Influence of limb positioning during image acquisition on femoral torsion measurements: implications for surgical planning

ABSTRACT Femoral torsion is an important parameter to accurately quantify when planning for the correction of structural pathomorphology. The purpose of this study was to quantify the influence of limb positioning during image acquisition and of alignment techniques on femoral torsion measurements, by measuring the change in femoral torsion angle, upon digital rotations that simulate flexion/extension and adduction/abduction positions of the femur. Femoral torsion measurements were reduced up to 1° and increased up to 0.35° per each degree of flexion and abduction, respectively. The estimation of femoral torsion measurements yielded a difference up to 5.8° between the aligned and non-aligned cases.


Introduction
Femoral torsion describes the forward or backward axial rotation of the proximal femur in relation to the distal femoral condyles. Femoral torsion is most commonly measured as the difference between two angles on axial MRI or CT images, one measured at a proximal location and the other at a distal location on the femur. The proximal angle is formed by the femoral neck axis and a horizontal line (Figure 1 Angle 2), whereas the distal angle is formed between a line that defines the posterior femoral condylar axis and a horizontal line (Figure 1 Angle 1). Femoral torsion abnormality can have profound implications for the diagnosis and treatment of lower extremity disorders, such as patellofemoral pain (PFP) syndrome, hip instability, and femoroacetabular impingement syndrome (FAIS) (Kudrna 2005;Piva et al. 2006;Sankar et al. 2018;Wang et al. 2021). In severe cases of femoral torsion abnormality, a proximal and/or distal de-rotational osteotomy is performed to correct the axial misalignment at the affected lower extremity joint or joints, therefore accurate measures of femoral torsion in these cases are essential to plan for this surgical correction (Lerch et al. 2020).
Measures of femoral torsion play an important role in the management of clinical hip conditions, such as FAIS and hip instability (Kudrna 2005;Sankar et al. 2018;Scorcelletti et al. 2020;Wang et al. 2021). Excessive femoral ante-torsion is associated with conditions of hip instability, whereas excessive femoral retro-torsion is linked to conditions of FAIS (Westermann and Willey 2021;Arshad et al. 2021) (Figure 2). Lerch and colleagues found that 1 in 10 patients with FAIS also demonstrate severe abnormality in femoral torsion (Lerch et al. 2018). Patients with excessive femoral ante-torsion have significantly greater range of motion for internal rotation and smaller range of motion for external rotation, when compared to people with retro-torsion or normal femoral torsion values (Hartigan et al. 2017;Kraeutler et al. 2018;Sankar et al. 2018). Therefore, dynamic mechanical impingement could be reduced by femoral ante-torsion and femoral retro-torsion may exacerbate this dynamic mechanical impingement. Although arthroscopic surgery for FAIS addresses the local causes of bony impingement associated with cam and/or pincer pathomorphology, these arthroscopic surgical procedures do not address femoral torsion abnormality leading to persistent pain and symptoms. Some studies have shown that accounting for femoral retro-torsion abnormality during surgical planning improves clinical outcome scores following hip arthroscopy (Hartigan et al. 2017;Kraeutler et al. 2018;Sankar et al. 2018). For this reason, accurate femoral torsion measures are important to include in the diagnostic workup of FAIS. However, the image based evaluation of femoral torsion also demonstrates some ambiguity in the most accurate measurement technique, and is known to be influenced by patient positioning, therefore, is an area that warrants further research using more sophisticated three-dimensional (3D) imagingbased methods (Banerjee et al. 2014;Schmaranzer et al. 2020).
Multiple factors have been shown to affect femoral torsion measurements such as the anatomical landmarks chosen to define the proximal femoral neck axis (Hernandez et al. 1981;Jarrett et al. 2010;Fuller et al. 2018;Schmaranzer et al. 2019) and the distal femoral axis (i.e. posterior condylar alignment, epicondylar alignment, etc. (Kingsley and Olmsted 1948;Weiner et al. 1978;Egund and Palmer 1984;Murphy et al. 1987;Yoshioka et al. 1987), and the orientation of the limb during image acquisition (Jarrett et al. 2010;Morvan et al. 2017;Jamali et al. 2017). The choice of the method used to define the anatomical landmarks may yield different values of femoral torsion angles by up to 20° (Kaiser et al. 2016;Hartel et al. 2016;Schmaranzer et al. 2019;Scorcelletti et al. 2020), while limb positioning can influence femoral torsion by 12.5° in the same participant (Morvan et al. 2017). This is an important variability when considering torsion angle measurements ranging from −20° to 50° (Sankar et al. 2018). The relaxed position of the hip includes slight flexion, abduction, and external rotation (ER), which is the common posture assumed at rest in people with painful hip joint pathology. Sometimes the orientation of the limb during image acquisition can be controlled during the scan set up, however, in cases of significant pain, accommodations must be made to limb position. The other factors that can affect femoral torsion measures are directly related to the alignment axes selected for the femoral torsion measurement itself, therefore, are not necessarily impacted by limb orientation. Differences in limb position can be accounted for by performing stereo-radiographic measurements (i.e. virtual alignment of the femur) (Morvan et al. 2017), yet these techniques are not readily or clinically applicable. Therefore, new ways to account for limb orientation during a diagnostic imaging scan used to evaluate femoral torsion, such as computed tomography (CT), are needed to account for the discrepancy caused by limb orientation during the scan acquisition.
First steps in developing a method towards accurate femoral torsion measurements, is to understand the effect of using different alignment techniques on femoral torsion measurement and to define the scope of the impact that limb position alteration has on femoral torsion measurements. The aim of this study was to quantify how the variability in limb positioning during image acquisition influences femoral torsion measurements. This was accomplished using an algorithmic approach applied to the 3D femoral models generated from CT scans from a large imaging database. The algorithmic approach incrementally rotated the femur into different angles of hip flexion/extension and hip abduction/adduction to determine how the femoral torsion angle changed based on different hip positions. Additionally, the study aimed to determine how the choice of using a alignment technique defines a different range of normality in femoral torsion measurements. The present study could help to unveil the importance of implementing standard alignment procedures in the surgical planning stages for femoral osteotomies.

