Statistical Shape Modeling of Femur Shape Variability in Female Patients with Hip Dysplasia

Abstract

Although increasing evidence suggests that abnormal femur geometry in developmental dysplasia of the hip (DDH) may contribute to intra-articular damage and the development of hip osteoarthritis, a comprehensive 3D description of femoral abnormalities in DDH remains incomplete. Statistical shape modeling (SSM) was used to quantify three-dimensional (3D) geometric variation among femurs in female patients with DDH and control subjects. SSM correspondence points (n = 8,192) were placed on each femur using a gradient descent energy function to derive mean DDH and control femoral shapes and principal component analysis (PCA) was then used to describe shape variation. PCA results were associated with common 2D radiographic measures of femur shape using general linear models. For patients with DDH, the first eight principal components (modes) captured 90.9% of the cumulative variance accounted for (VAF). Notably, mode 2 captured 23.6% VAF and described variation in femoral version, the neck-shaft angle, and femoral neck length, while mode 3 captured 16.4% VAF and described variation in femoral version, femoral head size, and femoral offset. SSM captured complex geometric deformities in DDH, which may not be fully described by 2D measures of the acetabulum and proximal femur alone. By determining the primary shape variations among femurs in cases of DDH, SSM may further understanding of pathologies on the femoral side of dysplastic hips, in context with more commonly recognized acetabular deformities. This article is protected by copyright. All rights reserved

INTRODUCTION

Developmental dysplasia of the hip (DDH) is a structural pathology characterized by a shallow acetabulum that fails to provide full coverage and stabilization of the femoral head.^1–3 This abnormal bone structure results in altered stress on the intra-articular cartilage and labrum^4,5, which increases the risk of developing hip osteoarthritis (OA) by upwards of 4.3 told.^6,7 To prevent or slow development of hip OA, hip preservation surgery for DDH involves reorienting the acetabulum relative to the femoral head to provide more complete coverage and aims to establish normal joint loading.^8–10 Currently, diagnosis and surgical correction of DDH primarily focus on the acetabulum, yet abnormal femoral shape is present in many DDH cases, with excessive femoral anteversion, femoral head asphericity and increased coxa valga being the most commonly reported.^11–14

Further understanding the 3D shape variability of femurs in cases of DDH may help identify abnormal articulation between the femur and acetabulum and how each structure contributes to mechanisms of intra-articular damage. Understanding the shape variability within this population may also better elucidate shape morphology similarities and differences in patients with DDH and other proximal femur pathologies (e.g. femoroacetabular impingement syndrome), which are poorly defined. Furthermore, shape variability of the distal femur may be relevant to the DDH population because it can affect lower extremity alignment and transmission of loads from the ground to the hip joint. Greater knowledge about proximal and distal femur shape in DDH can inform pre-surgical planning, and provide insight regarding the varied long-term joint survivorship within this population.¹⁵

Statistical shape modeling (SSM) is a population-based statistical tool that can objectively quantify shape variation.^16,17 SSM involves a distribution of corresponding points across a set of shapes representing a population of interest to characterize the location and relative magnitude of shape variability among individuals within that population.^18,19 SSM has been used to further the understanding of shape variability in a variety of orthopaedic populations^18,20–27, yet it has not yet been applied in a DDH population.

Current clinical measures to classify hip geometry use a limited set of discrete features on the acetabulum (e.g. lateral aspect of acetabular rim) and femur (e.g. deviation from a best fit circle) based on plain radiographic images or a series of two-dimensional (2D) images from computed tomography (CT) or magnetic resonance imaging (MRI).^1,2,28,29 However, 2D descriptions of geometry may misidentify (or fail to identify) deformities and cannot adequately describe 3D geometry, which can hinder diagnosis and treatment planning. If established, the relationships between 3D shape variation and clinical measures could further refine the diagnostic tools that most completely describe DDH pathology.

To advance our understanding of geometric pathologies in DDH, the primary objective of this investigation was to develop a SSM of femurs in patients with symptomatic DDH and describe the most common types of 3D shape variation. The second objective was to test for associations between SSM descriptions of shape variation and measures acquired from 2D radiographs and functional measures of hip joint ROM.

