Generation of a 3D proximal femur shape from a single projection 2D radiographic image

3D-DXA Based Finite Element Modelling for Femur Strength Prediction: Evaluation Against QCT

Osteoporosis is characterised by the loss of bone density resulting in an increased risk of fragility fractures. The clinical gold standard for diagnosing osteoporosis is based on the areal bone mineral density (aBMD) used as a surrogate for bone strength, in combination with clinical risk factors. Finite element (FE) analyses based on quantitative computed tomography (QCT) have been shown to estimate bone strength better than aBMD. However, their application in the osteoporosis clinics is limited due to exposure of patients to increased X-rays radiation dose. Statistical modelling methods (3D-DXA) enabling the estimation of 3D femur shape and volumetric bone density from dual energy X-ray absorptiometry (DXA) scan have been shown to improve osteoporosis management. The current study used 3D-DXA based FE analyses to estimate femur strength from the routine clinical DXA scans and compared its results against 151 QCT based FE analyses, in a clinical cohort of 157 subjects. The linear regression between the femur strength predicted by QCT-FE and 3D-DXA-FE models correlated highly (coefficient of determination R2 = 0.86) with a root mean square error (RMSE) of 397 N. In conclusion, the current study presented a 3D-DXA-FE modelling tool providing accurate femur strength estimates noninvasively, compared to QCT-FE models.

2D-3D reconstruction of the proximal femur from DXA scans: Evaluation of the 3D-Shaper software

Introduction: Osteoporosis is currently diagnosed based on areal bone mineral density (aBMD) computed from 2D DXA scans. However, aBMD is a limited surrogate for femoral strength since it does not account for 3D bone geometry and density distribution. QCT scans combined with finite element (FE) analysis can deliver improved femoral strength predictions. However, non-negligible radiation dose and high costs prevent a systematic usage of this technique for screening purposes. As an alternative, the 3D-Shaper software (3D-Shaper Medical, Spain) reconstructs the 3D shape and density distribution of the femur from 2D DXA scans. This approach could deliver a more accurate estimation of femoral strength than aBMD by using FE analysis on the reconstructed 3D DXA. Methods: Here we present the first independent evaluation of the software, using a dataset of 77 ex vivo femora. We extend a prior evaluation by including the density distribution differences, the spatial correlation of density values and an FE analysis. Yet, cortical thickness is left out of this evaluation, since the cortex is not resolved in our FE models. Results: We found an average surface distance of 1.16 mm between 3D DXA and QCT images, which shows a good reconstruction of the bone geometry. Although BMD values obtained from 3D DXA and QCT correlated well (r ² = 0.92), the 3D DXA BMD were systematically lower. The average BMD difference amounted to 64 mg/cm³, more than one-third of the 3D DXA BMD. Furthermore, the low correlation (r ² = 0.48) between density values of both images indicates a limited reconstruction of the 3D density distribution. FE results were in good agreement between QCT and 3D DXA images, with a high coefficient of determination (r ² = 0.88). However, this correlation was not statistically different from a direct prediction by aBMD. Moreover, we found differences in the fracture patterns between the two image types. QCT-based FE analysis resulted mostly in femoral neck fractures and 3D DXA-based FE in subcapital or pertrochanteric fractures. Discussion: In conclusion, 3D-Shaper generates an altered BMD distribution compared to QCT but, after careful density calibration, shows an interesting potential for deriving a standardized femoral strength from a DXA scan.

Validation of 3D finite element models from simulated DXA images for biofidelic simulations of sideways fall impact to the hip

Computed tomography (CT)-derived finite element (FE) models have been proposed as a tool to improve the current clinical assessment of osteoporosis and personalized hip fracture risk by providing an accurate estimate of femoral strength. However, this solution has two main drawbacks, namely: (i) 3D CT images are needed, whereas 2D dual-energy x-ray absorptiometry (DXA) images are more generally available, and (ii) quasi-static femoral strength is predicted as a surrogate for fracture risk, instead of predicting whether a fall would result in a fracture or not. The aim of this study was to combine a biofidelic fall simulation technique, based on 3D computed tomography (CT) data with an algorithm that reconstructs 3D femoral shape and BMD distribution from a 2D DXA image. This approach was evaluated on 11 pelvis-femur constructs for which CT scans, ex vivo sideways fall impact experiments and CT-derived biofidelic FE models were available. Simulated DXA images were used to reconstruct the 3D shape and bone mineral density (BMD) distribution of the left femurs by registering a projection of a statistical shape and appearance model with a genetic optimization algorithm. The 2D-to-3D reconstructed femurs were meshed, and the resulting FE models inserted into a biofidelic FE modeling pipeline for simulating a sideways fall. The median 2D-to-3D reconstruction error was 1.02 mm for the shape and 0.06 g/cm³ for BMD for the 11 specimens. FE models derived from simulated DXAs predicted the outcome of the falls in terms of fracture versus non-fracture with the same accuracy as the CT-derived FE models. This study represents a milestone towards improved assessment of hip fracture risk based on widely available clinical DXA images.

