Bio-Medical Materials and Engineering 25 (2015) 213–220 DOI 10.3233/BME-151271 IOS Press
213
Study of hip fracture risk by DXA-based patient-specific finite element model Zannatul Ferdous a and Yunhua Luo a,b,∗ a b
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, Canada Department of Anatomy, Southern Medical University, Guangzhou, China
Received 4 September 2013 Accepted 30 October 2014 Abstract. A number of factors may have effects on hip fracture, for example, bone mineral density (BMD), body weight and height, femur length, femoral neck length, etc. It is not clear which factor(s) has the dominant effect on hip fracture. Therefore, the factors were investigated by a previously developed DXA (dual energy X-ray absorptiometry) based finite element model. The finite element model is patient-specific, as all information required in constructing the model was extracted from the patient’s hip DXA image. DXA images of 180 patients were obtained from the Manitoba Bone Mineral Density Database. For each patient, a finite element model was constructed and fracture risk indices (FRI) were calculated at the three critical locations on the hip, i.e. the femoral neck, the intertrochanter and the subtrochanter. Possible correlations between the fracture risk indices and the factors were then investigated. The obtained results indicated that, for hip fractures resulted from lateral fall, areal BMD and patient’s body weight are two dominant factors, but effects from the other factors are not trivial. The study suggested that hip fracture is the result of combined effects from all the factors. Therefore, use of areal BMD alone in clinical assessment of fracture risk is not reliable. Keywords: Hip fracture risk, dual energy X-ray absorptiometry (DXA), bone mineral density (BMD), finite element model, fracture factors
1. Introduction Osteoporosis is the degradation of bone tissue and deterioration of bone strength with a consequential increase in bone fragility and susceptibility of fracture. In Canada, prevalence of osteoporosis is reported to be 21.3% in women and 5.5% in men over age 50 [1]. Osteoporosis patients have much higher risk of bone fracture than healthy people, usually caused by low traumatic events such as fall from standing height and even a hard sneezing. Hip fracture has a high incidence rate in osteoporosis patients especially among the elderly [1–3]. Hip fracture has been a main cause of morbidity and mortality for osteoporosis patients, and it has also been a substantial source of health care expenditure [1,4–6]. Accurately assessment of hip fracture risk is important for preventing hip fracture. Proximal femoral areal bone mineral density (BMD) captured by dual energy X-ray absorptiometry (DXA) has been used as a standard reference in screening osteoporosis and a surrogate for assessing hip fracture risk. However, assessment of hip fracture risk using only femoral BMD is not reliable [7–9], as hip fracture is governed integrally by a number of factors that include other factors such as body weight and femoral geometry beside *
Address for correspondence: Yunhua Luo, Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 2N2. E-mail: [email protected]. 0959-2989/15/$35.00 © 2015 – IOS Press and the authors. All rights reserved
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Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
femoral BMD. Finite element models based on engineering mechanical theories are able to integrate all the involved factors and provide more reliable assessment of hip fracture risk [5,10]. A DXA-based patient-specific finite element model has been proposed in [10]. Understanding how the involved factors affecting hip fracture risk have significant clinical applications [11–13]. In this reported research, the DXA-based finite element model developed in [10] was applied to investigate the factors affecting hip fracture. 2. Method and materials 2.1. DXA-based patient-specific finite element model and fracture risk index DXA is the imaging modality recommended by the World Health Organization (WHO) to measure BMD, for the purpose of screening and monitoring osteoporosis. DXA uses a low X-ray dosage. The radiation received by the patient during the scan is less than that of an around airline trip from the west to the east coast in the United States. DXA is the most widely used and also the most thoroughly studied bone density measurement technology. In DXA scanning, two X-ray beams with different energy levels are projected to the concerned part of the patient’s body. The BMD is determined from absorption of each beam by the bone, after subtracting the absorption by the soft tissues. However, due to the projection nature of DXA, the obtained DXA image is two-dimensional and the BMD measured is areal rather than volumetric, i.e. the bone mineral content in per unit area with the unit of gram per square centimeter (g/cm2 ) in clinic. BMD is the main determinant of bone elasticity modulus and strength. Large experimental studies [14] have shown that correlations between bone elasticity and volumetric BMD (g/cm3 ) are mostly in the form of exponential function. By experimental studies using cadaveric femur bones, Buijs et al. [15] also established a correlation, in the form of exponential function, between bone elasticity modulus and areal (or projected) BMD (g/cm2 ) that can be measured from DXA. The DXA-based finite element (FE) model developed in [10] is briefly described in the following for completeness. As DXA image is inherently two-dimensional, an equivalent plane stress model was adopted. In construction of the FE model, patient hip DXA image is taken as an input for extracting geometrical data and material property of the proximal femur. The contour of the proximal femur is segmented from the DXA image and used to generate a finite element mesh. The projected femur bone is considered as a pointwise inhomogeneous material and material properties such as elasticity modulus (E) and yield stress (σY ) are correlated to areal BMD (ρ) by empirical functions, E = 2980 × ρ1.05 MPa,
σY = 37.4 × ρ1.39 MPa.