Data
All analyses were performed on anonymised-computed tomography (CT) data part of the SOMA database (Schröder et al. 2014;Schmidt et al. 2018). All CT scans in the database had been obtained per local legal and regulatory requirements, which included ethics board approval and patient informed consent, where applicable. CT scans in the database had been acquired exclusively for medical indications, such as polytrauma (20%), CT angiography (70%) and other reasons (i.e. total joint replacement) (10%). Automated morphometric measurements based on CT scans of the femur were performed with the Stryker Anatomy Analysis Tool (version 5.4). Anatomical features that were required for assessing the femoral alignment during image acquisition and femoral torsion measurements were selected on a correspondent model and automatically mapped onto the CT scans in the database using statistical shape modelling technique (SSM) (Schröder et al. 2014). The femoral head centre was defined by the centre of the best-fitted sphere on the bone surface of the femoral head. Femoral torsion was measured using the three-dimensional surface reconstructions by measuring the angle between the neck axis and the posterior condylar axis projected onto the transverse plane (Fuller et al. 2018). This Figure 1. In the standard radiological practice, femoral torsion is measured on axial MRI or CT slices as the angle formed between the posterior condylar axis (red solid line) and the femoral neck axis (blue solid line) based on axial or reformatted slices. In other words, femoral torsion can be obtained by subtracting Angle 2 from Angle 1, where Angle 1 is the angle formed between the posterior condylar axis and the horizontal line (red dashdot line) and Angle 2 is the angle formed between the femoral neck axis and the horizontal line (blue dash-dot line). This figure is representative of the Jarett method where the neck axis is drawn on a single coronal reformatted axial oblique image parallel to the long axis of the femoral neck (Jarrett et al. 2010). method differs from common slice-based methods for measuring femoral torsion in that the neck axis is based on the threedimensional femoral neck rather than based on (reformatted/ superimposed) slices. All cases (n = 2890) were visually inspected and samples with incorrect landmarks, clear signs of osteoarthritis, bone deformities, or osteophytes were excluded. The final count of femurs included in the analysis was 2727 (1373 left, 1354 right, 1422 males, 1300 females, 5 gender unknown).