Prediction of osteoporotic hip fracture in postmenopausal women through patient-specific FE analyses and machine learning

A great challenge in osteoporosis clinical assessment is identifying patients at higher risk of hip fracture. Bone Mineral Density (BMD) measured by Dual-Energy X-Ray Absorptiometry (DXA) is the current gold-standard, but its classification accuracy is limited to 65%. DXA-based Finite Element (FE) models have been developed to predict the mechanical failure of the bone. Yet, their contribution has been modest. In this study, supervised machine learning (ML) is applied in conjunction with clinical and computationally driven mechanical attributes. Through this multi-technique approach, we aimed to obtain a predictive model that outperforms BMD and other clinical data alone, as well as to identify the best-learned ML classifier within a group of suitable algorithms. A total number of 137 postmenopausal women (81.4 ± 6.95 years) were included in the study and separated into a fracture group (n = 89) and a control group (n = 48). A semi-automatic and patient-specific DXA-based FE model was used to generate mechanical attributes, describing the geometry, the impact force, bone structure and mechanical response of the bone after a sideways-fall. After preprocessing the whole dataset, 19 attributes were selected as predictors. Support Vector Machine (SVM) with radial basis function (RBF), Logistic Regression, Shallow Neural Networks and Random Forest were tested through a comprehensive validation procedure to compare their predictive performance. Clinical attributes were used alone in another experimental setup for the sake of comparison. SVM was confirmed to generate the best-learned algorithm for both experimental setups, including 19 attributes and only clinical attributes. The first, generated the best-learned model and outperformed BMD by 14pp. The results suggests that this approach could be easily integrated for effective prediction of hip fracture without interrupting the actual clinical workflow.

Image-based finite-element modeling of the human femur

Fracture is considered a critical clinical endpoint in skeletal pathologies including osteoporosis and bone metastases. However, current clinical guidelines are limited with respect to identifying cases at high risk of fracture, as they do not account for many mechanical determinants that contribute to bone fracture. Improving fracture risk assessment is an important area of research with clear clinical relevance. Patient-specific numerical musculoskeletal models generated from diagnostic images are widely used in biomechanics research and may provide the foundation for clinical tools used to quantify fracture risk. However, prior to clinical translation, in vitro validation of predictions generated from such numerical models is necessary. Despite adopting radically different models, in vitro validation of image-based finite element (FE) models of the proximal femur (predicting strains and failure loads) have shown very similar, encouraging levels of accuracy. The accuracy of such in vitro models has motivated their application to clinical studies of osteoporotic and metastatic fractures. Such models have demonstrated promising but heterogeneous results, which may be explained by the lack of a uniform strategy with respect to FE modeling of the human femur. This review aims to critically discuss the state of the art of image-based femoral FE modeling strategies, highlighting principal features and differences among current approaches. Quantitative results are also reported with respect to the level of accuracy achieved from in vitro evaluations and clinical applications and are used to motivate the adoption of a standardized approach/workflow for image-based FE modeling of the femur.

A Mouse Model for Skeletal Structure and Function Changes Caused by Radiation Therapy and Estrogen Deficiency