(1)
The proximal femur is completely fixed at the bottom in finite element analysis. The patient’s weight is applied on the femoral head as a uniformly distributed load and an impact force that is three times of the patient’s body weight is applied at the great trochanter. The resulting finite element model is shown in Fig. 1(a). The constructed finite element model is patient specific, as the DXA image is taken from the patient and the geometry and material properties are all extracted from or related to the patient’s hip DXA image. Stress distribution over the proximal femur for a specific patient can be obtained by finite element analysis with the above described finite element model. By examining the performance of nine stress- and strain-based failure theories against mechanical testing results of human femoral bones, Keyak et al. [16] found that shear/distortion is an important
Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
(a)
215
(b)
Fig. 1. (a) DXA-based finite element model; (b) critical locations of femur fracture. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.)
failure mode during femoral fracture and the von Mises criterion may be the most accurate for predicting fracture locations. It has also been demonstrated by experiments that the human proximal femur behaves linearly elastic up to failure under physiological loading conditions [17]. Based on the above study results, the ratio of von Mises stress induced by external forces and material yield stress, as defined in Eq. (2), can be used to evaluate material integrity at a specific material point, η=
von Mises Stress . Yield Stress
(2)
If it is assumed that bone yielding is not allowed in normal physical activities, the index defined in Eq. (2) can be adopted as fracture risk index of bone, i.e., if η < 1, fracture would not occur at the point; otherwise, if η 1, the bone would fracture. It should be noted that the ratio in Eq. (2) is a function of location. Previous studies [18–21] have shown that hip fractures most often occur at three locations, i.e., the femoral neck, the intertrochanter and the subtrochanter. Correspondingly in clinical practice, average areal BMD are taken from the three critical regions as shown in Fig. 1(b) for assessing osteoporosis. To be consistent with the previous studies and clinical practice, the average fracture risk index over the three critical regions are defined in Eq. (3) and adopted in our study, η dA η¯ = A , A dA
(3)
where A is the area of a region of interest. 2.2. Factors affecting hip fracture and clinical cohorts The factors that may have effects on hip fracture include: areal BMD over the three regions, body weight, femur length, femoral neck length, femoral neck width and femoral neck angle. These factors affect the fracture risk index defined in Eq. (3) via material properties, loading conditions and geometric
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Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model Table 1 Statistics of the 180 clinical cases Parameters Age (years) Weight (kg) Height (cm) BMD (g/cm2 ) Femoral neck Intertrochanter Total hip
Mean value (±SD) 65.93 (±8.65) 61.65 (±13.77) 159.5 (±5.60) 0.7336 (±0.1343) 0.5803 (±0.1512) 0.7436 (±0.1585)
Fig. 2. Definition of geometric factors affecting hip fracture.
dimensions in the finite element model. Areal BMD is directly related to bone elasticity modulus and yield stress by Eq. (1); body weight is used as loading in the finite element model. The rest parameters affect the geometry of the finite element model. Definitions of the geometric parameters are shown in Fig. 2. The length of the proximal femur (H) is taken as proportional to the patient’s body height and it is measured from the top most point of the femur head to the bottom of the proximal femur. The femoral neck width (W) is the diameter of the narrowest femoral neck. The femoral neck length (L) is defined as the distance between the two tangent points of the line of narrowest neck width with the contour of the proximal femur at, respectively, the femoral head and the great trochanter. The femoral neck angle (α) is the angle between the narrowest neck diameter and the horizontal line. To investigate effects of the factors on hip fracture risk, hip DXA images of total 180 osteoporosis patients were obtained from the Manitoba Bone Mineral Density Database (MBMDD) under an approval of health research ethics issued by the provincial Research Ethics Board. In the Province of Manitoba, Canada, BMD testing with DXA has been available since 1990. Results of all clinical DXA scans performed are maintained in the MBMDD, along with patient demographics, clinical risk factors, and anthropomorphic measures (weight, height, BMI, soft tissue composition percentage of lean and fat). Statistical data of the 180 cases are provided in Table 1. For each case, a patient-specific finite element model was constructed. After performing finite element convergence test and region sensitivity test, stress distribution over the proximal femur was obtained by finite element analysis. Fracture risk indices at the three critical locations were calculated using the obtained finite element stresses. Correlations between fracture risk index and the mentioned factors, i.e., areal BMD, body weight, femur length, femoral neck length, femoral neck width and femoral neck angle, were investigated. 3. Results and discussions Distributions of areal BMD and elasticity modulus over the proximal femur in one of the clinical cases are shown in Fig. 3(a) and (b), respectively. As can be seen from the figures, bone has denser areal BMD also has higher elasticity modulus, especially the cortical bone has much higher elasticity modulus than cancellous bone. It must be pointed out that the large areal BMD over the femoral head is partially due to
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(a)
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(b)
Fig. 3. (a) Distribution of areal BMD (g/cm2 ); (b) Distribution of bone elasticity modulus (Pa). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.)
