Axial Scan Orientation and the Tibial Tubercle Trochlear Groove Distance: Error Analysis and Correction

Transcription

1 Musculoskeletal Imaging Original Research Yao et al. MRI Measurements of the TT-TG Distance Musculoskeletal Imaging Original Research Lawrence Yao 1 Neville Gai 1 Robert D. Boutin 2 Yao L, Gai N, Boutin RD Keywords: knee, MRI, patellofemoral instability, tibial tubercle, trochlear groove DOI: /AJR Received June 29, 2013; accepted after revision October 11, This study was supported in part by the National Institutes of Health Clinical Center, Intramural Research Program. 1 Department of Radiology and Imaging Sciences, NIH Clinical Center, 10 Center Dr, Bethesda, MD Address correspondence to L. Yao (lyao@cc.nih.gov). 2 Department of Radiology, University of California, Sacramento, CA. AJR 2014; 202: X/14/ American Roentgen Ray Society Axial Scan Orientation and the Tibial Tubercle Trochlear Groove Distance: Error Analysis and Correction OBJECTIVE. The tibial tubercle (TT) trochlear groove (TG) distance is an important metric in the assessment of patellofemoral dysfunction and is routinely measured on axial MRI and CT. This study examines error in measurements of the TT-TG distance related to variance in axial MRI scan orientation. SUBJECTS AND METHODS. Isotropic 3D turbo spin-echo MRI of the extended knee was performed in 12 healthy subjects. The z-axis of the scanner defines the perpendicular to a routine axial plane, and the anatomic axial plane is parallel to the knee joint. Isotropic MRI was reformatted into routine and anatomic axial planes and in axial planes simulating 5 of femoral adduction and abduction relative to the anatomic plane. A method for correcting the TT-TG distance to account for variable axial scan orientation is presented. RESULTS. Five degrees of simulated femoral abduction is associated with a mean increase in the TT-TG distance of 38% (SD = 17%), whereas 5 of simulated femoral adduction is associated with a mean decrease in the TT-TG distance of 51% (SD = 39%). The average deviation of the routine axial plane from the anatomic axial plane was 5.0 abduction (SD = 2.3 ). The simplest correction method reduced the mean discrepancy in the observed TT-TG distance by 68% and 72% in simulated femoral abduction and adduction, respectively. CONCLUSION. The TT-TG distance is sensitive to small changes in femoral alignment and should be interpreted with caution if axial image acquisition is not standardized. Knowing the vertical separation of the TT from the TG facilitates a simplified correction of the TT-TG distance, which is as effective as more complex corrections. P atellofemoral maltracking or instability is a common clinical syndrome with multiple predisposing or causative factors. If surgical treatment of patellofemoral syndrome is contemplated, the selection of an appropriate operative procedure is guided by key anatomic features and associated measurements. One popular metric is the transverse offset between the tibial tubercle (TT) and trochlear groove (TG) or TT-TG distance. Excessive lateralization of the TT increases the lateral force vector acting on the patella and predisposes to lateral patellar subluxation. Measurement of the TT-TG distance was originally described as a radiographic analog to the Q angle, which is measured clinically [1]. The TT-TG distance was measured on axial radiographs obtained tangential to the patellofemoral articulation with the knee flexed 30. Subsequently, CT became the favored method for measuring the TT-TG distance by superimposing an axial image through the TT on an- other axial image through the TG [2]. CT was shown to be superior for the measurement of the TT-TG distance by eliminating projectional errors inherent to radiography [3]. More recently, MRI has been validated as a reliable means of measuring the TT-TG distance using axial MR images and a digital workstation [4 6]. Reported normative ranges for the TT-TG distance have varied. Several studies suggest that a normal TT-TG distance is 10 mm or less [5, 7, 8]. A TT-TG distance greater than 15 mm in patients with patellofemoral instability may predict limited benefit from physical therapy [7]. A TT-TG distance greater than 20 mm is widely considered to be abnormal [2, 9] and suggests that a distal realignment procedure may be beneficial in the setting of patellofemoral syndrome [8, 10]. Because the TT-TG distance serves as a potential branch point in treatment decision making for patellofemoral syndrome, the reliability of the TT-TG distance measurement is essential. AJR:202, June