Radiation therapy and estrogen deficiency can damage healthy bone and lead to an increased fracture risk. The goal of this study is to develop a mouse model for radiation therapy using a fractionated biologically equivalent dose for cervical cancer treatment in both pre- and postmenopausal women. Thirty-two female C57BL/6 mice 13 weeks of age were divided into four groups: Sham + non-irradiated (SHAM + NR), Sham + irradiated (SHAM + IRR), ovariectomy + non-irradiated (OVX + NR) and ovariectomy + irradiated (OVX + IRR). The irradiated mice received a 6 Gy dose of X-rays to the hindlimbs at Day 2, Day 4 and Day 7 (18 Gy total). Tissues were collected at Day 35. DEXA, microCT analysis and FEA were used to quantify structural and functional changes at the proximal tibia, midshaft femur, proximal femur and L1 vertebra. There was a significant (p < 0.05) decline in proximal tibia trabecular BV/TV from (1) IRR compared to NR mice within Sham (- 46%) and OVX (- 41%); (2) OVX versus Sham within NR mice (- 36%) and IRR mice (- 30%). With homogenous material properties applied to the proximal tibia mesh using FEA, there was (1) an increase in whole bone (trabecular + cortical) structural stiffness from IRR compared to NR mice within Sham (+ 10%) and OVX (+ 15%); (2) a decrease in stiffness from OVX versus Sham within NR mice (- 18%) and IRR mice (- 14%). Fractionated irradiation and ovariectomy both had a negative effect on skeletal microarchitecture. Ovariectomy had a systemic effect, while skeletal radiation damage was largely specific to trabecular bone within the X-ray field.

Assessment of finite element models for prediction of osteoporotic fracture

With increasing life expectancy and mortality rates, the burden of osteoporotic hip fractures is continually on an upward trend. In terms of prevention, there are several osteoporosis treatment strategies such as anti-resorptive drug treatments, which attempt to retard the rate of bone resorption, while promoting the rate of formation. With respect to prediction, several studies have provided insights into obtaining bone strength by non-invasive means through the application of FE analysis. However, what valuable information can we obtain from FE studies that have focused on osteoporosis research, with respect to the prediction of osteoporotic fractures? This paper aims to fine studies that have used FE analysis to predict fractures in the proximal femur through a systematic search of literature using PUBMED, with the main objective of supporting the diagnosis of osteoporosis. The focus of these FE studies is first discussed, and the methodological aspects are summarized, by mainly comparing and contrasting their meshing properties, material properties, and boundary conditions. The implications of these methodological differences in FE modelling processes and propositions with the aim of consolidating or minimalizing these differences are further discussed. We proved that studies need to start converging in terms of their input parameters to make the FE method applicable to clinical settings. This, in turn, will decrease the time needed for in vitro tests. Current advancements in FE analysis need to be consolidated before any further steps can be taken to implement engineering analysis into the clinical scenario.

Review of 2-D/3-D Reconstruction Using Statistical Shape and Intensity Models and X-Ray Image Synthesis: Toward a Unified Framework

Patient-specific three-dimensional (3-D) bone models are useful for a number of clinical applications such as surgery planning, postoperative evaluation, as well as implant and prosthesis design. Two-dimensional-to-3-D (2-D/3-D) reconstruction, also known as model-to-modality or atlas-based 2-D/3-D registration, provides a means of obtaining a 3-D model of a patient's bones from their 2-D radiographs when 3-D imaging modalities are not available. The preferred approach for estimating both shape and density information (that would be present in a patient's computed tomography data) for 2-D/3-D reconstruction makes use of digitally reconstructed radiographs and deformable models in an iterative, non-rigid, intensity-based approach. Based on a large number of state-of-the-art 2-D/3-D bone reconstruction methods, a unified mathematical formulation of the problem is proposed in a common conceptual framework, using unambiguous terminology. In addition, shortcomings, recent adaptations, and persisting challenges are discussed along with insights for future research.

Analysis of the evolution of cortical and trabecular bone compartments in the proximal femur after spinal cord injury by 3D-DXA

Marked trabecular and cortical bone loss was observed at the proximal femur short-term after spinal cord injury (SCI). 3D-DXA provided measurement of vBMD evolution at both femoral compartments and cortical thinning, thereby suggesting that this technique could be useful for bone analysis in these patients.

INTRODUCTION

SCI is associated with a marked increase in bone loss and risk of osteoporosis development short-term after injury. 3D-DXA is a new imaging analysis technique providing 3D analysis of the cortical and trabecular bone from DXA scans. The aim of this study was to assess the evolution of trabecular macrostructure and cortical bone using 3D-DXA in patients with recent SCI followed over 12 months.

METHODS

Sixteen males with recent SCI (< 3 months since injury) and without antiosteoporotic treatment were included. Clinical assessment, bone mineral density (BMD) measurements by DXA, and 3D-DXA evaluation at proximal femur (analyzing the integral, trabecular and cortical volumetric BMD [vBMD] and cortical thickness) were performed at baseline and at 6 and 12 months of follow-up.

