Statistical shape modeling of the proximal femur bone for hip implant design optimization

Abstract

The femur is the major load-bearing skeletal component in the human body, and its proximal end is prone to either osteoporosis or high-energy injury-related fractures. When a fracture occurs, prosthetic implants, depending on the type and level of injury, are used to restore the normal biomechanics of the bone. Fracture fixation and the subsequent bone healing process depend on several factors, including the anatomical fitting quality of the prosthetic implant utilized. However, the standard commercially available prosthetic implants are generic, and commonly implants are designed and validated based on a limited set of cadaver bones, which may result in the incompatibility of implants to all patient groups. Utilization of an incompatible implant for patients may cause implant-related complications. In recent years, generic implants have been optimized for a specific population group on the basis of anatomical data obtained from the target population to improve the fitting quality of implants to the intended anatomical region. This study aimed to develop a statistical shape model (SSM) of the proximal femur bone and to carry out morphometric analysis of the femoral neck-shaft angle (NSA). The shape modelling process followed sequential steps, including image segmentation and 3D surface reconstruction, manual annotation of anatomical landmarks, establishment of surface correspondence across datasets, and model building via principal component analysis. Additionally, femoral NSA measurements are implemented. The quality of the SSM was validated through shape quality metrics: compactness, specificity, and generality. The validation result revealed that the first eleven principal components of the SSM represented 92.85% of the total variance in the model. Similarly, the specificity and generalizability of the model were approximately 1.33 mm and 0.83 mm, respectively.

Introduction

The femur is the longest and main load-bearing skeletal component in the human body. Its proximal end articulates with the acetabulum of the hipbone to form the hip joint (ball and socket joint), which allows the leg to move at all angles. The proximal femur (PF) region is highly vulnerable to fractures, mainly in the femoral neck and trochanteric regions¹. Globally, approximately 1.6 million proximal femur or hip fractures are estimated to occur annually². Among all fractures in the human body, proximal femur fractures account for 14%, and in terms of cost, it accounts nearly 72% of the total number of fractures³. Although there are limited data concerning the prevalence of proximal femur fractures in Ethiopia, a previous study indicated that out of the 115 patients referred abroad within one year for treatment, 41 (36%) underwent hip joint replacement surgery⁴. In another study, 50 locally treated total hip replacements (THRs) were reported⁵. These studies revealed the incidence of proximal femur fractures in Ethiopia.

Proximal femur fractures are typically treated with various prosthetic implants, depending on the level and type of injury. However, the quality of fixation and fracture healing is influenced by several factors, including bone shape variability and the availability of appropriately sized fixation implants that accommodate this variability in the population. Consequently, incorporating shape variability through systematic quantification is vital for developing fixation plates or prosthetic implants that fit the given population⁶. In recent years, population-specific implants have been introduced in arthroplasty to improve implant alignment accuracy and minimize implant-related complications associated with standard generic implants⁷. Aldieri et al.⁸ created three-dimensional statistical models of the proximal femur that combined shape and intensity information to predict the risk of hip fractures better, showing that the combined shape and intensity model was significantly more accurate than standard areal bone mineral density (aBMD) analysis. Bergiers et al.⁹ used statistical shape modeling (SSM) on retrieved metal-on-metal acetabular cups to identify the location of edge wear in vivo, showing that the parameters of implant positioning, especially the angle of inclination and anteversion, significantly affected the distribution of wear. Dupraz et al.¹⁰ developed population-specific statistical shape models (SSMs) to inform the design of total knee arthroplasty (TKA) implants and demonstrated that SSM-derived anatomical parameters were effective in optimizing implant sizing. De Angelis et al.¹¹ employed statistical shape modeling (SSM) to model the pelvic anatomy of patients with severe acetabular damage and demonstrated that the SSM-derived hip center of rotation was accurate compared with surgical planning and the opposite side, thereby validating the preoperative planning and positioning of the implant in complex hip revisions. Schmid et al.¹² proposed a statistical shape and intensity modeling (SSIM) method for data augmentation in medical imaging. They reported that the combination of shape and intensity synthesis had a positive effect on deep learning-based segmentation of pathological hip bones compared with traditional data augmentation methods. Betti et al.¹³ proposed a statistical shape model of the femoral medullary canal on the basis of CT scans, and they found that segment-specific analysis reveals substantial anatomical variation, thus facilitating the design of personalized distal femoral orthopedic implants.

In this context, the statistical shape modeling (SSM) technique has played a significant role in objectively quantifying and identifying anatomical variations in largely scattered data, and in performing population-based evaluations. The basic idea in SSM is to establish the average model and the main pattern of legal variations in shapes and spatial relationships of structures for the given training datasets¹⁴. This method is used to parametrize shape variability by providing an appropriate representation of shape and allowing shape constraints to be applied. The SSM enables us to build a flexible shape model from a set of shape instances to ensure that each shape fits the largest number of subjects in the given population of interest¹⁵. Despite these advancements, the majority of SSM-based studies on the proximal femur in humans have focused on European, North American, and Asian populations. There is a considerable dearth of morphometric and statistical shape modeling studies on African populations. In Ethiopia, although hip fractures constitute a considerable percentage of orthopedic surgical cases, there is a lack of quantitative studies on the morphology of the proximal femur based on three-dimensional CT images. The absence of a population-specific geometric model may obstruct the design and development of anatomically compatible implants for the population group.

