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Prediction of femoral fracture load using automated finite element modeling
Journal of Biomechanics 31 (1998) 125 — 133
Prediction of femoral fracture load using automated finite element modeling Joyce H. Keyak!,",#,*, Stephen A. Rossi",#, Kimberly A. Jones", Harry B. Skinner!,",# ! Department of Orthopaedic Surgery, University of California Irvine Medical Center, Orange, CA, U.S.A. " Rehabilitation Research and Development Service, Department of Veterans Affairs Medical Center, San Francisco, CA, U.S.A. # Bioengineering Graduate Group, University of California, San Francisco/Berkeley, CA, U.S.A. Received in final form 17 November 1997
Abstract Hip fracture is an important cause of morbidity and mortality among the elderly. Current methods of assessing a patient’s risk of hip fracture involve local estimates of bone density (densitometry), and are limited by their inability to account for the complex structural features of the femur. In an effort to improve clinical and research tools for assessing hip fracture risk, this study investigated whether automatically generated, computed tomographic (CT) scan-based finite element (FE) models can be used to estimate femoral fracture load in vitro. Eighteen pairs of femora were examined under two loading conditions — one similar to loading during the stance phase of gait, and one simulating impact from a fall. The femora were then mechanically tested to failure and regression analyses between measured fracture load and FE-predicted fracture load were performed. For comparison, densitometry measures were also examined. Significant relationships were found between measured fracture load and FE-predicted fracture load (r"0.87, stance; r"0.95, fall; r"0.97, stance and fall data pooled) and between measured fracture load and densitometry data (r"0.78, stance; r"0.91, fall). These results indicate that this sophisticated technique, which is still early in its development, can achieve precision comparable to that of densitometry and can predict femoral fracture load to within !40% to #60% with 95% confidence. Therefore, clinical use of this approach, which would require additional X-ray exposure and expenditure for a CT scan, is not justified at this point. Even so, the potential advantages of this CT/FE technique support further research in this area. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Hip fracture; Osteoporosis; Finite element; Femur; Bone strength
1. Introduction Hip fracture is an important cause of morbidity and mortality among the elderly. In the U.S.A. over 260,000 hip fractures occur each year in patients 65 yr of age or older (Graves, 1992). A great proportion of these fractures lead to permanent disability and/or death (Cummings et al., 1985; Kenzora et al., 1984; Mullen and Mullen, 1992; White et al., 1987), and in about 50% of all cases, recovery is not achieved within one year (Holbrook et al., 1984; Miller, 1978). The high cost of treatment, estimated at $7.1 billion annually in the U.S.A.
*Correspondence address: Department of Orthopaedic Surgery, University of California Irvine Medical Center, 101 City Drive South, Orange, CA 92868-5382, U.S.A. Tel.: (714) 456 5754; fax: (714) 456 7547; e-mail: [email protected]. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S0021-9290(97)00123-1
(Praemer et al., 1992), and the disabling nature of this injury point to the importance of preventing hip fracture. An inexpensive and accurate means of assessing hip fracture risk would enable patients at high risk to be identified so that preventive measures could be taken. Current methods of assessing hip fracture risk are based on the assumption that reduced bone strength is related to fracture incidence and employ two-dimensional (2-D) or three-dimensional (3-D) imaging techniques (i.e. densitometry), such as dual-energy X-ray absorptiometry (DXA) or quantitative computed tomography (QCT), to obtain estimates of bone mineral density in the femur or other bones (Cann, 1988; Cummings et al., 1993; Glueer et al., 1994; Grampp et al., 1993; Lang et al., 1991; Mazess et al., 1988; Melton et al., 1986; Perloff et al., 1991; Riggs et al., 1982; Vega et al., 1991). These methods have been only partly successful in identifying patients who fracture, and are inherently limited by
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their inability to account for complex geometry, bone heterogeneity, loading conditions, or variable fracture location. Attempts to improve densitometry-based techniques have been directed at developing better predictors of femoral fracture load by including simple measures of femoral geometry in the evaluation (Alho et al., 1988; Courtney et al., 1994, 1995; Faulkner et al., 1993; Lotz and Hayes, 1990), or by performing 2-D structural engineering analyses (Beck et al., 1990; Gies et al., 1985). However, these efforts have resulted in only marginal improvements. In an effort to improve clinical and research tools for assessing hip fracture risk, this study investigated whether automatically generated, computed tomographic (CT) scan-based finite element (FE) models can be used to estimate femoral fracture load. To address this question, two loading conditions were studied in vitro — one similar to loading during the stance phase of gait, and one simulating impact from a fall. Mechanical testing was performed to evaluate the FE models. For comparison with a simpler approach, two QCT-based densitometry measures were also examined.
2. Methods Matched pairs of fresh-frozen human cadaveric proximal femora were obtained from 10 female and eight male Caucasian donors ages 52—92 yr (mean, 70.3 yr). Specimens were screened for blood-borne pathogens and were provided by tissue banks (seven cases) and the local anatomy department (11) from donors age 50 yr or older. Causes of death were cardiovascular disease (eight cases), hemorrhage (two), cancer (three), other illnesses (three), and unknown (two). One femur from each pair was randomly selected for examination in a stance-like load configuration; force was applied to the femoral head and directed within the coronal plane at 20° to the shaft axis (Frankel, 1960), and the shaft was restrained (Fig. 1a). The contralateral femur was examined in a configuration simulating impact from an oblique fall backward and to the side, similar to loading investigated previously (Backman, 1957; Lotz and Hayes, 1990); opposing forces were applied to the femoral head and greater trochanter at 60° to the shaft and 70° to the major axis of the elliptical cross-section of the neck, and the shaft was restrained (Fig. 1b). The distal end of the shaft of each proximal femur was embedded in polymethylmethacrylate (PMMA) to provide mechanical restraint. This PMMA base also served as a coordinate system that was fixed relative to the femur and facilitated accurate modeling of the applied load. A PMMA cup was molded (but not bonded) to the femoral head, and was later used to distribute the force applied during mechanical testing. For the femora tested
in the fall configuration, a cup was also made for the greater trochanter. For FE model generation, the femur and attached PMMA base were immersed in water and placed atop a calibration phantom (0—200 mg cm~3 K HPO in 2 4 water) (Lang et al., 1991), and a CT scan of the femur was taken using a GE 9800 Research Scanner (General Electric, Milwaukee, WI, U.S.A.) (80 kVp, 280 mAs, contiguous 3.0 mm-thick slices, 1.08 mm pixels, 320]320 matrix, standard reconstruction). The CT scan data were transferred to an Indigo Iris computer (Silicon Graphics, Mountain View, CA), and a 3-D FE model using heterogeneous linear isotropic mechanical properties was automatically generated for each femur (Keyak et al., 1990). Linear, eight-noded cube-shaped elements measuring 3 mm on a side were used so that the elements matched the thickness of the CT scan images. The FE models, which each took about 30 min to generate, consisted of 6876—19,151 nodes and 5152—15,552 elements, depending on femur size (Fig. 2). The elastic modulus and strength of each element were computed as follows. The CT scan data were calibrated in terms of K HPO equivalent density, and apparent 2 4 ash density was estimated from these data using the relation reported by Les et al. (1994) for equine bone. This relation is close to one found previously for human tibial trabecular bone (Keyak et al., 1994) and is valid for both cortical and trabecular bone. Modulus and strength were computed from ash density using reported correlations for trabecular bone (Keyak et al., 1994) and cortical bone (Keller, 1994) (Table 1). To speed FE analysis, all elements with a modulus below 5 MPa were assigned a new modulus of 0.01 MPa (essentially zero), and the remaining element moduli were grouped, requiring an adjustment of no more than$2.5% for each element, to obtain approximately 170 modulus values. The final moduli which met this$2.5% criterion were 5.125, 5.381, 2 , 21,531, 22,607 MPa, or equivalently, 5.125] (1.05)n~2 MPa, where n"2, 3, 2 , 174. A constant Poisson’s ratio of 0.4 was assumed (Reilly and Burstein, 1975; Van Buskirk and Ashman, 1981). Boundary conditions were applied to the FE models to represent the conditions of mechanical testing with a quasi-static force of 1000 N. Force magnitude was arbitrary because model linearity enabled the stress/strain results to be scaled to obtain results for any magnitude. For each model, the direction and location of the applied force were extrapolated from CT scan coordinates of the PMMA base attached to the femur, thereby enabling accurate representation of the experimental loads. Force was equally divided over nodes on the loaded portion of the femoral head, and the distal portion of the model was fully restrained at the level corresponding to the most proximal portion of the PMMA base. For the fall load configuration, nodes representing the portion of the greater trochanter that was in contact
J.H. Keyak et al. / Journal of Biomechanics 31 (1998) 125—133
Fig. 1. Stance (a) and fall (b) loading conditions used in this study. The FE models attempted to represent these conditions.