Fig. 4. Finite element convergence test result. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ BME-151271.)
overlapping of the femoral head and the pelvis bone in DXA scanning. Based on the theory of material mechanics, the resulted high elasticity modulus in the femoral head may change the local distribution of stresses; it should not affect the stress level over the rest part of the proximal femur. Result of finite element convergence test is plotted in Fig. 4. It can be noticed that the convergence process has oscillations and not as smooth as in the finite element analysis of engineering materials. This is due to the consideration of bone inhomogeneity in the study. For one of the clinical cases, the obtained distributions of effective (or von Mises) stress and pointwise fracture risk index calculated using definition in Eq. (2) are plotted respectively in Fig. 5(a) and (b). It can be observed that stress level in the cortical bone is much higher than that in the cancellous bone. However, it does not mean fracture risk index in the cortical bone is also higher, as cortical bone has higher BMD and thus higher yield stress. The calculated correlation coefficients between FRI at the three locations and the investigated factors are given in Table 2. It should be noted that the listed areal BMD in the second column of the table were taken respectively from the three locations. A large correlation coefficient with a small p-value (usually p < 0.05) indicates there exists a strong correlation [22]. It can be observed, among these factors, fracture risk is
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Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
(a)
(b)
Fig. 5. (a) Distribution of effective (von Mises) stress (Pa); (b) Distribution of pointwise fracture risk index (FRI). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.) Table 2 Correlation coefficients (p-value) between FRI at the three locations and different factors Location at femur Femoral neck
Areal BMD −0.33 (0.001)
Body weight 0.52 (0.001)
Femur length 0.13 (0.1062)
Neck length 0.11 (0.1175)
Neck width 0.1618 (0.0267)
Neck angle 0.09 (0.2637)
Intertrochanter
−0.67 (0.001)
0.18 (0.017)
0.20 (0.01)
0.20 (0.009)
0.3346 (0.001)
0.00 (0.9676)
Subtrochanter
−0.43 (0.001)
0.57 (0.001)
0.29 (0.0009)
0.32 (0.001)
0.2825 (0.0002)
0.03 (0.6759)
influenced mainly by areal bone density and patient’s body weight, followed by the other factors. It can also be observed that at different location, the factors may have different roles in hip fracture. Over the intertrochanter, FRI strongly correlates to areal bone density (r = −0.67, p < 0.001), which is consistent with the results reported by Lang et al. [23] and Cheng et al. [24]. However, at the femoral neck and the subtrochanter, FRI has stronger correlation with patient’s body weight, as indicated by the respective correlation coefficients, r = 0.52 (p < 0.001) and r = 0.57 (p < 0.001). On the other hand, correlation between FRI and neck angle at the three locations is low and may even not exit, as the corresponding p-values are very large. Similar observation has been made by Faulkner et al. in their investigation [13]. Correlations between FRI and proximal femur length, femoral neck length, and femoral neck width are moderate at the intertrochanter and subtrochanter, and low at the femoral neck. It is also evident from Table 2 that FRI and proximal femur length, which was taken as proportional to patient’s height, have a weak to moderate positive correlation at the three sections. This outcome is in agreement with those from population based cohort study, i.e., taller people are in higher risk of hip fracture than shorter people [25]. However, there are two observations from Table 2 that seems not consistent with and even contradicting to the theories of Structural Mechanics. One is that FRI at the three locations only has very week positive correlation with femoral neck length; the other is that FRI at the three locations has positive correlation with femoral neck width (or neck diameter). If the proximal femur is considered as a beam, cf. Fig. 1(a), a longer femoral neck would generate a larger bending moment by the weight acting
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219
on the femoral head and thus a higher fracture risk. On the other hand, if the femoral neck width is increased, the resistance of beam cross-section to bending moment should be increased and the fracture risk should be reduced. Similar discrepancies have already reported in the literature [26–28]. The above discrepancies may be caused by several reasons. First, it may be caused by the unique loading condition considered in the study. The resultant force of the uniformly distributed force on the femoral head was approximately along the femoral neck axis. Therefore, the force on the femoral neck was mainly an axial force. Second, the femoral neck length may coincide with the femoral moment arm [29,30]. Third, it has been found in our study that femoral neck width (or diameter) is strongly correlated to femoral neck length (correlation coefficient r = 0.8714, p < 0.001), indicating that a thicker femoral neck is also longer. In addition, a thicker femoral neck may also have low areal BMD [31]. Several aspects of the reported study need be improved in the future. For example, the forces acting on the femoral head and the greater trochanter induced in lateral fall were determined using a statistical model. The impact forces may be different for a specific subject due to their individual anthropometric differences such as body height and weight. Moreover, the direction of fall and the energy absorbed during impact are also important issues that deserve further consideration. 