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Automation of a DXA-based finite element tool for clinical assessment of hip fracture risk
Accepted Manuscript
Automation of a DXA-based Finite Element Tool for Clinical Assessment of Hip Fracture Risk Yunhua Luo , Sharif Ahmed , William D. Leslie PII: DOI: Reference:
S0169-2607(17)31028-3 10.1016/j.cmpb.2017.11.020 COMM 4551
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
12 August 2017 15 November 2017 24 November 2017
Please cite this article as: Yunhua Luo , Sharif Ahmed , William D. Leslie , Automation of a DXAbased Finite Element Tool for Clinical Assessment of Hip Fracture Risk, Computer Methods and Programs in Biomedicine (2017), doi: 10.1016/j.cmpb.2017.11.020
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Highlights DXA-based finite element model for assessing hip fracture risk in sideways fall; Completely automated computer program with hip DXA as the only input; Greatly improved short-term precision after automation; Better performance than femoral BMD in discrimination test.
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Automation of a DXA-based Finite Element Tool for Clinical Assessment of Hip Fracture Risk Yunhua Luo 1,2,*, Sharif Ahmed 1 and William D. Leslie 3,4 1
Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada
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Department of Biomedical Engineering, University of Manitoba, Winnipeg, Canada
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Department of Radiology, University of Manitoba, Winnipeg, Canada
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Department of Internal Medicine, University of Manitoba, Winnipeg, Canada * Corresponding author: [email protected]
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ABSTRACT
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Finite element analysis of medical images is a promising tool for assessing hip fracture risk. Although a number of finite element models have been developed for this purpose, none of them have been routinely used in clinic. The main reason is that the computer programs that implement the finite element models have not been completely automated, and heavy training is required before clinicians can effectively use them. By using information embedded in clinical dual energy X-ray absorptiometry (DXA), we completely automated a DXA-based finite element (FE) model that we previously developed for predicting hip fracture risk. The automated FE tool can be run as a standalone computer program with the subject’s raw hip DXA image as input. The automated FE tool had greatly improved short-term precision compared with the semiautomated version. To validate the automated FE tool, a clinical cohort consisting of 100 prior hip fracture cases and 300 matched controls was obtained from a local community clinical center. Both the automated FE tool and femoral bone mineral density (BMD) were applied to discriminate the fracture cases from the controls. Femoral BMD is the gold standard reference recommended by the World Health Organization for screening osteoporosis and for assessing hip fracture risk. The accuracy was measured by the area under ROC curve (AUC) and odds ratio (OR). Compared with femoral BMD (AUC=0.71, OR=2.07), the automated FE tool had a considerably improved accuracy (AUC=0.78, OR=2.61 at the trochanter). This work made a large step toward applying our DXA-based FE model as a routine clinical tool for the assessment of hip fracture risk. Furthermore, the automated computer program can be embedded into a website as an internet application. KEY WORDS: hip fracture, dual energy X-ray absorptiometry (DXA), finite element model, fracture risk, automation 1. INTRODUCTION
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Fall-induced hip fracture is a common health risk among elderly people, especially for those who have osteoporosis [1-4]. Osteoporosis can significantly reduce bone strength, it is a ‘silent’ disease as it has no symptom until first fracture. Therefore, subjects of high fracture risk must be diagnosed by clinicians using a reliable assessment tool. A number of tools for assessing fracture risk have been developed from either population-based statistical models [5-9] or biomechanical models [10-16]. The existing clinical tools are almost exclusively based on statistical models. T-score calculated from femoral bone mineral density (BMD) is the gold standard reference for screening osteoporosis and for assessing fracture risk [17, 18]. However, extensive clinical studies showed that the majority of patients who sustain low-trauma fractures have T-scores within the WHO (World Health Organization) safe range [19-22]. Therefore, researchers were motivated to develop assessment tools to consider multiple clinical risk factors [23]. Among these tools FRAX (Fracture Risk Assessment Tool) is the most popular one, which is a web-based calculator to predict an individual’s 10-year probability of hip fracture. However, FRAX still has limited accuracy even though 12 clinical risk factors are considered [5, 23-25]. The main reasons are: the considered clinical factors are biomechanically dependent and some important biomechanical variables such as fall-induced impact force are missing [26].
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In view of the limitations of population-based tools, researchers have turned their attention to biomechanical approaches. Theoretically, biomechanical modeling has the potential to more accurately predict an individual’s fracture risk than statistical approaches, as biomechanical models are based on well-established mechanical principles. A large number of finite element (FE) models have been developed to determine bone strength and to assess fracture risk. Most of the FE models are constructed from QCT (quantitative computed tomography) [11, 16, 2734], since QCT contains actual material and geometry information required to construct a three-dimensional finite element model. However, QCT uses high dosage of radiation and it is not recommended for routine clinical examination [35]. To meet the current clinical needs, DXA-based finite element models [36, 37] have also been developed, although construction of accurate finite element models from DXA images is more challenging and assumptions must be introduced.
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Nevertheless, none of the finite element models have been used routinely in clinic. Indeed, there are still unresolved technical issues in the finite element models [27], for example, the discrepancy among different bone material models [38], the lack of a generally accepted risk threshold for clinical intervention and the inconsistency among risk measurements produced by different finite element models. However, even after the technical issues are all resolved, there is still an obstacle for clinical application, that is, the computer programs that implement the finite element models have not been completely automated. User intervention that often requires the knowledge of finite element analysis (FEA) does not appeal to clinicians. We developed a DXA-based FE model for the prediction of hip fracture risk [37, 39]. In this study, we completely automate the computer program with simple input, so that the automated DXAbased FE tool can be used by clinicians with a minimum training and no knowledge of FEA is required.
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2. AUTOMATION OF DXA-BASED FINITE ELEMENT (FE) MODEL
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The procedure of our DXA-based finite element analysis [37, 39] is shown in Figure 1. The only input required by the procedure is a raw hip DXA, for example, the enCore file (with extension of DFF) generated by GE Lunar. The procedure starts with a clinical hip DXA of the concerned subject and includes the following steps: (1) Clinical regions of interest (ROI) are identified; (2) Proximal femur is segmented from the DXA and a contour of the femur is obtained; (3) A finite element mesh is generated from the femur contour; (4) Material properties are assigned; (5) Loading and constraint conditions are applied; (6) Stress distributions in the femur are obtained by a finite element analysis; (7) Fracture risk index is calculated over the clinical ROIs. The main challenge in automation of the procedure is the generation of a finite element model from hip DXA image without any user intervention. The automation of the DXA-based finite element procedure is described below.
