Trabecular Bone Contributes to Strength of the Proximal Femur Under Mediolateral Impact in the Avian N. Passi A. Gefen1 e-mail: [email protected] Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel Background: Osteoporosis in long bones involves loss of cortical thickness and of the trabecular microarchitecture. Deterioration and weakening of trabecular bone tissue during osteoporosis imposes greater physiological loads on the cortical shell. However, it is unclear whether trabecular bone significantly contributes to the strength of whole bones under non-physiological impact loads. Method of Approach: We hypothesize that trabecular tissue in epiphyses of long bones contributes to resisting and distributing impact loads. To test this hypothesis, we caused artificial trabecular bone loss in proximal femora of adult hens but did not alter the bone cortex. Subsequently, we compared the energy required to fracture the proximal part of femora with missing trabecular tissue with the energy required to fracture control femora, by means of a Charpy test. Results: Extensive loss of trabecular bone in hens (over 0.50 grams or ⬃71% weight fraction) significantly reduced the energy required to fracture the whole proximal femur in mediolateral impacts (from ⬃0.37 joule in controls to ⬃0.20 joule after extraction of core trabecular tissue). Conclusions: These findings indicate that trabecular bone in the proximal femur is important for distributing impact loads applied to the cortex, and support the concept that in treating osteoporosis to prevent hip fractures, it is just as important to prevent trabecular bone loss as it is important to prevent loss of cortical thickness. 关DOI: 10.1115/1.1835366兴 Keywords: Mechanical Properties, Fracture, Aging, Osteoporosis, Chicken 1 Introduction Osteoporosis is responsible for about 300 000 hip fractures per year in the United States 关1,2兴. The initial bone loss in the proximal femur is of trabecular bone, and loss of cortical thickness follows 关3–5兴. In postmenopausal osteopenic American women, bone loss in the proximal femur consists of ⬃35% of cortical thickness and ⬃50% of trabecular epiphyseal tissue 关3,4兴. It is commonly accepted that as trabecular tissue deteriorates and weakens, more physiological loads are borne by the cortical shell. However, it is unclear whether this manifests under nonphysiological, traumatic impact loads. Specifically, it is unclear whether fragility of an osteopenic femur under a traumatic impact load is caused by decreased cortical thickness, lack of trabecular support, or a combination of both. In order to study the contribution of trabecular bone to strength of a whole epiphyseal and metaphyseal bone under impact, we developed a simple in vitro model using a chicken femur subjected to a pendulum impact. The mechanical properties of avian bones have received less attention in the literature with respect to mammalian bones. Nev1 To whom correspondence should be addressed. Contributed by the Bioengineering Division for publication in the JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received by the Bioengineering Division December 9, 2003; revision received August 18, 2004. Associate Editor: David Fyhrie. 198 Õ Vol. 127, FEBRUARY 2005 ertheless, several comparative studies of mechanical properties of avian and mammalian long bones were conducted in the 1940s 关6兴, and all showed consistent similarity in mechanical properties of femoral bones between mammals and birds. The overlapping properties included the elastic modulus of cortical bone 共17 to 20 GPa兲, ultimate tensile strength of the femoral diaphysis when tested under 3-point bending 共100 to 300 MPa兲, and failure tensile strain when tested in 3-point bending 共6 000 to 14 000 microstrain兲 关7–10兴. Differences between mechanical properties of mammals and birds within these limited ranges were considered to reflect minor skeletal adaptations to the specific mechanical functions related to locomotion of the species 关10,11兴. It should be mentioned that intrinsic fatigue strength of whole chicken bone 共tibia兲 is only 60% that of human 关12兴, but for single-impact testing, chicken bones can still serve as a valid substitute for human bones. Gross structural differences between human and avian femurs are more apparent. In humans, the femur is the longest and most massive bone, but in birds it is reduced in size and mass compared with the tibiotarsus of the avian skeleton 共Fig. 1; left scheme兲. Importantly, both birds and humans have a very distinctive ball joint on their proximal femurs. The microstructural characteristics of cortical and cancellous bone in humans and hens are very similar. The density of cortical bone in mature hens 共in the tibia兲 was reported to be 1.79 ⫾0.19 g/cc (mean⫾standard deviation, 关13兴兲, which is well within the range of cortical bone densities reported for the human proximal femur 共1.5–2 g/cc 关14兴兲. Likewise, apparent density of avian trabecular bone, 0.3 g/cc in hens 关15兴 and 0.4 g/cc in turkeys 关16兴, is in the range of apparent trabecular bone density in human proximal femora 共0.2–0.6 g/cc 关14,17兴兲. Trabecular bone volume in hens 共14% in epiphyses of several medullary bones, 关18兴兲 also resembles that in the femoral neck of humans 共17%, 关19兴兲. Taken together, the above-listed similarities in mechanical and structural properties indicate that the chicken femur is an adequate model for the purpose of the present study. Considering also their availability and low cost, long