METHODS

Patient Selection

CT images from 76 female patients with DDH were retrospectively included from the Washington University School of Medicine Department of Orthopaedic Surgery. All patients were skeletally mature (age: 27.4 ± 8.1 years [range: 15 – 50 years]), had BMI: 24.5 ± 3.2 kg/m² [range: 17.1 – 33.7 kg/m²], had undergone a CT scan of the hip and knees as part of clinical care, and provided written consent to be included as part of a larger Institutional Review Board-approved study. Diagnoses of DDH were made by an orthopaedic surgeon (JCC, JJN) based on radiographic measures (lateral center-edge angle³⁰ (LCEA) < 20°) and presence of symptoms, and were identified as candidates for periacetabular osteotomy surgery. CT images were acquired using a Siemens SOMATOM Definition AS+ scanner (100 kVp tube voltage; 512 × 512 acquisition matrix; 1.0 pitch; 100 mA tube current). Hip images (femoral head to lesser trochanter) were acquired with a 0.6 mm slice thickness and knee images (proximal tibial plateau to superior of the femoral condyles and trochlear groove) were acquired with a 3 mm slice thickness and resampled to 0.6 mm. Femurs with a diagnosis of Legg-Calvé-Perthes or Slipped Capital Femoral Epiphysis, as well as previous surgery, were excluded.

With Institutional Review Board approval, CT scans for control subjects were retrospectively included from female patients who presented to the emergency department of our institution. Inclusion criteria for control images included: CT scan of the whole femur (proximal femur to tibial plateau), aged: 15 – 40 years, BMI < 30 kg/m², and no radiographic evidence of DDH. Of 123 potential candidates, 24 subjects met the inclusion criteria. Images were acquired using a Siemens SOMATOM Definition Flash scanner (120 kVP voltage; 512 × 512 acquisition matrix; 1.0 pitch; 100 mA tube current) with a 1 mm slice thickness and resampled to 0.6 mm.

Clinical Descriptors of Morphology

Radiographic measurements to describe DDH were acquired from a series of x-ray images using previously described methods (Fig. 1a)³¹. Acetabular shape was described using the LCEA (anteroposterior view), acetabular inclination (AI) (anteroposterior view), and the anterior center edge angle (ACEA) (false-profile view). Femoral head shape was described using the α-angle (Dunn view) and head-neck offset (HNO) (Dunn view). Additional descriptors of femur shape included the neck-shaft angle (NSA) (anteroposterior view), overall femoral version (oblique CT image, Fig. 1b), supratrochanteric and infratrochanteric version³² (oblique and axial CT, Fig. 1c).

Figure 1.

Radiographic descriptors of morphology from a) 2D radiographs b) volumetric CT images and c) 3D surface reconstruction from.

Standardized radiographic images were not available for the retrospective control group. Therefore, only global femoral version, supratrochanteric and infratrochanteric version were measured. Control values for the remaining radiographic descriptors were acquired from previously published investigations.

3D Reconstruction and Preprocessing

The proximal and distal femur bone geometries of the DDH group, and whole femurs of the control group, were segmented and reconstructed from CT image data in Amira (v6.4.0, Thermo Scientific, Waltham, MA). The femoral shaft was created by linear interpolation between the most inferior and superior slice of the proximal and distal image sets, respectively (Fig. 2). For consistent shape comparison to the DDH group, proximal and distal femur geometries of the control group were created by cropping the whole femur 6 cm distal to the most medial prominence of the lesser trochanter and 6 cm proximal to the lateral condyles, respectively (Fig. 2). These geometries were then linearly interpolated, as previously described. To reduce segmentation and linear interpolation artifact, 3D reconstructions were triangulated and smoothed. To remove overall variability in femur size, which is known to vary significantly based on demographics (age, height), each femur was rigidly scaled to an arbitrarily chosen “master” femur²⁹ (Fig. 2). Femurs were then aligned using an iterative closest point optimization algorithm to minimize the root mean square distance between surfaces in Amira (inter-iteration RMS < 0.0001) (Fig. 2). Finally, femurs were converted to binary volumes with a 512 × 512 × 512 bounding box and isotropic voxel resolution of 1.0 mm × 1.0 mm × 1.0 mm.

Figure 2.

SSM pipeline. Reconstructions from CT images were aligned with an iterative closest point optimization; correspondence particles were placed on each femur to identify the mean shape and all dimensions of variation. PCA was used to identify primary modes of variation.