Figure 1 DXA-based finite element analysis of hip fracture risk
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2.1 Segmentation of Proximal Femur
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The proximal femur is automatically segmented from hip DXA scan using information extracted from native DXA file. The steps are shown in Figure 2. (a) The contour of whole hip, including proximal femur and pelvis, is identified from hip DXA scan. (b) The region containing femoral head is extracted from the DXA file, and the contour of pelvis is removed. (c) A circle is fitted into the femoral head region. (d) The circle and the remaining femur contour are merged, and the outline of proximal femur is obtained.
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Figure 2 Segmentation of proximal femur
2.2 Identification of Regions of Interest (ROIs)
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On the basis of clinical studies [40-43], the majority of hip fractures occur at one of three locations, i.e. femoral neck, intertrochanter and femoral shaft as shown in Figure 3(a). An algorithm has been developed to automatically identify the three regions of interest and it is illustrated in Figure 3 (b) – (d). First, the narrowest cross-section of femoral neck is located by finding the shortest distance between points on the two opposite sides of the neck. Femoral neck axis is obtained as a line normal to the narrowest femoral neck and passing through the middle point. Then, femoral shaft axis is determined by linear regression using central points of six shaft cross-sections. Intertrochanteric cross-section is defined as the bi-section line of the neck-shaft angle. Femoral shaft cross-section is located below the neck-shaft intersection point at a distance of 1.5 times of the neck width. All the regions of interest have a width of 10 mm.
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Figure 3 Automatic identification of regions of interest at femoral neck, intertrochanter and femoral shaft (subtrochanter).
2.3 Finite Element Model and Generation of Finite Element Mesh DXA is inherently two-dimensional as a result of X-ray projection. Therefore, only a twodimensional finite element model can be constructed from DXA image. After examining the available two-dimensional mechanical models, it appears that the plane stress model is the only option. The femur bone has irregular and non-uniform cross-section, its material distribution is also spatial. None of the assumptions in the plane stress model are strictly satisfied. However, 5
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application of the plane stress model to femur bone can still be justified based on the loading conditions in sideways fall [44], which is the most critical situation leading to hip fracture. As the femur is connected to the pelvis and the tibia by joints that cannot transfer large torques, it can be reasonably assumed that the femur mainly experiences bending during sideways fall. The bone material behaves like ‘fibres’ in resisting bending moment.
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Consider a composite engineering beam consisting of fibers that is intended to resist the moments as shown in Figure 4. The beam has a non-rectangular cross-section and it does not satisfy the assumptions of plane stress model. Based on beam theory, the contribution of the fibers to resistance of the moments is determined by their distance from the neutral line, and is independent of their horizontal location. Therefore, the fibers can be replaced by a uniformly distributed material that has an equivalent contribution in resisting the moments. The rest material over the beam cross-section can be ‘converted’ into a uniform thickness in the similar way. The equivalent cross-section satisfies all the requirements of plane stress model. The DXA imaging process can be considered as such a homogenization operation.
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Figure 4 Equivalent cross-section produced by material projection
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The nearest-nodes finite element method (NN-FEM) [45, 46] was adopted in this study, because NN-FEM is able to construct high-order finite elements from simplex meshes and NN-FEM has much lower requirement on the quality of finite element meshes [47]. Techniques for generating simplex mesh are well developed and automated. Various software for generating simplex meshes consisting of three-node triangle elements are available. However, to make the DXA-based FE tool seamless, we developed our own computer codes for mesh generation [46]. The mesh density was determined by a series of convergence tests. One convergence curve is provided in Figure 5(a) and a sample finite element mesh is shown in Figure 5(b), where the fracture risk index (FRI) will be described in Section 2.6 and defined in Equation (7).
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FRI vs no of nodes 0.82
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FRI at clinical trochanteric ROI
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Figure 5 (a) Convergence of Fracture Risk Index (FRI) with the number of finite element nodes; (b) a sample finite element mesh producing converged FRI
2.4 Assignment of Element Material Properties
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In the automated DXA-based FE tool, bone mechanical properties are assigned based on bone density. A large number of equations have been established from experimental data to calculate bone elasticity modulus and yield stress from bone density [38]. We adopted the following equations developed by Morgan et al [48, 49].
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Elasticity modulus,
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compressive yield stress,
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{
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and tensile yield stress, {
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Bone density required in the above equations is apparent volumetric density (g/cm3). But bone density measured by DXA is areal bone mineral density (g/cm2). Bone mineral density is equivalent to ash density and it can be converted into apparent density by [50],
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Areal BMD ( , g/cm2) can be converted into volumetric BMD ( , g/cm3) using the diameter at the narrowest femoral neck ( , cm) [51], (5)
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Sample distributions of bone mechanical properties calculated from Equations (1) – (5) for one clinical case are displayed in Figure 6. It should be noticed that the high BMD over the femoral head in Figure 6(a) is caused by overlaping of femoral head and pelvis in DXA.
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Figure 6 Bone mechanical properties assigned based bone mineral density. (a) Areal bone mineral density; (b) elasticity modulus; (c) compressive yield stress; (d) tensile yield stress.
2.5 Application of Loading/Constraint Conditions
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Loading/constraint conditions simulating a sideways fall are considered in the automated DXAbased FE tool. Impact force (F, Newton) induced in sideways fall can be estimated from the subject’s sex, body weight (W, Newton), height (H, centimeter) and hip soft-tissue thickness (T, millimeter) using the following equations [44], (6)
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The actual loading and constraint conditions occurring in a real-world sideways fall are very complicated. We simplified the conditions for the purpose of assessing the relative risk of hip fracture among elderly people. The simplified conditions are shown in Figure 7. The impact force calculated by Equation (6) is applied over the great trochanter; the distal femur is completely constrained; at the contact surface between the femoral head and the pelvis, the femoral head is partly constrained.