2 Yao et al. Although the TT-TG distance has been widely studied and is commonly applied in clinical MRI practices, the method of prescribing the axial (transverse) images on which it is measured is not explicit or clearly standardized and may also be subject to variances in extremity positioning or MR receiver coil design. For this study, we hypothesized that a variation in axial scan plane orientation leads to a systematic error in the TT-TG distance measurement. We also hypothesized that an analytic correction model can reduce these potential errors in TT-TG distance measurements. Subjects and Methods Twelve healthy subjects underwent a standardized MRI examination at 3 T (Achieva, Philips Healthcare) using a rigid multichannel receiver coil (PMS Sense Hi Res, Invivo). The knee was positioned in full extension. Informed consent was obtained from all subjects in accordance with the institutional review board approved study protocol. The MRI study included an isotropic 3D intermediate-weighted or balanced turbo spin-echo (TSE) sequence that uses a relaxation enhancement radiofrequency pulse; spatially nonselective, partial, refocusing radiofrequency pulses; and an excitation radiofrequency pulse modified to minimize echo spacing and improve slab profile. The scanning parameters for the 3D isotropic sequence included the following: TR/TE, 650/35; echo-train length, 22; half-fourier phase sampling; sensitivity-encoding in 2D; and voxel size, mm. Isotropic 3D MRI facilitates image reformation in arbitrary orientations without altering in-plane image resolution. Three-dimensional isotropic TSE images were reformatted into four separate axial scans, each differing slightly in obliquity, as defined by rotation around the anteroposterior axis. Image reformations were generated and archived using open-source PACs workstation software (OsiriX, version 4.1.1, Antoine Rosset). For the purposes of this study, the routine axial plane is defined as the plane perpendicular to the axis of the scanner bore (0 angulation). An axial plane parallel to the knee joint, as visualized on a straight coronal reformation through the center of the knee, is defined as the anatomic axial plane (Fig. 1). Three-dimensional TSE images were reformatted in the anatomic axial plane; the routine axial plane; and axial planes rotated 5 and 5 about the anteroposterior axis relative to the anatomic axial plane simulating mild femoral abduction and abduction, respectively (Fig. 1). An experienced musculoskeletal radiologist measured the TT-TG distance on the reformatted axial images. For the purposes of this study, the TT was defined as the most anterior aspect of the proximal TT (Fig. 2A) and the TG was defined as the deepest aspect of the TG (Fig. 2B). Additional measurements were recorded for use in the correction models: the femoral condylar angle (ε), defined as the angle formed between the coronal plane and the plane tangent to the posterior-most aspects of the medial and lateral femoral condyles (Fig. 2B); the vertical distance (D) between the TT and TG landmarks (Fig. 3); and the anteroposterior offset (d) between the TT and TG (Fig. 3). The deviation of the routine axial imaging plane from the anatomic axial plane (θ), as defined by a rotation about the anteroposterior axis, was also tabulated (Fig. 1). All measurements were performed using routine measurement and cross-referencing tools available in OsiriX. An analytic approach for correcting an observed TT-TG distance to an expected TT-TG distance if axial images are variably rotated about the anteroposterior axis is presented in Appendix 1, suggesting three potential correction models. Model 1 assumes that the femoral condylar axis (defined as ε) remains constant independent of axial scan obliquity (θ). Model 2 extends the assumptions of model 1 and also assumes that the anteroposterior offset of the TT and TG is negligible (d = 