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Fig. 2. One of the FE models used in this study. This model contained 14,534 nodes and 11,604 cube elements measuring 3 mm on a side.
with the PMMA cup were restrained in the direction of the applied load. The models were analyzed using ABAQUS software (version 5.4, Hibbitt, Karlsson, and Sorensen, Providence, RI). To predict the fracture load of a femur, a factor of safety (FOS) for each element was computed at the element centroid using the distortion energy theory of failure: FOS" element strength (derived from the CT scan data) . element von Mises stress (computed the FE model) FOS less than one indicated element failure. Elements at the model surface were disregarded because partial volume effects made results at the surface unreliable. Neglecting these elements may have been a source of error if fracture began at the bone surface; however, this error was partially offset by the fact that, on average, these elements consisted of only 50% bone by volume and therefore played a minor structural role. In addition, multiple elements were used to identify the fracture load (see below), thereby reducing the effect of disregarding individual surface elements. The predicted femoral fracture load (F ) was defined FE as the load at the onset of local material failure, as indicated by the element FOS values. This methodology assumed that fracture began in the region where FOS values were less than one. Because failure of just a few
finite elements was thought to be structurally insignificant and could have been prone to artifacts, F was FE defined a priori as the load at which the factors of safety for 15 contiguous nonsurface elements were less than 1 (Fig. 3).1 Linearity of the models enabled F to be FE computed after a single FE analysis by simply finding the 15 contiguous elements with lowest FOS and then scaling the load, FE data, and FOS data until those 15 FOS values were less than or equal to 1. This post-processing of the FE data was performed in just a few minutes using in-house software. After F was computed, the measured femoral fracFE ture load (F ) was determined by mechanical testing to M%!4 failure under displacement control at 0.5 mm s~1 (Bionix 858 Test System, MTS, Eden Prairie, MN). Grease was placed between the PMMA cups and loading platens to minimize transverse forces. F was defined as the load M%!4 at the first peak of the force—displacement curve. Given the definition of F used in this study, a more appropriFE ate definition of F would have been the load at the M%!4 measured onset of failure. However, this latter definition could not be implemented because the onset of failure was, by nature, highly localized and consequently had a negligible effect on the force—displacement curve. As a result, F tended to overstate the load at the onset of M%!4 failure. To provide comparative data for one currently available technology, two QCT-based densitometry measures were examined. For the femora tested in the stance configuration, average density in the subcapital region (o ) SC was computed (Esses et al., 1989). For the femora tested in the fall configuration, intertrochanteric density (o ) IT multiplied by intertrochanteric area (A ) was obtained IT (Lotz and Hayes, 1990). These densitometry measures were selected a priori, and were computed using the same CT scan, calibration, and geometry data that were used to generate the FE models. The abilities of the FE models and densitometry measures to predict F were assessed separately for M%!4 each loading condition by performing simple linear regression on F vs F , and on F vs densitometry M%!4 FE M%!4 values. When the data appeared not to be linearly related and did not satisfy the assumption of homoscedasticity (tested by a Spearman rank correlation between the absolute values of the residuals and F ), power relations M%!4 were computed by performing simple linear regression on logarithmic transformations of the data. For the FE approach, the data for the two loading conditions were compared by pooling the data and
1F was relatively insensitive to the number of contiguous elements FE required by the failure criterion as long as more than 8—10 elements were required. As the number of elements was increased from 11 to 15, F increased by 0.4—5% (mean, 2.7%) for the stance condition and FE 0—11% (mean, 5.1%) for the fall condition.
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Table 1 Relationships used to compute modulus and strength from ash density! Relationship
Density range
Correlation coefficient
Reference
E"33,900 o2.20 !4) E"10,200 o2.01 !4) E"5307 o #469" !4)# S"137 o1.88 !4) S"114 o1.72# !4)
o 40.27 g cm~3 !4) o 50.6 g cm~3 !4) 0.27(o (0.6 g cm~3 !4) o (0.317 g cm~3 !4) o 50.317 g cm~3 !4)
0.92 0.82 — 0.96 0.94
Keyak et al. (1994) Keller (1994) — Keyak et al. (1994) Keller (1994)
!E"elastic modulus (MPa); S" strength (MPa); o "apparent ash density (g cm~3). !4) " This equation represents linear interpolation between the extremes of the two previous relations for modulus. # The strength correlations were similar and intersected at o "0.317 g cm~3. !4)
Fig. 3. Failure locations computed for the stance loading condition (top) and fall loading condition (bottom) for a matched pair of femora. (Posterior views are on the left, and medial views are on the right.) Elements with factors of safety below one are shown, with the 15 contiguous elements shown in black.
performing backward stepwise regression (F-toremove"3.9, p"0.0565; F-to-enter"4.0, p"0.0535). The initial regression equation took the form F "b #b G#b GF #b F , M%!4 0 1 2 FE 3 FE
where G was a dummy variable equal to#1 for the stance configuration and !1 for the fall configuration, and b , b , b , and b were determined by the regression 0 1 2 3 analysis. Significance of the terms containing G would indicate that the relationship between F and F M%!4 FE
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depended on loading condition. The change in coefficient of determination (R2) caused by removal of terms during the stepwise regression indicated the amount of additional variance in F that had been accounted for by M%!4 those terms. Finally, to determine whether the use of two, theoretically non-independent data points from each donor influenced the final regression equation, an additional multiple regression analysis that accounted for between-subjects variability was performed (Glantz and Slinker, 1990), and the coefficients of the resulting equation and the original equation were compared using t-tests with a"0.05. Comparison of the CT/FE technique and densitometry methods utilized a limited data set of 18 pairs, so statistically significant differences between the methods were not expected. Rigorous statistical comparison of correlation coefficients for the two methods would have required over 100 pairs of specimens, assuming underlying correlation coefficients of 0.8 and 0.9, 80% statistical power, and a"0.05 (Zar, 1984).
3. Results F and F were linearly related for the stance M%!4 FE configuration [r"0.867, p(0.0001, standard error of the estimate (S.E.E)"1.56 kN; Fig. 4a] and non-linearly related for the fall configuration [r"0.949, p(0.0001, S.E.E."0.0909 log (kN); Fig. 4b]. Logarithmic trans10 formations of the data were required for the fall configuration due to both nonlinearity and heteroscedasticity of the data (p"0.008). Data for one femur to be tested in the fall condition were lost due to mechanical error.
When the data for both loading conditions were pooled, logarithmic transformations were again necessary (Spearman test, p(0.0001), and backward stepwise regression revealed that the regression equation did not depend on loading condition (p"0.08). More importantly, inclusion of the terms related to loading condition increased R2 from 0.936 to 0.947, indicating that these terms accounted for only an additional 1.1% of the variance in F . In addition, the coefficients of the M%!4 regression equation were not significantly different after accounting for between-subjects variability. Therefore, the data for both loading conditions were described by a single power relation between F and F [r"0.967, M%!4 FE p(0.0001, S.E.E."0.0970 log (kN); Fig. 5]. This equa10 tion and the equation for the fall loading condition alone were nearly identical, further supporting the finding that the relationships for the stance and fall configurations were the same. Finally, the 95% confidence interval for an additional observation for this relationship spanned from !40% to #60% of F (Fig. 5). M%!4 Significant correlations between F and the denM%!4 sitometry data were found for the stance (r"0.781, p"0.0001, S.E.E."1.95 kN; Fig. 6a) and fall (r"0.906, p(0.0001, S.E.E."0.568 kN; Fig. 6b) loading conditions. These correlation coefficients were not significantly different from those for the CT/FE technique. However, statistical power was low, as explained previously.