Thus, the current study aims to establish a statistical shape model of the proximal femur in 3D using data from Ethiopian patients who underwent a CT scan. This study also aims to establish a scientific basis for optimizing the design of hip implants and developing orthopedic solutions for the Ethiopian population by understanding the primary modes of anatomical variation and the key geometric parameters of the femur, particularly femoral neck-shaft angle, relevant to the fixation and positioning of hip implants.

Methods

The general procedure used in this study for the development of the statistical shape model of the proximal femur from CT scan images is demonstrated. It consists of a series of steps, including the collection of CT images, image segmentation and 3D surface reconstruction, surface mesh refinement or preprocessing, correspondence establishment through landmark identification and registration, statistical shape model development, and model validation. The overall workflow of the modeling process is shown in Fig. 1.

Fig. 1.

General workflow of the modeling process.

Description of the image data

After submitting a letter to Jimma University to access CT image data, permission was granted, and one hundred two bilateral pelvic CT images were retrospectively collected from three different hospitals: Jimma University Medical Center, ALERT Hospital, and Myungsung Christian Medical (MCM) General Hospital. All patients underwent CT scans in the supine position with an imaging interval ranging from the entire pelvis to the proximal femur. CT scans were performed with nominal settings: tube voltage 120kVp, tube current 80–493 mA, and slice thickness 1.25–5 mm. The CT scan images were stored and imported into Digital Imaging and Communications in Medicine (DICOM) format for easier digital transfer and storage. For all the proximal femurs, CT images with signs of trauma such as fractures and joint disease, and demonstrating metallic implants, were excluded. Additionally, images that are too blurred and difficult for optimal segmentation in bone contours were also excluded. The collected bones were classified as healthy if they did not present any abnormal morphological feature or sign of joint disease, such as osteoarthritis. All patients’ proximal femur bones considered functional at the time of scanning by a radiologist are incorporated in the datasets. After defining the inclusion and exclusion criteria as described, 24 right proximal femora and a few left proximal femora were deemed healthy by a radiologist. Finally, 24 right proximal femora (14 males and 10 females) were included in this study, and the left proximal femora were excluded from the datasets due to the following reason. In statistical shape modeling, to increase the sample size, mirroring the left femur to match the right (or vice versa) is a common preprocessing technique. However, it introduces several key limitations, primarily stemming from physiological, functional, and pathological asymmetries between the two sides, and significant side-to-side differences exist between the left and right femur^16,17. The main limitations in mirroring include that while the left and right femurs are generally similar, they are not perfectly symmetric, such as leg dominance, which can lead to differences in bone density, structural rigidity, and specific geometric features (e.g., torsion or neck-shaft angle)¹⁸. The paper published by Pierre et al. suggests that even if overall right and left femur geometric, densitometric, and structural properties are not significantly different from one another, absolute left–right differences for individual patients can be significant, especially in the case of structural rigidity properties, and should be considered in separate clinical and research studies¹⁹. Therefore, in this study, only the right proximal femur is used to build the SSM. The number of right proximal femur CT scan images was limited because of the unavailability of CT scan images of the pelvic bones in scanning centers that were considered. Additionally, since the full-length femur bone was not available for the entire training set from all scanning centers, the right proximal femur bone was the region of interest for this study. The age at the time of scanning varied from 25 to 64 years, and a mean ± standard deviation (STD) age of 42 ± 8.7 years was considered to construct the proximal femur SSM. The Patient’s demography at the time of scanning is described in Table 1.

Table 1.

Patient demography at time of scanning.

No	Sex	Age	Slice thickness (T)	Dose info	Data obtained from
1	M	42	T:3 mm	480 mA, 120 kV	ALERT Hospital
2	F	37	T:4 mm	493 mA, 120 kV	ALERT Hospital
3	M	33	T:3 mm	458 mA, 120 kV	ALERT Hospital
4	M	36	T:5 mm	492 mA, 120 kV	ALERT Hospital
5	M	25	T:2.5 mm	310 mA, 120 kV	ALERT Hospital
6	F	28	T:3 mm	179 mA, 120 kV	ALERT Hospital
7	M	33	T:5 mm	335 mA, 120kv	ALERT Hospital
8	F	55	T:4 mm	315 mA, 120 kV	ALERT Hospital
9	M	44	T:4 mm	100 mA, 120 kV	ALERT Hospital
10	F	38	T:5 mm	347 mA, 120 kV	ALERT Hospital
11	M	39	T:2.5 mm	304 mA, 120 kV	ALERT Hospital
12	M	64	T:2.5 mm	368 mA, 120 kV	ALERT Hospital
13	M	41	T:3 mm	339 mA, 120 kV	ALERT Hospital
14	M	53	T:3 mm	301 mA, 120 kV	ALERT Hospital
15	M	36	T:3 mm	300 mA, 120 kV	ALERT Hospital
16	F	48	T:2.5 mm	300 mA, 120 kV	MCM General Hospital
17	M	59	T:1.3 mm	135 mA, 120 kV	MCM General Hospital
18	F	37	T:1.3 mm	80 mA, 120 kV	MCM General Hospital
19	F	40	T:5 mm	147 mA, 120 kV	MCM General Hospital
20	M	52	T:5 mm	80 mA,120 kV	MCM General Hospital
21	F	40	T:5 mm	107 mA, 120 kV	MCM General Hospital
22	M	48	T:3.8 mm	80 mA, 120 kV	MCM General Hospital
23	F	29	T:1.25 mm	–	Jimma University Medical Center
24	F	51	T:1.25 mm	–	Jimma University Medical Center

Image segmentation and 3D surface reconstruction

In this paper, a semi-automatic segmentation technique was performed using the global thresholding method to segment the CT data. The segmentation was held through global thresholding (Otsu-based) method with a combination of masking techniques utilized in 3D slicer v4.10.2 software. The thresholding technique is expressed in Eq. (1.1).

