A new hip fracture risk index derived from FEA-computed proximal femur fracture loads and energies-to-failure

Abstract

Introduction

Osteoporosis is among the most common and costly metabolic bone diseases [1], causing bones to become weak and brittle and greatly increasing the risk of fracture [2, 3]. Although osteoporosis can affect any bone in the human body, osteoporotic fractures of the proximal femur are the most devastating outcome of the disease, often signaling an end to independent living in the functional elderly. Fracture risk assessment and risk stratification through screening are necessary to reduce the incidence of hip fracture. The areal bone mineral density (aBMD) extracted from the dual-energy X-ray absorptiometry (DXA), a 2D-projection technique, sometimes provides limited information about skeletal factors on fracture risk [4, 5].

Quantitative CT (QCT) imaging is one of the most powerful methods for assessing bone quality in the proximal femur; after three-dimensional (3D) segmentation of the proximal femur, features such as volumetric bone mineral density (BMD) of the cortical and trabecular bone and bone geometry can be computed. Although DXA has undergone many years of development and has benefited from multiple studies of large cohorts and QCT measures have not undergone as much analysis, QCT has the potential to provide improved prediction of hip fracture once additional research and development are performed [6]. QCT is much more sensitive to changes in trabecular BMD and can identify reductions in trabecular BMD well before DXA. DXA aBMD combines cortical and trabecular bone into one measure, thereby obscuring measurements of trabecular BMD and reducing the sensitivity of DXA to changes in trabecular BMD. When bone loss is rapid, such as during use of glucocorticoids or during spaceflight, trabecular bone is lost first, and use of DXA aBMD understates bone loss because cortical bone is superimposed over trabecular bone [7, 8]. Patient-specific finite element analysis (FEA) from QCT images incorporates bone geometry, cortical thickness, and the three-dimensional distribution of bone density in the proximal femur to compute the force (fracture load) necessary to break the proximal femur in a particular loading condition. The fracture load can be defined as the force at the onset of fracture (the yield strength) or the maximum force the proximal femur withstands before complete fracture (the ultimate strength or load capacity), which are calculated using FEA with linear or nonlinear material properties, respectively. FEA-computed fracture loads are the most robust measure of proximal femoral structural integrity and, therefore, hip fracture risk [9, 10]. In particular, the ultimate strength or load capacity of the proximal femur which is computed with nonlinear FEA is associated with incident hip fracture in men and women, and in men even after controlling for aBMD [11].

Finite element models compute the force necessary to break the proximal femur when forces and other boundary conditions are applied to reflect a specific loading condition, such as single-limb stance during walking or impact onto the greater trochanter from a fall in a specific direction [11]. Although the FEA-computed yield or ultimate strengths for different loading conditions are individually associated with incident hip fracture, and are mutually correlated, each yield and ultimate strength for each loading condition provides different structural information about the proximal femur that contributes to a subject’s overall hip fracture risk. The energy transferred to the proximal femur prior to reaching ultimate failure in a particular loading condition may also be associated with fracture risk. Therefore, in this study we used principal component analysis (PCA) to examine a combination of the FEA-computed yield and ultimate strengths and energies-to-failure in various loading conditions to obtain a more robust measure of fracture risk than individual FEA-computed strengths. Principal component analysis is a commonly used method to reduce the dimensionality of data by selecting the most important features that capture the most information [12]. PCA can also speed up the algorithm for prediction by getting rid of correlated variables which do not contribute to decision making [13]. Therefore, we employed PCA to develop a global FEA-computed hip fracture risk index based on the FE model results of 110 hip fracture subjects and 235 age- and sex-matched control subjects in a subset of the AGES-Reykjavik study [14]. PCA is one of the most widely used dimension reduction techniques to transform a large number of variables into a smaller number of variables by identifying the correlations and patterns, while preserving most of the valuable information. The objectives of this study were (1) to construct a global FEA-computed fracture risk index derived from the most important FE parameters of fracture risk based on PCA that is associated with incident hip fracture and (2) to determine if the global FEA-computed fracture risk index, after adjusting for aBMD and covariates, can predict hip fracture better than the FE yield strength, ultimate failure load and energy-to-failure in a single loading condition or their combination in four different loading conditions.

Methods

Results

Within the male sample, the fracture and control groups were not significantly different with respect to age, height, weight, and the three energies-to-failure in the fall loading conditions (PLenergy, Penergy, Lenergy) at the time of the CT scan (p-value > 0.120; Table 1). However, the remaining nine FE parameters were significantly lower in each fracture group than in the respective control group (p-value < 0.001). In contrast, within the female sample, the fracture and control groups were significantly different with respect to weight (p-value = 0.036). As for the male group, age, height, and the three energies-to-failure in the fall loading conditions in the female group (PLenergy, Penergy, Lenergy) were not significantly different between fracture and control groups (p-value > 0.513). Similarly to the male group, the remaining nine FE parameters were also significantly lower in each fracture group than in the respective control group (Lu, p-value = 0.007; all others, p-value < 0.001; Table 1).

