Introduction. Acetabular bone defects are still challenging to quantify. Numerous classification schemes have been proposed to categorize the diverse kinds of defects. However, these classification schemes are mainly descriptive and hence it remains difficult to apply them in pre-clinical testing, implant development and pre-operative planning. By reconstructing the native situation of a defect pelvis using a Statistical Shape Model (SSM), a more quantitative analysis of the bone defects could be performed. The aim of this study is to develop such a SSM and to validate its accuracy using relevant clinical scenarios and parameters. Methods. An SSM was built on the basis of segmented 66 CT dataset of the pelvis showing no orthopedic pathology. By adjusting the SSM's so called modes of shape variation it is possible to synthetize new 3D pelvis shapes. By fitting the SSM to intact normal parts of an anatomical structure, missing or pathological regions can be extrapolated plausibly. The validity of the SSM was tested by a Leave-one-out study, whereby one pelvis at a time was removed from the 66 pelvises and was reconstructed using a SSM of the remaining 65 pelvises. The reconstruction accuracy was assessed by comparing each original pelvis with its reconstruction based on the root-mean-square (RMS) surface error and five clinical parameters (center of rotation, acetabulum diameter, inclination, anteversion, and volume). The influence of six different numbers of shape variation modes (reflecting the degrees of freedom of the SSM) and four different mask sizes (reflecting different clinical scenarios) was analyzed. Results. The Leave-one-out study showed that the reconstruction errors decreased when the number of shape variation modes included in the SSM increased from 0 to 20, but remained almost constant for higher numbers of shape variation modes. For the SSM with 20 shape variation modes, the RMS of the reconstruction error increased with increasing mask size, whereas the other parameters only increased from Mask_0 to Mask_1, but remained almost constant for Mask_1, Mask_2 and Mask_3. Median reconstruction errors for Mask_1, Mask_2, and Mask_3 were approximately 3 mm in Center of Rotation (CoR) position, 2 mm in Diameter, 3° in inclination and anteversion, as well as 5 ml in volume. Discussion. This is the first study analyzing and showing the feasibility of a quantitative analysis of acetabular bone defects using a SSM-based reconstruction method in the clinical scenario of a defect or implant in both acetabuli and incomplete CT-scans. Validation results showed acceptable reconstruction accuracy, also for clinical scenarios in which less healthy bone remains. Further studies could apply this method on a larger number of defect pelvises to obtain quantitative measures of acetabular bone defects

Background. Degeneration of the shoulder joint is a frequent problem. There are two main types of shoulder degeneration: Osteoarthritis and cuff tear arthropathy (CTA) which is characterized by a large rotator cuff tear and progressive articular damage. It is largely unknown why only some patients with large rotator cuff tears develop CTA. In this project, we investigated CT data from ‘healthy’ persons and patients with CTA with the help of 3D imaging technology and statistical shape models (SSM). We tried to define a native scapular anatomy that predesignate patients to develop CTA. Methods. Statistical shape modeling and reconstruction:. A collection of 110 CT images from patients without glenohumeral arthropathy or large cuff tears was segmented and meshed uniformly to construct a SSM. Point-to-point correspondence between the shapes in the dataset was obtained using non-rigid template registration. Principal component analysis was used to obtain the mean shape and shape variation of the scapula model. Bias towards the template shape was minimized by repeating the non-rigid template registration with the resulting mean shape of the first iteration. Eighty-six CT images from patients with different severities of CTA were analyzed by an experienced shoulder surgeon and classified. CT images were segmented and inspected for signs of glenoid erosion. Remaining healthy parts of the eroded scapulae were partitioned and used as input of the iterative reconstruction algorithm. During an iteration of this algorithm, 30 shape components of the shape model are optimized and the reconstructed shape is aligned with the healthy parts. The algorithm stops when convergence is reached. Measurements. Automatic 3D measurements were performed for both the healthy and reconstructed shapes, including glenoid version, inclination, offset and critical shoulder angle. These measurements were manually performed on the mean shape of the shape model by a surgeon, after which the point-to-point correspondence was used to transfer the measurements to each shape. Results. The critical shoulder angle was found to be significantly larger for the CTA scapulae compared to the references (P<0.01). When analyzing the classified scapulae significant differences were found for the version angle in the scapulae of group 4a/4b and the critical shoulder angle of group 3 when compared to the references (P<0.05). Conclusion. Patients with CTA have a larger critical shoulder angle compared with reference patients. Some significant differences are found between the scapulae from patients in different stages of CTA and healthy references, however the differences are smaller than the accuracy of the SSM reconstruction. Therefore, we are unable to conclude that there is a predisposing anatomy in terms of glenoid version, inclination or offset for CTA

