Statistical shape and appearance models for fast and automated estimation of proximal femur fracture load using 2D finite element models

Investigation of the process intergrowth of bone tissue into the hole in titanium implants (Experimental research)

INTRODUCTION

Despite the use of modern implants, complications such as nonunion and avascular necrosis of the femoral head are observed in femoral neck fractures (FNF). We have created a new perforated I-beam implant for FNF osteosynthesis and developed a new osteosynthesis philosophy based not only on the mechanical and biomechanical interaction of the bone-implant system, but also on the interaction of the biological properties of the bone and the implant. The purpose of the work is to study the interaction of the biological process of the bone - its regeneration (germination) of bone tissue into the holes of the implant.

MATERIALS AND METHODS

The experiment was carried out on fourteen Chinchilla rabbits in accordance with all international standards. A perforated implant specially made of titanium (ChM, Poland) was surgically implanted into the proximal femur. The implant measurements were as follows: length - 6 mm, width - 3 mm, thickness - 2 mm, 2 holes with a diameter of 2 mm. The 14 rabbits were divided into 7 groups. After 1, 2, 3, 4, 5, 10 and 12 weeks the animals were withdrawn from the experiment according to the standard rules in sequential order. The preparations were placed in a formalin solution and sent to the pathomorphology laboratory (CITO, Russia) for histological studies.

RESULTS

Weekly histopathological studies revealed a gradual transition from the organization of a hematoma to the formation of mature bone tissue in the holes of the implants. The titanium implant is bioinert and did not cause any visible reactions from the bone tissue. Simultaneous integration of vascular proliferation and newly formed bone tissue into the implant holes were revealed. On 10-12-week preparations, the formation of trabecular structures of mature bone tissue was revealed in the holes of the implants and elements of adipose and bone marrow tissue were observed. Macroscopic examination of 4-5-week preparations showed almost complete filling of the holes with bone tissue. On 10-12-week preparations, the bone tissue in the holes of the implants did not differ from the bone tissue surrounding the implant. The processes of formation of mature bone tissue in the holes of the implants were similar to the processes of physiological bone healing (regeneration) at the fracture site.

CONCLUSIONS

The obtained results show the following: 1.The titanium implant is bioinert and does not cause any visible reactions from the bone tissue; 2. There is a gradual process of formation of new vessels, and then the formation of new bone tissue in the holes of the implant instead of the one damaged during implantation. Thus, the results of this experiment indirectly confirm our assumption that a perforated implant for FNF osteosynthesis will participate not only in the mechanical and biomechanical interaction of the bone-implant system, but will also include the 3rd element in this system - the biological properties of the bone itself. We assume that these properties of the new implant will increase blood flow in the femoral neck and partially replenish the volume of bone tissue destroyed during osteosynthesis which does not occur with FNF osteosynthesis by any of the known implants.

Stochastic failure analysis of proximal femur using an isogeometric analysis based nonlocal gradient-enhanced damage model

BACKGROUND AND OBJECTIVE

Medical imaging-based finite element methods are more accurate tools for fracture risk prediction than the traditional aBMD based methods. However, these methods have drawbacks like geometric errors, high computational cost, mesh-dependent results, etc. In this article, the authors have proposed an isogeometric analysis-based nonlocal gradient-enhanced damage model to overcome some of these issues. Moreover, there are uncertainties in the values of input parameters for such analysis due to various measurement errors. Hence, stochastic analysis is performed to quantify the effect of these parametric uncertainties on the fracture behavior of the proximal femur.

METHODS

Computed Tomography images of a patient are used to create a 2D proximal femur model with a heterogeneous description of material properties. A numerical model based on gradient-enhanced nonlocal continuum damage mechanics is used for fracture analysis of proximal femur to overcome the issues related to mesh dependency in traditional continuum damage mechanics models. Further, a multipatch isogeometric solver is developed to solve the governing equations. Monte Carlo simulations are used to understand the effect of parametric uncertainties on the fracture behavior of the proximal femur.