1.1

where T is the threshold value; x, y are the coordinates of the threshold value point, p (x, y) and f (x, y) are points located in the gray level image pixels. Hence, an image thresholding is defined as Eq. (1.2).

1.2

The result of the thresholding is a binary image, where pixels with an intensity value of 1 correspond to objects, whereas pixels with a value of 0 correspond to the background image.

In Fig. 2a, the white regions correspond to bone structures, whereas the gray regions represent surrounding soft tissues, including fat and muscle. During the thresholding process, pixel intensities associated with muscle and fat were classified as background, while pixel intensities corresponding to bone were identified as the region of interest. An initial threshold value (T) was therefore applied to achieve preliminary segmentation of the image. The segmented image is composed of two groups of pixels: pixels whose values are above or equal to the threshold value and those whose value is below the threshold value (f(x,y)<T). For accurate results, the threshold value is iteratively determined and used until the best segmentation result is achieved. The approximate thresholding lower value range from 125 to 244 with a mean value of 149.4. In Fig. 2a, the bronze area represents bone, and the black area represents the external background of the CT image. The bone areas comprise both the pelvic area and the proximal femur; however, the current study is limited to the proximal femur only as the region of interest. Since both areas have similar intensity values in the CT image, thresholding alone was insufficient. This implies that grey-level separation alone was inadequate for the segmentation process.

Fig. 2.

(a) Original CT image before further processing in 3D slicer software (b) Results of preliminary segmentation via Otsu-based global thresholding technique.

As illustrated in Fig. 3b, the two anatomical regions were separated via the “Paint” and “Islands” modules in 3D Slicer. Segmenting the femoral part from the ball and socket joint is challenging because of the similarity of the pixel value and the deep interconnection of the head of the femur with the acetabulum of the hip bone. Therefore, segmenting the case requires considerable effort. To segment the femoral head from the acetabulum of the pelvis part, in the course of masking through the “Paint” module, should cover only the femoral part without touching or including the component of the pelvic part. Otherwise, if we consciously or unconsciously include a very small component of the pelvis bone segmentation of the femoral head from the acetabulum will no longer be accomplished.

Fig. 3.

(a) Results of segmentation via the global thresholding module in 3D slicer after segmenting the fat and muscle tissue from the CT image (b) Showing the 3D surface reconstruction of the segmented image.

In this work, only bone information was needed as regions representing fat and muscle tissues were included in the exterior region, thereby remaining with only two regions as shown in Fig. 4a. This means that accurate masking through the “Paint” module of the target region leads to the two bony regions being distinctively shaded with different colors in 3D view in 3D slicer software, as shown in Fig. 4b, if not, the two regions are seen as overlapping with the same color, as shown in Fig. 4b. The results of the segmentation process were evaluated to ensure that they were representative of the objects in the CT images. The segmentation was evaluated via empirical goodness evaluation methods that assess the quality of the segmented images as described in²⁰. After the segmentation was evaluated, the segmented images were converted to 3D surfaces via the surface generation technique of volume rendering and smoothed through the smoothing module in the 3D Slicer software. The 3D surface generation was performed on the default value of vertices in the 3D slicer to carry much shape/form information for the proximal femur. The large number of nodes and triangles that represented the 3D surfaces resulted in large Stereo Lithography (STL) files with no gain in topology and therefore were further processed to reduce sizes and to make the meshes isotropic, i.e., making the mesh triangles uniform across the regions of the meshes. Tests performed by Mutsvangwa et al. revealed that isotropic vertex establishment improved the process of establishing dense correspondence for registration²¹.

Fig. 4.

(a) Results of segmentation via the paint and masking module in a 3D slicer to segment the femur (b) Final segmentation result of the proximal femur bone in 3D view.

Surface mesh refining and smoothing

After segmentation and 3D surface reconstruction in a 3D slicer, surface meshes might contain holes, non-uniform triangles, and many node points without topological significance. Hence, surface mesh refinement, through hole filling, mesh re-meshing, and further smoothing were performed through the filling of holes via the “Fill Hole Freeform” Module in Materialise, 3-Matic software. As shown in Fig. 5a, the mesh is composed of a rough surface, and in Fig. 5b, the mesh is smoothed and uniform. The mesh refinement process was performed as follows: first, a uniform mesh generation was performed, and second, an isotropic (equilateral triangle) mesh generation was performed. The mesh refinement and smoothing of the meshes reduced the number of points and triangles.

Fig. 5.

Surface mesh refining and smoothing, (a) shows a mesh before re-meshing and smoothed and (b) shows a mesh after uniform mesh re-meshing and smoothing.

After hole filling, re-meshing was performed to generate a uniform triangle mesh, establish simplification of excess triangle nodes, and further smoothing to remove outliers. The quality of the mesh was evaluated by how well the elements resemble equilateral triangles, in terms of smoothness, and the maintenance of the features of the proximal femur. The quality of elements’ smoothness was evaluated by inspecting in the Materialise 3-Matic software with shape measures related to triangle properties, such as length and angle of triangles. The smoothed and re-meshed surface meshes have isotropic vertices with an average element size (triangle edge size) of 1.0 mm and a sharp edge angle of 60°.