Figure 7 Simplified loading/constraint conditions simulating a sideways fall. 9
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2.6 Finite Element Analysis of Stresses and Calculation of Fracture Risk Index (FRI)
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Femur stresses produced by impact force in sideways fall are obtained by finite element analysis. We developed and automated computer codes for solving finite element equations and for calculating stresses. Figure 8(a) shows a sample distribution of von Mises stress in the femur. A number of locations on the femur have high stresses, but not all of them are critical locations. Bone is a highly heterogeneous material and its material strength varies from location to location, therefore, a high stress does not mean high risk of material failure at the point. A previous study [52] has shown that femur bone has a linear elastic behavior up to facture. Therefore, the ratio of von Mises stress to the corresponding yield stress at a critical point is adopted to measure the integrity of bone. If the ratio is larger than one, bone failure will start at the point. Figure 8(b) displays the ratio of von Mises stress to yield stress. Bone has different compressive and tensile yield stress [48, 49]. To simplify calculation, it is assumed that a point located in the lateral side of the neck/shaft axes (see Figure 3) has principal compressive stress and Equation (2) is applied to calculate the yield stress, otherwise Equation (3) is used.
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Figure 8 (a) Distribution of von Mises stress obtained by finite element analysis; (b) the ratio of von Mises stress to yield stress
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The ratio of von Mises stress to yield stress averaged over a region of interest is defined as fracture risk index (FRI) [37],
Where and interest.
(7) are respectively von Mises and yield stress, A is the area of the region of
The fracture risk index (FRI) defined in Equation (7) can be used as a classifier of hip fracture risk. FRI = 1 is the theoretical threshold. If FRI > 1, the subject will suffer hip fracture if the subject has a sideways fall.
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3. CLINICAL STUDY
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Short-term precision and the ability of discriminating clinical fracture cases from matched controls are the two important performance indicators of clinical tools for assessing hip fracture risk. To study the performance of the automated DXA-based FE tool, clinical cases were acquired from St. Boniface Hospital in Winnipeg under an approval of human subject research ethics, with personal information such as patient name and residence address removed before acquisition. Each case had a unique identifier that was used through this study. 3.1 Short-term precision test
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Short-term precision, also termed short-term repeatability or reproducibility, is the capability of a diagnostic tool to produce the same measurement value for the same subject when the tool is operated by the same or different technologist at different time when no actual variation is expected in the measurement. Short-term precision can be measured by the coefficient of variation (CV, %) [53]. A smaller CV (%) represents a better short-term precision. The coefficient of variation is calculated by the following equations [53]. ∑
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In the above equations, m is the number of clinical cases; and are respectively the initial and repeated measurement that are separated by a short-time period; In this study, they are the fracture risk index corresponding to the initial and repeated DXA scan. ̅ is the average of the two measurements; and is standard deviation in the measurements of case j.
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Good short-term precision is necessary for a clinician to know small change in the measurement caused by either clinical treatment or by disease development. A clinical cohort of 100 pairs of hip DXA scans were acquired for this study. Time intervals separating the paired DXA are listed in Table 1. Table 1 Time interval between paired DXA scanning
Number of Cases
< 1 day 1 – 7 days 8 – 10 days 55 35 10
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For the clinical cases, fracture risk index of the initial and repeated scan in each pair were predicted using the automated DXA-based FE tool. Coefficients of variation was calculated according to Equations (8a) – (8d). 3.2 Discrimination test
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Fracture risk index (FRI) generated by the automated DXA-based FE tool can be used as a classifier of hip fracture. The ability of FRI to discriminate clinical hip fracture cases from matched controls can be measured by the area under the ROC (receiver operating characteristic) curve, or AUC in short, and odds ratio (OR) [54-56]. ROC is a graphical plot that illustrates the probability of a diagnostic tool to correctly classify a case if the threshold is changed. AUC is the overall accuracy of the tool for all possible thresholds, with AUC = 1 representing a perfect classification, and AUC = 0.5 indicating no classification ability at all. Although the theoretical threshold of fracture risk index is one, the actual optimal threshold is affected by factors such as the type of DXA scanner and the quality of DXA image, and the optimal threshold should be determined by clinical calibration. Therefore, AUC is an appropriate performance measurement for this study. Odds ratio (OR) measures the association between FRI value and actual fracture outcome. OR > 1 indicates that a larger FRI is associated with a higher risk of hip fracture. The larger the OR, the stronger the association is.
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A clinical cohort consisting of 400 women, including 100 prior hip fractures and 300 matched controls, was acquired for this discrimination study. In the selection of the cohort, the following criteria were used: (1) women age≥ 65 years; (2) femoral neck T-score below -1; and (3) no osteoporosis treatment. The clinical data of the subjects are provided in Table 2.
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Table 2 Statistics of fracture and control group
Fracture Group Control Group 76±9 75±12 63.2±10.3 63.8±11.4 158.8±4.7 158.1±6.2 -2.4 -2.3
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Age (years) Weight (kg) Height (cm) Femoral Neck T-score
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Hip fracture risk indices were predicted by the automated FE tool in batch processing. The only operation required from the user was to provide the location where the 400 hip DXA files are stored. The fracture status of each case was not known to the tool user. The FRI values predicted by the tool were sent to St. Boniface Hospital for an independent statistics analysis. AUC and OR values were calculated using SAS (SAS Institute, Version 9.3). 4. RESULTS The average processing time for each case was about 15 seconds when the cases were processed in batch. If processed cases by case, the processing time was about 17 seconds. Both are acceptable for clinical practice. 12
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Short-term precision of FRI and BMD expressed by coefficient of variation (CV, %) are presented in Table 3. In general, BMD still has the best short-term precision; automated DXA-based FE tool greatly improved the precision compared with the previous semi-automated version. Table 3 Short-term precision (CV, %)
Femoral Neck Trochanter Sub-trochanter 1.94 2.58 4.05 4.53 4.96 6.87 1.12 1.16 -
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FRI (automated) FRI (semi-automated) BMD (clinical)
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In the discrimination test, FRI of six cases was not calculated by the automated FE tool due to poor quality of the DXA images. It turned out the six cases included one fracture case and five controls. Therefore, the actual cases used in this study included 99 prior hip fractures and 295 controls. Average FRI with standard deviation at the three anatomic sites are provided in Table 4. Correlations between FRI and age/BMI (body mass index) are presented in Table 5. The obtained AUC values with 95% CI (confidence interval) are listed in Table 6. The OR values adjusted with age and body mass index are provided in Table 7. According to the results in Table 6, FRI at trochanter was considerably more accurate than femoral BMD in discriminating clinical fracture cases from matched controls. Table 7 shows that FRI had much stronger association with actual fracture outcome than femoral BMD at all sites, and the association at trochanter was the strongest.