For the multiple linear regression analyses (Table 2), after controlling for four demographic parameters (age, sex, height, and weight) and interactions, the FE parameters except for Pu, and energies-to-failure in the fall loading conditions were associated with hip fracture (p-value < 0.1). However, Pu was significantly lower in each fracture group than in the respective control group when not controlling for demographic parameters and interactions (p-value < 0.001) (Table 1) and had the higher R² = 0.5217 (Table 2). Note that the interaction of fracture and weight was not retained in our analysis since all p-values for this interaction were greater than 0.1. Therefore, we considered nine hip fracture-related FE parameters (Sy, Su, Senergy, Py, Pu, PLy, PLu, Ly, and Lu) in the following analysis. PCA was applied to these nine FE parameters, which were inherently highly correlated. The proportions of variance explained by the first principal component (PC1) were 83.31%, 78.23%, and 80.65% for the whole sample, male sample, and female sample, respectively. We found that PC1 of the FE parameters was the only significant predictor for hip fracture (p-value < 0.001 in the whole sample, male sample, and female sample). Therefore, we referred to PC1 as the global FEA computed fracture risk index. Using the LGOCV, we found that the performance of using PC1 along with aBMD_CT and covariates, or the nine FE parameters combined along with aBMD_CT and covariates, were better than that of only using aBMD_CT and covariates to predict hip fracture (Table 3). In particular, we observed the superior predictive performance within the whole sample and male sample of PC1 compared with FE parameters combined for all nine classification models; however, within the female sample, FE parameters combined had greater AUC than PC1. Logistic regression and PLS had the greatest AUCs among nine models (Table 3), and were chosen as the two best models. For PLS and logistic based on stratified resampling (Figs. 1 and ​and2),2), in the whole sample, logistic performed better than the PLS by using PC1 and FE parameters combined along with aBMD_CT and covariates, which were also better than Logistic using aBMD_CT and covariates (p-value < 0.001). In contrast, within the male sample, PLS using PC1 and FE parameters combined with aBMD_CT and covariates was better than PLS using aBMD_CT and covariates (p-value < 0.001).

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Fig. 1

The predictive performance of logistic and PLS based on stratified resampling. The values over the lines indicated the p-values obtained from the one-sided Student’s t-test. The values on top of the boxes indicated the average AUCs by using PC1 along with aBMD_CT and covariates (PC1 + aBMD_CT + Cov) versus using aBMD_CT and covariates (aBMD_CT + Cov) or FE parameters combined with aBMD_CT and covariates (FE combined + aBMD_CT + Cov). Notes: The abbreviations of FE parameters are yield strength (force at onset of fracture) calculated during single-limb stance (Sy) and impact from a fall onto the posterior (Py), posterolateral (PLy), and lateral (Ly) aspects of the greater trochanter; ultimate strength (failure load capacity) calculated during single-limb stance (Su) and impact from a fall onto the posterior (Pu), posterolateral (PLu), and lateral (Lu) aspects of the greater trochanter; energy-to-failure calculated during single-limb stance (Senergy) and impact from a fall onto the posterior (Penergy), posterolateral (PLenergy), and lateral (Lenergy) aspects of the greater trochanter

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Fig. 2

The predictive performance of PLS using each FE parameters compared with that of using PC1. The values over the lines indicated the p-values were obtained from the one-sided Student’s t-test. The values on top of the boxes indicated the average AUCs by using PC1 along with aBMD_CT and covariates (PC1 + aBMD_CT + Cov) versus using each of FE parameters along with aBMD_CT and covariates (* + aBMD_CT + Cov)

We performed ANOVA for AUC based on logistic. We observed that the resampled AUCs with aBMD_CT and covariates were different with the resampled AUCs with PC1 or FE parameters combined in the whole sample (p-value = 0.05) and in the male sample (p-value = 0.01), but no such difference was found in the female sample (p-value = 0.68). According to ANOVA for AUC based on PLS, the difference was still observed in the male sample with p-value < 0.01. Remarkably, within the female sample, a distinct pattern emerged from PLS, which is consistent with the Student’s t-test results shown in Fig. 1. There were different resampled AUCs in the female sample with p-value = 0.05. In contrast, in the whole sample, there was no difference observed (p-value = 0.97).