4. Conclusions The uncovered correlations between FRI and the investigated factors in the reported study clearly demonstrated that use of areal BMD alone as hip fracture predictor is not reliable, as hip fracture is also simultaneously dependent on several other factors such as body weight and femur geometry. At different location on the proximal femur, the factors may have a different role in hip fracture. Hip fracture is the result of the combined effects from the involved factors. For hip fractures resulted from lateral fall, areal BMD and patient’s weight are the two dominant factors. However, the effects of the rest factors are not trivial as indicated by the values of their correlation coefficients. For the number of involved factors and the complicated correlations between FRI and the factors, it is suggested that DXA-based finite element modeling should be adopted in clinical assessment of hip fracture risk. Acknowledgements The reported research has been supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Manitoba Health Research Council (MHRC), which are gratefully acknowledged. Special thanks are directed to Ms. Linda Ward at the St. Boniface General Hospital, Winnipeg, for preparing the DXA images used in the reported research. References [1] M.E. Wiktorowicz and R. Goeree, Economic implications of hip fracture: health service use, institutional care and cost in Canada, Osteoporosis International 12 (2001), 271–278. [2] G.S. Keene, M.J. Parker and G.A. Pryor, Mortality and morbidity after hip fractures, British Medical Journal 307 (1993), 1248–1250. [3] J. Stevens, K.A. Mack et al., Self-reported falls and fall-related injuries among persons aged 65 years United States, 2006, Journal of Safety Research 39 (2008), 345–349. [4] B.L. Riggs and L.J. Melton III, The world wide problem of osteoporosis: insights afforded by epidemiology, Bone 17 (1995), S505–S511.
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[5] B. Borah, G.J. Gross et al., Three dimensional micro imaging, finite element modeling and rapid prototyping provide unique insights into bone architecture in osteoporosis, The Anatomical Record 265 (2001), 101–110. [6] J.C. Davis, M.C. Robertson et al., International comparison of cost of falls in older adults living in the community: a systematic review, Osteoporosis International 21 (2010), 1295. [7] T.J. Beck, A.C. Looker et al., Structural trends in the aging femoral neck and proximal shaft: analysis of the third national health and nutrition examination survey dual-energy X-ray absorptiometry data, Journal of Bone and Mineral Research 15 (2000), 2297–2304. [8] D. Marshall, O. Johnell and H. Wedel, Meta-analysis of how well measures of bone mineral density predict occurrence of osteoporotic fractures, British Medical Journal 312 (1996), 1254–1259. [9] S.A. Wainwright, L.M. Marshall et al., Hip fracture in women without osteoporosis, The Journal of Clinical Endocrinology and Metabolism 90 (2005), 2787–2793. [10] Y. Luo, Z. Ferdous and W.D. Leslie, A preliminary dual-energy X-ray absorptiometry-based finite element model for assessing osteoporotic hip fracture risk, Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 225(12) (2011), 1188–1195. [11] Y. Maeda, N. Sugano et al., Comparison of femoral morphology and bone mineral density between femoral neck fractures and trochanteric fractures, Clinical Orthopaedics and Related Research 469 (2011), 884–889. [12] J. Panula, M. Savela et al., The impact of proximal femur geometry on fracture type: a comparison between cervical and trochanteric fractures with two parameters, Scandinavian Journal of Surgery 97 (2008), 266–271. [13] K.G. Faulkner, S.R. Cummings et al., Simple measurement of femoral geometry predicts hip fracture: the study of osteoporotic fractures, Journal of Bone and Mineral Research 8 (1993), 1211–1217. [14] B. Helgason, E. Perilli et al., Mathematical relationships between bone density and mechanical properties: a literature review, Clin. Biomech. 23 (2008), 135–146. [15] J.O.D. Buijs and D. Dragomir-Daescu, Validated finite element models of the proximal femur using two-dimensional projected geometry and bone density, Computer Methods and Programs in Biomedicine 104 (2011), 168–174. [16] J.H. Keyak and S.A. Rossi, Prediction of femoral fracture load using finite element models: an examination of stress- and strain-based failure theories, Journal of Biomechanics 33 (2000), 209–214. [17] M.M. Juszczyk, L. Cristofolini and M. Viceconti, The human proximal femur behaves linearly elastic up to failure under physiological loading conditions, Journal of Biomechanics 44 (2011), 2259–2266. [18] R.Y. Hinton and G.S. Smith, The association of age, race, and sex with the location of proximal femoral fractures in the elderly, Journal of Bone and Joint Surgery 75 (1993), 752–759. [19] R.Y. Hinton, D.W. Lennox et al., Relative rates of fracture of the hip in the United States geographic, sex, and age variations, Journal of Bone and Joint Surgery 77 (1995), 695–702. [20] J.D. Michelson, A. Myers, R. Jinnah, Q. Cox and M. Van Natta, Epidemiology of hip fractures among the elderly: Risk factors for fracture type, Clinical Orthopaedics and Related Research 311 (1995), 129–135. [21] M.R. Karagas, G.L. Lu-Yao et al., Heterogeneity of hip fracture: age, race, sex, and geographic patterns of femoral neck and trochanteric fractures among the US elderly, American Journal of Epidemiology 