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Table 4 Average FRI (±SD)
Anatomic Site
Fracture Group Control Group 1.37±0.32 1.12±0.44 0.55±0.09
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Femoral Neck Trochanter Subtrochanter
p-value as compared to controls
1.28±0.32 0.87±0.26 0.48±0.13
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Table 5 Correlation between FRI and age/BMI
Anatomic Site Femoral Neck Trochanter Subtrochanter
Age (p-value) BMI (p-value) 0.25 (p<0.05) -0.23 (p<0.05) 0.27 (p<0.05) -0.28 (p<0.05) 0.17 (p<0.05) 0.11 (p=0.09)
Table 6 Area under ROC curve (AUC) with 95% CI
FRI Femoral-Neck BMD
Femoral Neck Trochanter Sub-trochanter 0.70 (0.63, 0.77) 0.78 (0.72, 0.83) 0.74 (0.68, 0.80) 0.71 (0.65, 0.78) Referent 13
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p-value compared to referent
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Table 7 Odds ratio (OR) with 95% CI (per SD change)
Femoral Neck FRI adjusted with age and BMI
Trochanter
Sub-trochanter
2.13 (1.54, 2.94) 2.61 (1.83, 3.72) 2.28 (1.68, 3.09)
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FRI adjusted for age, BMI and 1.36 (1.04, 1.75) 1.74 (1.37, 2.24) 2.11 (1.65, 2.65) femoral neck BMD FRI adjusted for FRAX score 0.99 (0.81, 1.20) 1.31 (1.05, 1.65) 1.53 (1.24, 1.92) (with femoral-neck BMD) Femoral-Neck BMD 2.08 (1.57, 2.76)
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5. DISCUSSION
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The large improvement in short-term precision of our DXA-based FE tool is mainly attributed to the automation of femur contour segmentation. In the previous semi-automated version [37], manual operation is required in segmentation of femur contour, which introduces random error. Automated segmentation in the new version is able to eliminate the random error and thus improves the short-term precision. However, even the automated FE tool still has much lower short-term precision than BMD. There are a number of reasons. First, FRI is a functions of a number of variables affecting hip fracture risk, BMD is one of them. The other variables include the projected femur geometry, body weight and height, hip soft-tissue thickness, etc. The worst short-term precision in the variables will determine the short-term precision of FRI. Second, BMD used in clinic is an average over region of interest. The averaging operation is able to improve short-term precision [37]. However, BMD used in the DXA-based FE model is a point-wise map. Change of patient positioning in DXA scanning may introduce difference in the map. Third, also the most important, a small difference in the BMD will be amplified by the material model in Equations (1) – (3) that are nonlinear exponential functions.
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Theoretically, FRI produced by the DXA-based FE model is a better fracture risk predictor than BMD. Hip fracture is often resulted by impact force induced in accidental fall. If the impact force exceeds the femur strength, the femur will fracture. Hip fracture risk is thus jointly determined by impact force and femur strength, and the latter is further decided by femur bone quality that is mainly represented by BMD, and femur size. FRI predicted by the FE model is able to consider all the involved variables, while BMD is only one of them. This explains why FRI had better performance than femoral BMD in the test. That FRI at trochanter had better performance than at other sites is probably due to that the majority of fracture sites in the clinical cohort are actually at trochanter. The region of trochanter is dominated by trabecular bone that has much lower strength than cortical bone, and it is covered by very little soft tissue. If a subject has a sideways fall, the large impact force will directly act on the weak trabecular 14
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bone. Reported clinical studies show that the trochanteric region is indeed a dominant site of hip fractures [42, 57, 58]. The results in Table 5 indicate that hip fracture risk increases with age among elderly women, which is consistent with clinical observations [41, 59-61]. The reason is that bone loss is accelerated for post-menopause women and bone density is a main determinant of bone strength. The results also suggest that for elderly women, BMI is a protective factor for hip fracture at the femoral neck and intertrochanter, but not at the subtrochanter. Hip fracture at the femoral neck and intertrochanter is caused by the impact force that is directly applied at the great trochanter in sideways fall [65-67]. For a subject with higher BMI, the soft-tissue over the great trochanter is likely thicker, which is able to more effectively attenuate the impact force and thus to reduce FRI. But fracture at subtrochanter is probably caused by bending moment generated by the body weight, if the lower extremity is partly or completely constrained in fall. A subject of higher BMI probably experience a larger bending moment at the subtrochanter, and thus has a higher FRI. One major difference between our DXA-based FE model and the previously developed ones [54, 55] is in the consideration of subject-specific impact force induced in sideways fall. Most previous finite element models only consider bone strength in evaluation of fracture risk. Bone strength is indeed one important determinant of hip fracture risk, but fall-induced impact force must be also considered because the impact force has large variation from subject to subject, and it is determined by the subject’s anthropometric parameters. Since fall-induced impact force is considered, this model is helpful to evaluate fracture risk among elderly people who are prone to fall.
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However, there are still a number of limitations in this study and in our FE model. First, our FE model is two-dimensional and simplifications have been introduced as in the other similar models [10, 36]. Our model is theoretically not accurate as three-dimensional FE models constructed from QCT (quantitative computed tomography) [30, 62, 63]. Therefore, our model can only be used to assess relative fracture risk among individuals, it does not have the ability to predict when and where the fracture will occur. Second, information of fall orientation (sideways, forward or backward) is not available from the clinical records, and fall orientation may have significant effect on fracture outcome [64-67]. Currently, our FE model can only deal with impact force in sideways fall by Equation (6). There is a need to extend the equation to accommodate forward and backward fall.
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6. CONCLUSION
In conclusion, this study made a step toward the application of our DXA-based FE model as a clinical tool for assessment of hip fracture risk. As the next step, we will apply our model in prospective studies and in validations of cross clinical centers and DXA scanners. The automated standalone computer program will be distributed to clinical centers. Furthermore, the computer program will be embedded into a web-site as an internet application, so that clinicians over the world will be able to use the tool. ACKNOWLEDGEMENT 15
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The reported research has been supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and Research Manitoba, which are gratefully acknowledged.