Statistical Shape Modeling

The optimization techniques used within the SSM are described in detail elsewhere.¹⁸ Briefly, surfaces from Amira were processed within ShapeWorks software¹⁶ by converting each to i distance transform, which defines each 3D shape to include the physical distance of each voxel in shape space relative to a global origin within an image volume¹⁹, and volumes were automatically cropped to a cuboid volume of 124 × 98 × 442 bounding box size. Within ShapeWorks, 8,192 correspondence particles were placed on each femur using a gradient descent energy function that balances the ensemble entropy of particle distribution on each shape surface.¹⁶ Particle configurations were then used to generate separate mean shapes for the DDH and control groups.

Quantitative Analysis

The Hotelling T² test was used to test for significant differences in mean shapes between the DDH and control groups. Inter-group differences in mean shapes were then expressed as the distance between mean DDH shape relative to the mean control shape. Global, supratrochanteric, and infratrochanteric femoral version measurements were compared across the DDH and control groups using a two-tailed independent samples t-test. Levene’s test was used to assess equality of variance, and if significant the unequal variance independent t-test was used.

Principal component analysis (PCA) was used to reduce the high-dimensionality of variation across all correspondence particles to a set of linearly uncorrelated modes of variation. PCA yields a series of non-zero eigenvalues that characterize the amount of variance explained within an orthonormal eigenvector. PCA ranks each uncorrelated dimension of variation as “modes,” based on order of the eigenvalues; thus, modes of higher rank describe larger amounts of overall shape variation. A parallel analysis, which is used to quantify the inherent noise of shape variation within the sample population, was used to determine the number of statistically significant modes of variation.³³ To identify the location of variation in relation to the mean femur, the absolute maximum distance of each PCA mode at ± 2 standard deviations from the mean shape was determined. Because SSM and PCA were applied separately for both the DDH and control groups, the PCA modes identified for each group are independent from one another.

PCA results were quantified using a loading factor (λ), which is a scaling factor that relates the mean shape (μ) and its direction of variation (eigenvector) to the amount of variation (eigenvalue):

$$\text{eigenvalue}=\mu +\lambda (\text{eignvector})$$ (1)

Statistical relationships between loading factors and 2D radiographs were determined using a general linear model to represent a multiple linear regression between independent (λ) and dependent (2D radiographs) variables with Bonferroni corrections to control for Type I error. The Shapiro-Wilk test was used to assess the normality of the data. If non-normal, distributions were transformed to normal using a logarithmic transformation. Level of significance for all statistical analyses was set at α = 0.05 and performed using R³⁴ and SPSS (v24.0, SPSS Inc., Chicago, IL).

RESULTS

Group Comparison

The mean DDH and control shapes were significantly different (P < 0.001, T² = 62.4). The largest morphological difference was observed proximally in the femoral head, in which the mean DDH shape was more anteverted and had a larger femoral neck length (Fig. 3).

Figure 3.

Mean shapes of the DDH and control groups. Contour plots show the distance of the mean DDH shape relative to the mean control shape.

Clinical Descriptors of Morphology

Global and supratrochanteric femoral version of the DDH group was significantly greater than that of our control subjects (P = 0.007, t = 3.358; P = 0.002, t = −3.129, respectively) (Table 1). No differences were found in infratrochanteric version across groups. Other radiographic measures of the DDH group were outside typical mean ranges for control femurs described in the literature (Table 1).

Table 1.

Mean ± 1 SD 2D radiographic measures of the femur and acetabulum. For the control group, radiographic measurements requiring x-rays were taken from the literature. Measures of version (global, supratrochanteric, and infratrochanteric) were measured from the CT images of the current sample.

Radiographic Measure (view)	DDH Group	Control Group(ref)
Lateral center edge angle (Anteroposterior view)	13.9° ± 6.4°	>20°31
Anterior center edge angle (false-profile view)	17.0° ± 9.5°	25° – 35°31
Acetabular inclination (Anteroposterior view)	15.3° ± 5.6°	0° – 10°31
α-Angle (Dunn view)	53.0° ± 14.4°	<50°49
Neck-shaft angle (Anteroposterior view)	135.3° ± 6.5°	120° – 135°49
Head-neck offset (Dunn view)	4.4 mm ± 2.3 mm	<9 mm50
Global Version (CT)	28.8° ± 12.0° *	20.1° ± 6.2° *
Supratrochanteric Version (CT)	28.9° ± 12.3° *	38.7 ° ± 15.7° *
Infratrochanteric Version (CT)	−21.6° ± 12.1°	−16.3 ° ± 9.8°

^*indicates significant difference between groups (P < 0.05).