143 (1996), 677–682. [22] P. Armitage, G. Berry and J.N.S. Matthews, Statistical Methods in Medical Research, 4th edn, Blackwell Science, 2002. [23] T.F. Lang, J.H. Keyak et al., Volumetric quantitative computed tomography of the proximal femur: precision and relation to bone strength, Bone 21 (1997), 101–108. [24] X.G. Cheng, G. Lowet et al., Assessment of the strength of proximal femur in vitro: relationship to femoral bone mineral density and femoral geometry, Bone 20 (1997), 213–218. [25] B.Y. Farahmand, K. Michaïelsson et al., Body size and hip fracture risk, Epidemiology 11 (2000), 214–219. [26] S. Gnudi, C. Ripamonti et al., Geometry of proximal femur in prediction of hip fracture in osteoporotic women, British Journal of Radiology 72 (1999), 729–733. [27] C.C. Glüer, S.R. Cummings et al., Prediction of hip fractures from pelvic radiographs: the study of osteoporotic fractures. The study of osteoporotic fractures research group, Journal of Bone and Mineral Research 9 (1994), 671–677. [28] F. Rivadeneira, M.C. Zillikens et al., Femoral neck BMD is a strong predictor of hip fracture susceptibility in elderly men and women because it detects cortical bone instability: the Rotterdam study, Journal of Bone and Mineral Research 22 (2007), 1781–1790. [29] H. Ulusoy, A. Bilgici et al., A new value of proximal femur geometry to evaluate hip fracture risk: true moment arm, Hip International 18 (2008), 101–107. [30] M.I. Wani, M.M. Wani et al., Subtrochanteric fractures – current management options, The Internet Journal of Orthopedic Surgery 17 (2010), 2. [31] S. Kaptoge, T.J. Beck et al., Prediction of incident hip fracture risk by femur geometry variables measured by hip structural analysis in the study of osteoporotic fractures, Journal of Bone and Mineral Research 23 (2008), 1892–1904.
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213
Study of hip fracture risk by DXA-based patient-specific finite element model Zannatul Ferdous a and Yunhua Luo a,b,∗ a b
Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, Canada Department of Anatomy, Southern Medical University, Guangzhou, China
Received 4 September 2013 Accepted 30 October 2014 Abstract. A number of factors may have effects on hip fracture, for example, bone mineral density (BMD), body weight and height, femur length, femoral neck length, etc. It is not clear which factor(s) has the dominant effect on hip fracture. Therefore, the factors were investigated by a previously developed DXA (dual energy X-ray absorptiometry) based finite element model. The finite element model is patient-specific, as all information required in constructing the model was extracted from the patient’s hip DXA image. DXA images of 180 patients were obtained from the Manitoba Bone Mineral Density Database. For each patient, a finite element model was constructed and fracture risk indices (FRI) were calculated at the three critical locations on the hip, i.e. the femoral neck, the intertrochanter and the subtrochanter. Possible correlations between the fracture risk indices and the factors were then investigated. The obtained results indicated that, for hip fractures resulted from lateral fall, areal BMD and patient’s body weight are two dominant factors, but effects from the other factors are not trivial. The study suggested that hip fracture is the result of combined effects from all the factors. Therefore, use of areal BMD alone in clinical assessment of fracture risk is not reliable. Keywords: Hip fracture risk, dual energy X-ray absorptiometry (DXA), bone mineral density (BMD), finite element model, fracture factors
1. Introduction Osteoporosis is the degradation of bone tissue and deterioration of bone strength with a consequential increase in bone fragility and susceptibility of fracture. In Canada, prevalence of osteoporosis is reported to be 21.3% in women and 5.5% in men over age 50 [1]. Osteoporosis patients have much higher risk of bone fracture than healthy people, usually caused by low traumatic events such as fall from standing height and even a hard sneezing. Hip fracture has a high incidence rate in osteoporosis patients especially among the elderly [1–3]. Hip fracture has been a main cause of morbidity and mortality for osteoporosis patients, and it has also been a substantial source of health care expenditure [1,4–6]. Accurately assessment of hip fracture risk is important for preventing hip fracture. Proximal femoral areal bone mineral density (BMD) captured by dual energy X-ray absorptiometry (DXA) has been used as a standard reference in screening osteoporosis and a surrogate for assessing hip fracture risk. However, assessment of hip fracture risk using only femoral BMD is not reliable [7–9], as hip fracture is governed integrally by a number of factors that include other factors such as body weight and femoral geometry beside *
Address for correspondence: Yunhua Luo, Department of Mechanical Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 2N2. E-mail: [email protected]. 0959-2989/15/$35.00 © 2015 – IOS Press and the authors. All rights reserved
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Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