4. Discussion In an effort to improve clinical and research tools for assessing hip fracture risk, we have shown that automatically generated CT scan-based FE models can predict
Fig. 4. Measured fracture load versus FE-predicted fracture load for the stance configuration (a) and fall configuration (b). These highly significant relationships indicate that CT scan-based FE models can be used to estimate femoral fracture load. Dashed lines indicate the bounds of the 95% confidence intervals for the regression equations (short dashes) and additional observations (long dashes).
J.H. Keyak et al. / Journal of Biomechanics 31 (1998) 125—133
femoral fracture load in vitro for two very different loading conditions with a precision of !40% to #60%. This level of precision is comparable to that of the densitometry-based measures examined here. With respect to accuracy, the CT/FE technique tends to underestimate F , as indicated by the regression results. However, M%!4 this underestimation can be attributed to the fact that F was defined as the load at the onset of failure, FE
Fig. 5. Measured fracture load versus FE-predicted fracture load when data for both load configurations were pooled. A single power relation described the data for both configurations, indicating the robustness of the CT/FE technique. Circles and triangles indicate femora tested in the stance and fall configurations, respectively. Dashed lines indicate the bounds of the 95% confidence intervals for the regression equation (short dashes) and additional observations (long dashes).
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whereas F was defined as the load at the first peak of M%!4 the force-displacement curve. Therefore, the underestimation of F should not be viewed as a limitation M%!4 of the CT/FE technique, but rather as a result of the experimental method. The precision of the CT/FE technique is comparable to that of densitometry methods reported previously. For the stance configuration, the correlation for the CT/FE technique (r"0.87) is as strong as correlations found in previous studies using dual photon absorptiometry (r"0.74) (Beck et al., 1990), QCT (r"0.79) (Alho et al., 1988), and engineering-related methods (r"0.89 in two studies) (Beck et al., 1990; Gies et al., 1985). For the fall configuration, the correlation coefficient for the CT/FE technique (r"0.95) is statistically comparable to coefficients for the strongest correlations reported by Courtney et al. (1994, 1995) (r"0.80—0.96), who used DXA and loading representing impact from a fall to the side. It should be noted that the CT/FE technique is still in its infancy and significant improvements in precision may be achieved through refinements, most importantly in the area of material representation. For example, the current approach relied upon isotropic material properties that had been determined by testing specimens in compression in their most stiff and strong direction; element moduli and strengths for the other directions were therefore overstated. Use of anisotropic mechanical properties (Ciarelli et al., 1991; Keyak et al., 1994; Reilly and Burstein, 1975; Van Buskirk and Ashman, 1981) and accounting for the fact that bone material strength is about 30% lower in tension than in compression (Currey, 1970; Keaveny et al., 1994a,b; Reilly and Burstein, 1975) may improve FE model predictions. However, such
Fig. 6. Measured fracture load versus subcapital density for the stance configuration (a), and measured fracture load versus intertrochanteric density multiplied by area for the fall configuration (b). The correlation coefficients for these regression equations are statistically comparable to those for the CT/FE technique (Fig. 4). Dashed lines indicate the bounds of the 95% confidence intervals for the regression equations (short dashes) and additional observations (long dashes).
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improvements would require special failure theories, and none have been validated for bone at this time. A more practical first step toward improving model precision may be achieved by simply using smaller elements to better represent material heterogeneity and bone geometry. Finally, restriction of the analysis to linear material behavior, which maintained computational time at practical levels, was an important limitation because it precluded modeling past the onset of failure. The ability of the FE models to account for loading condition represents a major advance over densitometry techniques, making it possible to calculate fracture loads for real-life loading conditions on a patient-specific basis. These fracture loads can then be compared with loads occurring in vivo in order to assess fracture risk, either for research or for clinical applications. Specifically, use of this technology in research may help us identify the most risky loading conditions and improve our understanding of the mechanisms of hip fracture so that preventive measures, either medical (Ettinger, 1985, 1993; Liberman et al., 1995; Reid et al., 1994; Stone, 1993) or biomechanical (Lauritzen et al., 1993), can be directed optimally. The results of the present study are applicable to most of the elderly population because there were no restrictions based on medical history. Although all donors were Caucasian, lack of diversity should not affect generality of the results because the CT/FE technique can account for differences in bone size and density, the most important race-related parameters. Three of the donors died from cancer, and the cancer had metastasized extensively to the bones in one of these cases. In addition, it is likely that other femora came from donors with other diseases or treatments that could have affected bone strength. Despite these potentially confounding variables, there were no obvious outliers in the data. This result is especially surprising in the case of the femora with metastatic tumors, as it has not been shown that the material property relationships used in generating the FE models are valid for bone with tumors. Thus, these results suggest that CT scan-based FE models may be useful for assessing fracture load in highly pathological conditions. This study has shown that automatically generated CT scan-based FE models can be used to estimate femoral fracture load under two very different loading conditions. However, the precision of this technique is comparable to that of densitometry methods such as DXA and QCT. Therefore, clinical use of this approach, which would require additional X-ray exposure and expenditure for a full CT scan of the femur, is not justified at this stage of development. Even so, the potential advantages of this CT/FE technique, i.e. its ability to account for the effects of 3-D geometry, material heterogeneity, and loading conditions, all at relatively low cost, support further research in this area.
Acknowledgements This work was funded by the Department of Veterans Affairs, Rehabilitation R & D Service. Mechanical testing was performed at the University of California, San Francisco Orthopaedic Biomechanics Laboratory. Femora were provided by the University of California, San Francisco Tissue Bank; University of California, San Francisco Department of Anatomy; University of California, Irvine Organ and Tissue Bank; and National Disease Research Interchange. The authors thank Marina Pejcic for her assistance. References Alho, A., Husby, T., Hoiseth, A., 1988. Bone mineral content and mechanical strength. An ex vivo study of human femora at autopsy. Clinical Orthopaedics and Related Research 227, 292—297. Backman, S., 1957. The proximal end of the femur. Investigations with special reference to the etiology of femoral neck fractures. Anatomical studies. Roentgen projections. Theoretical stress calculations. Experimental production of fractures. Acta Radiologica Supplementum 146. Beck, T.J., Ruff, C.B., Warden, K.E., Scott, W.W., Jr., Rao, G.U., 1990. Predicting femoral neck strength from bone mineral data. A structural approach. Investigative Radiology 25, 6—18. Cann, C.E., 1988. Quantitative CT for determination of bone mineral density: a review. Radiology 166, 509—521. Ciarelli, M.J., Goldstein, S.A., Kuhn, J.L., Cody, D.D., Brown, M.B., 1991. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. Journal of Orthopaedic Research 9, 674—682. Courtney, A.C., Wachtel, E.F., Myers, E.R., Hayes, W.C., 1994. Effects of loading rate on strength of the proximal femur. Calcified Tissue International 55, 53—58. Courtney, A.C., Wachtel, E.F., Myers, E.R., Hayes, W.C., 1995. Agerelated reductions in the strength of the femur tested in a fall-loading configuration. Journal of Bone and Joint Surgery 77-A, 387—395. Cummings, S.R., Kelsey, J.L., Nevitt, M.C., O’Dowd, K.J., 1985. Epidemiology of osteoporosis and osteoporotic fractures. Epidemiologic Reviews 7, 178—208. Cummings, S.R., Black, D.M., Nevitt, M.C., Browner, W., Cauley, J., Ensrud, K., Genant, H.K., Palermo, L., Scott, J., Vogt, T.M., 1993. Bone density at various sites for prediction of hip fractures. The Lancet 341, 72—75. Currey, J.D., 1970. The mechanical properties of bone. Clinical Orthopaedics and Related Research 73, 210—231. Esses, S.I., Lotz, J.C., Hayes, W.C., 1989. Biomechanical properties of the proximal femur determined in vitro by single-energy quantitative computed tomography. Journal of Bone and Mineral Research 4, 715—722. Ettinger, B., Genant, H.K., Cann, C.E., 1985. Long-term estrogen replacement therapy prevents bone loss and fractures. Annals of Internal Medicine. 102, 319—324. Ettinger, B., 1993. An update for the obstetrician-gynecologist on advances in the diagnosis, prevention, and treatment of postmenopausal osteoporosis. Current Opinion in Obstetrics and Gynecology 5, 396—403. Faulkner, K.G., Cummings, S.R., Black, D., Palermo, L., Glueer, C.C., Genant, H.K., 1993. Simple measurement of femoral geometry predicts hip fracture: The study of osteoporotic fractures. Journal of Bone and Mineral Research 8, 1211—1217.
