Statistical analysis of the inter-individual variations of the bone shape, volume fraction and fabric and their correlations in the proximal femur

Quantitative Analysis of Primary Compressive Trabeculae Distribution in the Proximal Femur of the Elderly

OBJECTIVE

As osteoporosis progresses, the primary compressive trabeculae (PCT) in the proximal femur remains preserved and is deemed the principal load-bearing structure that links the femoral head with the femoral neck. This study aims to elucidate the distribution patterns of PCT within the proximal femur in the elderly population, and to assess its implications for the development and optimization of internal fixation devices used in hip fracture surgeries.

METHODS

This is a retrospective cohort study conducted from March 2022 to April 2023. A total of 125 patients who underwent bilateral hip joint CT scans in our hospital were enrolled. CT data of the unaffected side of the hip were analyzed. Key parameters regarding the PCT distribution in the proximal femur were measured, including the femoral head's radius (R), the neck-shaft angle (NSA), the angle between the PCT-axis and the head-neck axis (α), the distance from the femoral head center to the PCT-axis (δ), and the lengths of the PCT's bottom and top boundaries (L-bottom and L-top respectively). The impact of gender differences on PCT distribution patterns was also investigated. Student's t-test or Mann-Whitney U test were used to compare continuous variables between genders. The relationship between various variables was investigated through Pearson's correlation analysis.

RESULTS

PCT was the most prominent bone structure within the femoral head. The average NSA, α, and δ were 126.85 ± 5.85°, 37.33 ± 4.23°, and 0.39 ± 1.22 mm, respectively, showing no significant gender differences (p > 0.05). Pearson's correlation analysis revealed strong correlations between α and NSA (r = -0.689, p < 0.001), and R and L-top (r = 0.623, p < 0.001), with mild correlations observed between δ and NSA (r = -0.487, p < 0.001), and R and L-bottom (r = 0.427, p < 0.001). Importantly, our study establishes a method to accurately localize PCT distribution in true anteroposterior (AP) radiographs of the hip joint, facilitating precise screw placement in proximal femur fixation procedures.

CONCLUSION

Our study provided unprecedented insights into the distribution patterns of PCT in the proximal femur of the elderly population. The distribution of PCT in the proximal femur is predominantly influenced by anatomical and geometric factors, such as NSA and femoral head size, rather than demographic factors like gender. These insights have crucial implications for the design of internal fixation devices and surgical planning, offering objective guidance for the placement of screws in hip fracture treatments.

A combined active shape and mean appearance model for the reconstruction of segmental bone loss

This study investigates the novel combination of an active shape and mean appearance model to estimate missing bone geometry and density distribution from sparse inputs simulating segmental bone loss of the femoral diaphysis. An active shape Gaussian Process Morphable model was trained on healthy right femurs of South African males to model shape. The density distribution was approximated based on the mean appearance of computed tomography images from the training set. Estimations of diaphyseal resections were obtained by probabilistic fitting of the active shape model to sparse inputs consisting of proximal and distal femoral data on computed tomography images. The resulting shape estimates of the diaphyseal resections were then used to map the mean appearance model to the patients' missing bone geometry, constructing density estimations. In this way, resected bone surfaces were estimated with an average error of 2.24 (0.5) mm. Density distributions were approximated within 87 (0.7) % of the intensity of the original target images before the simulated segmental bone loss. These results fall within the acceptable tolerances required for surgical planning and reconstruction of long bone defects.

Noninvasive shape-fitting method quantifies cam morphology in femoroacetabular impingement syndrome: Implications for diagnosis and surgical planning

There are considerable limitations associated with the standard 2D imaging currently used for the diagnosis and surgical planning of cam-type femoroacetabular impingement syndrome (FAIS). The aim of this study was to determine the accuracy of a new patient-specific shape-fitting method that quantifies cam morphology in 3D based solely on preoperative MRI imaging. Preoperative and postoperative 1.5T MRI scans were performed on n = 15 patients to generate 3D models of the proximal femur, in turn used to create the actual and the virtual cam. The actual cams were reconstructed by subtracting the postoperative from the preoperative 3D model and used as reference, while the virtual cams were generated by subtracting the preoperative 3D model from the virtual shape template produced with the shape-fitting method based solely on preoperative MRI scans. The accuracy of the shape-fitting method was tested on all patients by evaluating the agreement between the metrics of height, surface area, and volume that quantified virtual and actual cams. Accuracy of the shape-fitting method was demonstrated obtaining a 97.8% average level of agreement between these metrics. In conclusion, the shape-fitting technique is a noninvasive and patient-specific tool for the quantification and localization of cam morphology. Future studies will include the implementation of the technique within a clinically based software for diagnosis and surgical planning for cam-type FAIS.

