Introduction

The increase in the elderly population and the growing concern about the consequences of fractures, together with insufficient rates of detection of situations of bone fragility¹,², has increased the indication of the assessment of fracture risk in people of both sexes older than 64 years³. The dualenergy X-ray absorptiometry (DXA) technique is currently the clinical standard for this type of bone measurement.

Nowadays, when evaluating the risk of fracture, different methods are applied, although the most widely used include the presence of clinical risk factors and the measurement of areal bone mineral density (BMD). Bone measurements are made in the proximal femur and lumbar spine using DXA. However, BMD only allows a limited assessment of the mechanical determinants of bone fracture⁴,⁵.

Finite element analysis (FE) has been applied to assess bone resistance in volumetric bone models, based on computed tomography (CT) scans, precisely identifying the subject-specific mechanical determinants of fracture. This type of analysis includes the three-dimensional geometry of the bone, the quantity and distribution of bone tissue, and the loads to which the bone is subjected⁶. With this process, the limitations of the BMDa are overcome. CT-based models of FE have been extensively validated ex vivo^{7 12}, and have shown better performance compared to a BMD in predicting proximal femur resistance in vitro⁶,¹³. A significant association between bone fractures and estimated resistance with FE has also been reported in an in vivo study¹⁴.

Numerical models have also addressed fracture risk classification in recent years. In this sense, the bone resistance obtained from the analysis by FE is a better classifier than the BMDa¹⁵,¹⁶. Falcinelli et al.¹⁵ studied the effect of the load condition on fracture through bone resistance. In this study, in the analysis of ROC curves (Receiving Operating Characteristic), the area under the curve (AUC), both in position and under multiple load conditions, was higher than the values obtained for the BMDa. Qasim et al.¹⁶ pointed out that bone strength calculated from CT images with FE was a more reliable predictor of fracture than BMDa obtained with DXA. Both studies used logistic regression to classify fractures.

Nishiyama et al.¹⁷ classified 35 cases of women suffering osteoporotic fractures through femur resistance obtained using a FE model based on quantitative CT (QCT), comparing their classification power with the vBMD. The results obtained with the vector support machine technique showed AUC values of 0.79 and 0.94 for trochanter and neck fractures, respectively. Despite the achievement obtained in this type of study, QCT-based FE models are far from becoming routine clinical practice. Recently, DXA-based three-dimensional (3D) FE models allowed discrimination of fracture cases with AUC >0.80 by using the major principal stress (MPS) as a parameter for discrimination, analyzing for bone tissue type, class of fracture and gender.

A possible improvement of the mechanical analysis of the femur fracture encompasses the study of fracture by regions, which allows filtering the most relevant data of the calculation. However, robust criteria are required to correctly estimate high fracture risk areas and optimize analysis. Furthermore, in most published numerical studies, simulation of a lateral fall has focused on a single load vector. In real conditions, the main load vector, origin of the fracture, may have a different orientation from that assumed in the FE models, affecting the distribution of internal loads and, consequently, the most relevant areas of interest. Some authors¹⁸ have already expressed the need for a broader approach in simulating the load component, among the various determining factors of bone fracture. In the only study in which three fall load conditions were simulated¹⁹, differences in the results were evident.

Therefore, our hypothesis was that the analysis of one of the first diagnostic radiographs of the fracture allows us to infer the spatial orientation of the main load, and to identify the weakest structural sector of the proximal femur, by simulating FE fall. Our objective, then, was to verify, in a case-control study of proximal femur fractures, whether the association of biomechanical parameters related to bone resistance derived from DXA-based

FE models improves, taking into account the most advanced representations of the loads associated with the fall and the most affected areas of the bone.

Materials and methods

Subjects

The methodology applied in this study and the use of clinical data and medical images were evaluated by the ethics committee of the University Hospital Mutua de Terrasa, receiving their approval in November 2016.