Coordinate system
To assess limb position during image acquisition, a standard coordinate system was introduced ( Figure 3).
The coronal plane was defined by the centre of the femoral head and the medial and lateral posterior condyles. The transverse and sagittal planes were established perpendicular to this plane. Flexion extension was defined as a rotation around the medial lateral (ML) line with respect to the femoral head centre ( Figure 3). Adduction/abduction was defined as rotation around the anterior-posterior (AP) line with respect to the femoral head centre ( Figure 3). Distances between the centre of the femoral head and a point centred between the medial and lateral posterior condyles were measured in antero-posterior, medial-lateral, and superior-inferior directions, where the AP direction was related to the amount of flexion/extension, the ML distance to the amount of ab/adduction, and the superior-inferior distances to the femur length during image acquisition. Thus, the degrees Figure 3. Coordinate system centered at the center of the femoral head (red point). The x axis corresponds to the medial-lateral (ML) direction, the y axis to the anteroposterior (AP) direction and the z axis to the superior-inferior direction. Flexion/extension is defined as the rotation around the x axis with respect to the femoral head center, while adduction/abduction is the rotation around the y axis with respect to the femoral head center. The center of the posterior condyles is represented with a green point.
of rotation in flexion/extension and in adduction/abduction can be expressed in terms of AP and ML distances in mm, respectively, when the distance between the femoral head centre and the condylar centre is known ( Figure 4).

Effect of limb positioning on femoral torsion measurement assessed via an algorithmic approach
Femoral torsion was mathematically computed as the angle (blue angle θ in Figure 5(d)) between the posterior condylar axis vector (purple vector p * in Figure 5(a,b)) and the projection of the femoral neck axis vector (orange vector n 00 * in Figure 5(d)) onto the transverse plane (purple plane in Figure 5). Therefore, the variables that influence the femoral torsion measurements include the x, y, and z components of the femoral neck axis (n * ) and the rotation angles (α and β); the femoral length did not influence femoral torsion. The entire process to measure femoral torsion following the algorithmic approach is described in Appendix A.
The effect of limb orientation on femoral torsion measurement was assessed by measuring the change in femoral torsion angle, upon steps of 1° variation in the rotation angles α and β, in order to simulate positions of flexion/extension (rotation around the medial-lateral axis) and adduction/abduction (rotation around the anterior-posterior axis), respectively. Similarly, the variation of femoral torsion angle per % change in the x, y and z components of the femoral neck axis vector was estimated for a 400-mm-long femur (average femur length in the dataset). The x (ML), the y (AP) and the z (superior-inferior) components of the neck axis vector represented the neck length, the neck version and the neck-shaft angle, respectively. An empirical estimation of the influence of limb positioning on femoral torsion measurements was provided in Appendix B as a confirmation of the results obtained with the algorithmic approach.

Effect of the application of alignment techniques on femoral torsion measurements
Femoral torsion was measured on the transverse plane under different 3D position conditions: (1) No alignment (CT scan orientation as used in clinical practice standard); (2) Epicondylar alignment technique (alignment commonly used for hip arthroplasty); (3) Posterior condylar alignment technique (alignment requiring less and more reproducible landmarks).
Femoral torsion was measured as the angle formed on the transverse plane between the posterior condylar axis and the femoral neck axis, where the transverse plane is: • perpendicular to the line connecting the centre of the femoral head to the centre of the femoral posterior condyles for the posterior condylar alignment technique; • perpendicular to the line connecting the centre of the femoral head to the centre of the centre of the femoral epicondyles for the epicondylar alignment technique.
The ranges of femoral torsion measurements obtained with the different alignment techniques outlined above were then compared. To quantify the number of cases with an inconsistent femoral torsion measurement due to no alignment, the percentage of cases was plotted against the difference in femoral torsion due to alignment. . Conversion from mm distance between the femoral head center (green) and the condylar center (red) in the anterior-posterior direction (left) or mediallateral direction (right) to the flexion/extension angle (yellow) or adduction/abduction angle (purple) when the length between the femoral head center and the condylar center (pink arrow) are known.