femoral BMD. Finite element models based on engineering mechanical theories are able to integrate all the involved factors and provide more reliable assessment of hip fracture risk [5,10]. A DXA-based patient-specific finite element model has been proposed in [10]. Understanding how the involved factors affecting hip fracture risk have significant clinical applications [11–13]. In this reported research, the DXA-based finite element model developed in [10] was applied to investigate the factors affecting hip fracture. 2. Method and materials 2.1. DXA-based patient-specific finite element model and fracture risk index DXA is the imaging modality recommended by the World Health Organization (WHO) to measure BMD, for the purpose of screening and monitoring osteoporosis. DXA uses a low X-ray dosage. The radiation received by the patient during the scan is less than that of an around airline trip from the west to the east coast in the United States. DXA is the most widely used and also the most thoroughly studied bone density measurement technology. In DXA scanning, two X-ray beams with different energy levels are projected to the concerned part of the patient’s body. The BMD is determined from absorption of each beam by the bone, after subtracting the absorption by the soft tissues. However, due to the projection nature of DXA, the obtained DXA image is two-dimensional and the BMD measured is areal rather than volumetric, i.e. the bone mineral content in per unit area with the unit of gram per square centimeter (g/cm2 ) in clinic. BMD is the main determinant of bone elasticity modulus and strength. Large experimental studies [14] have shown that correlations between bone elasticity and volumetric BMD (g/cm3 ) are mostly in the form of exponential function. By experimental studies using cadaveric femur bones, Buijs et al. [15] also established a correlation, in the form of exponential function, between bone elasticity modulus and areal (or projected) BMD (g/cm2 ) that can be measured from DXA. The DXA-based finite element (FE) model developed in [10] is briefly described in the following for completeness. As DXA image is inherently two-dimensional, an equivalent plane stress model was adopted. In construction of the FE model, patient hip DXA image is taken as an input for extracting geometrical data and material property of the proximal femur. The contour of the proximal femur is segmented from the DXA image and used to generate a finite element mesh. The projected femur bone is considered as a pointwise inhomogeneous material and material properties such as elasticity modulus (E) and yield stress (σY ) are correlated to areal BMD (ρ) by empirical functions, E = 2980 × ρ1.05 MPa,
σY = 37.4 × ρ1.39 MPa.
(1)
The proximal femur is completely fixed at the bottom in finite element analysis. The patient’s weight is applied on the femoral head as a uniformly distributed load and an impact force that is three times of the patient’s body weight is applied at the great trochanter. The resulting finite element model is shown in Fig. 1(a). The constructed finite element model is patient specific, as the DXA image is taken from the patient and the geometry and material properties are all extracted from or related to the patient’s hip DXA image. Stress distribution over the proximal femur for a specific patient can be obtained by finite element analysis with the above described finite element model. By examining the performance of nine stress- and strain-based failure theories against mechanical testing results of human femoral bones, Keyak et al. [16] found that shear/distortion is an important
Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
(a)
215
(b)
Fig. 1. (a) DXA-based finite element model; (b) critical locations of femur fracture. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.)
failure mode during femoral fracture and the von Mises criterion may be the most accurate for predicting fracture locations. It has also been demonstrated by experiments that the human proximal femur behaves linearly elastic up to failure under physiological loading conditions [17]. Based on the above study results, the ratio of von Mises stress induced by external forces and material yield stress, as defined in Eq. (2), can be used to evaluate material integrity at a specific material point, η=
von Mises Stress . Yield Stress
(2)
If it is assumed that bone yielding is not allowed in normal physical activities, the index defined in Eq. (2) can be adopted as fracture risk index of bone, i.e., if η < 1, fracture would not occur at the point; otherwise, if η 1, the bone would fracture. It should be noted that the ratio in Eq. (2) is a function of location. Previous studies [18–21] have shown that hip fractures most often occur at three locations, i.e., the femoral neck, the intertrochanter and the subtrochanter. Correspondingly in clinical practice, average areal BMD are taken from the three critical regions as shown in Fig. 1(b) for assessing osteoporosis. To be consistent with the previous studies and clinical practice, the average fracture risk index over the three critical regions are defined in Eq. (3) and adopted in our study, η dA η¯ = A , A dA
(3)
where A is the area of a region of interest. 2.2. Factors affecting hip fracture and clinical cohorts The factors that may have effects on hip fracture include: areal BMD over the three regions, body weight, femur length, femoral neck length, femoral neck width and femoral neck angle. These factors affect the fracture risk index defined in Eq. (3) via material properties, loading conditions and geometric
216
Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model Table 1 Statistics of the 180 clinical cases Parameters Age (years) Weight (kg) Height (cm) BMD (g/cm2 ) Femoral neck Intertrochanter Total hip
Mean value (±SD) 65.93 (±8.65) 61.65 (±13.77) 159.5 (±5.60) 0.7336 (±0.1343) 0.5803 (±0.1512) 0.7436 (±0.1585)
Fig. 2. Definition of geometric factors affecting hip fracture.
