2004;11:251–7. [2] Erkman MJ, Walker PS. A study of knee geometry applied to the design of condylar prostheses. Biomed Eng 1974;9(1):14–7. [3] Nuno N, Ahmed AM. Three-dimensional morphometry of the femoral condyles. Clin Biomech 2003;18(10):924–32. [4] Siu D, Rudan J, Wevers HW, Griffiths P. Femoral articular shape and geometry. J Arthroplasty 1996;11(2):166–73. [5] Yoshioka Y, Siu D, Cooke TD. The anatomy and functional axes of the femur. J Bone Jt Surg 1987;69A(6):873–80. [6] Matsuda S, Miura H, Nagamine R, Mawatari T, Tokunaga M, Nabeyama R, et al. Anatomical analysis of the femoral condyle in normal and osteoarthritic knees. J Orthop Res 2004;22(1):104–9. [7] Blaha JD, Mancinelli CA, Simons WH. Using the transepicondylar axis to define the sagittal morphology of the distal part of the femur. J Bone Jt Surg 2002;84A(suppl 2):48–55. [8] Tillman MD, Smith KR, Bauer JA, Cauraugh JH, Falsetti AB, Pattishall JL. Differences in three intercondylar notch geometry indices between males and females: a cadaver study. Knee 2002;9(1):41–6. [9] Kasis Ag, Pacheco RJ, Hekal W, Farhan MJ, Smith DM, Ali AM. The precision and accuracy of templating the size of unicondylar knee arthroplasty. Knee 2004;11:395–8. [10] Nagamine R, Miura H, Bravo CV, Urabe K, Matsuda S, Miyanishi K, et al. Anatomic variations should be considered in total knee arthroplasty. J Orthop Sci 2005;5:232–7.
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