0). Model 3 extends the assumptions of model 2 and also assumes that the femoral condylar axis coincides with the reference coronal plane (ε = 0). The intrasubject differences for TT-TG measurements made on the various axial imaging series were tested for significance using a Wilcoxon test. The reduction in error (R) or discrepancy for a corrected TT-TG distance (T c ) versus an observed Fig. 1 Isotropic 3D MR image of knee of healthy 25-year-old man. Image was reformatted in straight coronal plane. Routine axial plane that is perpendicular to scanner bore or tabletop (dashed white lines) defines angulation (θ) of zero. Isotropic MRI data were also reformatted in angled axial planes as shown by solid black line (5 simulated femoral abduction) and by dashed black line (5 simulated femoral adduction). Isotropic MRI data were also reformatted in axial plane parallel to knee joint, which is referred to as anatomic axial plane and is shown by solid white line. TT-TG distance (T o ) was expressed as follows: R = [ T o T a T c T a ] / T o T a, where T a is the TT-TG distance measured on the corresponding anatomic axial image, an ad hoc A B Fig. 2 Isotropic 3D turbo spin-echo (TSE) MR images of knee of healthy 25-year-old man (same volunteer as in Fig. 1). A, Isotropic 3D TSE MR image reformatted in reference axial plane at level of tibial tubercle (TT) illustrates anterior-most portion of TT used as landmark for measurement (white dot). B, MR image obtained more cephalad than A from same axial reformatted series as A illustrates location of trochlear groove (TG) and projected location of TT. TT-TG distance is distance between projected TT (white dot) and TG (black dot), measured along line parallel to femoral condylar axis (black line). Femoral condylar axis typically deviated from reference coronal plane of scanner (dashed white line), defining femoral condylar axis angle (ε). LFC = lateral femoral condyle, MFC = medial femoral condyle, dotted black line = line perpendicular to femoral condylar axis passing through TG, dotted white line - line perpendicular to the femoral condylar axis passing through projected TT AJR:202, June 2014

3 MRI Measurements of the TT-TG Distance TABLE 1: Tibial Tubercle (TT) Trochlear Groove (TG) Distances on Three TT-TG Distance (mm) Fig. 3 Isotropic 3D turbo spin-echo (TSE) MR image of knee of healthy 25-year-old man (same volunteer as in Figs. 1 and 2) reformatted in straight sagittal plane parallel to scanner bore, or z-axis, and passing through tibial tubercle (TT) (white dot). Location of trochlear groove (TG) (black dot) is projected from more medial sagittal image, illustrating vertical separation of TT from TG (D) and anteroposterior offset of TT from TG (d). These measures are used in correction model described in Appendix 1. Solid black and white lines are horizontal lines passing through projected TG and TT, respectively. Dashed black and white lines are vertical lines passing through projected TG and TT, respectively. standard for the TT-TG distance for the purposes of this study. Reductions in discrepancies for TT-TG distance measured on axial images in simulated femoral abduction or adduction versus anatomic axial images by the three correction models were tested for significant differences with a Friedman statistic, and pairwise differences were examined with a Wilcoxon test with Bonferroni correction. Results The TT-TG measurements in the anatomic axial plane and in 5 of simulated femoral abduction and adduction are summarized in Table 1. Five degrees of simulated femoral abduction is associated with a mean increase in the TT-TG distance of 3.4 mm, or 38% (SD = 1.0 mm or 17%; p < 0.01), whereas 5 of simulated femoral adduction is associated with a mean decrease in the TT-TG distance of 4.3 mm, or 51% (SD = 1.6 mm or 39%; p < 0.01). The group average deviation of the routine axial plane from the anatomic axial plane was 5.0 (range, ; SD = 2.3 ), indicating that the femur is typically abducted relative to the z-axis of the scanner. The TT-TG distance as measured on routine or straight (nonangled) axial images is consistently greater than the TT-TG distance measured on anatomic axial images (mean difference = 3.0 mm, or 34%; SD = 2.1 mm, or 34%; SD = 