RESULTS

vBMD significantly decreased at integral, trabecular, and cortical compartments at 6 months (- 8.8, - 11.6, and - 2.4%), with a further decrease at 12 months, resulting in an overall decrease of - 16.6, - 21.9, and - 5.0%, respectively. Cortical thickness also decreased at 6 and 12 months (- 8.0 and - 11.4%), with the maximal decrease being observed during the first 6 months. The mean BMD losses by DXA at femoral neck and total femur were - 17.7 and - 21.1%, at 12 months, respectively.

CONCLUSIONS

Marked trabecular and cortical bone loss was observed at the proximal femur short-term after SCI. 3D-DXA measured vBMD evolution at both femoral compartments and cortical thinning, providing better knowledge of their differential contributory role to bone strength and probably of the effect of therapy in these patients.

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.

Prediction of incident hip fracture with the estimated femoral strength by finite element analysis of DXA Scans in the study of osteoporotic fractures

A bone fractures only when loaded beyond its strength. The purpose of this study was to determine the association of femoral strength, as estimated by finite element (FE) analysis of dual-energy X-ray absorptiometry (DXA) scans, with incident hip fracture in comparison to hip bone mineral density (BMD), Fracture Risk Assessment Tool (FRAX), and hip structure analysis (HSA) variables. This prospective case-cohort study included a random sample of 1941 women and 668 incident hip fracture cases (295 in the random sample) during a mean ± SD follow-up of 12.8 ± 5.7 years from the Study of Osteoporotic Fractures (n = 7860 community-dwelling women ≥67 years of age). We analyzed the baseline DXA scans (Hologic 1000) of the hip using a validated plane-stress, linear-elastic finite element (FE) model of the proximal femur and estimated the femoral strength during a simulated sideways fall. Cox regression accounting for the case-cohort design assessed the association of estimated femoral strength with hip fracture. The age-body mass index (BMI)-adjusted hazard ratio (HR) per SD decrease for estimated strength (2.21; 95% CI, 1.95-2.50) was greater than that for total hip (TH) BMD (1.86; 95% CI, 1.67-2.08; p < 0.05), FN BMD (2.04; 95% CI, 1.79-2.32; p > 0.05), FRAX scores (range, 1.32-1.68; p < 0.0005), and many HSA variables (range, 1.13-2.43; p < 0.005), and the association was still significant (p < 0.05) after further adjustment for hip BMD or FRAX scores. The association of estimated strength with incident hip fracture was strong (Harrell's C index 0.770), significantly better than TH BMD (0.759; p < 0.05) and FRAX scores (0.711-0.743; p < 0.0001), but not FN BMD (0.762; p > 0.05). Similar findings were obtained for intracapsular and extracapsular fractures. In conclusion, the estimated femoral strength from FE analysis of DXA scans is an independent predictor and performs at least as well as FN BMD in predicting incident hip fracture in postmenopausal women.

Use of DXA-based finite element analysis of the proximal femur in a longitudinal study of hip fracture

Bone mineral density (BMD) measured by dual-energy X-ray absorptiometry (DXA) is used for clinical assessment of fracture risk; however, measurements that incorporate bone strength could improve predictive ability. The aim of this study was to determine whether bone strength derived from finite element (FE) analysis was associated with hip fracture risk in a longitudinal study. We studied 728 women (mean age 82 years), 182 with subsequent hip fracture. FE models were generated from baseline DXA scans of the hip to determine femoral bone strength and load-to-strength ratio (LSR). The baseline LSR was significantly higher in fracture cases (median 1.1) compared with controls (0.7, p < 0.0001). Femoral strength and BMD were also significantly lower in cases (median 1820 N, 0.557 g/cm(2)) compared with controls (2614 N, 0.618 g/cm(2) ) both p < 0.0001. Fracture risk increased per standard deviation decrease in femoral strength (odds ratio [OR] = 2.2, 95% confidence interval [CI] 1.8-2.8); femoral neck (FN) BMD (OR = 2.1, 95% CI 1.7-2.6); total hip BMD (OR = 1.8, 95% CI 1.5-2.1); and per SD increase in LSR (OR = 1.8, 95% CI 1.5-2.1). After adjusting for FN BMD, the odds ratio for femoral strength (OR = 1.7, 95% CI 1.2-2.4) and LSR (OR = 1.4, 95% CI 1.1-1.7) remained significantly greater than 1. The area under the curve (AUC) for LSR combined with FN BMD (AUC 0.69, 95% CI 0.64-0.73) was significantly greater than FN BMD alone (AUC 0.66, 95% CI 0.62-0.71, p = 0.004). Strength and LSR remained significant when adjusted for prevalent fragility fracture, VFA, and FRAX score. In conclusion, the DXA-based FE model was able to discriminate incident hip fracture cases from controls in this longitudinal study independently from FN BMD, prior fracture, VFA, and FRAX score. Such an approach may provide a useful tool for better assessment of bone strength to identify patients at high risk of hip fracture who may benefit from treatment to reduce fracture risk.