RESULTS

The developed numerical framework is used to solve the fracture problem of proximal femur under single leg stance loading conditions. The obtained results are validated by comparing the load-displacement response and the crack path with that given in the literature. Stochastic analysis is performed by considering a ±5% variation in the elastic modulus, damage initiation strain, and the neck-shaft angle values.

CONCLUSION

The proposed numerical framework can correctly predict the damage initiation and propagation in a proximal femur. The results reveal that the heterogeneous nature of material properties of bone plays a significant role in determining the fracture characteristics of the proximal femur. Further, the results of the stochastic analysis reveal that the parametric uncertainties in the neck-shaft angle have a much more significant influence on the results of the analysis than the parametric uncertainties in the elastic modulus and damage initiation strain.

Femoral strength can be predicted from 2D projections using a 3D statistical deformation and texture model with finite element analysis

Ultimate force of the proximal human femur can be predicted using Finite Element Analysis (FEA), but the models rely on 3D computed tomography images. Landmark-based statistical appearance models (SAM) and B-Spline transformation-based statistical deformation models (SDM) have been used to estimate 3D images from 2D projections, which facilitates model generation and reduces the radiation dose. However, there is no literature on the accuracy of SDM-based FEA models of bones with respect to experimental results. In this study, a methodology for an enhanced SDM with textural information is presented. The statistical deformation and texture models (SDTMs) are based on a set of 37 quantitative CT (QCT) images. They were used to estimate 3D images from two or one projections of the set in a leave-one-out setup. These estimations where then used to create FEA models. The ultimate force predicted by FEA models estimated from two or one projection using the SDTMs were compared to the experimental ultimate force from a previous study on the same femora and to the results of standard QCT-based FEA models. High correlations between predictions and experimental measurements were found for FEA models reconstructed from 2D projections with R²=0.835 when based on two projections and R²=0.724 when using one projection. The correlations were comparable to those reached with standard QCT-based FE-models with the experimental results (R²=0.795). This study shows the high potential of SDTM-based 3D image reconstruction and FEA modelling from 2D projections to predict femoral ultimate force.

Clinical relevance of augmented statistical shape model of the scapula in the glenoid region

OBJECTIVE

To illustrate (a) whether a statistical shape model (SSM) augmented with anatomical landmark set(s) performs better fitting and provides improved clinical relevance over non-augmented SSM and (b) which anatomical landmark set provides the best augmentation strategy for predicting the glenoid region of the scapula.

METHODS

Scapula SSM was built using 27 dry bone CT scans and augmented with three anatomical landmark sets (16 landmarks each) resulting in three augmented SSMs (aSSM_proposed, aSSM_set1, aSSM_set2). The non-augmented and three augmented SSMs were then used in a non-rigid registration (regression) algorithm to fit to six external scapular shapes. The prediction error by each type of SSM was evaluated in the glenoid region for the goodness of fit (mean error, root mean square error, Hausdorff distance and Dice similarity coefficient) and for four anatomical angles (critical shoulder angle, lateral acromion angle, glenoid inclination, glenopoar angle).

RESULTS

Inter- and intra-observer reliability for landmark selection was moderate to excellent (ICC>0.74). Prediction error was significantly lower for SSM_{non-augmented} for mean (0.9 mm) and root mean square (1.15 mm) distances. Dice coefficient was significantly higher (0.78) for aSSM_proposed compared to all other SSM types. Prediction error for anatomical angles was lowest using the aSSM_proposed for critical shoulder angle (3.4°), glenoid inclination (2.6°), and lateral acromion angle (3.2°).

CONCLUSION AND SIGNIFICANCE

The conventional SSM robustness criteria or better goodness of fit do not guarantee improved anatomical angle accuracy which may be crucial for certain clinical applications in pre-surgical planning. This study provides insights into how SSM augmented with region-specific anatomical landmarks can provide improved clinical relevance.