26%). Value The mean vertical separation of the TT and TG was 47.2 mm (SD = 6.8 mm), whereas the mean anteroposterior separation of the TT and TG was 0.2 mm (SD = 2.4 mm). The mean angle between the femoral condylar axis and the coronal plane of the scanner was 5.7 (SD = 4.0 ). The simplest correction method (model 3) reduced the error in the observed TT-TG distance by a mean of 68% and 72% in cases of simulated hip abduction and adduction, respectively (Table 2). There were statistically significant differences in error reduction between the models for TT-TG distance measured in simulated abduction (p < 0.03) but not for TT-TG distance measured in simulated adduction. For TT-TG distance measured in simulated abduction, correction by model 1 was statistically superior to that by model 3 (p < 0.05). In absolute terms, the differences in the corrected TT-TG distance by the three models were extremely small (Table 3). The dependencies of the corrected or predicted TT-TG distance by the three models on the tilt of the axial imaging plane (θ), the Anatomic a Adduction 5 b Abduction 5 c Median Mean SD Maximum Minimum 4.9 ± a Axial scan that is aligned with the knee joint. b Axial image in 5 relative simulated femoral abduction. c Axial image in 5 simulated femoral adduction. anteroposterior offset of the TT from the TG (d), and the femoral condylar axis angle (ε) are illustrated in Figures 4 6. The preponderant influence of the tilt angle (θ) on the TT-TG distance is clear. In each illustration, clinically extreme values for fixed parameters are chosen to accentuate the small or negligible differences in the TT-TG distance predicted by the three correction models. Discussion The TT-TG distance is helpful in selecting appropriate patients for distal patellar realignment procedures and may also guide operative decisions about how far the TT should be moved. The TT-TG distance may be predictive of recurrent patellar dislocation [2] and of the most likely site of a medial patellofemoral ligament tear in cases of patellar dislocation [11]. The mean difference in the TT-TG distance between patients who have suffered a patellar dislocation and control subjects has been reported to be 4 mm [12]. Thus, differences in the TT-TG distance on the order of 5 mm or less may TABLE 2: Reduction in Discrepancy of Tibial Tubercle (TT) Trochlear Groove (TG) Distance by Correction Models Fractional Reduction in Discrepancy Between TT-TG Distance Measured on Anatomic Scan a and TT-TG Distance Measured on Other Model 1 Model 2 Model 3 Abduction 5 b Mean SD Adduction 5 c Mean SD a Axial scan that is aligned with the knee joint. b Axial image in 5 simulated femoral adduction. c Axial image in 5 relative simulated femoral abduction. AJR:202, June

4 Yao et al. be clinically significant and may influence clinical decision making. In this study, we wanted to quantify the effect of minor variations in axial plane prescription, as commonly encountered in clinical practice, on the TT-TG distance. Even relatively minor effects of such variation on the TT-TG distance could be important given the clinical significance of relatively small differences in the TT-TG distance. TABLE 3: Absolute Differences in Corrected Tibial Tubercle (TT) Trochlear Groove (TG) Distance by Correction Model Absolute Difference in Corrected TT-TG Distance (mm) Model 1 Model 2 Model 1 Model 3 Model 2 Model 3 Abduction 5 a Mean b SD Adduction 5 c Mean SD Note All mean intrasubject differences in the corrected TT-TG distance by the three correction models are less than 0.1 mm. a Axial image in 5 simulated femoral adduction. b Significant difference (p < 0.05). c Axial image in 5 relative simulated femoral abduction. Observed TT-TG (mm) Observed TT-TG (mm) Tilt angle (Θ [ ]) Anteroposterior Offset of TT From TG (d [mm]) + Model 1 Model 2 Model 3 + Model 3 Model 2 Model 1 Fig. 5 Tibial tubercle (TT) trochlear groove (TG) distance predicted by three correction models as function of anteroposterior offset of TT from TG (d) when tilt angle (θ) is 10. Influence of d is negligible, and preponderant effect is related to tilt angle. For this illustration, vertical separation of TT and TG is assumed to be 50 mm, femoral condylar axis (ε) is assumed to be 25 from