J.H. Keyak et al. / Journal of Biomechanics 31 (1998) 125—133 Frankel, V.H., 1960. The Femoral Neck: Function, Fracture Mechanism, Internal Fixation; An Experimental Study. Almqvist and Wiksell, Stockholm. Gies, A.A., Carter, D.R., Sartoris, D.J., Sommer, F.G., 1985. Femoral neck strength predicted from dual energy projected radiography. Transactions of the Orthopaedic Research Society 10, 357. Glantz, S.A., Slinker, B.K., 1990. Primer of Applied Regression and Analysis of Variance, pp. 381—390. McGraw-Hill, New York. Glueer, C.C., Cummings, S.R., Pressman, A., Li, J,, Glueer, K., Faulkner, K.G., Grampp, S., Genant, H.K., the Study of Osteoporotic Fractures Research Group., 1994. Prediction of hip fractures from pelvic radiographs: the study of osteoporotic fractures. Journal of Bone and Mineral Research 9, 671—677. Grampp, S., Jergas, M., Glueer, C.C., Lang, P., Brastow, P., Genant, H.K., 1993. Radiologic diagnosis of osteoporosis. Current methods and perspectives. Radiologic Clinics of North America 31, 1133—1145. Graves, E., 1992. Detailed diagnoses and procedures, national hospital discharge survey, 1990. Vital and Health Statistics, Series 13, no. 113. Pub. (PHS)92-1774, U.S. Dept. of Health and Human Services, Public Health Svc., National Center for Health Statistics, Hyattsville, Maryland. Holbrook, T.L., Grazier, K., Kelsey, J.L., Stauffer, R.N., 1984. The Frequency of Occurrence, Impact and Cost of Selected Musculoskeletal Conditions in the United States. American Academy of Orthopaedic Surgeons, Chicago, IL. Keaveny, T.M., Guo, X.E., Wachtel, E.F., McMahon, T.A., Hayes, W.C., 1994a. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. Journal of Biomechanics 27, 1127—1136. Keaveny, T.M., Wachtel, E.F., Ford, C.M., Hayes, W.C., 1994b. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. Journal of Biomechanics 27, 1137—1146. Keller, T.S., 1994. Predicting the compressive mechanical behavior of bone. Journal of Biomechanics 27, 1159—1168. Kenzora, J.E., McCarthy, R.E., Lowell, J.D., Sledge, C.B., 1984. Hip fracture mortality. Relation to age, treatment, preoperative illness, time of surgery, and complications. Clinical Orthopaedics and Related Research 186, 45—56. Keyak, J.H., Lee, I.Y., Skinner, H.B., 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. Journal of Biomedical Materials Research 28, 1329—1336. Keyak, J.H., Meagher, J.M., Skinner, H.B., Mote, C.D., Jr, 1990 Automated three-dimensional finite element modelling of bone: a new method. Journal of Biomedical Engineering 12, 389—397. Lang, P., Steiger, P., Faulkner, K., Gluer, C., Genant, H.K., 1991. Osteoporosis. Current techniques and recent developments in quantitative bone densitometry. Radiologic Clinics of North America 29, 49—76. Lauritzen, J.B., Petersen, M.M., Lund, B., 1993. Effect of external hip protectors on hip fractures. The Lancet 341, 11—13. Les, C.M., Keyak, J.H., Stover, S.M., Taylor, K.T., Kaneps, A.J., 1994. The estimation of material properties in the equine metacarpus using
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quantitative computed tomography. Journal of Orthopaedic Research 12, 822—833. Liberman, U.A., Weiss, S.R., Broll, J., Minne, H.W., Quan, H., Bell, N.H., Rodriguez-Portales, J., Downs, R.W., Dequeker, J., Favus, M., Seeman, E., Recker, R.R., Capizzi, T., Santora, A.C., Lombardi, A., Shah, R.V., Hirsch, L.J., Karpf, D.B., 1995. Effect of oral alendronate on bone mineral density and the incidence of fractures in postmenopausal osteoporosis. New England Journal of Medicine 333, 1437—1443. Lotz, J.C., Hayes, W.C., 1990. The use of quantitative computed tomography to estimate risk of fracture of the hip from falls. Journal of Bone and Joint Surgery 72-A, 689—700. Mazess, R.B., Barden, H., Ettinger, M., Schultz, E., 1988. Bone density of the radius, spine, and proximal femur in osteoporosis. Journal of Bone and Mineral Research 3, 13—18. Melton, L.J., III, Wahner, H.W., Richelson, L.S., O’Fallon, W.M., Riggs, B.L. 1986. Osteoporosis and the risk of hip fracture. American Journal of Epidemiology 124, 254—261. Miller, C.W., 1978. Survival and ambulation following hip fracture. Journal of Bone and Joint Surgery 60-A, 930—934. Mullen, J.O., Mullen, N.L., 1992. Hip fracture mortality. A prospective, multifactorial study to predict and minimize death risk. Clinical Orthopaedics and Related Research 280, 214—222. Perloff, J.J., McDermott, M.T., Perloff, K.G., Blue, P.W., Enzenhauer, R., Sieck, E., Chantelois, A.E., Dolbow, A., Kidd, G.S., 1991. Reduced bone-mineral content is a risk factor for hip fractures. Orthopaedic Review 20, 690—698. Praemer, A., Furner, S., Rice, D.P., 1992. Musculoskeletal Conditions in the United States. American Academy of Orthopaedic Surgeons, Chicago, IL. Reid, I.R., Wattie, D.J., Evans, M.C., Gamble, G.D., Stapleton, J.P., Cornish, J., 1994. Continuous therapy with pamidronate, a potent bisphosphonate, in postmenopausal osteoporosis. Journal of Clinical Endocrinology and Metabolism, 79, 1595—1599. Reilly, D.T., Burstein, A.H., 1975. The elastic and ultimate properties of compact bone tissue. Journal of Biomechanics 8, 393—405. Riggs, B.L., Wahner, H.W., Seeman, E., Offord, K.P., Dunn, W.L., Mazess, R.B., Johnson, K.A., Melton, L.J., III, 1982. Changes in bone mineral density of the proximal femur and spine with aging: Differences between the postmenopausal and senile osteoporosis syndromes. Journal of Clinical Investigation 70, 716—723. Stone, M., 1993. Didronel PMO. British Journal of Hospital Medicine 49, 275—277. Van Buskirk, W.C., Ashman, R.B., 1981. The elastic moduli of bone. Trans. American Society of Mechanical Engineers (Applied Mechanics Division) 45, 131—143. Vega, E., Mautalen, C., Gomez, H., Garrido, A., Melo, L., Sahores, A.O., 1991. Bone mineral density in patients with cervical and trochanteric fractures of the proximal femur. Osteoporosis International 1, 81—86. White, B.L., Fisher, W.D., Laurin, C.A., 1987. Rate of mortality for elderly patients after fracture of the hip in the 1980’s. Journal of Bone and Joint Surgery 69-A, 1335—1340. Zar, J.H., 1984. Biostatistical Analysis, pp. 115—118, 309—315. PrenticeHall, Englewood Cliffs, NJ.