Anatomical landmark identification and annotation

After re-meshing and smoothing of surface meshes, anatomical landmark identification and annotation are performed to establish surface mesh correspondence through registration. Landmarks are points within a dataset upon which correspondence is preserved. These landmark points need to be easily identifiable and reproducible in each session by different annotators at different times without ambiguity. Similarly, the number of landmark points to be annotated shall cover all regions of the proximal femur, i.e., not be concentrated only in some regions of the object. Annotating many landmark points in a Statistical Shape Model (SSM) might provide a high-resolution capture of local morphology, surface curvature, and detailed shape variations, which improves modeling accuracy. However, this often leads to increased computational cost, requires a larger training set to prevent overfitting, and makes finding consistent correspondence across shapes difficult²². However, minimizing the number of landmark points has advantages for manual point placement in terms of making the process simpler and quicker, reducing the time burden required for image processing, and also minimizing overfitting with a small training set²². Considering these facts, nine anatomical landmark points that are easily identifiable and reproducible in each session by different annotators at different times without ambiguity, with optimal coverage of all regions of the proximal femur, are selected in this study. Table 2 provides the nine identified anatomical landmark points.

Table 2.

The nine annotated landmark points and their anatomical descriptions.

Landmark No	Anatomical landmark description
1	At the fovea capitis
2	At the tip of greater trochanter
3	At the trochanteric crust
4	At the center of the less trochanter
5	At neck axis end point
6	At the neck and shaft axis meeting point
7	At head and neck meeting point (center)
8	At the starting point of femoral axis
9	At the cut end of the shaft body (center)

After that, these nine anatomical landmark points were annotated manually by two operators twice each, with more than 24-h interval between annotations. A time interval between the operator’s annotation processes was introduced to avoid recall bias.

Basically, landmark annotations have dual purposes. First, it is the base for initial rigid registration. Second, landmarks are used as a reliability test since the correspondence of datasets depends on the identified landmark points. That is, landmark reliability tests are used as a direct way to validate the model. The annotation of landmarks was performed manually via the Scalismo platform developed by the Graphics and Vision Research Group at the University of Basel, Switzerland. Here, the precedence of the landmark annotation in each operator and in each session is accordingly shown in the sequences in Fig. 6.

Fig. 6.

Anatomical landmarks (blue points) selected on the 3D proximal femur.

From the two sets of landmark annotations, intraobserver and interobserver values were computed via Eqs. (1.3) and (1.4), respectively, to determine the reproducibility of the nine identified anatomical landmark points.

1.3

where, , and are the landmark coordinates from the first sets of both operators’ annotations, likewise, , and are the landmark coordinates from the second set of both operators’ annotations.

1.4

where, and represent an average of operator 1 measurement and , and belong to an average measurement of operator 2, measurements at a time i.

Once the precision error is computed for those specific landmarks across the population, the global error is computed. The global error is the average of those averages and denotes the error made by the observer for the whole dataset.

Registrations for correspondence

To establish dense correspondence, a set of registrations was performed. First, rigid alignment is used to collect all the training datasets into a common coordinate system, i.e., normalizing the pose of an object with respect to some reference shape from datasets, followed by iterating the closest point²³. Second, a parametric non-rigid registration algorithm was used as a model fitting optimizer, which optimizes the problem via gradient-based optimization. To perform the actual optimization, the workflow starts from building the Gaussian process (GP) model. The method works by fitting a reference shape (selected from the sample datasets, with the prerequisite that it has the representative topology of that species of shapes) to the targets.

Figure 7a shows the initial positions of the target surface mesh (red) and reference surface mesh (yellow), Fig. 7b shows the results after rigid alignment or transformation of the target mesh from its original position to the reference mesh position, and Fig. 7c shows the results after iterative closet point based rigid registration of the target mesh with the reference mesh. Note that we used here not reference the mesh directly, but passed the mesh from which we find the closest points as an argument. The reason is that this will later be iteratively transformed to come closer to the target meshes.

Fig. 7.

(a) Initial positions, (b) Rigid alignment, (c) ICP registrations.

The kernel used for the modeling is the Gaussian kernel, which is a particularly simple kernel that enforces smooth deformations as shown in Eq. 1.5. A kernel function representing how the mean shape deforms was defined as:

1.5

where, l is the span parameter that defines the bandwidth or the range over which deformations are correlated, i.e., it refers to the radius from a point (x) on the mesh within which other points also undergo deformation when a deformation is applied to the point (x) and s is the parameter representing the scale/magnitude of the deformation vector to which a point (x) is subjected, i.e., it determines the variance. Here, the values of the tunable parameters were empirically found with l = 15 mm and s = 30 mm using the Scalismo software, which provided the best deformation characteristics for fitting the training samples. Fig. 8a shows the initial positions of the target mesh (blue) and reference mesh (red), Fig. 8b shows the iterative closest point (ICP) rigid registration of the target mesh with the reference mesh, and Fig. 8c shows the model fitting result in which the reference mesh deforms and fits to the target mesh.

Fig. 8.

(a) Initial position, (b) rigid alignment, (c) Parametric, nonrigid registration.

The parametric, non-rigid registration was performed across the twenty-four 3D surfaces to establish dense correspondence as a model fitting process. After model fitting, through registration, the deformed surface model was used as a representation of the 3D surface. From the twenty-four 3D surfaces, only one reference shape was used for the model fitting process, and for all twenty-four 3D surfaces, the deformed surfaces were in dense correspondence .