In particular, we observed the superior predictive performance in male sample of PC1 compared with the predictive performance of each FE parameter based on PLS (p-value = 0.02 for Ly; all others, p-value < 0.01) (Fig. 2). For the female sample, all of the AUCs of PLS using one of the FE parameters were greater than the corresponding AUC using PC1 with p-value > 0.1, except for Ly (p-value = 0.0145). We also observed similar predictive performance based on logistic. In the male sample, the predictive performance using PC1 was better than the predictive performance of each FE parameter (p-value = 0.02 for Su; p-value = 0.04 for Ly; all others, p-value < 0.01). In the female sample, all of the AUCs of logistic using one of the FE parameters were similar to the corresponding AUC using PC1 with p-value > 0.1, except for Ly (p-value < 0.01) and Senergy (p-value = 0.04).

Discussion

This is the first study to construct a global FEA-computed risk index by principal component analysis based on multiple fracture-related FEA-computed fracture loads and energies under different loading conditions. The global FEA-computed fracture risk index, after adjusting for aBMD_CT and covariates, predicted hip fracture better than each individual FE parameter (yield strength, ultimate failure load, and energy-to-failure) and also better than the FE parameters combined in the whole sample and the male sample but not the female sample (Figs. 1 and ​and2;2; Table 3). Meanwhile, predicting fracture in the female sample was inherently more difficult than predicting fracture in the male sample because the difference between female fracture and control subjects is much smaller than that for males. In our previous work [11], the age-matched design of this study enhanced our ability to explore gender differences in proximal femoral strength and incident hip fracture as a function of age. In particular, our cross-sectional analysis of age-related FE parameter (Su, PLu, Pu, and Lu) loss by gender and fracture status may explain why proximal femoral strength was strongly associated with incident hip fracture in men but much less so in women (Table 2).

Although the FE parameters are individually associated with incident hip fracture, and are mutually highly correlated, they each provide different structural information about the proximal femur that can influence a subject’s overall fracture risk. The superior performance, in both men and women, of the assessment of hip fracture risk by using the global FEA-computed risk index and FE parameters combined along with aBMD_CT and covariates compared with aBMD_CT and covariates is not surprising. The CT-derived total femur aBMD was considered, which has a strong correlation with aBMD from DXA (r = 0.935) [9]. The predictive performance by incorporating information from FE parameters was better than only using aBMD_CT and covariates in the male sample and female sample (Fig. 1; Table 3), implying that the FE parameters can provide additional information in the assessment of hip fracture risk by incorporating bone geometry, cortical thickness, and the three-dimensional distribution of bone density in the proximal femur. Meanwhile, the global FEA-computed risk index plus the aBMD from DXA was better than the aBMD only (Fig. 1; Table 3). Although aBMD from DXA correlated with bone weakness and fragility fracture [22], DXA is a 2D-projection technique that poorly accounts for bone geometry and size and is a poor predictor of hip fracture in subjects with osteopenia (T-scores between −1 and −2.5). Thus, aBMD provides limited information about skeletal factors on fracture risk. However, several studies have been conducted using 2D-derived indices other than aBMD which showed better and independent predictive capacity, such as the hip structure analysis techniques [23], the 2D FEA [24], and the hip axis length [25]. With the emergence of QCT scan-based FE modeling, better estimates of proximal femoral strength have become possible [26]. Our study employed three-dimensional (3D) FE models from QCT scans, which explicitly represent the 3D geometry and distribution of material properties that make each femur structurally and mechanically unique and is therefore more robust than two-dimensional (2D) models from DXA. Principles of physics dictate that hip fracture occurs when an excessive force is applied to the proximal femur, i.e., when the applied force exceeds the force that the proximal femur can support. This force, which varies with the type of loading and force direction, is known as the proximal femoral strength, fracture load [11, 20], or load capacity [15] computed using patient-specific FEA. Patient-specific FEA-computed fracture loads and energies are the most robust measures of proximal femoral structural integrity and, therefore, benefitted for evaluating the hip fracture risk. The comparison of QCT FEA-computed fracture loads and energies and other measurements derived from 2D images deserves further study.

Conclusions

In summary, FEA-computed fracture loads and energies were associated with incident hip fracture in most of loading conditions that were examined, and the global FEA-computed fracture risk index that was investigated by principal component analysis increased hip fracture risk prediction accuracy in the male sample more than that in the female sample. The global FEA-computed fracture risk index was most strongly associated with incident hip fracture in men after accounting for aBMD from DXA and other clinical and demographic parameters. Thus, FE parameters from 3D FE models includes information about hip fracture beyond that of aBMD from 2D models, especially in the male sample. The significance and complexity of these findings, particularly with respect to sex and age effects, indicate that additional studies of FE modeling for hip fracture risk assessment are likely to enhance our understanding of this significant public health problem.

Acknowledgements

Footnotes

References