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Automation of a DXA-based Finite Element Tool for Clinical Assessment of Hip Fracture Risk Yunhua Luo , Sharif Ahmed , William D. Leslie PII: DOI: Reference:
S0169-2607(17)31028-3 10.1016/j.cmpb.2017.11.020 COMM 4551
To appear in:
Computer Methods and Programs in Biomedicine
Received date: Revised date: Accepted date:
12 August 2017 15 November 2017 24 November 2017
Please cite this article as: Yunhua Luo , Sharif Ahmed , William D. Leslie , Automation of a DXAbased Finite Element Tool for Clinical Assessment of Hip Fracture Risk, Computer Methods and Programs in Biomedicine (2017), doi: 10.1016/j.cmpb.2017.11.020
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Highlights DXA-based finite element model for assessing hip fracture risk in sideways fall; Completely automated computer program with hip DXA as the only input; Greatly improved short-term precision after automation; Better performance than femoral BMD in discrimination test.
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Automation of a DXA-based Finite Element Tool for Clinical Assessment of Hip Fracture Risk Yunhua Luo 1,2,*, Sharif Ahmed 1 and William D. Leslie 3,4 1
Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada
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Department of Biomedical Engineering, University of Manitoba, Winnipeg, Canada
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Department of Radiology, University of Manitoba, Winnipeg, Canada
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Department of Internal Medicine, University of Manitoba, Winnipeg, Canada * Corresponding author: [email protected]
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ABSTRACT
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Finite element analysis of medical images is a promising tool for assessing hip fracture risk. Although a number of finite element models have been developed for this purpose, none of them have been routinely used in clinic. The main reason is that the computer programs that implement the finite element models have not been completely automated, and heavy training is required before clinicians can effectively use them. By using information embedded in clinical dual energy X-ray absorptiometry (DXA), we completely automated a DXA-based finite element (FE) model that we previously developed for predicting hip fracture risk. The automated FE tool can be run as a standalone computer program with the subject’s raw hip DXA image as input. The automated FE tool had greatly improved short-term precision compared with the semiautomated version. To validate the automated FE tool, a clinical cohort consisting of 100 prior hip fracture cases and 300 matched controls was obtained from a local community clinical center. Both the automated FE tool and femoral bone mineral density (BMD) were applied to discriminate the fracture cases from the controls. Femoral BMD is the gold standard reference recommended by the World Health Organization for screening osteoporosis and for assessing hip fracture risk. The accuracy was measured by the area under ROC curve (AUC) and odds ratio (OR). Compared with femoral BMD (AUC=0.71, OR=2.07), the automated FE tool had a considerably improved accuracy (AUC=0.78, OR=2.61 at the trochanter). This work made a large step toward applying our DXA-based FE model as a routine clinical tool for the assessment of hip fracture risk. Furthermore, the automated computer program can be embedded into a website as an internet application. KEY WORDS: hip fracture, dual energy X-ray absorptiometry (DXA), finite element model, fracture risk, automation 1. INTRODUCTION
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Fall-induced hip fracture is a common health risk among elderly people, especially for those who have osteoporosis [1-4]. Osteoporosis can significantly reduce bone strength, it is a ‘silent’ disease as it has no symptom until first fracture. Therefore, subjects of high fracture risk must be diagnosed by clinicians using a reliable assessment tool. A number of tools for assessing fracture risk have been developed from either population-based statistical models [5-9] or biomechanical models [10-16]. The existing clinical tools are almost exclusively based on statistical models. T-score calculated from femoral bone mineral density (BMD) is the gold standard reference for screening osteoporosis and for assessing fracture risk [17, 18]. However, extensive clinical studies showed that the majority of patients who sustain low-trauma fractures have T-scores within the WHO (World Health Organization) safe range [19-22]. Therefore, researchers were motivated to develop assessment tools to consider multiple clinical risk factors [23]. Among these tools FRAX (Fracture Risk Assessment Tool) is the most popular one, which is a web-based calculator to predict an individual’s 10-year probability of hip fracture. However, FRAX still has limited accuracy even though 12 clinical risk factors are considered [5, 23-25]. The main reasons are: the considered clinical factors are biomechanically dependent and some important biomechanical variables such as fall-induced impact force are missing [26].
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In view of the limitations of population-based tools, researchers have turned their attention to biomechanical approaches. Theoretically, biomechanical modeling has the potential to more accurately predict an individual’s fracture risk than statistical approaches, as biomechanical models are based on well-established mechanical principles. A large number of finite element (FE) models have been developed to determine bone strength and to assess fracture risk. Most of the FE models are constructed from QCT (quantitative computed tomography) [11, 16, 2734], since QCT contains actual material and geometry information required to construct a three-dimensional finite element model. However, QCT uses high dosage of radiation and it is not recommended for routine clinical examination [35]. To meet the current clinical needs, DXA-based finite element models [36, 37] have also been developed, although construction of accurate finite element models from DXA images is more challenging and assumptions must be introduced.
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Nevertheless, none of the finite element models have been used routinely in clinic. Indeed, there are still unresolved technical issues in the finite element models [27], for example, the discrepancy among different bone material models [38], the lack of a generally accepted risk threshold for clinical intervention and the inconsistency among risk measurements produced by different finite element models. However, even after the technical issues are all resolved, there is still an obstacle for clinical application, that is, the computer programs that implement the finite element models have not been completely automated. User intervention that often requires the knowledge of finite element analysis (FEA) does not appeal to clinicians. We developed a DXA-based FE model for the prediction of hip fracture risk [37, 39]. In this study, we completely automate the computer program with simple input, so that the automated DXAbased FE tool can be used by clinicians with a minimum training and no knowledge of FEA is required.
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2. AUTOMATION OF DXA-BASED FINITE ELEMENT (FE) MODEL
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The procedure of our DXA-based finite element analysis [37, 39] is shown in Figure 1. The only input required by the procedure is a raw hip DXA, for example, the enCore file (with extension of DFF) generated by GE Lunar. The procedure starts with a clinical hip DXA of the concerned subject and includes the following steps: (1) Clinical regions of interest (ROI) are identified; (2) Proximal femur is segmented from the DXA and a contour of the femur is obtained; (3) A finite element mesh is generated from the femur contour; (4) Material properties are assigned; (5) Loading and constraint conditions are applied; (6) Stress distributions in the femur are obtained by a finite element analysis; (7) Fracture risk index is calculated over the clinical ROIs. The main challenge in automation of the procedure is the generation of a finite element model from hip DXA image without any user intervention. The automation of the DXA-based finite element procedure is described below.