reference coronal plane (external rotation), and TT-TG distance is assumed to be 15 mm on axial image where θ = 0. Fig. 4 Predicted tibial tubercle (TT) trochlear groove (TG) distance by three correction models as function of axial tilt angle (θ) if TT-TG distance is equal to 15 mm on axial image where θ = 0. TT-TG distance values predicted by three models over commonly encountered range of axial tilt angles ( 10 to 10 ) are nearly identical. For this illustration, vertical separation of TT and TG is assumed to be 50 mm, TT is assumed to be 15 mm anterior to TG, and femoral condylar axis (ε) is assumed to be 25 from reference coronal plane (external rotation). Observed TT-TG (mm) Transverse MR images are often obtained as straight axial images, perpendicular to the longitudinal axis of the scanner bore and perpendicular to the scanner table the same manner in which CT images are routinely acquired. Alternatively, axial MR images are commonly oriented perpendicular to the femoral shaft axis or parallel to the plane of the knee joint. Knee alignment relative to the scanner bore or z-axis can also vary. Variance in femoral and knee alignment may be greater on open-architecture scanners or couch scanners, which permit greater degrees of relative hip or femoral abduction. Our study findings confirm the hypothesis that minor alterations in axial scan plane orientation significantly influence the observed TT-TG distance. In our study, just 5 of relative femoral abduction or adduction is associated with mean changes in the TT-TG distance that approach 40%. We found that straight or nonangled axial images acquired on a high-field-strength closed-bore magnet system using a rigid multichannel receiver coil deviated on average 5 from the anatomic axial plane, simulating relative femoral abduction. Greater degrees of relative femoral abduction are associated with a larger observed TT-TG distance. Interpretation and comparison of published TT-TG values measured on radiography, CT, and MRI should consider the potential systematic effect of uncontrolled minor variations in relative femoral abduction or adduction. The results of our study also confirm the hypothesis that a correction model can reduce discrepancies in the TT-TG distance re Femoral Condylar Angle (ε [ ]) + Model 3 Model 2 Model 1 Fig. 6 Predicted variation of tibial tubercle (TT) trochlear groove (TG) distance by three correction models as function of femoral condylar axis angle (ε) when TT-TG distance is equal to 15 mm on anatomic axial image (θ = 0 ). Influence of ε is negligible (< 1 mm) over common range of ε values. For this illustration, vertical separation of TT and TG is assumed to be 50 mm and anteroposterior offset of TT from TG (d) is assumed to be 15 mm. Positive ε denotes externally rotated femoral condylar axis AJR:202, June 2014

5 MRI Measurements of the TT-TG Distance lated to mild rotations of the axial scan plane. One additional measurement, the vertical separation of the TT from the TG (D), facilitates a significant correction of an observed TT-TG distance to a TT-TG distance that corresponds to a standard degree of relative femoral abduction or adduction. Our analysis illustrates that more comprehensive correction methods incorporating the femoral condylar axis angle and the anteroposterior offset of the TT from the TG offer negligible advantage over the simplest correction method. Our analytic approach to TT-TG distance correction assumes that the TT and TG represent fixed spatial landmarks independent of scan orientation. In reality, assignment of these landmarks may be influenced by alterations in depicted anatomy related to axial scan orientation. Despite this limitation, the correction method substantially minimizes the variance in the TT-TG distance related to common variable rotations of the axial plane about the anteroposterior axis and should be clinically useful. This study addresses the relative obliquity of axial imaging as defined by a single rotation about the anteroposterior axis. Additional systematic variances in the TT-TG distance might arise from relative rotation of the axial plane about the transverse axis or by rotation or flexion of the knee. Although MRI is typically performed with the patient