INTRODUCTION. Statistical shape models (SSM) have become a common tool to create reference models for design input and verification of total joint implants. In a recent discussion paper around Artificial Intelligence and Machine Learning, the FDA emphasizes the importance of independent test data [1]. A leave-one-out test is a standard way to evaluate the generalization ability of an SSM [2]; however, this test does not fulfill the independence requirement of the FDA. In this study, we constructed an SSM of the knee (femur and tibia). Next to the standard leave-one-out validation, we used an independent test set of patients from a different geographical region than the patients used to build the SSM. We assessed the ability of the SSM to predict the shapes of knees in this independent test set. METHODS. A dataset of 82 computed tomography (CT) scans of Caucasian patients (42 male, 40 female) from 11 different geographic locations in France, Germany, Austria, Italy and Australia were used as training set to make an SSM of the femur and tibia. A leave-one-out test was performed to assess the ability of the SSM to predict shapes within the training set. A test dataset of 4 CT scans of Caucasian patients from Russia were used for the validation. The SSM was fitted onto each of the femur and tibia shapes and the root mean square error (RMSE) was measured. RESULTS. The leave-one-out tests showed that the femur and tibia SSMs were able to predict patients in the input population with an RMSE of 0.59 ± 0.1 mm (average ± standard deviation) for the femur and 0.70 ± 0.1 mm for the tibia. The validation test showed that the femur and tibia SSMs were able to predict the shapes of the Russian patients with an RMSE 0.62 ± 0.1 mm for the femur and 0.71 ± 0.1 mm for the tibia. DISCUSSION. There were no significant differences in the ability of the SSM to predict femur and tibia shapes of patients in a new geographic region compared to the ability of the SSM to predict shapes within the training set. CONCLUSIONS. Based on this study, 11 different geographic locations in France, Germany, Austria, Italy and Australia provide a complete sample of the Caucasian population. Using an independent set of CT scans is a valuable tool to further validate the generalization ability of an SSM. For any figures or tables, please contact authors directly

Aims

The aim of this study was to optimize screw hole placement in an acetabulum cup implant to improve secondary initial fixation by identifying the region of thickest acetabulum bone. The “scratch fit” of modern acetabular cup implants with highly porous coatings is often adequate for initial fixation in primary total hip arthroplasty. Initial fixation must limit micromotion to acceptable levels to facilitate osseointegration and long term cup stability. Secondary initial fixation can be required in cases with poor bone quality or bone loss and is commonly achieved with bone screws and a cup implant with multiple screw holes. To provide maximum secondary initial fixation, the cup screw holes should be positioned to allow access to the limited region of thick pelvic bone.

This work was motivated by the need to capture the spectrum of anatomical shape variability rather than relying on analyses of single bones. A novel tool was developed that combines image-based modelling with statistical shape analysis to automatically generate new femur geometries and measure anatomical parameters to capture the variability across the population. To demonstrate the feasibility of the approach, the study used data from 62 Caucasian subjects (31 female and 31 male) aged between 43 and 106 years, with CT voxel size ranging 0.488 × 0.488 × 1.5 mm to 0.7422 × 0.7422 × 0.97 mm.

The scans were divided into female and male subgroups and high-quality subject-specific tetrahedral finite element (FE) meshes resulting from segmented femurs formed the so-called training samples. A source mesh of a segmented femur (25580 nodes, 51156 triangles) from the Visible Human dataset [Spitzer, 1996] was used for elastic surface registration of each considered target male and female subjects, followed by applying a mesh morphing strategy.

To represent the variations in bone morphology across the population, gender-based Statistical Shape Models (SSM) were developed, using Principal Component Analysis. These were then sampled using the principal components required to capture 95% of the variance in each training dataset to generate 1000 new anatomical shapes [Bryan, 2010; Blanc, 2012] and to automatically measure key anatomical parameters known to critically influence the biomechanics after hip replacement (Figure 1).