dimensions in the finite element model. Areal BMD is directly related to bone elasticity modulus and yield stress by Eq. (1); body weight is used as loading in the finite element model. The rest parameters affect the geometry of the finite element model. Definitions of the geometric parameters are shown in Fig. 2. The length of the proximal femur (H) is taken as proportional to the patient’s body height and it is measured from the top most point of the femur head to the bottom of the proximal femur. The femoral neck width (W) is the diameter of the narrowest femoral neck. The femoral neck length (L) is defined as the distance between the two tangent points of the line of narrowest neck width with the contour of the proximal femur at, respectively, the femoral head and the great trochanter. The femoral neck angle (α) is the angle between the narrowest neck diameter and the horizontal line. To investigate effects of the factors on hip fracture risk, hip DXA images of total 180 osteoporosis patients were obtained from the Manitoba Bone Mineral Density Database (MBMDD) under an approval of health research ethics issued by the provincial Research Ethics Board. In the Province of Manitoba, Canada, BMD testing with DXA has been available since 1990. Results of all clinical DXA scans performed are maintained in the MBMDD, along with patient demographics, clinical risk factors, and anthropomorphic measures (weight, height, BMI, soft tissue composition percentage of lean and fat). Statistical data of the 180 cases are provided in Table 1. For each case, a patient-specific finite element model was constructed. After performing finite element convergence test and region sensitivity test, stress distribution over the proximal femur was obtained by finite element analysis. Fracture risk indices at the three critical locations were calculated using the obtained finite element stresses. Correlations between fracture risk index and the mentioned factors, i.e., areal BMD, body weight, femur length, femoral neck length, femoral neck width and femoral neck angle, were investigated. 3. Results and discussions Distributions of areal BMD and elasticity modulus over the proximal femur in one of the clinical cases are shown in Fig. 3(a) and (b), respectively. As can be seen from the figures, bone has denser areal BMD also has higher elasticity modulus, especially the cortical bone has much higher elasticity modulus than cancellous bone. It must be pointed out that the large areal BMD over the femoral head is partially due to
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(b)
Fig. 3. (a) Distribution of areal BMD (g/cm2 ); (b) Distribution of bone elasticity modulus (Pa). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.)
Fig. 4. Finite element convergence test result. (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/ BME-151271.)
overlapping of the femoral head and the pelvis bone in DXA scanning. Based on the theory of material mechanics, the resulted high elasticity modulus in the femoral head may change the local distribution of stresses; it should not affect the stress level over the rest part of the proximal femur. Result of finite element convergence test is plotted in Fig. 4. It can be noticed that the convergence process has oscillations and not as smooth as in the finite element analysis of engineering materials. This is due to the consideration of bone inhomogeneity in the study. For one of the clinical cases, the obtained distributions of effective (or von Mises) stress and pointwise fracture risk index calculated using definition in Eq. (2) are plotted respectively in Fig. 5(a) and (b). It can be observed that stress level in the cortical bone is much higher than that in the cancellous bone. However, it does not mean fracture risk index in the cortical bone is also higher, as cortical bone has higher BMD and thus higher yield stress. The calculated correlation coefficients between FRI at the three locations and the investigated factors are given in Table 2. It should be noted that the listed areal BMD in the second column of the table were taken respectively from the three locations. A large correlation coefficient with a small p-value (usually p < 0.05) indicates there exists a strong correlation [22]. It can be observed, among these factors, fracture risk is
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Z. Ferdous and Y. Luo / Study of hip fracture risk by DXA-based patient-specific finite element model
(a)
(b)
Fig. 5. (a) Distribution of effective (von Mises) stress (Pa); (b) Distribution of pointwise fracture risk index (FRI). (Colors are visible in the online version of the article; http://dx.doi.org/10.3233/BME-151271.) Table 2 Correlation coefficients (p-value) between FRI at the three locations and different factors Location at femur Femoral neck
Areal BMD −0.33 (0.001)
Body weight 0.52 (0.001)
Femur length 0.13 (0.1062)
Neck length 0.11 (0.1175)
Neck width 0.1618 (0.0267)
Neck angle 0.09 (0.2637)
Intertrochanter
−0.67 (0.001)
0.18 (0.017)
0.20 (0.01)
0.20 (0.009)
0.3346 (0.001)
0.00 (0.9676)
Subtrochanter
−0.43 (0.001)
0.57 (0.001)
0.29 (0.0009)
0.32 (0.001)
0.2825 (0.0002)
0.03 (0.6759)