Prediction of femoral fracture load using automated finite element modeling Joyce H. Keyak!,",#,*, Stephen A. Rossi",#, Kimberly A. Jones", Harry B. Skinner!,",# ! Department of Orthopaedic Surgery, University of California Irvine Medical Center, Orange, CA, U.S.A. " Rehabilitation Research and Development Service, Department of Veterans Affairs Medical Center, San Francisco, CA, U.S.A. # Bioengineering Graduate Group, University of California, San Francisco/Berkeley, CA, U.S.A. Received in final form 17 November 1997
Abstract Hip fracture is an important cause of morbidity and mortality among the elderly. Current methods of assessing a patient’s risk of hip fracture involve local estimates of bone density (densitometry), and are limited by their inability to account for the complex structural features of the femur. In an effort to improve clinical and research tools for assessing hip fracture risk, this study investigated whether automatically generated, computed tomographic (CT) scan-based finite element (FE) models can be used to estimate femoral fracture load in vitro. Eighteen pairs of femora were examined under two loading conditions — one similar to loading during the stance phase of gait, and one simulating impact from a fall. The femora were then mechanically tested to failure and regression analyses between measured fracture load and FE-predicted fracture load were performed. For comparison, densitometry measures were also examined. Significant relationships were found between measured fracture load and FE-predicted fracture load (r"0.87, stance; r"0.95, fall; r"0.97, stance and fall data pooled) and between measured fracture load and densitometry data (r"0.78, stance; r"0.91, fall). These results indicate that this sophisticated technique, which is still early in its development, can achieve precision comparable to that of densitometry and can predict femoral fracture load to within !40% to #60% with 95% confidence. Therefore, clinical use of this approach, which would require additional X-ray exposure and expenditure for a CT scan, is not justified at this point. Even so, the potential advantages of this CT/FE technique support further research in this area. ( 1998 Elsevier Science Ltd. All rights reserved. Keywords: Hip fracture; Osteoporosis; Finite element; Femur; Bone strength
1. Introduction Hip fracture is an important cause of morbidity and mortality among the elderly. In the U.S.A. over 260,000 hip fractures occur each year in patients 65 yr of age or older (Graves, 1992). A great proportion of these fractures lead to permanent disability and/or death (Cummings et al., 1985; Kenzora et al., 1984; Mullen and Mullen, 1992; White et al., 1987), and in about 50% of all cases, recovery is not achieved within one year (Holbrook et al., 1984; Miller, 1978). The high cost of treatment, estimated at $7.1 billion annually in the U.S.A.
*Correspondence address: Department of Orthopaedic Surgery, University of California Irvine Medical Center, 101 City Drive South, Orange, CA 92868-5382, U.S.A. Tel.: (714) 456 5754; fax: (714) 456 7547; e-mail: [email protected]. 0021-9290/98/$19.00 ( 1998 Elsevier Science Ltd. All rights reserved. PII S0021-9290(97)00123-1
(Praemer et al., 1992), and the disabling nature of this injury point to the importance of preventing hip fracture. An inexpensive and accurate means of assessing hip fracture risk would enable patients at high risk to be identified so that preventive measures could be taken. Current methods of assessing hip fracture risk are based on the assumption that reduced bone strength is related to fracture incidence and employ two-dimensional (2-D) or three-dimensional (3-D) imaging techniques (i.e. densitometry), such as dual-energy X-ray absorptiometry (DXA) or quantitative computed tomography (QCT), to obtain estimates of bone mineral density in the femur or other bones (Cann, 1988; Cummings et al., 1993; Glueer et al., 1994; Grampp et al., 1993; Lang et al., 1991; Mazess et al., 1988; Melton et al., 1986; Perloff et al., 1991; Riggs et al., 1982; Vega et al., 1991). These methods have been only partly successful in identifying patients who fracture, and are inherently limited by
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their inability to account for complex geometry, bone heterogeneity, loading conditions, or variable fracture location. Attempts to improve densitometry-based techniques have been directed at developing better predictors of femoral fracture load by including simple measures of femoral geometry in the evaluation (Alho et al., 1988; Courtney et al., 1994, 1995; Faulkner et al., 1993; Lotz and Hayes, 1990), or by performing 2-D structural engineering analyses (Beck et al., 1990; Gies et al., 1985). However, these efforts have resulted in only marginal improvements. In an effort to improve clinical and research tools for assessing hip fracture risk, this study investigated whether automatically generated, computed tomographic (CT) scan-based finite element (FE) models can be used to estimate femoral fracture load. To address this question, two loading conditions were studied in vitro — one similar to loading during the stance phase of gait, and one simulating impact from a fall. Mechanical testing was performed to evaluate the FE models. For comparison with a simpler approach, two QCT-based densitometry measures were also examined.
2. Methods Matched pairs of fresh-frozen human cadaveric proximal femora were obtained from 10 female and eight male Caucasian donors ages 52—92 yr (mean, 70.3 yr). Specimens were screened for blood-borne pathogens and were provided by tissue banks (seven cases) and the local anatomy department (11) from donors age 50 yr or older. Causes of death were cardiovascular disease (eight cases), hemorrhage (two), cancer (three), other illnesses (three), and unknown (two). One femur from each pair was randomly selected for examination in a stance-like load configuration; force was applied to the femoral head and directed within the coronal plane at 20° to the shaft axis (Frankel, 1960), and the shaft was restrained (Fig. 1a). The contralateral femur was examined in a configuration simulating impact from an oblique fall backward and to the side, similar to loading investigated previously (Backman, 1957; Lotz and Hayes, 1990); opposing forces were applied to the femoral head and greater trochanter at 60° to the shaft and 70° to the major axis of the elliptical cross-section of the neck, and the shaft was restrained (Fig. 1b). The distal end of the shaft of each proximal femur was embedded in polymethylmethacrylate (PMMA) to provide mechanical restraint. This PMMA base also served as a coordinate system that was fixed relative to the femur and facilitated accurate modeling of the applied load. A PMMA cup was molded (but not bonded) to the femoral head, and was later used to distribute the force applied during mechanical testing. For the femora tested
in the fall configuration, a cup was also made for the greater trochanter. For FE model generation, the femur and attached PMMA base were immersed in water and placed atop a calibration phantom (0—200 mg cm~3 K HPO in 2 4 water) (Lang et al., 1991), and a CT scan of the femur was taken using a GE 9800 Research Scanner (General Electric, Milwaukee, WI, U.S.A.) (80 kVp, 280 mAs, contiguous 3.0 mm-thick slices, 1.08 mm pixels, 320]320 matrix, standard reconstruction). The CT scan data were transferred to an Indigo Iris computer (Silicon Graphics, Mountain View, CA), and a 3-D FE model using heterogeneous linear isotropic mechanical properties was automatically generated for each femur (Keyak et al., 1990). Linear, eight-noded cube-shaped elements measuring 3 mm on a side were used so that the elements matched the thickness of the CT scan images. The FE models, which each took about 30 min to generate, consisted of 6876—19,151 nodes and 5152—15,552 elements, depending on femur size (Fig. 2). The elastic modulus and strength of each element were computed as follows. The CT scan data were calibrated in terms of K HPO equivalent density, and apparent 2 4 ash density was estimated from these data using the relation reported by Les et al. (1994) for equine bone. This relation is close to one found previously for human tibial trabecular bone (Keyak et al., 1994) and is valid for both cortical and trabecular bone. Modulus and strength were computed from ash density using reported correlations for trabecular bone (Keyak et al., 1994) and cortical bone (Keller, 1994) (Table 1). To speed FE analysis, all elements with a modulus below 5 MPa were assigned a new modulus of 0.01 MPa (essentially zero), and the remaining element moduli were grouped, requiring an adjustment of no more than$2.5% for each element, to obtain approximately 170 modulus values. The final moduli which met this$2.5% criterion were 5.125, 5.381, 2 , 21,531, 22,607 MPa, or equivalently, 5.125] (1.05)n~2 MPa, where n"2, 3, 2 , 174. A constant Poisson’s ratio of 0.4 was assumed (Reilly and Burstein, 1975; Van Buskirk and Ashman, 1981). Boundary conditions were applied to the FE models to represent the conditions of mechanical testing with a quasi-static force of 1000 N. Force magnitude was arbitrary because model linearity enabled the stress/strain results to be scaled to obtain results for any magnitude. For each model, the direction and location of the applied force were extrapolated from CT scan coordinates of the PMMA base attached to the femur, thereby enabling accurate representation of the experimental loads. Force was equally divided over nodes on the loaded portion of the femoral head, and the distal portion of the model was fully restrained at the level corresponding to the most proximal portion of the PMMA base. For the fall load configuration, nodes representing the portion of the greater trochanter that was in contact
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Fig. 1. Stance (a) and fall (b) loading conditions used in this study. The FE models attempted to represent these conditions.