Single x-ray transmission system for bone mineral density determination

Bones are the support of the body. They are composed of many inorganic compounds and other organic materials that all together can be used to determine the mineral density of the bones. The bone mineral density is a measure index that is widely used as an indicator of the health of the bone. A typical manner to evaluate the quality of the bone is a densitometry study; a dual x-ray absorptiometry system based study that has been widely used to assess the mineral density of some animals' bones. However, despite the success stories of utilizing these systems in many different applications, it is a very expensive method that requires frequent calibration processes to work properly. Moreover, its usage in small species applications (e.g., rodents) has not been quite demonstrated yet. Following this argument, it is suggested that there is a need for an instrument that would perform such a task in a more reliable and economical manner. Therefore, in this paper we explore the possibility to develop a new, affordable, and reliable single x-ray absorptiometry system. The method consists of utilizing a single x-ray source, an x-ray image sensor, and a computer platform that all together, as a whole, will allow us to calculate the mineral density of the bone. Utilizing an x-ray transmission theory modified through a version of the Lambert-Beer law equation, a law that expresses the relationship among the energy absorbed, the thickness, and the absorption coefficient of the sample at the x-rays wavelength to calculate the mineral density of the bone can be advantageous. Having determined the parameter equation that defines the ratio of the pixels in radiographies and the bone mineral density [measured in mass per unit of area (g/cm(2))], we demonstrated the utility of our novel methodology by calculating the mineral density of Wistar rats' femur bones.

Reconstructing the 3D shape and bone mineral density distribution of the proximal femur from dual-energy X-ray absorptiometry

The accurate diagnosis of osteoporosis has gained increasing importance due to the aging of our society. Areal bone mineral density (BMD) measured by dual-energy X-ray absorptiometry (DXA) is an established criterion in the diagnosis of osteoporosis. This measure, however, is limited by its two-dimensionality. This work presents a method to reconstruct both the 3D bone shape and 3D BMD distribution of the proximal femur from a single DXA image used in clinical routine. A statistical model of the combined shape and BMD distribution is presented, together with a method for its construction from a set of quantitative computed tomography (QCT) scans. A reconstruction is acquired in an intensity based 3D-2D registration process whereby an instance of the model is found that maximizes the similarity between its projection and the DXA image. Reconstruction experiments were performed on the DXA images of 30 subjects, with a model constructed from a database of QCT scans of 85 subjects. The accuracy was evaluated by comparing the reconstructions with the same subject QCT scans. The method presented here can potentially improve the diagnosis of osteoporosis and fracture risk assessment from the low radiation dose and low cost DXA devices currently used in clinical routine.

Comparison of 3D finite element analysis derived stiffness and BMD to determine the failure load of the excised proximal femur

INTRODUCTION

Bone mineral density (BMD) is currently the preferred surrogate for bone strength in clinical practice. Finite element analysis (FEA) is a computer simulation technique that can predict the deformation of a structure when a load is applied, providing a measure of stiffness (N mm(-1)). Finite element analysis of X-ray images (3D-FEXI) is a FEA technique whose analysis is derived from a single 2D radiographic image.

METHODS

18 excised human femora had previously been quantitative computed tomography scanned, from which 2D BMD-equivalent radiographic images were derived, and mechanically tested to failure in a stance-loading configuration. A 3D proximal femur shape was generated from each 2D radiographic image and used to construct 3D-FEA models.

RESULTS

The coefficient of determination (R(2)%) to predict failure load was 54.5% for BMD and 80.4% for 3D-FEXI.

CONCLUSIONS

This ex vivo study demonstrates that 3D-FEXI derived from a conventional 2D radiographic image has the potential to significantly increase the accuracy of failure load assessment of the proximal femur compared with that currently achieved with BMD. This approach may be readily extended to routine clinical BMD images derived by dual energy X-ray absorptiometry.