Principal Component Analysis

The first eight PCA modes were significantly non-spurious for the DDH group, based on parallel analysis and described 90.9% of the total variance accounted for (VAF) (Fig. 4). Specifically, mode 1 captured 28.6% VAF, followed by mode 2 at 23.6%, mode 3 at 16.4%, mode 4 at 8.1%, mode 5 at 6.6%, mode 6 at 2.8%, mode 7 at 2.0%, and mode 8 at 1.7% of the VAF. For the control group, the first seven modes were significant following parallel analysis and described 91.6% of the total VAF (Fig. 4).

Figure 4.

Scree plot showing the cumulative shape variation in significant PCA modes of the DDH (blue) and control (green) groups. PCA modes are ordered based upon the associated eigenvalue (left axis), which determined the cumulative shape variation (right axis). SSM and PCA were run separately for each group; DDH and control PCA modes are independent from one another.

Specifically, for the DDH group, variation in mode 1 was most substantial in the width of the femur (Fig. S–1, Supplemental Video 1). Mode 2 primarily described variation in proximal femoral version, the neck-shaft angle, and femoral neck length (Fig. 5, Table 2, Supplemental Video 2). Mode 3 described variation in distal femoral version, femoral head size, and femoral offset (Fig 5, Table 2, Supplemental Video 3). Shape variations captured in modes 4 through 8 were subtle and primarily included variation in proximal femur shape (Fig. S–2 – S–6; Supplemental Videos 4–8). For the control group, mode 1 described variation in the neck shaft angle and the width of the femoral condyles. Mode 2 described variation in height and width of the greater trochanter.

Figure 5.

Shape variation captured in PCA modes 2 and 3 of the DDH group. Within each mode, shape variations are shown at ±2 standard deviations from the mean shape. Contour plots identify areas of deviation with respect to the mean shape. Maximum deviation occurred at the proximal femur in Mode 2 and at the distal femur in Mode 3. Red lines qualitatively identify the greatest components of variation captured within each mode.

Table 2.

Location and value of the maximum distance of each significant PC A mode from the mean for the DDH group. Locations are with respect to the global origin and axes shown (i.e. positive z-coordinate indicates more proximal location).

	Mode	Value (mm)	Coordinate (x, y, z)
	1	8.52	(25.80, 16.34, −95.08)
	2	9.64	(7.05, 4.30, 209.46)
	3	7.05	(20.73, 46.50, −161.17)
	4	5.44	(−9.78, 3.57, 225.30)
	5	5.88	(−6.24, −2.36, 126.48)
	6	3.19	(−30.27, −2.36, 99.68)
	7	4.09	(−2.62, 22.07, −159.16)
	8	3.86	(−6.24, −10.50, 179.89)

General Linear Regression

The general linear regression model identified multiple radiographic measures that were significantly (P < 0.05) associated with PCA loading factors (Table 3). There was a significant relation between shape variation in PCA mode 2 and the LCEA (P = 0.002), the neck-shaft angle (P < 0.001), global femoral version (P < 0.001), and infratrochanteric version (P = 0.001). In addition, shape variation described in PCA mode 3 was also significantly related to global femoral version (P < 0.001) and infratrochanteric version (P < 0.001).

Table 3.

Standardized beta coefficients determined from the general linear regression models. Highlight indicates significant relationships (P< 0.05/9 = 0.006) between 2D radiographic measures and PCA loading factors.