DXA test data from 111 patients of both sexes with indication of bone densitometry were used, which had been explored in the CETIR department at the University Hospital Mutua de Terrassa. All patients presented osteoporosis, according to the WHO classification, (T-score of lumbar spine, neck of the femur or total area of the femur <-2.5). There was no selection in patients with fracture under the criterion of a T-score >-2.5. Of these patients, 62 had recently suffered a fracture in one of the sectors of the proximal third of the femur after a fortuitous fall (group of cases), and 49 patients, with similar characteristics in terms of age, weight, height, and category according to T-score, had no history of previous fracture (control group). Patient data have been described in table 1, considering the type of fracture and gender.

Table 1. Number of patients recruited by group, sex and type of fracture 

ROC-AUC analysis

Following the guidelines of the study by Ruiz Wills et al.²¹, the discrimination power of six parameters was tested: the BMDv related to the DXA images extrapolated in 3D, and 5 parameters derived from the FE simulations, ie, the maximum principal deformation, the MPE, the SED, the maximum main voltage and the MPS. The analysis considered the groups of patients (cases and controls), type of fracture (neck and trochanter), type of bone (trabecular and cortical) and gender (female and male). The area under the ROC curve was used to quantify the discriminating power of the evaluated parameters. In addition, a 5 and 4 iteration cross validation was applied for the neck fracture and trochanter discriminations, respectively. This technique is used in artificial intelligence instruments to validate the generated models, guaranteeing that the partition between training and test data is independent. It consists of repeating and calculating the arithmetic mean obtained from the evaluation measurements on different partitions. The cross validation process is repeated during k iterations, with each of the possible subsets of test data. Finally, the arithmetic mean of the results of each iteration is performed to obtain a single result. This method is very accurate since it is evaluated from K combinations of training and test data.

Figure 1. Limiting conditions of the simulations: A) impact simulations, and B) static simulations 

Results

Region of interest (ROI)

The impact simulation allowed identifying areas in the femur with maximum MPS values. The neck fracture group showed 15,023 elements (geometrically regular fragments into which the bone volume is divided after meshing the finite elements) with high MPS values, while the trochanter group had 42,880 elements (Figure 2). The number of elements identified is 17.9% and 37% lower than the elements used in a previous study carried out in our group for the neck and trochanter, respecti-vely²¹. The area identified for each type of fracture coincided 95% of the time with the fracture line of the available post-fracture X-ray images (Figure 3). As a result, the identified elements were used to carry out the ROC-AUC analysis and classification.

Figure 2. Area with high values of major main tension (MPS). The blueelements correspond to the element for neck fractures and the redelements are for the trochanter fracture 

Figure 3. Comparison between the fracture line and the critical areaidentified for a neck fracture case with high values of major majorstress (MPS) 

ROC analysis

ROC analysis was carried out regarding the patients' gender. As shown in table 1, the number of men was very small compared to the number of women for both types of fractures. To avoid any misinterpretation of the results, the analysis was applied only to the female population. Table 2 presents the AUC values obtained in the analysis. In trabecular bone, the lowest AUC values were 0.65 for the BMV, and the highest were 0.82 for the MPS, followed by the SED with 0.76, for patients with neck fractures. Trochanteric fracture cases showed similar results, with AUC values of 0.72, 0.82, and 0.83 for BMD, SED, and maximum principal tension, respectively. The maximum AUC value was 0.93 for the MPS. Regarding cortical bone, the BMDv had AUC values of 0.57 and 0.61 for neck and trochanter fractures, respectively. The MPS for trochanter cases provided the highest AUC value: 0.80.

Table 2. AUC values, in the analysis of ROC curves (average cross-validation) for women by ROI and type of bone tissue 

AUC: area under the curve; ROC: receiving operating characteritics; ROI: region of interest

Classification

Based on the results obtained in the previous section, the SVM technique was applied to the data for women, trabecular bone in neck and trochanter fractures. The confusion matrix for neck fracture showed that the 15 patients without fracture (15/26) were correctly classified, and there was a perfect classification of fracture cases (Figure 4a). For trochanter fractures, 17 (17/23) and 13 (13/15) control and fracture cases were correctly classified, respectively (Figure 4b).