MRI-- and CT--based metrics for the quantification of arthroscopic bone resections in femoroacetabular impingement syndrome

The purpose of this in vitro study was to quantify the bone resected from the proximal femur during hip arthroscopy using metrics generated from magnetic resonance imaging (MRI) and computed tomography (CT) reconstructed three-dimensional (3D) bone models. Seven cadaveric hemi-pelvises underwent both a 1.5 T MRI and CT scan before and following an arthroscopic proximal femoral osteochondroplasty. The images from MRI and CT were segmented to generate 3D proximal femoral surface models. A validated 3D--3D registration method was used to compare surface--to--surface distances between the 3D models before and following surgery. The new metrics of maximum height, mean height, surface area and volume, were computed to quantify bone resected during osteochondroplasty. Stability of the metrics across imaging modalities was established through paired sample t--tests and bivariate correlation. Bivariate correlation analyses indicated strong correlations between all metrics (r = 0.728--0.878) computed from MRI and CT derived models. There were no differences in the MRI- and CT-based metrics used to quantify bone resected during femoral osteochondroplasty. Preoperative- and postoperative MRI and CT derived 3D bone models can be used to quantify bone resected during femoral osteochondroplasty, without significant differences between the imaging modalities.

A computational framework for canonical holistic morphometric analysis of trabecular bone

Bone is a remarkable, living tissue that functionally adapts to external loading. Therefore, bone shape and internal structure carry information relevant to many disciplines, including medicine, forensic science, and anthropology. However, morphometric comparisons of homologous regions across different individuals or groups are still challenging. In this study, two methods were combined to quantify such differences: (1) Holistic morphometric analysis (HMA) was used to quantify morphometric values in each bone, (2) which could then be mapped to a volumetric mesh of a canonical bone created by a statistical free-form deformation model (SDM). Required parameters for this canonical holistic morphometric analysis (cHMA) method were identified and the robustness of the method was evaluated. The robustness studies showed that the SDM converged after one to two iterations, had only a marginal bias towards the chosen starting image, and could handle large shape differences seen in bones of different species. Case studies were performed on metacarpal bones and proximal femora of different primate species to confirm prior study results. The differences between species could be visualised and statistically analysed in both case studies. cHMA provides a framework for performing quantitative comparisons of different morphometric quantities across individuals or groups. These comparisons facilitate investigation of the relationship between spatial morphometric variations and function or pathology, or both.

Anatomically Parameterized Statistical Shape Model: Explaining Morphometry through Statistical Learning

Objective: Statistical shape models (SSMs) are a popular tool to conduct morphological analysis of anatomical structures which is a crucial step in clinical practices. However, shape representations through SSMs are based on shape coefficients and lack an explicit one-to-one relationship with anatomical measures of clinical relevance. While a shape coefficient embeds a combination of anatomical measures, a formalized approach to find the relationship between them remains elusive in the literature. This limits the use of SSMs to subjective evaluations in clinical practices. We propose a novel SSM controlled by anatomical parameters derived from morphometric analysis. Methods: The proposed anatomically parameterized SSM (ANAT_SSM) is based on learning a linear mapping between shape coefficients (latent space) and selected anatomical parameters (anatomical space). This mapping is learned from a synthetic population generated by the standard SSM. Determining the pseudo-inverse of the mapping allows us to build the ANAT_SSM. We further impose orthogonality constraints to the anatomical parameterization (OC-ANAT_SSM) to obtain independent shape variation patterns. The proposed contribution was evaluated on two skeletal databases of femoral and scapular bone shapes using clinically relevant anatomical parameters within each (five for femoral and six for scapular bone). Results: Anatomical measures of the synthetically generated shapes exhibited realistic statistics. The learned matrices corroborated well with the obtained statistical relationship, while the two SSMs achieved moderate to excellent performance in predicting anatomical parameters on unseen shapes. Conclusion: This study demonstrates the use of anatomical representation for creating anatomically parameterized SSMs and as a result, removes the limited clinical interpretability of standard SSMs. Significance: The proposed models could help analyze differences in relevant bone morphometry between populations, and be integrated in patient-specific pre-surgery planning or in-surgery assessment.