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Fig. 2. One of the FE models used in this study. This model contained 14,534 nodes and 11,604 cube elements measuring 3 mm on a side.
with the PMMA cup were restrained in the direction of the applied load. The models were analyzed using ABAQUS software (version 5.4, Hibbitt, Karlsson, and Sorensen, Providence, RI). To predict the fracture load of a femur, a factor of safety (FOS) for each element was computed at the element centroid using the distortion energy theory of failure: FOS" element strength (derived from the CT scan data) . element von Mises stress (computed the FE model) FOS less than one indicated element failure. Elements at the model surface were disregarded because partial volume effects made results at the surface unreliable. Neglecting these elements may have been a source of error if fracture began at the bone surface; however, this error was partially offset by the fact that, on average, these elements consisted of only 50% bone by volume and therefore played a minor structural role. In addition, multiple elements were used to identify the fracture load (see below), thereby reducing the effect of disregarding individual surface elements. The predicted femoral fracture load (F ) was defined FE as the load at the onset of local material failure, as indicated by the element FOS values. This methodology assumed that fracture began in the region where FOS values were less than one. Because failure of just a few
finite elements was thought to be structurally insignificant and could have been prone to artifacts, F was FE defined a priori as the load at which the factors of safety for 15 contiguous nonsurface elements were less than 1 (Fig. 3).1 Linearity of the models enabled F to be FE computed after a single FE analysis by simply finding the 15 contiguous elements with lowest FOS and then scaling the load, FE data, and FOS data until those 15 FOS values were less than or equal to 1. This post-processing of the FE data was performed in just a few minutes using in-house software. After F was computed, the measured femoral fracFE ture load (F ) was determined by mechanical testing to M%!4 failure under displacement control at 0.5 mm s~1 (Bionix 858 Test System, MTS, Eden Prairie, MN). Grease was placed between the PMMA cups and loading platens to minimize transverse forces. F was defined as the load M%!4 at the first peak of the force—displacement curve. Given the definition of F used in this study, a more appropriFE ate definition of F would have been the load at the M%!4 measured onset of failure. However, this latter definition could not be implemented because the onset of failure was, by nature, highly localized and consequently had a negligible effect on the force—displacement curve. As a result, F tended to overstate the load at the onset of M%!4 failure. To provide comparative data for one currently available technology, two QCT-based densitometry measures were examined. For the femora tested in the stance configuration, average density in the subcapital region (o ) SC was computed (Esses et al., 1989). For the femora tested in the fall configuration, intertrochanteric density (o ) IT multiplied by intertrochanteric area (A ) was obtained IT (Lotz and Hayes, 1990). These densitometry measures were selected a priori, and were computed using the same CT scan, calibration, and geometry data that were used to generate the FE models. The abilities of the FE models and densitometry measures to predict F were assessed separately for M%!4 each loading condition by performing simple linear regression on F vs F , and on F vs densitometry M%!4 FE M%!4 values. When the data appeared not to be linearly related and did not satisfy the assumption of homoscedasticity (tested by a Spearman rank correlation between the absolute values of the residuals and F ), power relations M%!4 were computed by performing simple linear regression on logarithmic transformations of the data. For the FE approach, the data for the two loading conditions were compared by pooling the data and
1F was relatively insensitive to the number of contiguous elements FE required by the failure criterion as long as more than 8—10 elements were required. As the number of elements was increased from 11 to 15, F increased by 0.4—5% (mean, 2.7%) for the stance condition and FE 0—11% (mean, 5.1%) for the fall condition.
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Table 1 Relationships used to compute modulus and strength from ash density! Relationship
Density range
Correlation coefficient
Reference
E"33,900 o2.20 !4) E"10,200 o2.01 !4) E"5307 o #469" !4)# S"137 o1.88 !4) S"114 o1.72# !4)
o 40.27 g cm~3 !4) o 50.6 g cm~3 !4) 0.27(o (0.6 g cm~3 !4) o (0.317 g cm~3 !4) o 50.317 g cm~3 !4)
0.92 0.82 — 0.96 0.94
Keyak et al. (1994) Keller (1994) — Keyak et al. (1994) Keller (1994)
!E"elastic modulus (MPa); S" strength (MPa); o "apparent ash density (g cm~3). !4) " This equation represents linear interpolation between the extremes of the two previous relations for modulus. # The strength correlations were similar and intersected at o "0.317 g cm~3. !4)
Fig. 3. Failure locations computed for the stance loading condition (top) and fall loading condition (bottom) for a matched pair of femora. (Posterior views are on the left, and medial views are on the right.) Elements with factors of safety below one are shown, with the 15 contiguous elements shown in black.
performing backward stepwise regression (F-toremove"3.9, p"0.0565; F-to-enter"4.0, p"0.0535). The initial regression equation took the form F "b #b G#b GF #b F , M%!4 0 1 2 FE 3 FE
where G was a dummy variable equal to#1 for the stance configuration and !1 for the fall configuration, and b , b , b , and b were determined by the regression 0 1 2 3 analysis. Significance of the terms containing G would indicate that the relationship between F and F M%!4 FE
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depended on loading condition. The change in coefficient of determination (R2) caused by removal of terms during the stepwise regression indicated the amount of additional variance in F that had been accounted for by M%!4 those terms. Finally, to determine whether the use of two, theoretically non-independent data points from each donor influenced the final regression equation, an additional multiple regression analysis that accounted for between-subjects variability was performed (Glantz and Slinker, 1990), and the coefficients of the resulting equation and the original equation were compared using t-tests with a"0.05. Comparison of the CT/FE technique and densitometry methods utilized a limited data set of 18 pairs, so statistically significant differences between the methods were not expected. Rigorous statistical comparison of correlation coefficients for the two methods would have required over 100 pairs of specimens, assuming underlying correlation coefficients of 0.8 and 0.9, 80% statistical power, and a"0.05 (Zar, 1984).
3. Results F and F were linearly related for the stance M%!4 FE configuration [r"0.867, p(0.0001, standard error of the estimate (S.E.E)"1.56 kN; Fig. 4a] and non-linearly related for the fall configuration [r"0.949, p(0.0001, S.E.E."0.0909 log (kN); Fig. 4b]. Logarithmic trans10 formations of the data were required for the fall configuration due to both nonlinearity and heteroscedasticity of the data (p"0.008). Data for one femur to be tested in the fall condition were lost due to mechanical error.
When the data for both loading conditions were pooled, logarithmic transformations were again necessary (Spearman test, p(0.0001), and backward stepwise regression revealed that the regression equation did not depend on loading condition (p"0.08). More importantly, inclusion of the terms related to loading condition increased R2 from 0.936 to 0.947, indicating that these terms accounted for only an additional 1.1% of the variance in F . In addition, the coefficients of the M%!4 regression equation were not significantly different after accounting for between-subjects variability. Therefore, the data for both loading conditions were described by a single power relation between F and F [r"0.967, M%!4 FE p(0.0001, S.E.E."0.0970 log (kN); Fig. 5]. This equa10 tion and the equation for the fall loading condition alone were nearly identical, further supporting the finding that the relationships for the stance and fall configurations were the same. Finally, the 95% confidence interval for an additional observation for this relationship spanned from !40% to #60% of F (Fig. 5). M%!4 Significant correlations between F and the denM%!4 sitometry data were found for the stance (r"0.781, p"0.0001, S.E.E."1.95 kN; Fig. 6a) and fall (r"0.906, p(0.0001, S.E.E."0.568 kN; Fig. 6b) loading conditions. These correlation coefficients were not significantly different from those for the CT/FE technique. However, statistical power was low, as explained previously.