Statistical analysis
All statistical analyses were performed in R (R Core Team (2017). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria). Normal distributions were confirmed with Kolmogorov-smirnoff tests. Femoral torsion was compared between different standard alignments using ANOVA with a TukeyHSD post-hoc test. A Levene's test was used to assess the equality of variances. For the purpose of showing the error in femoral torsion due to not considering limb orientation, Bland-Altman plots comparing different alignments were included. To assess the relation between femoral position and femoral torsion, linear regression was performed (and no consistent pattern for residuals was confirmed). Ranges of measurements are described by the 95% confidence intervals or as mean ± standard deviation as indicated in the text. A p-value less than 0.05 was considered statistically significant.

Effect of limb positioning on femoral torsion measurement assessed via an algorithmic approach
The algorithmic approach estimated that (for a median neck axis vector), for every degree of increase in flexion (AP direction), torsion decreased by 1.0°, while for every degree of increase in abduction (ML direction), torsion increased by 0.35° (Figure 6). However for cases with a varying neck axis (within the 95% CI) the change in torsion was up to 1.21° and as low as 0.8° per degree of flexion, and up to 0.53° and as low as 0.04° per degree of abduction. Figure 7 exemplifies the effect of accentuated flexion and extension positions of the limb on the femoral torsion angles θ, for the purpose to visualise the great influence of limb positioning on femoral torsion measurements.
The average femur orientation was 5.2° ± 0.9° of flexion and 3.8° ± 2.2° of abduction. The ranges of all variables for the 2727 specimen are shown in Table 1. The flexion angle (α) ranged (95%CI) between 3.4° and 6.9° and the adduction angle (β) between −0.6° adduction to 8° of abduction. The femoral neck axis vector pointed downwards (indicated by negative sign), laterally (indicated by positive sign) and frequently posteriorly (with positive sign). The average distance between the femoral head centre to the posterior condylar centre (representative of femur length) was 401 ± 31 mm and ranged between (95% CI) 340-461 mm.
Per percent increase in the neck axis vector components, torsion decreased by 0.22° for ML component which is representative of neck length (95% CI variation in component results in torsion change of: 5.78°), increased by 0.78° for the AP component which is representative of forward inclination or neck version (95% CI variation in component results in torsion change of: 31.7°) and decreased by 0.09° for superior-inferior component which is representative of upward inclination or neck-shaft angle (95% CI variation in torsion: 2.24°). This result indicates that forward/backward inclination of the limb is the main factor influencing torsion measurements. These results were confirmed by empirical measurements provided in Appendix B.

Effect of the application of alignment techniques on femoral torsion measurements
The normal range of femoral torsion (95% CI) was −8° to 25° for posterior alignment, −5° to 29° for epicondylar alignment and −5° to 34° for the original scanning orientation (Figure 8). Femoral torsion measured without alignment was significantly greater than femoral torsion measured with posterior alignment (average difference 5.8° ± 2.1°, p < 0.001, Figure 9(a)) or femoral torsion measured with epicondylar alignment (average difference 2.5° ± 1.7°, p < 0.001, Figure 9(b)). Alignment significantly reduced the femoral torsion measurement range (p < 0.001); as shown by the narrower range (maximum-minimum) of 68° for posterior and 67° for epicondylar alignment compared to the range of 80° without any kind of alignment. Similarly, the interquartile ranges were smaller for posterior alignment (11.4°) and epicondylar alignment (11.3°) when compared to no alignment (13.2°, indicated as CT in Figure 8). Posterior condylar alignment technique is preferred over epicondylar alignment technique, since it requires less and more reproducible landmarks. On the other hand, the detection of epicondyles for the epicondylar alignment technique is less accurate, and it can Table 1. Range of variables for calculating femoral torsion and as used in Figure 5. The range between the column with the header 2.50% and 97.50% is the 95% confidence interval; the range between the column with the header 25% and 75% is the interquartile range; the column with the header 50% shows the median. SD refers to standard deviation. Femur length refers to the distance between femoral head centre and condylar centre.  be particularly challenging in patients with advanced osteoarthritis (Folinais et al. 2013). Bland-Altman plots comparing different alignments are shown in Figure 9, for the purpose of showing the error in femoral torsion due to not considering limb orientation. Figure 9(a) shows a proportional bias when comparing femoral torsion measurements performed with posterior condylar alignment and without alignment, with a larger deviation for higher torsion values (R 2 = 0.45 and p < 0.001). This result is consistent with the fact that femoral torsion is more influenced by larger × component of the neck axis vector, representing the neck length. On the other hand, there was a consistent bias when comparing femoral torsion measurements performed with posterior condylar alignment and epicondylar alignment techniques (Figure 9(b)).
The absolute difference between femoral torsion measured with posterior alignment technique and without alignment minus their mean shows that the error in femoral torsion measurement due to the lack of alignment is at least 1° for 62% of all cases, at least 3° for 12% of all cases and at least 5° for only 2% of all cases (Figure 10).