s knee in full extension, an influence of knee flexion on the TT-TG distance, owing to the screw-home mechanism, has been described [6]. Our correction model shows how the TT-TG distance is quite robust to variations in femoral rotation and the anteroposterior offset of the TT from the TG (d). This robustness is explained by the method of TT-TG measurement, which is taken parallel to the intercondylar axis rather than along the reference coronal plane; this method of measurement largely normalizes the influence of femoral rotation and of offsets of the TT from the TG perpendicular to the intercondylar axis. Another limitation of our study is that it is based on a small number of asymptomatic subjects and does not examine many additional sources of variability in the TT-TG distance, including observer variation. Several large studies report the reliability of TT-TG distance measurements on MRI [4 6]. Our analysis is designed only to test a potential underrecognized source of systematic error in TT-TG distance measurements and to propose and evaluate a corresponding method of TT-TG correction. Our small study group is statistically sufficient for these limited conceptual purposes. Measurements of the patellar tendon TG distance and the TT posterior cruciate ligament (PCL) distance have been proposed as alternatives to the TT-TG distance on MRI. The patellar tendon TG distance uses the center of the patellar tendon insertion and is typically a few millimeters greater than the TT-TG distance [13]. The TT-PCL distance has been proposed as a more valid indicator of lateralization of the TT in contradistinction to medialization of the TG [14]. Although we did not specifically evaluate the patellar tendon TG and the TT-PCL, these measurements would logically be similarly influenced by systematic variances in axial imaging plane rotation. In summary, the results of this study show that the TT-TG distance is sensitive to small changes in axial scan orientation and, by logical extension, in thigh or femoral positioning. The precision of the TT-TG distance would be improved by standardizing the orientation of axial images on the basis of internal landmarks. The plane of the knee joint serves as one practical and intuitive internal standard for orientating the required axial images. Lack of imaging standardization will broaden the variance of the normal clinical range of the TT-TG distance. An additional measurement of the vertical separation of the TT from the TG landmarks can facilitate a substantial normalization of the TT-TG distance to one that conforms to a standard or desired degree of relative femoral abduction and adduction. References 1. Goutallier D, Bernageau J, Lecudonnec B. The measurement of the tibial tuberosity: patella groove distanced technique and results. (in French) Rev Chir Orthop Reparatrice Appar Mot 1978; 64: Dejour H, Walch G, Nove-Josserand L, Guier C. Factors of patellar instability: an anatomic radiographic study. Knee Surg Sports Traumatol Arthrosc 1994; 2: Wagenaar FC, Koëter S, Anderson PG, Wymenga AB. Conventional radiography cannot replace CT scanning in detecting tibial tubercle lateralisation. Knee 2007; 14: Schoettle PB, Zanetti M, Seifert B, Pfirrmann CW, Fucentese SF, Romero J. The tibial tuberosity trochlear groove distance: a comparative study between CT and MRI scanning. Knee 2006; 13: Pandit S, Frampton C, Stoddart J, Lynskey T. Magnetic resonance imaging assessment of tibial tuberosity trochlear groove distance: normal values for males and females. Int Orthop 2011; 35: Dietrich TJ, Betz M, Pfirrmann CW, Koch PP, Fucentese SF. End-stage extension of the knee and its influence on tibial tuberosity trochlear groove distance (TTTG) in asymptomatic volunteers. Knee Surg Sports Traumatol Arthrosc 2014; 22: Wittstein JR, O Brien SD, Vinson EN, Garrett WE Jr. MRI evaluation of anterior knee pain: predicting response to nonoperative treatment. Skeletal Radiol 2009; 38: Tsavalas N, Katonis P, Karantanas AH. Knee joint anterior malalignment and patellofemoral osteoarthritis: an MRI study. Eur Radiol 2012; 22: Colvin AC, West RV. Patellar instability. J Bone Joint Surg Am 2008; 90: Koëter S, Diks MJ, Anderson PG, Wymenga AB. A modified tibial tubercle osteotomy for