Figure 4. Confusion matrix of Support Vector Machine (SVM) for women and trabecular bone: A) neck fracture, and B) trochanter fracture. In green are the true positive cases, in orange the true negatives, in yellow the false positives (type I error) and in red the false negatives (type II error) 

The number of type I errors (false positive, yellow in figure 4) was 11 (11/37) and 2 (2/15) for neck and trochanter fractures, respectively. Furthermore, in trochanteric fractures, 6 cases (6/23) were predicted as a control when, in fact, they fractured: this was a type II error (False negative, red in figure 4).

Equations 8 and 9 represent the linear Kernel equation of the trabecular bone for neck and trochanter fractures, respectively. The values represent the specific weight of each variable in the classification process. The variables SED, maximum main tension and MPS, all presented a greater weight than the BMDv, in cases of neck fracture. Regarding the trochanteric fracture, the MPS variable was the only one that exceeded BMDv. For both types of fractures, the variables related to deformation, that is, the maximum main deformation and the MPE were the least significant of all.

Mcuello = 1,31(DMOv) + 0,15 (Max. Prin. Strain) + 0,54 (MPE) + 1,96 (SED) + 1,80 (Max. Prin. Stress) - 2,60 (MPS) - 1,13 [8]

Mtrocánter = 1,33(DMOv) + 0,42 (Max. Prin. Strain) + 0,38 (MPE) + 1,17 (SED) + 0,49 (Max. Prin. Stress) + 2,15 - 1,87 [9]

Discussion

The impact simulations permitted the identification of critical elements, according to the high MPS values. This result led to refinement of ROI for static simulations (Figure 5). On the one hand, the selection of critical elements such as ROI makes it possible to exclude elements that could contribute noise in the identification of critical stress or deformation concentrations in these areas. On the other hand, refinement of ROI accelerated data extraction and analysis in general.

1: proposed fracture analysis zones in Ruiz Wills et al. (2019). 2: real areas.

Figure 5. Refinement of the region of interest for: a) neck fracture, and b) trochanter fracture 

Consideration of fracture areas is not common in the literature, and when considered, the ROI used is selected according to the anatomical region defined for each type of fracture. As far as we know, this is the first study to use mechanical fields obtained with FE simulations to define ROI for the neck and trochanter areas. This ROI coincides with the fracture lines observed on radiographs taken immediately after the fracture occurred. This result indicates that the impact model is valid for the identification of critical areas for fracture cases. It is relevant to mention that the ROI defined in our study came from the average of all the critical elements of the models for each type of fracture, that is, neck or trochanter.

The ROC-AUC analysis for the trabecular bone indicated that the AUC values for the SED, the maximum main tension and the MPS were higher than the values of the BMDv, for both the neck fracture and the trochanter (Table 2). The AUC for MPS increased its discriminating power by 2% (from 0.91 to 0.93) with the new ROI of the trochanter compared to that previously reported in the literature²¹. This increase may be small in absolute terms; however, a 2% increase in AUC values greater than 0.90 is an excellent result. AUC values for cortical bone in the ROI of the trochanter were 0.8, representing an improvement of 13% compared to the values reported in a previous study (0.67)²¹. These results indicate that the selection of the ROI for the analysis has an important influence on the discrimination results. Furthermore, this result confirms that MPS could be the best parameter for fracture classification, as presented in a previous study carried out in our laboratory²¹.

Classification analysis was carried out using a VSM only for trabecular bone and women. The results showed a perfect classification, with a sensitivity of 100%, of the cases of femoral neck fracture. Regarding patients without fracture, 58% of cases were classified as true negatives, that is, a specificity of 58%, and the rest of the cases were predicted as fractures. These 11 erroneous classified cases correspond to type I error (false positive), which means that the prediction says that the patient will suffer a fracture when this will not happen or has not yet happened, with the greatest inconvenience of asking the patient to undergo a test or take medicine when it is not necessary. This type of error, in clinical practice, would not be so bad, since steps could be taken to prevent the fracture that may not occur. On the contrary, if the prediction led to a type II error, it would be a worse scenario, since it would indicate that the patient will not suffer any fracture when it really will. No type II error was found for the classification of femoral neck fracture.