Figure 1 DXA-based finite element analysis of hip fracture risk
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2.1 Segmentation of Proximal Femur
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The proximal femur is automatically segmented from hip DXA scan using information extracted from native DXA file. The steps are shown in Figure 2. (a) The contour of whole hip, including proximal femur and pelvis, is identified from hip DXA scan. (b) The region containing femoral head is extracted from the DXA file, and the contour of pelvis is removed. (c) A circle is fitted into the femoral head region. (d) The circle and the remaining femur contour are merged, and the outline of proximal femur is obtained.
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Figure 2 Segmentation of proximal femur
2.2 Identification of Regions of Interest (ROIs)
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On the basis of clinical studies [40-43], the majority of hip fractures occur at one of three locations, i.e. femoral neck, intertrochanter and femoral shaft as shown in Figure 3(a). An algorithm has been developed to automatically identify the three regions of interest and it is illustrated in Figure 3 (b) – (d). First, the narrowest cross-section of femoral neck is located by finding the shortest distance between points on the two opposite sides of the neck. Femoral neck axis is obtained as a line normal to the narrowest femoral neck and passing through the middle point. Then, femoral shaft axis is determined by linear regression using central points of six shaft cross-sections. Intertrochanteric cross-section is defined as the bi-section line of the neck-shaft angle. Femoral shaft cross-section is located below the neck-shaft intersection point at a distance of 1.5 times of the neck width. All the regions of interest have a width of 10 mm.
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Figure 3 Automatic identification of regions of interest at femoral neck, intertrochanter and femoral shaft (subtrochanter).
2.3 Finite Element Model and Generation of Finite Element Mesh DXA is inherently two-dimensional as a result of X-ray projection. Therefore, only a twodimensional finite element model can be constructed from DXA image. After examining the available two-dimensional mechanical models, it appears that the plane stress model is the only option. The femur bone has irregular and non-uniform cross-section, its material distribution is also spatial. None of the assumptions in the plane stress model are strictly satisfied. However, 5
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application of the plane stress model to femur bone can still be justified based on the loading conditions in sideways fall [44], which is the most critical situation leading to hip fracture. As the femur is connected to the pelvis and the tibia by joints that cannot transfer large torques, it can be reasonably assumed that the femur mainly experiences bending during sideways fall. The bone material behaves like ‘fibres’ in resisting bending moment.
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Consider a composite engineering beam consisting of fibers that is intended to resist the moments as shown in Figure 4. The beam has a non-rectangular cross-section and it does not satisfy the assumptions of plane stress model. Based on beam theory, the contribution of the fibers to resistance of the moments is determined by their distance from the neutral line, and is independent of their horizontal location. Therefore, the fibers can be replaced by a uniformly distributed material that has an equivalent contribution in resisting the moments. The rest material over the beam cross-section can be ‘converted’ into a uniform thickness in the similar way. The equivalent cross-section satisfies all the requirements of plane stress model. The DXA imaging process can be considered as such a homogenization operation.
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Figure 4 Equivalent cross-section produced by material projection
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The nearest-nodes finite element method (NN-FEM) [45, 46] was adopted in this study, because NN-FEM is able to construct high-order finite elements from simplex meshes and NN-FEM has much lower requirement on the quality of finite element meshes [47]. Techniques for generating simplex mesh are well developed and automated. Various software for generating simplex meshes consisting of three-node triangle elements are available. However, to make the DXA-based FE tool seamless, we developed our own computer codes for mesh generation [46]. The mesh density was determined by a series of convergence tests. One convergence curve is provided in Figure 5(a) and a sample finite element mesh is shown in Figure 5(b), where the fracture risk index (FRI) will be described in Section 2.6 and defined in Equation (7).
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FRI vs no of nodes 0.82
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FRI at clinical trochanteric ROI
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Figure 5 (a) Convergence of Fracture Risk Index (FRI) with the number of finite element nodes; (b) a sample finite element mesh producing converged FRI
2.4 Assignment of Element Material Properties
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In the automated DXA-based FE tool, bone mechanical properties are assigned based on bone density. A large number of equations have been established from experimental data to calculate bone elasticity modulus and yield stress from bone density [38]. We adopted the following equations developed by Morgan et al [48, 49].
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Elasticity modulus,
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compressive yield stress,
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Bone density required in the above equations is apparent volumetric density (g/cm3). But bone density measured by DXA is areal bone mineral density (g/cm2). Bone mineral density is equivalent to ash density and it can be converted into apparent density by [50],
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Areal BMD ( , g/cm2) can be converted into volumetric BMD ( , g/cm3) using the diameter at the narrowest femoral neck ( , cm) [51], (5)
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Sample distributions of bone mechanical properties calculated from Equations (1) – (5) for one clinical case are displayed in Figure 6. It should be noticed that the high BMD over the femoral head in Figure 6(a) is caused by overlaping of femoral head and pelvis in DXA.
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Figure 6 Bone mechanical properties assigned based bone mineral density. (a) Areal bone mineral density; (b) elasticity modulus; (c) compressive yield stress; (d) tensile yield stress.
2.5 Application of Loading/Constraint Conditions
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Loading/constraint conditions simulating a sideways fall are considered in the automated DXAbased FE tool. Impact force (F, Newton) induced in sideways fall can be estimated from the subject’s sex, body weight (W, Newton), height (H, centimeter) and hip soft-tissue thickness (T, millimeter) using the following equations [44], (6)
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The actual loading and constraint conditions occurring in a real-world sideways fall are very complicated. We simplified the conditions for the purpose of assessing the relative risk of hip fracture among elderly people. The simplified conditions are shown in Figure 7. The impact force calculated by Equation (6) is applied over the great trochanter; the distal femur is completely constrained; at the contact surface between the femoral head and the pelvis, the femoral head is partly constrained.