Statistical Shape and Appearance Models: Development Towards Improved Osteoporosis Care

PURPOSE OF REVIEW

Statistical models of shape and appearance have increased their popularity since the 1990s and are today highly prevalent in the field of medical image analysis. In this article, we review the recent literature about how statistical models have been applied in the context of osteoporosis and fracture risk estimation.

RECENT FINDINGS

Recent developments have increased their ability to accurately segment bones, as well as to perform 3D reconstruction and classify bone anatomies, all features of high interest in the field of osteoporosis and fragility fractures diagnosis, prevention, and treatment. An increasing number of studies used statistical models to estimate fracture risk in retrospective case-control cohorts, which is a promising step towards future clinical application. All the reviewed application areas made considerable steps forward in the past 5-6 years. Heterogeneities in validation hinder a thorough comparison between the different methods and represent one of the future challenges to be addressed to reach clinical implementation.

Evaluation of Statistical Shape Modeling in Quantifying Femoral Morphologic Differences Between Symptomatic and Nonsymptomatic Hips in Patients with Unilateral Femoroacetabular Impingement Syndrome

Purpose

To determine whether statistical shape modeling can detect subtle morphologic differences in the shape of the proximal femur that correlate with clinical findings of unilateral femoroacetabular impingement syndrome.

Methods

Patients who had diagnoses of unilateral femoroacetabular impingement syndrome and who had existing computed tomography scans of their pelvises were included. Three-dimensional shape models in the form of triangle meshes were generated from the computed tomography images. Statistical shapes of cam-type and normal hips were compared to identify structural differences.

Results

The study included 33 hips in 17 subjects. Of the subjects, 7 (41.1%) were male, and 10 (58.9%) were female. The subjects ranged in age from 17-60 years of age (mean 36.3 ± 11.0 years old). The statistical shape modeling found mean shapes and modes after optimizing the groupwise correspondence. Symptomatic hips demonstrated 1 mm of thickening as compared to the femoral necks of asymptomatic hips, corresponding to cam lesions.

Conclusions

Symptomatic cam deformities were an average of 1 mm more prominent in the femoral neck region as compared to the asymptomatic hips when using statistical shape modeling. The present study provides a proof of the concept that statistical shape modeling can be used to examine and help define cam morphology and that subtle morphologic differences may account for developing femoroacetabular impingement syndrome.

Clinical Relevance

Using the methods presented in this study, it would be possible to define cam and pincer morphologies by creating statistical shape models, and this work could potentially lead to the development of a new classification system for femoroacetabular impingement syndrome lesions.

Trabecular bone patterning across the human hand

Hand bone morphology is regularly used to link particular hominin species with behaviors relevant to cognitive/technological progress. Debates about the functional significance of differing hominin hand bone morphologies tend to rely on establishing phylogenetic relationships and/or inferring behavior from epigenetic variation arising from mechanical loading and adaptive bone modeling. Most research focuses on variation in cortical bone structure, but additional information about hand function may be provided through the analysis of internal trabecular structure. While primate hand bone trabecular structure is known to vary in ways that are consistent with expected joint loading differences during manipulation and locomotion, no study exists that has documented this variation across the numerous bones of the hand. We quantify the trabecular structure in 22 bones of the human hand (early/extant modern Homo sapiens) and compare structural variation between two groups associated with post-agricultural/industrial (post-Neolithic) and foraging/hunter-gatherer (forager) subsistence strategies. We (1) establish trabecular bone volume fraction (BV/TV), modulus (E), degree of anisotropy (DA), mean trabecular thickness (Tb.Th) and spacing (Tb.Sp); (2) visualize the average distribution of site-specific BV/TV for each bone; and (3) examine if the variation in trabecular structure is consistent with expected joint loading differences among the regions of the hand and between the groups. Results indicate similar distributions of trabecular bone in both groups, with those of the forager sample presenting higher BV/TV, E, and lower DA, suggesting greater and more variable loading during manipulation. We find indications of higher loading along the ulnar side of the forager sample hand, with high site-specific BV/TV distributions among the carpals that are suggestive of high loading while the wrist moves through the 'dart-thrower's' motion. These results support the use of trabecular structure to infer behavior and have direct implications for refining our understanding of human hand evolution and fossil hominin hand use.