Discussion
The present investigation found that limb positioning during image acquisition greatly influences femoral torsion measurements. Femoral torsion measurement decreased by a degree per every degree of hip flexion when quantified using an algorithmic approach (see Figure 5), and the different amounts of hip flexion and extension were shown to vary torsion measures by more than 5° (see Figure 9). Frontal plane limb orientation was shown to increase femoral rotation up to 0.35 degrees per degree of hip abduction (see Figure 5). These results indicate that sagittal plane limb position (i.e flexion/ extension) influences femoral torsion more so than frontal plane femoral orientation, however, variability in limb positioning in either plane can influence femoral torsion measurements. Also, the choice of not aligning the femur versus using an alignment technique (i.e. posterior condylar alignment or epicondylar alignment) yields a difference up to 5.8° in femoral torsion measurement between the aligned and non-aligned cases (see Figure 8). When three-dimensional stereoradiographic measurements are performed, the patient positioning is less relevant because the leg orientation can be aligned during image post-processing and provide the most consistent measurement. However, three-dimensional stereoradiographic measurements are not accessible for all radiology centres. Therefore, strategies for limb alignment in neutral position should be implemented during image acquisition in order to improve the surgical planning stages for procedures, such as femoral osteotomies.
Alterations of femoral torsion measurement of 5° can influence the clinical interpretation of these measurements when determining between normal versus pathological morphologies. Beyond affecting the diagnostic evaluation process, inaccurate estimations of femoral torsion also alter the surgical planning phase, for example, the derotational femoral osteotomy correction can be overlooked due to too much flexion while scanning. The current study found that a limb positioning in the CT scanner other than neutral alignment can result in up to 5° change in femoral torsion measurements demonstrated in 98% of the cases (Figure 10). The greatest impact was demonstrated with the hip positioned in flexion/extension position. Morvan and colleagues (Morvan et al. 2017) also reported an average difference between measurements at neutral position and 5° of flexion/extension around 3°. On the other hand, Morvan and colleagues (Morvan et al. 2017) did not notice significant differences in femoral torsion measures between neutral and adduction/abduction positions. These results are not consistent with the current study findings where a small difference in femoral torsion was noted, although the magnitude of the change in torsion was minimal. These discrepancies in the results may be attributed to a different definition of flexion or to modifiable factors, such as patient's positioning during different imaging modalities that can be corrected for, or to morphological/anatomical non-modifiable factors that will still influence the measure and thus need to be accounted for. For instance, the current study corrected for a possible presence of internal rotation due to the patient's positioning during imaging. Figure 8, comparing femoral torsion performed with and without alignment, confirms that an alignment procedure should be performed before carrying out femoral torsion measurement, in order to correct for the effect of limb positioning, without particular preference for the chosen alignment technique. Alignment is also of fundamental importance in order to improve the reproducibility of the results. Regarding the differences in femoral torsion measurements depending on the landmarks and alignment technique used, the results of the present study, showing a difference up to 5.8° in femoral torsion measurement between the aligned and non-aligned cases, are in line with previous studies, which reported differences in mean values between methods up to 10° (Kaiser et al. 2016), and up to 20° for people with excessive anteversion (Kaiser et al. 2016;Schmaranzer et al. 2019). Clinically, procedures such as limb stabilisation strategies (taping the feet in neutral position) during scanning, should be used to promote reproducibility of limb positioning in cases involving surgical planning for hip morphologic pathologies (Malloy et al. 2019).
A limitation of this study was that the effect of internal/ external rotation was not investigated, because it was assumed that this would be mostly in-plane rotation, which does not affect the torsion measurement. The data considered for the current study was limited to 'normal' data and was not specific   to femoroacetabular impingement syndrome patients. The proposed methods are not able to distinguish if the additional torsion to correct for, is due to simulated flexion/extension or to the actual positioning of the patient's limb during image acquisition. The methods are also not apt to discern between infra and supra trochanteric version as they consider a combined rotation of shaft and neck rather than separate, but this is typical of the standard approaches. A 3D evaluation of femoral neck, considering both neck shaft angle and infra/supra trochanteric torsion of the femur, would allow for more accurate estimations of actual values of femoral torsion. Considering the separate rotation becomes particular important when a derotational femoral osteotomy (DFO) procedure is being planned in order to correct the aforementioned morphological disorders (while minor retroversion can be treated with arthroscopic femoroplasty, excessive retroversion requires a DFO treatment) (Matsuda et al. 2014;Edmonds et al. 2020). In these cases, the rotation of the femur can be assessed in a segmental way, which is unaffected by limb positioning. Following the segmental approach for torsion calculation, it has been made possible to show that most of the rotation of the femur is below the lesser trochanter, about 1/3 above and 2/3 below (Waisbrod et al. 2017;Alpay et al. 2020); average total femoral torsion was 22.6 ± 8.7°, proximal torsion 47.7 ± 10.6°, mid-torsion −33.4 ± 9.9°, and distal torsion 8.3 ± 3.2° (n = 30) (Ferlic et al. 2018).
In conclusion, limb positioning greatly influences femoral torsion measurements, with a major effect of flexion/extension positions. Over or under estimation of femoral torsion due to improper patient positioning during CT scans (and the lack of stereoradiographic measurements and/or alignment) could result in misdiagnosis and ultimately to surgical planning errors (Wang et al. 2021).