Associations between body mass index across adult life and hip shapes at age 60 to 64: Evidence from the 1946 British birth cohort

OBJECTIVE

To examine the associations of body mass index (BMI) across adulthood with hip shapes at age 60-64years.

METHODS

Up to 1633 men and women from the MRC National Survey of Health and Development with repeat measures of BMI across adulthood and posterior-anterior dual-energy X-ray absorptiometry bone mineral density images of the proximal femur recorded at age 60-64 were included in analyses. Statistical shape modelling was applied to quantify independent variations in hip mode (HM), of which the first 6 were examined in relation to: i) BMI at each age of assessment; ii) BMI gain during different phases of adulthood; iii) age first overweight.

RESULTS

Higher BMI at all ages (i.e. 15 to 60-64) and greater gains in BMI were associated with higher HM2 scores in both sexes (with positive HM2 values representing a shorter femoral neck and a wider and flatter femoral head). Similarly, younger age first overweight was associated with higher HM2 scores but only in men once current BMI was accounted for. In men, higher BMI at all ages was also associated with lower HM4 scores (with negative HM4 values representing a flatter femoral head, a wider neck and smaller neck shaft angle) but no associations with BMI gain or prolonged exposure to high BMI were found. Less consistent evidence of associations was found between BMI and the other four HMs.

CONCLUSION

These results suggest that BMI across adulthood may be associated with specific variations in hip shapes in early old age.

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

Including structural information of trabecular bone improves the prediction of bone strength and fracture risk. However, this information is available in clinical CT scans, only for peripheral bones. We hypothesized that a correlation exists between the shape of the bone, its volume fraction (BV/TV) and fabric, which could be characterized using statistical modeling. High-resolution peripheral computed tomography (HR-pQCT) images of 73 proximal femurs were used to build a combined statistical model of shape, BV/TV and fabric. The model was based on correspondence established by image registration and by morphing of a finite element mesh describing the spatial distribution of the bone properties. Results showed no correlation between the distribution of bone shape, BV/TV and fabric. Only the first mode of variation associated with density and orientation showed a strong relationship (R²>0.8). In addition, the model showed that the anisotropic information of the proximal femur does not vary significantly in a population of healthy, osteoporotic and osteopenic samples. In our dataset, the average anisotropy of the population was able to provide a close approximation of the patient-specific anisotropy. These results were confirmed by homogenized finite element (hFE) analyses, which showed that the biomechanical behavior of the proximal femur was not significantly different when the average anisotropic information of the population was used instead of patient-specific fabric extracted from HR-pQCT. Based on these findings, it can be assumed that the fabric information of the proximal femur follows a similar structure in an elderly population of healthy, osteopenic and osteoporotic proximal femurs.

3D-DXA: Assessing the Femoral Shape, the Trabecular Macrostructure and the Cortex in 3D from DXA images

The 3D distribution of the cortical and trabecular bone mass in the proximal femur is a critical component in determining fracture resistance that is not taken into account in clinical routine Dual-energy X-ray Absorptiometry (DXA) examination. In this paper, a statistical shape and appearance model together with a 3D-2D registration approach are used to model the femoral shape and bone density distribution in 3D from an anteroposterior DXA projection. A model-based algorithm is subsequently used to segment the cortex and build a 3D map of the cortical thickness and density. Measurements characterising the geometry and density distribution were computed for various regions of interest in both cortical and trabecular compartments. Models and measurements provided by the "3D-DXA" software algorithm were evaluated using a database of 157 study subjects, by comparing 3D-DXA analyses (using DXA scanners from three manufacturers) with measurements performed by Quantitative Computed Tomography (QCT). The mean point-to-surface distance between 3D-DXA and QCT femoral shapes was 0.93 mm. The mean absolute error between cortical thickness and density estimates measured by 3D-DXA and QCT was 0.33 mm and 72 mg/cm³. Correlation coefficients (R) between the 3D-DXA and QCT measurements were 0.86, 0.93, and 0.95 for the volumetric bone mineral density at the trabecular, cortical, and integral compartments respectively, and 0.91 for the mean cortical thickness. 3D-DXA provides a detailed analysis of the proximal femur, including a separate assessment of the cortical layer and trabecular macrostructure, which could potentially improve osteoporosis management while maintaining DXA as the standard routine modality.