patellar maltracking: results at two years. J Bone Joint Surg Br 2007; 89: Balcarek P, Ammon J, Frosch S, et al. Magnetic resonance imaging characteristics of the medial patellofemoral ligament lesion in acute lateral patellar dislocations considering trochlear dysplasia, patella alta, and tibial tuberosity trochlear groove distance. Arthroscopy 2010; 26: Balcarek P, Jung K, Frosch KH, Stürmer KM. Value of the tibial tuberosity trochlear groove distance in patellar instability in the young athlete. Am J Sports Med 2011; 39: Wilcox JJ, Snow BJ, Aoki SK, Hung M, Burks RT. Does landmark selection affect the reliability of tibial tubercle trochlear groove measurements using MRI? Clin Orthop Relat Res 2012; 470: Seitlinger G, Scheurecker G, Högler R, Labey L, Innocenti B, Hofmann S. Tibial tubercle posterior cruciate ligament distance: a new measurement to define the position of the tibial tubercle in patients with patellar dislocation. Am J Sports Med 2012; 40: (Appendix follows on next page) AJR:202, June

6 Yao et al. APPENDIX 1: Models for Correcting Tibial Tubercle (TT) Trochlear Groove (TG) Distance Measurements For conceptualizing the correction models, we adopt a coordinate system that is oriented to the patient so that the weight-bearing axis defines the craniocaudal axis and is denoted z (positive is craniad), the transverse axis is denoted x (positive is medial, or left, for a right knee; positive is medial, or right, for a left knee), and the anteroposterior axis is denoted y (positive is anterior). The origin of the coordinate system is set at the TT and in a routine axial plane (P 0 ), the angle of rotation, θ, of the imaging plane about the y-axis is assumed to be zero. In this routine axial plane, ε represents the angle between the femoral condylar axis and the x-axis, with a positive ε representing external rotation of the femur. The TG is identified on an axial image parallel to P 0 a distance D craniad to TT; if the anteroposterior offset of the TG from the TT is d, the coordinates of TG are as follows: ([T o d sin(ε)] / cos(ε), d, D), where T o is the observed TT-TG distance and a positive d indicates the TT is anterior to the TG. Relative abduction or adduction of the hip can be approximated by a rotation of the axial imaging plane around the y-axis by an angle θ; a positive θ corresponds to greater femoral abduction, and a negative θ corresponds to greater femoral adduction. The resulting x coordinate of the TG in the coordinates of a new axial imaging plane P 1 that has been rotated about the y-axis by an angle θ is as follows: [x 0 cos(θ) + D sin(θ)], where x 0 is the x coordinate of TG in the original, nonrotated axial imaging plane. We define v 0 as the unit vector perpendicular to the femoral condylar axis in P 0, with coordinates sin(ε), cos(ε), and 0. If we assume the femoral condylar axis remains essentially constant with small changes in θ, then the TT-TG distance (T ) on rotated axial images parallel to the plane P 1 is the distance from the TG and the line through the projection of TT on P 1 (TT ) that has direction v 0. In this context, projection is along the original nonrotated z-axis. This new distance T, or the adjusted TT-TG distance, can be expressed in P 1 as follows: T = v 0 (TG TT ) / v 0. TG has the following coordinates in P 1 : ([[T o d sin(ε)] / cos(ε)] cos(θ) + D sin(θ), d). Because TT and TT are at the origin (0, 0) and v 0 is a unit vector, then the following is true: T = v 0 TG. The adjusted TT-TG distance in the rotated axial plane P 1 can be spelled out by computing the cross product as follows: T = d sin(ε) (1 cos(θ)) + T o cos(θ) + D cos(ε) sin(θ). If the distance d is assumed to be negligible (d = 0), a simpler correction model (model 2) is as follows: T = T o cos(θ) + D cos(ε) sin(θ). If the femoral condylar axis is assumed to coincide with the coronal plane of the scanner or scan table (ε = 0), then an even simpler correction model (model 3) is as follows: T = T o cos(θ) + D sin(θ). Using these models, a TT-TG distance (T o ) measured on any given set of axial images can be translated to a TT-TG distance expected on axial images that are rotated by an angle θ about the y-axis relative to the original axial images (T ) AJR:202, June 2014