Figure 7 Simplified loading/constraint conditions simulating a sideways fall. 9
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2.6 Finite Element Analysis of Stresses and Calculation of Fracture Risk Index (FRI)
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Femur stresses produced by impact force in sideways fall are obtained by finite element analysis. We developed and automated computer codes for solving finite element equations and for calculating stresses. Figure 8(a) shows a sample distribution of von Mises stress in the femur. A number of locations on the femur have high stresses, but not all of them are critical locations. Bone is a highly heterogeneous material and its material strength varies from location to location, therefore, a high stress does not mean high risk of material failure at the point. A previous study [52] has shown that femur bone has a linear elastic behavior up to facture. Therefore, the ratio of von Mises stress to the corresponding yield stress at a critical point is adopted to measure the integrity of bone. If the ratio is larger than one, bone failure will start at the point. Figure 8(b) displays the ratio of von Mises stress to yield stress. Bone has different compressive and tensile yield stress [48, 49]. To simplify calculation, it is assumed that a point located in the lateral side of the neck/shaft axes (see Figure 3) has principal compressive stress and Equation (2) is applied to calculate the yield stress, otherwise Equation (3) is used.
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Figure 8 (a) Distribution of von Mises stress obtained by finite element analysis; (b) the ratio of von Mises stress to yield stress
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The ratio of von Mises stress to yield stress averaged over a region of interest is defined as fracture risk index (FRI) [37],
Where and interest.
(7) are respectively von Mises and yield stress, A is the area of the region of
The fracture risk index (FRI) defined in Equation (7) can be used as a classifier of hip fracture risk. FRI = 1 is the theoretical threshold. If FRI > 1, the subject will suffer hip fracture if the subject has a sideways fall.
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3. CLINICAL STUDY
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Short-term precision and the ability of discriminating clinical fracture cases from matched controls are the two important performance indicators of clinical tools for assessing hip fracture risk. To study the performance of the automated DXA-based FE tool, clinical cases were acquired from St. Boniface Hospital in Winnipeg under an approval of human subject research ethics, with personal information such as patient name and residence address removed before acquisition. Each case had a unique identifier that was used through this study. 3.1 Short-term precision test
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Short-term precision, also termed short-term repeatability or reproducibility, is the capability of a diagnostic tool to produce the same measurement value for the same subject when the tool is operated by the same or different technologist at different time when no actual variation is expected in the measurement. Short-term precision can be measured by the coefficient of variation (CV, %) [53]. A smaller CV (%) represents a better short-term precision. The coefficient of variation is calculated by the following equations [53]. ∑
√
(8a)
(8b)
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̅
̅ ̅)
(
̅) ]
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√ [(
(8c) (8d)
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In the above equations, m is the number of clinical cases; and are respectively the initial and repeated measurement that are separated by a short-time period; In this study, they are the fracture risk index corresponding to the initial and repeated DXA scan. ̅ is the average of the two measurements; and is standard deviation in the measurements of case j.
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Good short-term precision is necessary for a clinician to know small change in the measurement caused by either clinical treatment or by disease development. A clinical cohort of 100 pairs of hip DXA scans were acquired for this study. Time intervals separating the paired DXA are listed in Table 1. Table 1 Time interval between paired DXA scanning
Number of Cases
< 1 day 1 – 7 days 8 – 10 days 55 35 10
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For the clinical cases, fracture risk index of the initial and repeated scan in each pair were predicted using the automated DXA-based FE tool. Coefficients of variation was calculated according to Equations (8a) – (8d). 3.2 Discrimination test
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Fracture risk index (FRI) generated by the automated DXA-based FE tool can be used as a classifier of hip fracture. The ability of FRI to discriminate clinical hip fracture cases from matched controls can be measured by the area under the ROC (receiver operating characteristic) curve, or AUC in short, and odds ratio (OR) [54-56]. ROC is a graphical plot that illustrates the probability of a diagnostic tool to correctly classify a case if the threshold is changed. AUC is the overall accuracy of the tool for all possible thresholds, with AUC = 1 representing a perfect classification, and AUC = 0.5 indicating no classification ability at all. Although the theoretical threshold of fracture risk index is one, the actual optimal threshold is affected by factors such as the type of DXA scanner and the quality of DXA image, and the optimal threshold should be determined by clinical calibration. Therefore, AUC is an appropriate performance measurement for this study. Odds ratio (OR) measures the association between FRI value and actual fracture outcome. OR > 1 indicates that a larger FRI is associated with a higher risk of hip fracture. The larger the OR, the stronger the association is.
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A clinical cohort consisting of 400 women, including 100 prior hip fractures and 300 matched controls, was acquired for this discrimination study. In the selection of the cohort, the following criteria were used: (1) women age≥ 65 years; (2) femoral neck T-score below -1; and (3) no osteoporosis treatment. The clinical data of the subjects are provided in Table 2.
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Table 2 Statistics of fracture and control group
Fracture Group Control Group 76±9 75±12 63.2±10.3 63.8±11.4 158.8±4.7 158.1±6.2 -2.4 -2.3
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Age (years) Weight (kg) Height (cm) Femoral Neck T-score
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Hip fracture risk indices were predicted by the automated FE tool in batch processing. The only operation required from the user was to provide the location where the 400 hip DXA files are stored. The fracture status of each case was not known to the tool user. The FRI values predicted by the tool were sent to St. Boniface Hospital for an independent statistics analysis. AUC and OR values were calculated using SAS (SAS Institute, Version 9.3). 4. RESULTS The average processing time for each case was about 15 seconds when the cases were processed in batch. If processed cases by case, the processing time was about 17 seconds. Both are acceptable for clinical practice. 12
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Short-term precision of FRI and BMD expressed by coefficient of variation (CV, %) are presented in Table 3. In general, BMD still has the best short-term precision; automated DXA-based FE tool greatly improved the precision compared with the previous semi-automated version. Table 3 Short-term precision (CV, %)
Femoral Neck Trochanter Sub-trochanter 1.94 2.58 4.05 4.53 4.96 6.87 1.12 1.16 -
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FRI (automated) FRI (semi-automated) BMD (clinical)
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In the discrimination test, FRI of six cases was not calculated by the automated FE tool due to poor quality of the DXA images. It turned out the six cases included one fracture case and five controls. Therefore, the actual cases used in this study included 99 prior hip fractures and 295 controls. Average FRI with standard deviation at the three anatomic sites are provided in Table 4. Correlations between FRI and age/BMI (body mass index) are presented in Table 5. The obtained AUC values with 95% CI (confidence interval) are listed in Table 6. The OR values adjusted with age and body mass index are provided in Table 7. According to the results in Table 6, FRI at trochanter was considerably more accurate than femoral BMD in discriminating clinical fracture cases from matched controls. Table 7 shows that FRI had much stronger association with actual fracture outcome than femoral BMD at all sites, and the association at trochanter was the strongest.