Prediction of femoral strength using 3D finite element models reconstructed from DXA images: validation against experiments

Computed tomography (CT)-based finite element (FE) models may improve the current osteoporosis diagnostics and prediction of fracture risk by providing an estimate for femoral strength. However, the need for a CT scan, as opposed to the conventional use of dual-energy X-ray absorptiometry (DXA) for osteoporosis diagnostics, is considered a major obstacle. The 3D shape and bone mineral density (BMD) distribution of a femur can be reconstructed using a statistical shape and appearance model (SSAM) and the DXA image of the femur. Then, the reconstructed shape and BMD could be used to build FE models to predict bone strength. Since high accuracy is needed in all steps of the analysis, this study aimed at evaluating the ability of a 3D FE model built from one 2D DXA image to predict the strains and fracture load of human femora. Three cadaver femora were retrieved, for which experimental measurements from ex vivo mechanical tests were available. FE models were built using the SSAM-based reconstructions: using only the SSAM-reconstructed shape, only the SSAM-reconstructed BMD distribution, and the full SSAM-based reconstruction (including both shape and BMD distribution). When compared with experimental data, the SSAM-based models predicted accurately principal strains (coefficient of determination >0.83, normalized root-mean-square error <16%) and femoral strength (standard error of the estimate 1215 N). These results were only slightly inferior to those obtained with CT-based FE models, but with the considerable advantage of the models being built from DXA images. In summary, the results support the feasibility of SSAM-based models as a practical tool to introduce FE-based bone strength estimation in the current fracture risk diagnostics.

ASSESSMENT OF OSTEOPOROTIC FEMORAL FRACTURE RISK: FINITE ELEMENT METHOD AS A POTENTIAL REPLACEMENT FOR CURRENT CLINICAL TECHNIQUES

Femoral fracture risk prediction is a necessary step preceding effective pharmacological intervention or pre-operative planning. Current clinical methods for fracture risk prediction rely on 2D imaging methods and have limited predictive value. Researchers are therefore trying to find improved methods for fracture prediction. During last few decades, many studies have focused on integration of 3D imaging techniques and the finite element (FE) method to improve the accuracy of fracture assessment techniques. In this paper, we review the recent advances in FE and other techniques for predicting the risk of femoral fractures. Based on a number of selected studies, the different steps that are involved in generation of patient-specific FE models are reviewed with particular emphasis on the fracture criteria. The inaccuracies that might arise due to the imperfections of the involved steps are also discussed. It is concluded that compared to image- and geometry-based techniques, FE is a more promising approach for prediction of fracture loads. However, certain technological advancements in FE modeling protocols are required before FE modeling can be recruited in clinical settings.

Patient-specific bone modeling and analysis: the role of integration and automation in clinical adoption

Patient-specific analysis of bones is considered an important tool for diagnosis and treatment of skeletal diseases and for clinical research aimed at understanding the etiology of skeletal diseases and the effects of different types of treatment on their progress. In this article, we discuss how integration of several important components enables accurate and cost-effective patient-specific bone analysis, focusing primarily on patient-specific finite element (FE) modeling of bones. First, the different components are briefly reviewed. Then, two important aspects of patient-specific FE modeling, namely integration of modeling components and automation of modeling approaches, are discussed. We conclude with a section on validation of patient-specific modeling results, possible applications of patient-specific modeling procedures, current limitations of the modeling approaches, and possible areas for future research.