Disclosure statement
FML and MK are employees of Stryker and JWG, RCM and SJN are paid consultants of Stryker. MG and PM have no disclosures. We believe that the professional and financial affiliations did not biased the content of the manuscript

Funding
No specific funding was received for this work.

Appendices Appendix A. Mathematical description of the algorithmic approach used to quantify changes in femoral torsion with varying leg position
Changes in femoral torsion with varying leg position were quantified by mathematically describing the angle between the condylar axis and the neck axis on the axial plane. The section below explains the steps to obtain the mathematical formulation of femoral torsion: (1) Rotation of the femoral neck axis (to simulate flexion/extension or adduction/abduction). n * is the neck axis vector with components n x , n y , n z , corresponding to the medial-lateral component of the vector (representative of neck length), the anterior-posterior component of the vector (representative of neck version) and the superior-inferior component of the vector (representative of the neck shaft angle), respectively. The first step of the algorithmic approach consists in applying rotations to n * around x (ML direction) and y (AP direction) axes of angles α and β in order to simulate flexion/extension and adduction/abduction, respectively. The rotated neck axis, n 0 * , with components n x 0 , n y 0 , n z 0 , can be described as: (2) Projection of the (rotated) femoral neck axis onto the axial plane. The rotated neck axis vector n 0 * is projected onto the transverse plane at the condylar axis (with distance c) to obtain the rotated/projected neck axis vector n 00 * The average change in torsion was of 0.138° per mm in more anterior position of the femoral head when performing a rotation around the ML axis (flexion-extension) in steps of 0.9° and of 0.039° per mm in more lateral position of the femoral head when performing a rotation around the AP axis (adduction/abduction) in steps of 2.2° ( Figure B2). Assuming a femoral length of 400 mm, the average change in torsion, as measured using the empirical approach, was of 1.0° per degree of flexion and of 0.27° per degree of abduction which matched with the algorithmic observations. Figure B1. Femoral torsion boxplot or mean standard deviation (SD) for original position and adduction/abduction (mediolateral) and flexion/extension (anteroposterior) positions as measured empirically (n = 2727). Figure B2. Change in femoral torsion angle with changing limb orientation. a) Change in femoral torsion as it correlates to the change in distance between the centre of the femoral head and centre of the posterior condyles measured in the AP direction when performing a rotation around the ML axis (flexion-extension) in steps of 0.9°. b) Change in femoral torsion as it correlates to the change in distance between the centre of the femoral head and centre of the posterior condyles measured in the ML direction when performing a rotation around the AP axis (adduction-abduction) in steps of 2.2°. Each dot represents a sample and dots are connected through black lines. The yellow line represents the average slope.