		Standardized beta coefficient (top row) with P-value (bottom row)
	R2	λ1	λ2	λ3	λ4	λ5	λ6	λ7	λ8
Lateral center edge angle	0.230	−0.137 P = 0.206	−0.343 P = 0.002	0.018 P = 0.867	0.090 P = 0.406	−0.164 P = 0.132	−0.237 P = 0.030	0.110 P = 0.309	0.001 P = 0.994
Anterior center edge angle	0.187	−0.267 P = 0.018	−0.203 P = 0.073	0.116 P = 0.294	0.129 P = 0.245	−0.143 P = 0.201	−0.168 P = 0.131	0.004 P = 0.973	0.018 P = 0.870
Neck-shaft angle	0.312	0.033 P = 0.748	0.417 P < 0.001	0.028 P = 0.783	−0.261 P = 0.013	0.262 P = 0.012	0.155 P = 0.132	0.015 P = 0.883	0.065 P = 0.527
α-angle	0.108	0.048 P = 0.678	0.169 P = 0.153	−0.052 P = 0.653	−0.033 P = 0.776	−0.019 P = 0.872	0.216 P = 0.065	0.096 P = 0.411	−0.107 P = 0.363
Head-neck offset (Dunn)	0.074	0.158 P = 0.184	0.106 P = 0.377	−0.022 P = 0.853	0.145 P = 0.222	−0.042 P = 0.719	0.020 P = 0.865	−0.112 P = 0.345	0.037 P = 0.759
Acetabular inclination	0.276	0.156 P = 0.138	0.104 P = 0.327	−0.111 P = 0.289	−0.145 P = 0.168	0.111 P = 0.292	0.247 P = 0.020	−0.349 P = 0.001	0.152 P = 0.151
Global Version	0.865	−0.114 P = 0.014	0.648 P < 0.001	0.655 P < 0.001	0.023 P = 0.609	0.027 P = 0.556	0.013 P = 0.770	−0.061 P = 0.177	−0.010 P = 0.830
Supratrochanteric Version	0.251	−0.019 P = 0.855	−0.088 P = 0.416	0.155 P = 0.147	0.335 P = 0.002	−0.070 P = 0.509	0.082 P = 0.443	−0.301 P = 0.006	−0.101 P = 0.348
Infratrochanteric Version	0.462	−0.170 P = 0.062	0.324 P = 0.001	0.474 P < 0.001	−0.009 P = 0.921	−0.159 P = 0.081	−0.205 P = 0.025	0.166 P = 0.069	−0.030 P = 0.738

DISCUSSION

The primary objective of this investigation was to develop a SSM of the femur in a population diagnosed with symptomatic DDH. Our results indicate that the largest amount of variation among DDH femurs was in femoral version, which was most evident in the proximal femur. Furthermore, when compared to an average control shape, the greatest morphological differences occurred proximally, where the DDH femur demonstrates greater femoral anteversion and an increased femoral neck length. The considerable variability in femur geometry found within a relatively restricted and well-defined sample of patients (based on geometric features of the acetabulum) highlights the potential influence of the femur on symptom development and disease progression among patients with DDH. The second objective ws to identify associations between 3D modes of variation and common clinical measures of morphology. Our results suggested an association between 3D shape and measures of global version, as well as other measures commonly used for diagnostics of DDH (LCEA, NSA). Associations between complex 3D shape morphology and 2D radiographic measures may help improve the overall understanding of the heterogeneity of shape variability within the DDH population and inform new methods for diagnosis and evaluation.

The current SSM results revealed substantial variation in femoral version in PCA modes 2 and 3, indicating that this is one of the primary forms of femur shape variation within the DDH population. Our results indicated that the location of maximum deviation from the mean shape within PCA mode 2 occurred proximally, suggesting that femoral version variability is more prominently due to rotation of the proximal femur relative to the distal femur. Although not as prominent as proximal variability, SSM results of the DDH group also revealed substantial variation in distal femoral version as captured in PCA mode 3. Clinically, it is well established that extreme femoral version is associated with the development of hip OA³⁵ and worse outcomes after hip arthroscopy³⁶. However, the majority of prior research within this population has lacked a 3D description of shape variation, included only the proximal femur, and examined limited sample sizes, making the amount of variation in version difficult to quantify. It has previously been shown that increased femoral anteversion in femurs with DDH can be attributed to both supra-and infratrochanteric measures.³² Our results support the concept that while proximal morphology substantially influences version variability, abnormal version in DDH is a combined effect of distal and proximal femur variability. This finding may be of interest for surgical decision making about proper correction of the femur via de-rotational femoral osteotomy in conjunction with periacetabular osteotomy to improve the coverage of the femoral head and restore or preserve lower extremity alignment.³⁷

Comparison of DDH and control mean shapes can be used to identify the primary location of shape differences between groups. In the current study, the shapes of DDH femurs were significantly different than that of control femurs, with the greatest morphological differences occurring proximally resulting in significantly greater supratrochanteric version. Our results indicate that the morphological differences were primarily attributed to increased femoral anteversion in the DDH group, which is consistent with previous findings.^14,38 In addition to differences between mean shapes, the location and type of shape variation was fundamentally different across groups. The proximal variability that was most evident in DDH was in version, which differed from the control group who demonstrated variability in head sphericity and coxa valga. Understanding how the type and prevalence of shape variability in femurs of patients with DDH differs from that of a controls can inform studies of surgical treatment for DDH that aims to restore coverage of the femoral head and joint congruence closer to an asymptomatic control hip.^8,39 Specifically, identifying the location of version is of clinical relevance to help inform surgeons who are deciding whether to perform a derotational femoral osteotomy and its location, which is var,able.^40–42