influenced mainly by areal bone density and patient’s body weight, followed by the other factors. It can also be observed that at different location, the factors may have different roles in hip fracture. Over the intertrochanter, FRI strongly correlates to areal bone density (r = −0.67, p < 0.001), which is consistent with the results reported by Lang et al. [23] and Cheng et al. [24]. However, at the femoral neck and the subtrochanter, FRI has stronger correlation with patient’s body weight, as indicated by the respective correlation coefficients, r = 0.52 (p < 0.001) and r = 0.57 (p < 0.001). On the other hand, correlation between FRI and neck angle at the three locations is low and may even not exit, as the corresponding p-values are very large. Similar observation has been made by Faulkner et al. in their investigation [13]. Correlations between FRI and proximal femur length, femoral neck length, and femoral neck width are moderate at the intertrochanter and subtrochanter, and low at the femoral neck. It is also evident from Table 2 that FRI and proximal femur length, which was taken as proportional to patient’s height, have a weak to moderate positive correlation at the three sections. This outcome is in agreement with those from population based cohort study, i.e., taller people are in higher risk of hip fracture than shorter people [25]. However, there are two observations from Table 2 that seems not consistent with and even contradicting to the theories of Structural Mechanics. One is that FRI at the three locations only has very week positive correlation with femoral neck length; the other is that FRI at the three locations has positive correlation with femoral neck width (or neck diameter). If the proximal femur is considered as a beam, cf. Fig. 1(a), a longer femoral neck would generate a larger bending moment by the weight acting
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on the femoral head and thus a higher fracture risk. On the other hand, if the femoral neck width is increased, the resistance of beam cross-section to bending moment should be increased and the fracture risk should be reduced. Similar discrepancies have already reported in the literature [26–28]. The above discrepancies may be caused by several reasons. First, it may be caused by the unique loading condition considered in the study. The resultant force of the uniformly distributed force on the femoral head was approximately along the femoral neck axis. Therefore, the force on the femoral neck was mainly an axial force. Second, the femoral neck length may coincide with the femoral moment arm [29,30]. Third, it has been found in our study that femoral neck width (or diameter) is strongly correlated to femoral neck length (correlation coefficient r = 0.8714, p < 0.001), indicating that a thicker femoral neck is also longer. In addition, a thicker femoral neck may also have low areal BMD [31]. Several aspects of the reported study need be improved in the future. For example, the forces acting on the femoral head and the greater trochanter induced in lateral fall were determined using a statistical model. The impact forces may be different for a specific subject due to their individual anthropometric differences such as body height and weight. Moreover, the direction of fall and the energy absorbed during impact are also important issues that deserve further consideration. 4. Conclusions The uncovered correlations between FRI and the investigated factors in the reported study clearly demonstrated that use of areal BMD alone as hip fracture predictor is not reliable, as hip fracture is also simultaneously dependent on several other factors such as body weight and femur geometry. At different location on the proximal femur, the factors may have a different role in hip fracture. Hip fracture is the result of the combined effects from the involved factors. For hip fractures resulted from lateral fall, areal BMD and patient’s weight are the two dominant factors. However, the effects of the rest factors are not trivial as indicated by the values of their correlation coefficients. For the number of involved factors and the complicated correlations between FRI and the factors, it is suggested that DXA-based finite element modeling should be adopted in clinical assessment of hip fracture risk. Acknowledgements The reported research has been supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada and the Manitoba Health Research Council (MHRC), which are gratefully acknowledged. Special thanks are directed to Ms. Linda Ward at the St. Boniface General Hospital, Winnipeg, for preparing the DXA images used in the reported research. References [1] M.E. Wiktorowicz and R. Goeree, Economic implications of hip fracture: health service use, institutional care and cost in Canada, Osteoporosis International 12 (2001), 271–278. [2] G.S. Keene, M.J. Parker and G.A. Pryor, Mortality and morbidity after hip fractures, British Medical Journal 307 (1993), 1248–1250. [3] J. Stevens, K.A. Mack et al., Self-reported falls and fall-related injuries among persons aged 65 years United States, 2006, Journal of Safety Research 39 (2008), 345–349. [4] B.L. Riggs and L.J. Melton III, The world wide problem of osteoporosis: insights afforded by epidemiology, Bone 17 (1995), S505–S511.
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