Model validation

In SSM, before the model is used for any application, it has to be validated to ensure that the instances generated from the model are representative of the shape of the homologous series. Basically, in the SSM model, validation is assessed through four different tests²⁴. The first goodness test is directly computed on the corresponding points as differences to manually selected anatomical landmarks as described in Sect. “Landmark precision test”. The other three are indirect tests, which are computed using a PCA model based on the correspondence by conducting compactness, specificity, and generality tests through a leave-one-out cross-validation process on the model²⁵.

The compactness test measures the amount of variation in the training dataset as explained by each mode, via Eq. (1.6).

1.6

where is the largest eigenvalue, and is the cumulative variance of the mode.

The specificity test measures the ability of the model to produce instances that are valid in their resemblance to other shapes in the training dataset (Eq. 1.7).

1.7

where, N is the number of random sample sets, are randomly generated example shapes using m principal components/modes, and is the closest example of the training datasets to .

The generalization test measures the ability of the model to represent new shapes belonging to the class object of the training dataset (Eq. 1.8).

1.8

where, is the best model reconstruction of using m principal components, and is the excluded training instance.

Femoral neck-shaft angle measurement

In this study, to overcome measurement deviations for the femoral neck-shaft angle (NSA) of 3D proximal femur models in 3-Matic software, a mathematical fitting (least-squares) approach using the software’s analytical tools was employed as a standardized 3-Matic workflow. Therefore, by isolating anatomical regions (marking) of the proximal femur and using “Best Fit” primitives to define axes, a repeatable standard approach is developed as shown in Fig.9 (a) and (b). That means the femoral head, neck, and shaft regions are marked separately using the “Wave Brush” module in Materialise 3-Matic software as described in²⁶. The femoral neck axis is defined by fitting a best-fit sphere to the isolated femoral head surface by considering the sphere’s center (point A in Fig. 10a) as the first anchoring point in the procedure. Then, on the femoral neck an analytical curve was attached with “Create Curve” command in 3-Matic software as shown in Fig. 10a, and a sectioned cylinder (circle) was generated from the fitted curve. Then, the neck center is defined by fitting a best-fit cylinder or an inertia axis to the femoral neck surface, alternatively, creating a cross-section of the neck and setting its centroid (point B in Fig. 10a). Likewise, the line connecting point A and point B was defined as the 3D axis of the femoral neck^26,27.

Fig. 9.

Schematic diagram showing the femoral shaft axis and femoral neck axis plotting.

Fig. 10.

Schematic diagram showing one of the femoral neck-shaft angles measured (a) measurement of the actual bone and (b) measurement of the plotted lines.

Similarly, the femoral shaft axis is defined by fitting a best-fit cylinder to the proximal diaphysis (shaft) region by marking with the “Rectangular Mark” command in 3-Matic software. Then, analytical section cylinders were formed, and the centers of the two circles were connected with a straight line to create the femoral shaft axis, as shown in Fig. 10a. Finally, the angle is measured using the “Measure Angle” tool to select the two constructed axes. In 3D space, these axes may not intersect; the software will calculate the angle between the two 3D vectors accordingly²⁸.

In this study, to assess the reliability of the measurement method employed, the intra-class correlation (ICC) coefficient was used. After the sample size required in the reliability study is determined using the formula reported by Walter et al.²⁹, four observers made three repeated measurements of proximal femur samples. A repeated measures analysis of variance was applied to avoid a significant difference in the results of the study based on the suggestion proposed by Weir et al.³⁰. Proximal femora samples were subjected to repeated measurements in a fixed order by one senior attending orthopedic specialist with a minimum of a 24-h interval between trials to evaluate the intra-observer reliability. Three other subjects performed the same measurements on the same samples in an independent manner and a fixed order to assess inter-observer reliability.

The validation of the measurements’ consistency and reliability for intra-observer and inter-observer reliability was performed using the “MedCalc” statistical software package for Windows for biomedical research.

Results

Landmark precision test

A landmark precision test was conducted to determine the reliability of the annotated landmark points identified by the observers. The precision test was evaluated in terms of both intra-operator and inter-operator precision based on Eq. (1.3) and Eq. (1.4), respectively. Fig. 11 shows the intra-observer precision test results for each proximal femur for observer 1.

Fig. 11.

Intra-observer 1 land-marking precision.

The precision error of observer 1 ranged from a minimum error of 0.4 mm to a maximum error of 1.6 mm in the distance difference between the first and second sessions of landmark annotation. According to the precision test results, 79.6% of the total landmarks identified by observer 1 were annotated with high precision, and thus, the annotated landmarks were reliable for dense correspondence.

Figure 12 shows the intra- observer precision result for observer 2 and the precision error ranges from a minimum error of 0.28 mm to a maximum error of 0.9 mm in the distance difference between the first and second sessions of landmark annotation. In anatomical terms, the precision test results show that the identified and annotated landmark points were easily identifiable. According to the precision test results, 86.6% of the total landmarks identified by observer 2 were annotated with high precision, and thus, the annotated landmarks were reliable for dense correspondence. Fig. 13, shows the inter- observer reliability results for each proximal femur between observer 1 and observer 2 for the first trial.

Fig. 12.

Intra-observer 2 land-marking precision.

Fig. 13.

Inter-observer landmarking precision.