4. Discussion In an effort to improve clinical and research tools for assessing hip fracture risk, we have shown that automatically generated CT scan-based FE models can predict
Fig. 4. Measured fracture load versus FE-predicted fracture load for the stance configuration (a) and fall configuration (b). These highly significant relationships indicate that CT scan-based FE models can be used to estimate femoral fracture load. Dashed lines indicate the bounds of the 95% confidence intervals for the regression equations (short dashes) and additional observations (long dashes).
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femoral fracture load in vitro for two very different loading conditions with a precision of !40% to #60%. This level of precision is comparable to that of the densitometry-based measures examined here. With respect to accuracy, the CT/FE technique tends to underestimate F , as indicated by the regression results. However, M%!4 this underestimation can be attributed to the fact that F was defined as the load at the onset of failure, FE
Fig. 5. Measured fracture load versus FE-predicted fracture load when data for both load configurations were pooled. A single power relation described the data for both configurations, indicating the robustness of the CT/FE technique. Circles and triangles indicate femora tested in the stance and fall configurations, respectively. Dashed lines indicate the bounds of the 95% confidence intervals for the regression equation (short dashes) and additional observations (long dashes).
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whereas F was defined as the load at the first peak of M%!4 the force-displacement curve. Therefore, the underestimation of F should not be viewed as a limitation M%!4 of the CT/FE technique, but rather as a result of the experimental method. The precision of the CT/FE technique is comparable to that of densitometry methods reported previously. For the stance configuration, the correlation for the CT/FE technique (r"0.87) is as strong as correlations found in previous studies using dual photon absorptiometry (r"0.74) (Beck et al., 1990), QCT (r"0.79) (Alho et al., 1988), and engineering-related methods (r"0.89 in two studies) (Beck et al., 1990; Gies et al., 1985). For the fall configuration, the correlation coefficient for the CT/FE technique (r"0.95) is statistically comparable to coefficients for the strongest correlations reported by Courtney et al. (1994, 1995) (r"0.80—0.96), who used DXA and loading representing impact from a fall to the side. It should be noted that the CT/FE technique is still in its infancy and significant improvements in precision may be achieved through refinements, most importantly in the area of material representation. For example, the current approach relied upon isotropic material properties that had been determined by testing specimens in compression in their most stiff and strong direction; element moduli and strengths for the other directions were therefore overstated. Use of anisotropic mechanical properties (Ciarelli et al., 1991; Keyak et al., 1994; Reilly and Burstein, 1975; Van Buskirk and Ashman, 1981) and accounting for the fact that bone material strength is about 30% lower in tension than in compression (Currey, 1970; Keaveny et al., 1994a,b; Reilly and Burstein, 1975) may improve FE model predictions. However, such
Fig. 6. Measured fracture load versus subcapital density for the stance configuration (a), and measured fracture load versus intertrochanteric density multiplied by area for the fall configuration (b). The correlation coefficients for these regression equations are statistically comparable to those for the CT/FE technique (Fig. 4). Dashed lines indicate the bounds of the 95% confidence intervals for the regression equations (short dashes) and additional observations (long dashes).
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improvements would require special failure theories, and none have been validated for bone at this time. A more practical first step toward improving model precision may be achieved by simply using smaller elements to better represent material heterogeneity and bone geometry. Finally, restriction of the analysis to linear material behavior, which maintained computational time at practical levels, was an important limitation because it precluded modeling past the onset of failure. The ability of the FE models to account for loading condition represents a major advance over densitometry techniques, making it possible to calculate fracture loads for real-life loading conditions on a patient-specific basis. These fracture loads can then be compared with loads occurring in vivo in order to assess fracture risk, either for research or for clinical applications. Specifically, use of this technology in research may help us identify the most risky loading conditions and improve our understanding of the mechanisms of hip fracture so that preventive measures, either medical (Ettinger, 1985, 1993; Liberman et al., 1995; Reid et al., 1994; Stone, 1993) or biomechanical (Lauritzen et al., 1993), can be directed optimally. The results of the present study are applicable to most of the elderly population because there were no restrictions based on medical history. Although all donors were Caucasian, lack of diversity should not affect generality of the results because the CT/FE technique can account for differences in bone size and density, the most important race-related parameters. Three of the donors died from cancer, and the cancer had metastasized extensively to the bones in one of these cases. In addition, it is likely that other femora came from donors with other diseases or treatments that could have affected bone strength. Despite these potentially confounding variables, there were no obvious outliers in the data. This result is especially surprising in the case of the femora with metastatic tumors, as it has not been shown that the material property relationships used in generating the FE models are valid for bone with tumors. Thus, these results suggest that CT scan-based FE models may be useful for assessing fracture load in highly pathological conditions. This study has shown that automatically generated CT scan-based FE models can be used to estimate femoral fracture load under two very different loading conditions. However, the precision of this technique is comparable to that of densitometry methods such as DXA and QCT. Therefore, clinical use of this approach, which would require additional X-ray exposure and expenditure for a full CT scan of the femur, is not justified at this stage of development. Even so, the potential advantages of this CT/FE technique, i.e. its ability to account for the effects of 3-D geometry, material heterogeneity, and loading conditions, all at relatively low cost, support further research in this area.
Acknowledgements This work was funded by the Department of Veterans Affairs, Rehabilitation R & D Service. Mechanical testing was performed at the University of California, San Francisco Orthopaedic Biomechanics Laboratory. Femora were provided by the University of California, San Francisco Tissue Bank; University of California, San Francisco Department of Anatomy; University of California, Irvine Organ and Tissue Bank; and National Disease Research Interchange. The authors thank Marina Pejcic for her assistance. References Alho, A., Husby, T., Hoiseth, A., 1988. Bone mineral content and mechanical strength. An ex vivo study of human femora at autopsy. Clinical Orthopaedics and Related Research 227, 292—297. Backman, S., 1957. The proximal end of the femur. Investigations with special reference to the etiology of femoral neck fractures. Anatomical studies. Roentgen projections. Theoretical stress calculations. Experimental production of fractures. Acta Radiologica Supplementum 146. Beck, T.J., Ruff, C.B., Warden, K.E., Scott, W.W., Jr., Rao, G.U., 1990. Predicting femoral neck strength from bone mineral data. A structural approach. Investigative Radiology 25, 6—18. Cann, C.E., 1988. Quantitative CT for determination of bone mineral density: a review. Radiology 166, 509—521. Ciarelli, M.J., Goldstein, S.A., Kuhn, J.L., Cody, D.D., Brown, M.B., 1991. Evaluation of orthogonal mechanical properties and density of human trabecular bone from the major metaphyseal regions with materials testing and computed tomography. Journal of Orthopaedic Research 9, 674—682. Courtney, A.C., Wachtel, E.F., Myers, E.R., Hayes, W.C., 1994. Effects of loading rate on strength of the proximal femur. Calcified Tissue International 55, 53—58. Courtney, A.C., Wachtel, E.F., Myers, E.R., Hayes, W.C., 1995. Agerelated reductions in the strength of the femur tested in a fall-loading configuration. Journal of Bone and Joint Surgery 77-A, 387—395. Cummings, S.R., Kelsey, J.L., Nevitt, M.C., O’Dowd, K.J., 1985. Epidemiology of osteoporosis and osteoporotic fractures. Epidemiologic Reviews 7, 178—208. Cummings, S.R., Black, D.M., Nevitt, M.C., Browner, W., Cauley, J., Ensrud, K., Genant, H.K., Palermo, L., Scott, J., Vogt, T.M., 1993. Bone density at various sites for prediction of hip fractures. The Lancet 341, 72—75. Currey, J.D., 1970. The mechanical properties of bone. Clinical Orthopaedics and Related Research 73, 210—231. Esses, S.I., Lotz, J.C., Hayes, W.C., 1989. Biomechanical properties of the proximal femur determined in vitro by single-energy quantitative computed tomography. Journal of Bone and Mineral Research 4, 715—722. Ettinger, B., Genant, H.K., Cann, C.E., 1985. Long-term estrogen replacement therapy prevents bone loss and fractures. Annals of Internal Medicine. 102, 319—324. Ettinger, B., 1993. An update for the obstetrician-gynecologist on advances in the diagnosis, prevention, and treatment of postmenopausal osteoporosis. Current Opinion in Obstetrics and Gynecology 5, 396—403. Faulkner, K.G., Cummings, S.R., Black, D., Palermo, L., Glueer, C.C., Genant, H.K., 1993. Simple measurement of femoral geometry predicts hip fracture: The study of osteoporotic fractures. Journal of Bone and Mineral Research 8, 1211—1217.