Mapping anisotropy improves QCT-based finite element estimation of hip strength in pooled stance and side-fall load configurations

Hip fractures are one of the most severe consequences of osteoporosis. Compared to the clinical standard of DXA-based aBMD at the femoral neck, QCT-based FEA delivers a better surrogate of femoral strength and gains acceptance for the calculation of hip fracture risk when a CT reconstruction is available. Isotropic, homogenised voxel-based, finite element (hvFE) models are widely used to estimate femoral strength in cross-sectional and longitudinal clinical studies. However, fabric anisotropy is a classical feature of the architecture of the proximal femur and the second determinant of the homogenised mechanical properties of trabecular bone. Due to the limited resolution, fabric anisotropy cannot be derived from clinical CT reconstructions. Alternatively, fabric anisotropy can be extracted from HR-pQCT images of cadaveric femora. In this study, fabric anisotropy from HR-pQCT images was mapped onto QCT-based hvFE models of 71 human proximal femora for which both HR-pQCT and QCT images were available. Stiffness and ultimate load computed from anisotropic hvFE models were compared with previous biomechanical tests in both stance and side-fall configurations. The influence of using the femur-specific versus a mean fabric distribution on the hvFE predictions was assessed. Femur-specific and mean fabric enhance the prediction of experimental ultimate force for the pooled, i.e. stance and side-fall, (isotropic: r²=0.81, femur-specific fabric: r²=0.88, mean fabric: r²=0.86,p<0.001) but not for the individual configurations. Fabric anisotropy significantly improves bone strength prediction for the pooled configurations, and mapped fabric provides a comparable prediction to true fabric. The mapping of fabric anisotropy is therefore expected to help generate more accurate QCT-based hvFE models of the proximal femur for personalised or multiple load configurations.

A novel registration-based methodology for prediction of trabecular bone fabric from clinical QCT: A comprehensive analysis

Osteoporosis leads to hip fractures in aging populations and is diagnosed by modern medical imaging techniques such as quantitative computed tomography (QCT). Hip fracture sites involve trabecular bone, whose strength is determined by volume fraction and orientation, known as fabric. However, bone fabric cannot be reliably assessed in clinical QCT images of proximal femur. Accordingly, we propose a novel registration-based estimation of bone fabric designed to preserve tensor properties of bone fabric and to map bone fabric by a global and local decomposition of the gradient of a non-rigid image registration transformation. Furthermore, no comprehensive analysis on the critical components of this methodology has been previously conducted. Hence, the aim of this work was to identify the best registration-based strategy to assign bone fabric to the QCT image of a patient’s proximal femur. The normalized correlation coefficient and curvature-based regularization were used for image-based registration and the Frobenius norm of the stretch tensor of the local gradient was selected to quantify the distance among the proximal femora in the population. Based on this distance, closest, farthest and mean femora with a distinction of sex were chosen as alternative atlases to evaluate their influence on bone fabric prediction. Second, we analyzed different tensor mapping schemes for bone fabric prediction: identity, rotation-only, rotation and stretch tensor. Third, we investigated the use of a population average fabric atlas. A leave one out (LOO) evaluation study was performed with a dual QCT and HR-pQCT database of 36 pairs of human femora. The quality of the fabric prediction was assessed with three metrics, the tensor norm (TN) error, the degree of anisotropy (DA) error and the angular deviation of the principal tensor direction (PTD). The closest femur atlas (CTP) with a full rotation (CR) for fabric mapping delivered the best results with a TN error of 7.3 ± 0.9%, a DA error of 6.6 ± 1.3% and a PTD error of 25 ± 2°. The closest to the population mean femur atlas (MTP) using the same mapping scheme yielded only slightly higher errors than CTP for substantially less computing efforts. The population average fabric atlas yielded substantially higher errors than the MTP with the CR mapping scheme. Accounting for sex did not bring any significant improvements. The identified fabric mapping methodology will be exploited in patient-specific QCT-based finite element analysis of the proximal femur to improve the prediction of hip fracture risk.