The precision error by inter-operator ranges from a minimum error of zero to a maximum error of 1 mm between the first and second sessions of landmark annotation. In anatomical terms, the precision test results show that the identified and annotated landmark points were easily identifiable and repeatable between the sessions. According to the precision test result, 80.6% of the total landmarks identified by the inter-operator were annotated with high precision, and thus, the annotated and identified landmarks were reliable for dense correspondence establishment latert. Table 3 provides the number of landmarks scored in each landmark precision category for each observers.

Table 3.

The number of landmarks scored in each landmark precision category.

Observer	Number of landmarks scored in each landmark precision category
	Highly precise	Precise	Moderately precise	Imprecise
Observer 1	172	31	8	5
Observer 2	187	22	6	1
Inter-observer	174	29	8	5

From the precision test results in Table 3, out of the 216 total landmark points identified individually by observer 1, observer 2, and inter- observer, 172, 187, and 174 landmark points, respectively, were annotated with high precision.Table 4 provides the global error and the percentage of selected landmarks associated with the precision category of the annotated landmark points.

The results shown in Table 4 were the global error of the annotated landmark points for observer 1, observer 2, and inter-observer. The land-marking precision assessment was performed as described. It can be observed that for the proximal femur bone, landmarks were annotated with a global error of 0.69 mm, 0.57 mm, and 0.66 mm for observer 1, observer 2, and inter-observer, respectively.

Table 4.

Statistical analysis results of the precision errors of the landmark points.

	Proximal Femur bone
Global error (mm) for the dataset	Mean	STD
Global mean and standard deviation of mean errors of all landmarks
Observer 1	0.69	0.32
Observer 2	0.57	0.18
Inter- Observer	0.66	0.26

	Observer 1	Observer 2	Inter-observer
% of landmark selected associated with precisions category
% Highly precise	79.6%	86.6%	80.6%
% Precise	14.4%	10.2%	13.4%
% Moderately precise	3.7%	2.8%	3.7%
% Imprecise	2.3%	0.4%	2.3%

Surface mesh registrations

In this work, to establish dense correspondence (model fitting) across the datasets, parametric, non-rigid registration was performed. In this approach, since each target surface mesh is replaced by its corresponding fitted mesh after model fitting through deformable registration, the registration error is computed to evaluate how close the fitted mesh is to the target mesh. The error was measured by computing the point-to-point distances between each original mesh and its approximation through model fitting. The metric used was the mean squared distance between the fitted mesh and its corresponding original surface mesh. The mean squared distance determines how close points in one surface are to the corresponding points in the other surface, and the registration error is shown in Fig. 14.

Fig. 14.

A line graph illustrating the average mean distance error difference between the fitted mesh and its corresponding original target meshes during the model fitting process.

Model development

To visualize the main modes of anatomical variations or deviations encoded in the SSM of the individual proximal femur models, the mean shape model was twisted out from a standard deviation (STD) -3 to +3 along the directions of the first three principal components (PCs).

As shown in Fig. 15, the first row is mode 1, the second row is mode 2, and the third row is mode 3. The first column shows =-3 standard deviations, the second column shows the average (mean) shape, and the third column shows =+3 standard deviations from the mean. In mode 1, variation in the size of the proximal femur, especially in the shaft, surgical neck region, and greater trochanter region of the bone, is visualized. In mode 2, some form-related variations and the variations around the greater trochanter, surgical neck inclination, and the lesser trochanter of the proximal femur bone were also observed, as shown in the second row of Fig. 15. Mode 3 represented some size-related variations around the shaft and neck regions of the femur. In all three modes, the mentioned variations were manipulated through empirical visualization of the surface mushes.

Fig. 15.

The main modes of variation for the first three principal components of the proximal femur SSM.

Model validation

The quality of the statistical shape model developed was validated via shape quality metrics, including compactness, specificity, and generality tests. To evaluate the compactness of the model, model validation using a compactness metric is performed, and the compactness result shows that the first 11 PC components, approximately half of the PC components of the proximal femur model, represented 92.85% of the total variance, as was the case in^31,32, as shown in Fig. 16.

Fig. 16.

A line graph illustrating the compactness (cumulative variance) of the SSM (the blue arrow indicates the region where the first 11 principal components of the SSM represent 92.85% of its total variance).

To evaluate the SSM’s ability to generate instances that are similar to those in the training dataset, a specificity test is performed, and the results are shown in Fig. 17. The approximation error to generate similar instances in the training sets is averaged over the number of trails and the average distance between the instances and their respective nearest member in the training dataset is evaluated as shown in Fig. 17. The specificity test results indicate that as the number of principal components increases, the ability of the SSM to create an instance that is similar to the nearest member in the training set slowly changes its value. i.e., the SSM developed can generate instances that are similar in the training set with small instance differences, as was the case in³¹.

Fig. 17.

Line graph illustrating the specificity of the SSM.

Similarly, to evaluate the generalization ability of the developed SSM, a generalization test is performed through the leave-one-out cross-validation method. The generality test evaluates the model’s ability to effectively represent unseen instances that are outside the training set.

According to the results of the generality test, shown in Fig. 18, as the number of principal components increases, the ability of the SSM to generate unseen instances that are outside the training set, its value changes faster. That means the SSM developed can generate unseen instances that are outside the training set with a small error of generalizability as the number of training sets increases.

Fig. 18.

A line graph illustrating the generality of the SSM.