J.H. Keyak et al. / Journal of Biomechanics 31 (1998) 125—133 Frankel, V.H., 1960. The Femoral Neck: Function, Fracture Mechanism, Internal Fixation; An Experimental Study. Almqvist and Wiksell, Stockholm. Gies, A.A., Carter, D.R., Sartoris, D.J., Sommer, F.G., 1985. Femoral neck strength predicted from dual energy projected radiography. Transactions of the Orthopaedic Research Society 10, 357. Glantz, S.A., Slinker, B.K., 1990. Primer of Applied Regression and Analysis of Variance, pp. 381—390. McGraw-Hill, New York. Glueer, C.C., Cummings, S.R., Pressman, A., Li, J,, Glueer, K., Faulkner, K.G., Grampp, S., Genant, H.K., the Study of Osteoporotic Fractures Research Group., 1994. Prediction of hip fractures from pelvic radiographs: the study of osteoporotic fractures. Journal of Bone and Mineral Research 9, 671—677. Grampp, S., Jergas, M., Glueer, C.C., Lang, P., Brastow, P., Genant, H.K., 1993. Radiologic diagnosis of osteoporosis. Current methods and perspectives. Radiologic Clinics of North America 31, 1133—1145. Graves, E., 1992. Detailed diagnoses and procedures, national hospital discharge survey, 1990. Vital and Health Statistics, Series 13, no. 113. Pub. (PHS)92-1774, U.S. Dept. of Health and Human Services, Public Health Svc., National Center for Health Statistics, Hyattsville, Maryland. Holbrook, T.L., Grazier, K., Kelsey, J.L., Stauffer, R.N., 1984. The Frequency of Occurrence, Impact and Cost of Selected Musculoskeletal Conditions in the United States. American Academy of Orthopaedic Surgeons, Chicago, IL. Keaveny, T.M., Guo, X.E., Wachtel, E.F., McMahon, T.A., Hayes, W.C., 1994a. Trabecular bone exhibits fully linear elastic behavior and yields at low strains. Journal of Biomechanics 27, 1127—1136. Keaveny, T.M., Wachtel, E.F., Ford, C.M., Hayes, W.C., 1994b. Differences between the tensile and compressive strengths of bovine tibial trabecular bone depend on modulus. Journal of Biomechanics 27, 1137—1146. Keller, T.S., 1994. Predicting the compressive mechanical behavior of bone. Journal of Biomechanics 27, 1159—1168. Kenzora, J.E., McCarthy, R.E., Lowell, J.D., Sledge, C.B., 1984. Hip fracture mortality. Relation to age, treatment, preoperative illness, time of surgery, and complications. Clinical Orthopaedics and Related Research 186, 45—56. Keyak, J.H., Lee, I.Y., Skinner, H.B., 1994. Correlations between orthogonal mechanical properties and density of trabecular bone: use of different densitometric measures. Journal of Biomedical Materials Research 28, 1329—1336. Keyak, J.H., Meagher, J.M., Skinner, H.B., Mote, C.D., Jr, 1990 Automated three-dimensional finite element modelling of bone: a new method. Journal of Biomedical Engineering 12, 389—397. Lang, P., Steiger, P., Faulkner, K., Gluer, C., Genant, H.K., 1991. Osteoporosis. Current techniques and recent developments in quantitative bone densitometry. Radiologic Clinics of North America 29, 49—76. Lauritzen, J.B., Petersen, M.M., Lund, B., 1993. Effect of external hip protectors on hip fractures. The Lancet 341, 11—13. Les, C.M., Keyak, J.H., Stover, S.M., Taylor, K.T., Kaneps, A.J., 1994. The estimation of material properties in the equine metacarpus using
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quantitative computed tomography. Journal of Orthopaedic Research 12, 822—833. Liberman, U.A., Weiss, S.R., Broll, J., Minne, H.W., Quan, H., Bell, N.H., Rodriguez-Portales, J., Downs, R.W., Dequeker, J., Favus, M., Seeman, E., Recker, R.R., Capizzi, T., Santora, A.C., Lombardi, A., Shah, R.V., Hirsch, L.J., Karpf, D.B., 1995. Effect of oral alendronate on bone mineral density and the incidence of fractures in postmenopausal osteoporosis. New England Journal of Medicine 333, 1437—1443. Lotz, J.C., Hayes, W.C., 1990. The use of quantitative computed tomography to estimate risk of fracture of the hip from falls. Journal of Bone and Joint Surgery 72-A, 689—700. Mazess, R.B., Barden, H., Ettinger, M., Schultz, E., 1988. Bone density of the radius, spine, and proximal femur in osteoporosis. Journal of Bone and Mineral Research 3, 13—18. Melton, L.J., III, Wahner, H.W., Richelson, L.S., O’Fallon, W.M., Riggs, B.L. 1986. Osteoporosis and the risk of hip fracture. American Journal of Epidemiology 124, 254—261. Miller, C.W., 1978. Survival and ambulation following hip fracture. Journal of Bone and Joint Surgery 60-A, 930—934. Mullen, J.O., Mullen, N.L., 1992. Hip fracture mortality. A prospective, multifactorial study to predict and minimize death risk. Clinical Orthopaedics and Related Research 280, 214—222. Perloff, J.J., McDermott, M.T., Perloff, K.G., Blue, P.W., Enzenhauer, R., Sieck, E., Chantelois, A.E., Dolbow, A., Kidd, G.S., 1991. Reduced bone-mineral content is a risk factor for hip fractures. Orthopaedic Review 20, 690—698. Praemer, A., Furner, S., Rice, D.P., 1992. Musculoskeletal Conditions in the United States. American Academy of Orthopaedic Surgeons, Chicago, IL. Reid, I.R., Wattie, D.J., Evans, M.C., Gamble, G.D., Stapleton, J.P., Cornish, J., 1994. Continuous therapy with pamidronate, a potent bisphosphonate, in postmenopausal osteoporosis. Journal of Clinical Endocrinology and Metabolism, 79, 1595—1599. Reilly, D.T., Burstein, A.H., 1975. The elastic and ultimate properties of compact bone tissue. Journal of Biomechanics 8, 393—405. Riggs, B.L., Wahner, H.W., Seeman, E., Offord, K.P., Dunn, W.L., Mazess, R.B., Johnson, K.A., Melton, L.J., III, 1982. Changes in bone mineral density of the proximal femur and spine with aging: Differences between the postmenopausal and senile osteoporosis syndromes. Journal of Clinical Investigation 70, 716—723. Stone, M., 1993. Didronel PMO. British Journal of Hospital Medicine 49, 275—277. Van Buskirk, W.C., Ashman, R.B., 1981. The elastic moduli of bone. Trans. American Society of Mechanical Engineers (Applied Mechanics Division) 45, 131—143. Vega, E., Mautalen, C., Gomez, H., Garrido, A., Melo, L., Sahores, A.O., 1991. Bone mineral density in patients with cervical and trochanteric fractures of the proximal femur. Osteoporosis International 1, 81—86. White, B.L., Fisher, W.D., Laurin, C.A., 1987. Rate of mortality for elderly patients after fracture of the hip in the 1980’s. Journal of Bone and Joint Surgery 69-A, 1335—1340. Zar, J.H., 1984. Biostatistical Analysis, pp. 115—118, 309—315. PrenticeHall, Englewood Cliffs, NJ.