Analysis of the female and male training datasets revealed the following data for the five considered anatomical parameters: anteversion angle (12.6 ± 6.4° vs. 6.2 ± 7.5°), CCD angle (124.8 ± 4.7° vs. 126.3 ± 4.6°), femoral neck length (48.7 ± 3.8 mm vs. 52 ± 5 mm), femoral head radius (21.5 ± 1.3 mm vs. 24.9 ± 1.5 mm) and femur length (431.0 ± 17.6 mm vs. 474.5 ± 26.3 mm). However, using the SSM generated pool of 1000 femurs, the following data were computed for females against males: anteversion angle (10.5 ± 14.3° vs. 7.6 ± 7.2°), CCD angle (123.9 ± 5.8° vs. 126.7 ± 4°), femoral neck length (46.7 ± 7.7 mm vs. 51.5 ± 4.4 mm), femoral head radius (21.4 ± 1.2 mm vs. 24.9 ± 1.4 mm) and femur length (430.2 ± 16.1 mm vs. 473.9 ± 25.9 mm).

The highest variability was found in the anteversion of the females where the standard deviation in the SSM-based sample was increased to 14.3° from 6.4° in the original training dataset (Figures 2 & 3). The mean values for both females (10.5°) and males (7.6 °) were found close to the values of 10° and 7° reported in [Mishra, 2009] in 31 females and 112 males with a [2°, 25°] and [2°, 35°] range, respectively.

Femoral neck length of the female (male) subjects was 47.3 ± 6.2 mm (51.8 ± 4.1 mm) compared to 48.7 ± 3.8 mm (52 ± 5 mm) in the training dataset and 63.65 ± 5.15 mm in [Blanc, 2012] with n = 142, 54% female, 46% male and a [50.32–75.50 mm] range. For the measured CCD angle in both female (123.9 ± 5.8°) and male (126.7 ± 4°) subjects, a good correlation was found with reported values of 128.4 ± 4.75° [Atilla, 2007], 124.7 ± 7.4° [Noble, 1988] and 129.82 + 5.37° [Blanc, 2012].

In conclusion, the present study demonstrates that the proposed methodology based on gender-specific statistical shape modelling can be a valuable tool for automatically generating a large specific population of femurs to support implant design and planning of femoral reconstructive surgery.

INTRODUCTION

Automated MRI bone segmentation is one of the most challenging problems in medical imaging. To increase the segmentation robustness, a prior model of the structure could guide the segmentation. Statistical Shape Models (SSMs) are efficient examples for such application. We present an automated SSM construction approach of the scapula bone with an adapted initialisation to address the correspondences problem. Our innovation stems from the derivation of a robust SSM based on Watershed segmentation which steers the elastic registration at some critical zones.

The integration of statistical shape models (SSMs) for generating a patient-specific model from sparse data is widely spread. The SSM needs to be initially registered to the coordinate-system in which the data is acquired and then be instantiated based on the point data using some regressing techniques such as principal component analysis (PCR). Besides PCR, partial least squares regression (PLSR) could also be used to predict a patient-specific model. PLSR combines properties of PCR and multiple linear regression and could be used for shape prediction based on morphological parameters.

Both methods were compared on the basis of two SSMs, each of them constructed from 30 surface models of the proximal femur and the pelvis, respectively. Thirty leave-one-out trials were performed, in which one surface was consecutively left out and further used as ground truth surface model. Landmark data were randomly derived from the surface models and used together with the remaining 29 surface models to predict the left-out surface model based on PCR and PLSR, respectively. The prediction accuracy was analysed by comparing the ground truth model with the corresponding predicted model and expressed in terms of mean surface distance error.

According to their obtained minimum error, PCR (1.62 mm) and PLSR (1. 63 mm) gave similar results for a set of 50 randomly chosen landmarks. However PLSR seems to be more susceptible to a wrong selection of number of latent vectors, as it has a more variation in the error.

Although both regression methods gave similar results, decision needs to be done, how to select the optimal number of regressors, which is a delicate task. In order to predict a surface model based on morphological parameters using PLSR, the choice of the parameters and their optimal number needs to be carefully selected.