The SSM revealed a significant amount of femur shape variation in a population of patients who were diagnosed based on well-defined and constrained measures of acetabular shape. This is an important consideration given the relatively greater emphasis to acetabular deformities in both clinical and biomechanical analyses of DDH^43,44 This is quantitatively supported through moderate associations between shape variation and radiographic measures commonly used to describe femur morphology (neck-shaft angle and femoral version). Specifically, variation in PCA mode 2 was associated with the LCEA, which suggests a developmental relationship between the acetabulum and femur that may influence the severity of the dysplasia. Such a finding should be interpreted cautiously, but motivates the need for additional studies that quantify the mechanical relationship between femurs and acetabula through childhood and adolescence.

The current results also highlight the complexity of geometric deformities in DDH, which m ay not be comprehensively represented by 2D radiographs of the proximal femur alone. The relationships of 3D shape variation to 2D metrics elucidated with the current and future SSM may improve the overall understanding of the heterogeneity of shape variability within the DDH population and inform new methods for diagnosis and evaluation. Despite the evident proximal variation within PCA mode 2, the corresponding loading factor was not statistically significantly related to 2D measures of supratrochanteric femoral version. This lack of statistical significance may stem from the inherent difficulty of relating 2D metrics with limited reliability to complex 3D shapes.

PCA mode 1 accounted for the largest amount of VAF (28.6%), primarily describing variation in the scaling of femoral width. Although variation in femoral width is expected to vary based on demographics⁴⁵, we did not expect this to be the primary mode of variation within this population. Due to the retrospective nature of this study, there was variability in where the scan of the distal femur began, which could not be standardized post hoc. As a result, some femurs were imaged just superior to the epicondyles, while others included more of the distal femoral shaft. Consequently, the proximal to distal interpolation required to generate the whole femur likely introduced artificial variation in the width of the femur shaft, which cannot be directly quantified. Furthermore, when each femur was rigidly scaled to the size of the “master” femur, a scale factor was determined and uniformly applied in three orthogonal planes. Because differences in femur length tended to be greater than femur width differences, length was the driving determinant of the uniform scale factor. As a result, width variation found in PCA mode 1 was due, in part, to an artifact of the scaling procedure. Also, variation in femoral width was not prominent in the control group, in which the proximal and distal heights of the scans were standardized across image sets. Because the amount of natural versus spurious femoral width variation cannot be directly quantified, and femur width is unlikely to be of clinical significance to this population, we recommend caution when interpreting the implications of this variation.

There are several limitations to consider with this investigation. First, the SSM was not applied to the acetabulum. Because a comprehensive description of the 3D shape of femurs in patients with symptomatic DDH did not yet exist, we chose that as the focus of this investigation. Future work will implement simultaneous SSMs of shape variation in the acetabulum and femur. Second, the femur shaft was created based on linear interpolation between the proximal and distal CT images. Therefore, patient-specific shape variation within this region, including possible contribution to femoral version, was not identified by the SSM. Because image data were collected retrospectively and the proximal and distal femoral segments were isolated to minimize radiation exposure, this is an inherent limitation within this dataset. Third, this sample included only female patients and findings may not extrapolate to male patients with DDH. However, because females comprise most (72–80%) of patients presenting with DDH symptoms, these results represent the majority of the symptomatic clinical population.^46,47 Fourth, RMS alignment errors between femoral reconstructions may affect SSM results. To minimize any such effect, the femurs were aligned with an iterative closest point algorithm that included points across the entire femur surface and used a strict relative RMS error threshold of 0.1 mm. Thus, we expect any confounding alignment errors on SSM results to be negligible. Finally, interpretation of SSM results has inherent subjectivity. Thus, PCA loading values were used in this and other studies as objective descriptors of shape variability.^18,23 While subjectivity in SSM interpretation cannot be completely removed, additional objective measures, such as z-scores, may assist in future analyses to further identify shape variability not fully described by a single loading value from each orthogonal PCA mode.⁴⁸

By determining primary modes and locations of femur shape variation in femurs with DDH and comparing to controls, SSM may further clinical understanding of pathologies on the femoral side of dysplastic hips, in context with more commonly recognized acetabular deformities. Future work will apply SSM results from this study to better inform musculoskeletal models by including geometric descriptions of femurs within dysplastic hips. This can be used to elucidate the relative contributions of acetabular versus femoral deformities to pathologic intra-articular loading and soft-tissue damage.