Femoral neck-shaft angle measurement

The measurement result of the femoral neck-shaft angle varied from 110.07 to 136.26, with a mean ± standard deviation (STD) of 123.08 7.40. According to the measurement result, 12.5% of the samples had a femoral neck-shaft angle of greater than 130, 45.83% of the specimens had a femoral neck-shaft angle between 120 and 130 while 41.66% of the specimens had a femoral neck-shaft angle of between 110-120.

The measurement result for intra-observer and inter-observer reliability and consistency performed using the “MedCalc” statistical software package for Windows for biomedical research is shown in Fig. 19.

Fig. 19.

Intra-observer and inter-observer reliability of the measurements.

The validation of the measurements’ consistency and reliability for intra-observer and inter-observer reliability is shown in Tables 5 and 6, respectively.

Table 5.

Intra-observer and reliability of the measurements.

Intra-observer reliability of measurements
Observer A		Observer B		Observer C		Observer D
ICC	95% CI	ICC	95% CI	ICC	95% CI	ICC	95% CI
0.9888	0.9778 to 0.9948	0.9937	0.9877 to 0.9971	0.9947	0.9896 to 0.9975	0.9954	0.9910 to 0.9979

ICC, The intra-class correlation coefficient; CI, confidence interval.

Table 6.

Inter-observer reliability of the measurements.

Inter-observer reliability of measurements
Trial 1		Trial 2		Trial 3		Overall
ICC	95% CI	ICC	95% CI	ICC	95% CI	ICC	95% CI
0.9954	0.9915 to 0.9978	0.9960	0.9925 to 0.9981	0.9969	0.9942 to 0.9985	0.9986	0.9976 to 0.9993

Excellent intra-observer and inter-observer reliability (n = 24) were observed, with average ICC values of 0.99315 and 0.9986, respectively. The validation test results demonstrate an excellent degree of consistency among measurements in the current study, as was the case in²⁶.

Discussions

Landmark precision test

Owing to the ease of identifying the points by operators in a given session and covering all the parts of the object, nine anatomical landmark points were annotated manually via two observers, twice each, as shown in Fig. 6. The operators are experts in anatomical study. These landmark points were used as prior knowledge for initial registration. In addition, even though the landmark points are easily identifiable and reproducible across the training datasets, the occurrence of personal bias in each session of land-marking is natural. Hence, a landmark precision test was conducted to evaluate the annotated landmark points identified by observers with the best precision since the dense correspondence (model fitting) is influenced by the reliability of the annotated landmark points.

The precision test result revealed that more than 94% of the total landmarks were annotated precisely for both the observers and the inter-observer as well. It can be observed for the proximal femur bone that landmarks were annotated with a global error of 0.69 mm, 0.57 mm and 0.66 mm for observer 1, observer 2 and inter-observer, respectively. These results indicate that the annotated anatomical landmarks are easily identifiable and reproducible by observers precisely. Precise annotated landmark guides an effective dense correspondence (model fitting) across the datasets, which leads to efficient model development. From a topological perspective, the precision test results show that the identified and the annotated landmark points are easily identifiable with a small error, which enables optimal correspondence establishment later during model fitting.

Surface mesh registration

Surface registration is required for correspondence establishment across training sets. After all the training sets are transformed into a common coordinate system through rigid alignment, non-rigid registration based on a Gaussian process model fitting is performed, as shown in Fig. 8. Considering this as a model fit, a smooth Gaussian kernel was used as the model’s kernel. Model fitting by itself is trial and error, i.e., the registration result needs to be obtained by changing the tunable parameters that are the span (l) and the degree of deformation (s). After many iterations, model fitting through non-rigid registration is completed with an empirically determined span value of and degree of deformation for the Gaussian kernel. The termination of the model fitting ceases when the target mesh is adequately represented or mapped by the reference mesh, i.e., when it has an equal number of vertices or the same triangulation as the reference mesh. The same triangulation means that all the surface meshes share the same topology across the datasets. In the course of model fitting, since each target surface mesh was replaced by its corresponding fitted mesh after the registration, the degree of deformability of each bone was determined via visual inspection. This was validated by a numerical analysis of registration errors, which were computed to evaluate how close the fitted meshes were to the targets. The errors were measured by computing the point-to-point distances between each original mesh and its approximation or fit after registration through model fitting. The metric used was the mean squared distance between the fitted mesh and its corresponding original surface meshes as shown in Fig. 14.

Model development

The statistical shape model (SSM) was developed from only twenty-four subjects, and the findings of the study are dependent on the training set. Using principal component analysis, the anatomical variations across the twenty-four proximal femur models were quantified by twisting out the mean shape model from a standard deviation (STD) of -3 to +3 with the individual proximal femur models, as shown in Fig. 15. For the first mode, pure size variation in the shaft, neck, and head was observed from -3 STD to +3 STD. In addition, the femoral neck-shaft was more inclined from -3 STD to +3 STD. Similarly, from the -3 STD to the +3 STD, the greater trochanter becomes wider. For the second mode, the femoral neck-shaft was more inclined from -3 STD to +3 STD as shown in Fig. 15. Likewise, the greater trochanter becomes wider from -3 STD to +3 STD as shown in Fig. 15. For the third mode, pure size and shape variation was observed: from -3 STD to +3 STD the femoral neck becomes thicker, the greater trochanter is wider, and femoral neck-shaft inclination decreases slightly, as shown in Fig. 15. In a decreasing order of importance (from mode 1 to mode 3), these modes of variations show the most relevant changes in geometry witnessed in the studied population. In implant design perspective, these modes can be tuned to generate different sizes and geometries specific to the studied population. The above-mentioned anatomical variations are clinically relevant parameters in hip arthroplasty prosthesis. Hence, in the course of implant design optimization, considering these constraints is important to improve implant fitting during hip prosthesis surgery.