Statistical shape modeling (SSM) and statistical density modeling (SDM) are tools capable of describing the main modes of deviation in the shape and density distribution of the shoulder using a set of uncorrelated variables called principal components (PCs). We hypothesize that the first PC of the SDM, which scales overall density up/down, will be inversely correlated with age and will, on average, be greater for males than females. We also hypothesize that there is a correlation between some PCs of shape and density. SSM and SDM were developed for scapulae and humeri by segmenting surface meshes from computed tomographic images of 75 cadaveric shoulders. Bones were co-registered and defined by the same surface mesh. Volumetric tetrahedral meshes were defined for one of the specimens serving as base meshes for SDM. Base meshes were morphed to each individual bone's surface and superimposed upon the corresponding CT data to determine image intensity in Hounsfield units at each node. Principal component analysis was performed on the exterior shape and internal density distribution of bones. T-tests were performed to find any differences in PC scores between males and females, and Pearson correlation coefficients were calculated for age and PC scores. Finally, correlation coefficients between each of the PCs of the shape and density models were calculated. For the humerus, the first three PCs of the SDM were significantly correlated with age (ρ = 0.40, −0.46, and 0.36, all p ≤ 0.007). For the scapula, the first and ninth PCs showed such correlation (ρ = −0.31, and −0.32, all p ≤ 0.02). Statistically significant differences due to sex were found for the second to sixth SDM PCs of the humerus, with differences in average PC scores of 1, 1, −0.7, −0.8, and −0.6 standard deviations, respectively, for males relative to females. For the scapula, the second, fifth and seventh SDM PCs were significantly different between males and females, with average PC scores differing by 1.1, 0.7, and −0.6 standard deviations. Finally, for both bones, the first PC of SSM showed a weak but significant correlation with the second PC of the SDM (ρ = 0.47, p < 0.001 for the humerus, and ρ = 0.39, p < 0.001 for the scapula). The results of this study suggest that age has a significant influence on the first PC of the SDM, associated with scaling the density in the cortical boundary. Moreover, the negative correlation of age with the second PC of the humerus in SDM which mostly influences the thickness of the cortical boundary implies cortical thinning with age. The second PC of both bones differed significantly between males and females, implying that cortical thickness differs between sexes. Also, there was a significant correlation between the size of the bones and the thickness of the cortical boundary. These findings can help guide the designs of population-based prosthesis components

Introduction. A good anatomic fit of a Total Knee Arthroplasty is crucial to a good clinical outcome. The big variability of anatomies in the Asian and Caucasian populations makes it very challenging to define a design that optimally fits both populations. Statistical Shape Models (SSMs) are a valuable tool to represent the morphology of a population. The question is how to use this tool in practice to evaluate the morphologic fit of modern knee designs. The goal of our study was to define a set of bone geometries based on SSMs that well represent both the Caucasian and the Asian populations. Methods. A Statistical Shape Model (SSM) was built and validated for each population: the Caucasian Model is based on 120 CT scans from Russian, French, German and Australian patients. The Asian Model is based on 80 CT scans from Japanese and Chinese patients. We defined 7 Caucasian and 5 Asian bone models by using mode 1 of the SSM. We measured the antero-posterior (AP) and medio-lateral (ML) dimensions of the distal femur on all anatomies (input models and generated models) to check that those bone models well represent the studied population. In order to cover the whole population, 10 additional bone models were generated by using an optimization algorithm. First, a combined Asian-Caucasian SSM was generated of 92 patients, equally balanced between male and female, Caucasian and Asian. 10 AP/ML dimensions were defined to obtain a good coverage of the population. For a given AP/ML dimension, Markov chain Monte Carlo sampler was used to find the most average shape with AP/ML dimensions as close as possible to the target dimensions. The difference of the AP/ML dimensions of the generated models to the target dimensions was computed. A chi-squared distribution was used to assess how average the resulting shapes were compared to typical patient shapes. Results. The AP-ML dimensions of the 7 Caucasian bones and the 5 Asian bones well cover the range of the respective populations. For the Caucasian Femur, the AP/ML dimensions range from (53,6/64,9mm) for size 1 to (67,7/80,7mm) for size 7. For the Asian Femur, the AP/ML dimension range from (53,0/62,4mm) for size 1 to (60,5/72,4mm) for size 5. The dimensions of the 10 additionally generated bones differed in average (± 1 standard deviation) by 0,2±0,4mm in AP and 0,5±0,5mm in ML to the target dimensions. The maximal deviation was 0,9mm in AP and 1,0mm in ML. All 10 bones had a P-value of P < 10. -27. according to the chi-squared distribution. Conclusion. The proposed models of 7 Caucasian and 5 Asian bones well represent both populations. The 10 additional geometries enable to get a complete coverage of the population. Since they are very close to average, all these bone models provide more generalized reference shapes compared to individual patients. By performing a virtual implantation on those anatomies, the anatomical fit of implants to these populations can be evaluated. For any figures or tables, please contact authors directly