For trochanteric fractures, 68% of fracture cases were predicted as a fracture (68% sensitivity), with 6 patients predicted as a control when they fractured, i.e. type II error. A possible explanation could be the definition of ROI for trochanter analysis. Although the ROI was selected based on the critical mechanical fields, the ROI could include some elements that could really affect the results obtained. However, 89% of the control cases were classified as a control (specificity of 89%), and only 2 cases were obtained as a type I error. These results suggest that a larger number of patients may be necessary to extrapolate the results of trochanteric fracture case.

In both cases of fracture, the AUC value for fracture prediction was 0.79. For trochanteric fracture, these values coincide with the values reported in the literature for the same type of fracture¹⁹. These results suggest that the 3D-DXA-based volumetric femur model may work the same as the QCT-based FE models for the classification of trochanteric fractures. This would be a key point for the use of FE models in routine clinical practice, since DXA exploration can be applied to patients to make the predictive assessment of possible fractures. The AUC for neck fracture was lower than that reported in the literature using a model based on the QCT¹⁹. The AUC value highlights the total number of successfully classified cases, including fractures and controls. However, as previously discussed, there were no type II errors in the classification of neck fracture cases. Overall, these results also indicate that our model can be used to reliably predict neck fractures.

The present study presents certain limitations. The number of men needs to be increased. The extrapolation of the results obtained would be reinforced by the study of a greater number of men. This would provide a better understanding of fracture classification using FE models. Regarding the properties of the bone: the stiffness of the trabecular and cortical bone was calculated using empirical relationships based on BMDv. Macroscopic bone properties can be estimated from the nanoscale bone composition through the theory of homogenization²⁸-³¹. However, the stiffness estimate used in this study is accurate, since the fracture mechanism is outside the scope of our objective³². The model used in the drop simulations could only move in the direction of speed. Such a restriction could influence the mechanical response of the bone. However, the impact related to the lateral fall occurs in seconds or a fraction of seconds, and it is highly likely that the damaging force peak will actually occur in the direction of speed, just before impact. As such, restricting all degrees of freedom except in the direction of speed is a reasonable approach. Another point to consider is that the participation of the skin and soft tissues in the impact with the surface has not been taken into account. However, the subject-specific fall force used in the static simulation includes the influence of soft tissues²⁷. The subject-specific drop force used in the static simulations was set in one direction. The angle of force has been reported to affect the mechanical response of the bone³³,³⁴. The angle of application of the force was not modified in this study to simulate the maximum effect that the falling force can have on the mechanical response of the bone. The definition of ROI for neck and trochanter fractures needs to be improved. This study showed that the selection of ROI could influence the results obtained. Automatic subject-specific selection of critical elements can be implemented, by identifying significant differences between the mechanical field obtained from the simulations. This aspect needs to be further explored.

The next step would be to find a strong correlation between the MPS and the parameters derived from the DXA. To achieve this goal, the number of data must be increased to guarantee the accuracy of the correlation found. Once the correlation is established, MPS estimation and hip fracture prediction can be accomplished without the need for any numerical simulation, which can definitely save a lot of time in diagnosis. In this sense, the use of MPS as a fracture classifier/predictor in regular clinical practice may be possible in the near future.

The identification of the MPS variable, with a high predictive value for fragility bone fractures, opens a new stage in obtaining a diagnostic instrument that will potentially allow patients to be identified on the basis of decreased bone strength below of a subject-specific critical level. Inferring the result of this MPS variable from 3D bone measurements is the following objective and its integration with clinical fracture risk factors, not only with the application in femur fractures, but also in the main osteoporotic fractures.

Conclusions

DXA-based 3D FE femur models could be an appropriate tool for classifying patients who may suffer fractures. Defining specific regions of interest for the analysis area would improve the quality of the classification. As such, the definition must be done carefully. Overall, our results suggest that, in clinical practice, FE models of the femur from DXA scans can be used in routine practice to help prevent hip fractures. The number of examinations needs to be increased to define the correlation between MPS and DXA parameters, in order to avoid the use of simulation and accelerate the reliable classification of fracture patients. This point requires continuity in the line of studies and a careful review of the results, modeling a future fracture predictive instrument from DXA explorations with a biomechanical approach, including other well-recognized clinical risk factors.