Model validation

The validation result revealed that out of the twenty-four training datasets, the first eleven principal components represented for 92.85% of the total variance of the SSM, i.e., the SSM required only half the number of principal components to define 92.85% of the total variance, as was^31,32. In SSM, the model needs to be compact, i.e., within a smaller number of principal components; a higher value of cumulative variance is needed. Considering this, our SSM is compact since only half of the number of variables are required for the constructed shape model to define its population variance of approximately 93%. Similarly, the model represented an instance with an average error of specificity and generality, 1.33 mm and 0.82 mm, respectively. This means that the model was able to produce instances that are valid in their resemblance to other shapes in the training dataset with an average specificity error of 1.33 m, i.e., the SSM was able to efficiently represent unseen instances of the proximal femur in the datasets. The model was also able to represent new shape instances belonging to the class object of the training dataset with an average generality error of 0.82 mm. Based on the validation results, the shape of the developed model was sufficiently approximated from the training datasets. Owing to a lack of published evidence in the development and validation of the proximal femur SSM, comparisons with other methods is challenging.

Femoral neck-shaft angle measurement

Total hip arthroplasty (THA) or hip fracture fixation via prosthetic implants or fixation plate is a standard procedure for treating hip joint trauma and patients respond poorly to conventional medical therapy. However, implant-related complications might arise from anatomical variations among different population groups. The femoral neck-shaft angle (NSA) is one of the main design parameters that should be considered when designing hip prosthesis implants. The hip prototype must be created, and thus the hip stem-neck inclination must be optimized by taking into account the patient’s femoral morphology.

Even though the validation test demonstrates an excellent degree of consistency and reliability for intra-observer and inter-observer reliability, a slight NSA value difference is observed between the average SSM models and individually measured NSA values of proximal femurs. In this study, the measured values of the femoral NSA of the Ethiopian population vary from 110.07 to 136.26, and the mean ± standard deviation (STD) of 123.08 7.40. Meanwhile, the femoral NSA obtained from the average SSM model was 120.86. From this result, the mean neck-shaft angle obtained from the individual femur surfaces is slightly varied from that of the average SSM model developed from the datasets. This could be due to the reference bias at the time of mean shape model development, as well as due to personal bias in the course of a hypothetical marking of the femoral head, neck, and shaft with “Rectangular Mark,” since marking and curve sketching were performed by manually selecting the regions of interest.

Due to a lack of published evidence on proximal femur neck-shaft angle measurements in the Ethiopian population, the author was not able to compare the existing results with those of the local population. However, the femoral NSA measurement results of this study were compared with those of other population groups. For instance, the reported average femoral neck-shaft angle measurements of the Kenyans, Brazilians, Americans, and South Indians were 129.21, 130.47, 132.69, and 137.3^33,36, respectively.

The current study shows that the mean femoral NSA of the Ethiopian femora is smaller than that of the above-mentioned population groups. More specifically, it is much smaller than the American and Indian populations. Locally available THR implants are mainly acquired through donation from developed countries, especially from the United States of America³⁷. Thus, utilizing the standard commercially available hip implants may not be the best fit for Ethiopian patient groups and could be the cause of implants related complications. A recent study on 50 locally treated THR reported that previous partial hip replacement femur neck fractures were converted to THR in 6 patients, one patient lost in the acetabular component and referred later abroad, and one patient loose hip stem³⁷. Consequently, the mean SSM of this study could be used to optimize the available implants, and the femoral neck-shaft angle measurement could also be used to select implants closely related to the Ethiopian population.

Conclusion

In this study, the statistical shape model (SSM) of the proximal femur, including the main modes of variation and the morphometric analysis of femoral neck-shaft angle were conducted based on data from Ethiopian subjects. The quality of the developed model was validated via model quality metric tests (compactness, specificity, and generalization ability), and the validation results revealed that the model developed sufficiently approximated the shape from the training datasets. However, the SSM was developed from a few training datasets and collected from a limited region of the country, so the resulting SSM was expected to be limited in its ability to represent the entire population. Similarly, the mean femoral neck-shaft angle (NSA) and the standard deviation of femoral specimens collected from the Ethiopian population were estimated, and the results of this investigation could serve as a starting point for this population.

Future work and recommendations

In SSM, the number of training datasets needs to be representative of the given population. Additionally, morphometric information on shape variations in the population is vital for implant design and development because these parameters influence implant sizing and stability. In this study, the number of training samples is small due to the unavailability of pelvic CT images. Hence, in the future, a full-length shape model of the femur with a large number of training samples and its morphometric parameters could be developed to further improve the hip rotation and flexion as per the clinical standards and to enhance the reliability of measurement of the femoral head diameter, horizontal offset, and femoral neck-anteversion angle.

Author contributions

All authors contributed equally in this study. All authors read and approved the final manuscript.

Funding

Not applicable.

Data availability

The datasets used and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Declarations

Competing interests

The authors declare that they have no competing interests.

Ethical approval and consent to participate

This research has been approved by Jimma University’s research ethics institutional review board (IRB). This research has been performed in accordance with the ethical standards as laid down in the 1964\Declaration of Helsinki and its later amendments or comparable ethical standards. An informed written consent form was obtained from all participants prior to data collection.

Consent for publication

Not applicable.