With the increasing use of 3D medical imaging, it is possible to analyze 3D patient anatomy to extract features, trends and population specific shape information. This is applied to the development of ‘standard implants’ targeted to specific population groups. INTRODUCTION. Human beings are diverse in their physical makeup while implants are often designed based on some key measurements taken from the literature or a limited sampling of patient data. The different implant sizes are often scaled versions of the ‘average’ implant, although in reality, the shape of anatomy changes as a function of the size of patient. The implant designs are often developed based on a certain demographic and ethnicity and then, simply applied to others, which can result in poor design fitment [1]. Today, with the increasing use of 3D medical imaging (e.g. CT or MRI), it is possible to analyze 3D patient anatomy to extract features, trends and population specific shape information. This can be applied to the development of new ‘standard implants’ targeted to a specific population group [2]. PATIENTS & METHODS. Our population analysis was performed by creating a Statistical Shape Model (SSM) [3] of the dataset. In this study, 40 full Chinese cadaver femurs and 100 full Caucasian cadaver femurs were segmented from CT scans using Mimics®. Two different SSMs, specific to each population, were built using in-house software tools. These SSMs were validated using leave-one-out experiments, and then analyzed and compared in order to enhance the two population shape differences. RESULTS. An SSM is typically represented by an average model and a few independent modes of variation that capture most of the inherent variations in the data. Based on these main modes of variations, the shape features, e.g. length, thickness, curvature neck angle and femoral version, presenting largest variations were determined, and correlations between these features were calculated. Figure 1 represents the Caucasian and Chinese average models, and shows that while the length of these two models was significantly different, the AP and ML dimensions were similar, indicating a difference of morphology (other than a scaling) between the two populations. Figure 2 represents the first mode of variation that illustrates the variation of Chinese femur shape with size. As an example, the neck angle increases of 26° with an increase of 139 mm in femur length, indicative of the effect of changes in loading conditions on geometry as a function of size. CONCLUSION. The advantage of using more advanced statistical analyses is that the 3D data are probed in an unbiased fashion, allowing the most important parameters of variation to be determined. These analyses are thus particularly effective to compare different populations, to evaluate how well existing implant designs fit specific populations, and to highlight the design parameters that need to be adapted for good fitment of specific populations

INTRODUCTION. Understanding bone morphology is essential for successful computer assisted orthopaedic surgery, where definition of normal anatomical variations and abnormal morphological patterns can assist in surgical planning and evaluation of outcomes. The proximal femur was the anatomical target of the study described here. Orthopaedic surgeons have studied femoral geometry using 2D and 3D radiographs for precise fit of bone-implant with biological fixation. METHOD. The use of a Statistical Shape Model (SSM) is a promising venue for understanding bone morphologies and for deriving generic description of normal anatomy. A SSM uses measures of statistics on geometrical descriptions over a population. Current SSM construction methods, based on Principal Component Analysis (PCA), assume that shape morphologies can be modeled by pure point translations. Complicated morphologies, such as the femoral head-neck junction that has non-rigid components, can be poorly explained by PCA. In this work, we showed that PCA was impotent for processing complex deformations of the proximal femur and propose in its place our Principal Tangent Component (PTC) analysis. The new method used the Lie algebra of affine transformation matrices to perform simple computations, in tangent spaces, that corresponded to complex deformations on the data manifold. RESULTS. Both PCA and PTC were applied to the proximal femur dataset, from which selected femurs were reconstructed using the accumulation of components. PCA was deemed to have failed to reconstruct the surfaces because it required 65 components to achieve high coverage of the dataset. An important observation was that the head-neck junction was the most difficult section in the femur, requiring more components than other anatomical regions to reconstruct. This finding is consistent with the surgical observation that deformations occur in this junction for abnormal hip morphologies. PTC was successful in recovering 100% of the medical data using the only the first 5 components. We note that the encoding of deformation in PTC accounting for the performance increase. PTC outperformed PCA on the dataset in descriptive compactness. CONCLUSION. A standard SSM construction method was not adequate for analysing proximal femur surfaces because it could not easily model the complexity of non-rigid deformations at the head-neck junction. Principal tangent components, a novel method for using exponential maps on manifolds, accurately reconstructed the anatomical surfaces with very few components. Future work may include extending these concepts to describe joint diseases based on the shape of surfaces derived from volumetric data, such as CT or MRI. In conclusion, we have shown that differential geometry may be provide new insights to computational anatomy applications