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Table 4 Average FRI (±SD)
Anatomic Site
Fracture Group Control Group 1.37±0.32 1.12±0.44 0.55±0.09
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Femoral Neck Trochanter Subtrochanter
p-value as compared to controls
1.28±0.32 0.87±0.26 0.48±0.13
p<0.05
Table 5 Correlation between FRI and age/BMI
Anatomic Site Femoral Neck Trochanter Subtrochanter
Age (p-value) BMI (p-value) 0.25 (p<0.05) -0.23 (p<0.05) 0.27 (p<0.05) -0.28 (p<0.05) 0.17 (p<0.05) 0.11 (p=0.09)
Table 6 Area under ROC curve (AUC) with 95% CI
FRI Femoral-Neck BMD
Femoral Neck Trochanter Sub-trochanter 0.70 (0.63, 0.77) 0.78 (0.72, 0.83) 0.74 (0.68, 0.80) 0.71 (0.65, 0.78) Referent 13
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p-value compared to referent
-0.01
0.03
0.03
Table 7 Odds ratio (OR) with 95% CI (per SD change)
Femoral Neck FRI adjusted with age and BMI
Trochanter
Sub-trochanter
2.13 (1.54, 2.94) 2.61 (1.83, 3.72) 2.28 (1.68, 3.09)
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FRI adjusted for age, BMI and 1.36 (1.04, 1.75) 1.74 (1.37, 2.24) 2.11 (1.65, 2.65) femoral neck BMD FRI adjusted for FRAX score 0.99 (0.81, 1.20) 1.31 (1.05, 1.65) 1.53 (1.24, 1.92) (with femoral-neck BMD) Femoral-Neck BMD 2.08 (1.57, 2.76)
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5. DISCUSSION
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The large improvement in short-term precision of our DXA-based FE tool is mainly attributed to the automation of femur contour segmentation. In the previous semi-automated version [37], manual operation is required in segmentation of femur contour, which introduces random error. Automated segmentation in the new version is able to eliminate the random error and thus improves the short-term precision. However, even the automated FE tool still has much lower short-term precision than BMD. There are a number of reasons. First, FRI is a functions of a number of variables affecting hip fracture risk, BMD is one of them. The other variables include the projected femur geometry, body weight and height, hip soft-tissue thickness, etc. The worst short-term precision in the variables will determine the short-term precision of FRI. Second, BMD used in clinic is an average over region of interest. The averaging operation is able to improve short-term precision [37]. However, BMD used in the DXA-based FE model is a point-wise map. Change of patient positioning in DXA scanning may introduce difference in the map. Third, also the most important, a small difference in the BMD will be amplified by the material model in Equations (1) – (3) that are nonlinear exponential functions.
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Theoretically, FRI produced by the DXA-based FE model is a better fracture risk predictor than BMD. Hip fracture is often resulted by impact force induced in accidental fall. If the impact force exceeds the femur strength, the femur will fracture. Hip fracture risk is thus jointly determined by impact force and femur strength, and the latter is further decided by femur bone quality that is mainly represented by BMD, and femur size. FRI predicted by the FE model is able to consider all the involved variables, while BMD is only one of them. This explains why FRI had better performance than femoral BMD in the test. That FRI at trochanter had better performance than at other sites is probably due to that the majority of fracture sites in the clinical cohort are actually at trochanter. The region of trochanter is dominated by trabecular bone that has much lower strength than cortical bone, and it is covered by very little soft tissue. If a subject has a sideways fall, the large impact force will directly act on the weak trabecular 14
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bone. Reported clinical studies show that the trochanteric region is indeed a dominant site of hip fractures [42, 57, 58]. The results in Table 5 indicate that hip fracture risk increases with age among elderly women, which is consistent with clinical observations [41, 59-61]. The reason is that bone loss is accelerated for post-menopause women and bone density is a main determinant of bone strength. The results also suggest that for elderly women, BMI is a protective factor for hip fracture at the femoral neck and intertrochanter, but not at the subtrochanter. Hip fracture at the femoral neck and intertrochanter is caused by the impact force that is directly applied at the great trochanter in sideways fall [65-67]. For a subject with higher BMI, the soft-tissue over the great trochanter is likely thicker, which is able to more effectively attenuate the impact force and thus to reduce FRI. But fracture at subtrochanter is probably caused by bending moment generated by the body weight, if the lower extremity is partly or completely constrained in fall. A subject of higher BMI probably experience a larger bending moment at the subtrochanter, and thus has a higher FRI. One major difference between our DXA-based FE model and the previously developed ones [54, 55] is in the consideration of subject-specific impact force induced in sideways fall. Most previous finite element models only consider bone strength in evaluation of fracture risk. Bone strength is indeed one important determinant of hip fracture risk, but fall-induced impact force must be also considered because the impact force has large variation from subject to subject, and it is determined by the subject’s anthropometric parameters. Since fall-induced impact force is considered, this model is helpful to evaluate fracture risk among elderly people who are prone to fall.
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However, there are still a number of limitations in this study and in our FE model. First, our FE model is two-dimensional and simplifications have been introduced as in the other similar models [10, 36]. Our model is theoretically not accurate as three-dimensional FE models constructed from QCT (quantitative computed tomography) [30, 62, 63]. Therefore, our model can only be used to assess relative fracture risk among individuals, it does not have the ability to predict when and where the fracture will occur. Second, information of fall orientation (sideways, forward or backward) is not available from the clinical records, and fall orientation may have significant effect on fracture outcome [64-67]. Currently, our FE model can only deal with impact force in sideways fall by Equation (6). There is a need to extend the equation to accommodate forward and backward fall.
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6. CONCLUSION
In conclusion, this study made a step toward the application of our DXA-based FE model as a clinical tool for assessment of hip fracture risk. As the next step, we will apply our model in prospective studies and in validations of cross clinical centers and DXA scanners. The automated standalone computer program will be distributed to clinical centers. Furthermore, the computer program will be embedded into a web-site as an internet application, so that clinicians over the world will be able to use the tool. ACKNOWLEDGEMENT 15
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The reported research has been supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and Research Manitoba, which are gratefully acknowledged.
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