bones from chickens are advantageous for conducting experimental studies that require many specimens, as in our present destructive 共impact兲 tests. The effect of trabecular bone loss on whole bone mechanics under impact is critical to understanding the susceptibility to hip fractures among the osteopenic population. We hypothesize that trabecular bone in epiphyses of long bones contributes to resisting and distributing impact loads applied to the epiphyseal or metaphyseal cortex. This function may be analogous to the function of the trabecular lattice in distributing physiological 共joint and muscle兲 loads, however, since trabecular paths are aligned to provide maximal support in the directions of the physiological 共joint/ muscle兲 loads, the trabecular lattice is unlikely to be optimized for supporting nonphysiological impacts 共as during traumatic injury兲. To test whether the trabecular lattice in the avian contributes to strength under impact loading, we caused artificial trabecular bone loss in proximal femora of adult chickens 共but did not alter the bone cortex兲. Subsequently, we compared the energy required to fracture the proximal femora with missing trabecular tissue with the energy required to fracture control femora, by means of a Charpy test. 2 Methods We conducted pendulum fracture experiments on 142 femora of adult hens 共female chickens older than 10 months of age with completely ossified bones, classified as ‘‘baking chicken’’ or ‘‘stewing chicken’’ or ‘‘fowl’’ according to the definitions of the U.S. Department of Agriculture 关20兴兲. The weight of carcasses of these hens ranged between 2.3 and 3.2 kg, and the diameters of the central diaphysis of their femora ranged between 11 and 13 mm. Femora were obtained fresh from a local slaughterhouse and prepared for testing as described below less than 24 h after the hens were sacrificed. Copyright © 2005 by ASME Transactions of the ASME Fig. 1 Longitudinal cross sections through proximal femora of „a… poultry „with the limb skeleton shown on the left… and „b… human. Cross sections are scaled to similar size to allow comparisons of proportional thickness of the cortex and the trabecular architecture. Architecture of the avian femur was depicted based on anatomical observations by the authors. Dominant stresses on the human femoral cortex are marked with bold arrows „tension ]\; compression „\]…. In preparation for testing, the soft connective tissues were gently removed from the proximal end of the femora, and each femur was cut transversely at the center of the diaphysis. Through the open medullary canal, bone marrow was gently sucked out from the proximal femur. It has been reported that mechanical properties of bone specimens that were frozen at ⫺20°C 共for less than 100 days兲 and subsequently thawed to room temperature were indistinguishable from properties of fresh bones 共for trabecular tissue, cortical tissue, and whole bones兲 关21,22兴. Based on these reports, we stored the fresh cleaned bone specimens frozen at ⫺20°C until the day of testing 共no longer than 3 months from the time of freezing兲. Specimens were thawed to room temperature (25°C) 2 h before impact testing, and were kept moist until testing. Each femoral specimen was tested by applying an impact load distal to the ball of the hip joint, using a low impact pendulum testing machine 共LIPTM, Instron Dynatup POE 2000兲. This system incorporates a rigid, compound pendulum mounted on a reduced friction shaft assembly and a solid, vibration-free base 关Fig. 2共a兲兴. Upon release of the pendulum of the LIPTM, a standard Charpy hammer 关radius of curvature: 1.5 mm; Fig. 2共b兲兴 imposed an impact load on the specimen just distal to the femoral head while the ends of the specimen were held in specially designed jigs 关Fig. 2共b兲兴. To secure the specimen, a plastic tie strap was tightly wrapped around the distal part of the specimen and the corresponding jig 关Fig. 2共b兲兴. Specimens were consistently positioned so that the medial aspect of the femur was facing the Charpy hammer 关Fig. 2共b兲兴. This ensured that the lateral proximal aspect of the bone was subjected to maximal tensile stress during Journal of Biomechanical Engineering impact. The potential energy for producing the pendulum strike, E p , calculated as the product of pendulum weight and height of release with respect to the center of strike, was measured by the LIPTM system using a digital encoder connected to a PC for data acquisition and display. The energy required to fracture unaltered 共normal兲 chicken femora was measured first. Forty-eight specimens were divided into six groups that were subjected to increasing levels of potential 共release兲 energy (E p ), of 0.24 –0.36 joule (N⫽15), 0.37 joule (N⫽5), 0.48 joule (N⫽5), 0.58 joule (N⫽9), 0.87 joule (N ⫽9), and 1.19 joule (N⫽5). After each impact test, we classified the effect that the strike had on the specimen as one of three options: complete break ‘‘C,’’ partial break ‘‘P,’’ or nonbreak ‘‘NB.’’ Each femur specimen was only used once for impact testing, regardless of the outcome of the test. An additional 107 femoral specimens were used to determine the contribution of trabecular bone integrity to strength of the proximal femur under mediolateral impact. In this phase of the study, we applied E p levels that ranged between 0.15 joule and 0.41 joule on 12 unaltered specimens and on 95 specimens from which varying amounts of core epiphyseal trabecular tissue were removed 关Fig. 2共b兲兴. Specifically, we impacted 12 unaltered specimens, 20 altered specimens 共with trabecular bone removed兲 at E p levels of 0.18 joule or less, 21 altered specimens at 0.18⬍E p ⭐0.24 joule, 26 altered specimens at 0.24⬍E p ⭐0.30 joule, 26 altered specimens at 0.30⬍E p ⭐0.36 joule, and 2 altered specimens at E p levels of over 0.36 joule. Before extracting trabecular tissue, bone specimens were weighed using a precision digital scale 共resolution 0.01 g兲. A speFEBRUARY 2005, Vol. 127 Õ 199 Fig. 2 The experimental setup: „a… The low impact pendulum testing machine „LIPTM…; „b… illustrations of specimen preparation showing removal of core trabecular tissue „upper right… and the proximal femur specimen fixed prior to impact testing „left…. The Charpy hammer „design shown on bottom right… strikes under the femoral head. cial miniature hand drill was inserted via the medullary canal to remove core trabecular tissue 关Fig. 2共b兲兴. By slowly rotating the hollow-toothed head of the drill while it was pressing against the epiphysis, it was possible to remove varying weights of epiphyseal trabecular tissue, ranging between 0.03 g to 0.64 g. Care was taken during removal of the trabecular tissue not to damage or notch the cortex of bone. The weight of detached trabecular tissue was obtained by subtracting the weight of the specimen after drilling from its original weight. Femur specimens from which core trabecular tissue was removed were tested using the same testing procedure described for unaltered specimens. To approximate the weight fraction of trabecular epiphyseal tissue that was removed from the proximal femur, we studied 15 additional femora that were assigned for this purpose. Each specimen was cut along the longitudinal direction of the femur using a hand-held electrically powered saw equipped with a diamond200 Õ Vol. 127, FEBRUARY 2005 coated rotating minisaw blade 共Dremel Co.兲. The complete trabecular contents was manually scraped from the epiphysis and weighed. The mean weight, W T , was determined. The weight of trabecular tissue that was removed prior to each impact trial, W, was divided by W T to approximate the weight fraction of the trabecular tissue that was removed. To determine the strain rate to which bones were subjected during our impact tests, we instrumented three proximal femur specimens 共with trabecular tissue intact, and which had not been subjected to any previous testing兲 with strain gauges 共CEA-06240UZ-120, Micro-Measurements Co.兲. On each specimen, a strain gauge was mounted at the lateral aspect of the proximal femur 关Fig. 2共b兲兴 on a region opposite to the site of impact 共where maximal tension was expected兲. After the site of adhesion was dried locally 共but the rest of the specimen was kept moist兲, a strain gauge oriented longitudinally was fixed to the cortical surface Transactions of the ASME Fig. 3 Results of impact testing: „a… distribution of outcomes of impact testing of control specimens „ N Ä35… depending on the impact energy E p , and „b… outcomes of fracture tests with noncontrol specimens „ N Ä95… plotted as function of the amount of core trabecular tissue that was extracted from the epiphysis in each trial „absolute weight W and weight fraction in %…. A region of ‘‘no-break’’ outcomes „shaded… and a ‘‘break’’ threshold „dashed line… are marked. NBÄno break, PÄpartial break, CÄcomplete break. using superglue. The potential energy for impact was set as 0.3 joule, to correspond to the mean potential energy used during our experiments of trabecular removal. To verify uniformity of geometry among our test specimens, we measured cortical thickness in fifteen proximal epiphyses of new femora 共which had not been used in previous tests兲 around the region assigned for impact. We also measured the volume of fifteen other intact specimens by immersing them in distilled water. Subsequently, we verified uniformity in bone structural strength and stiffness among specimens by conducting slow 共1 mm/min兲 3-point bending experiments using an Instron electromechanical testing system 共model 5544兲 on ten additional new femora. To statistically test the hypothesis of this study, we conducted three one-way analysis of variance 共ANOVA兲 tests. The first ANOVA tested whether the removed trabecular weight (W) was different between the three fracture groups 共i.e., NB⫽nonbreak, P⫽partial break, or C⫽complete break). The second ANOVA tested whether the energy applied to impact the specimen (E p ) was different among the three fracture groups. Finally, the third ANOVA tested whether the interaction W⫻E p was different beJournal of Biomechanical Engineering tween the three fracture groups. The ANOVA which compared the interaction term (W⫻E p ) across the three fracture groups was used to test whether the effect of energy (E p ) on the fracture outcome 共NB, P, or C兲 depended on the value of extracted trabecular weight (W). Post hoc Tukey-Kramer multiple comparisons followed each ANOVA to identify specific differences between the parameters W, E p , and W⫻E p across the fracture outcome groups. A p value lower than 0.05 was considered statistically significant. 3 Results The distribution of test outcomes depending on the impact energy E p for the 48 unaltered specimens is shown in Fig. 3共a兲. The greatest impact energy E p 共1.19 joule兲 resulted in four complete breaks and one nonbreak. A lower E p energy of 0.37 joule resulted in four nonbreaks and one complete break. Additional tests (N ⫽15) conducted on control femora using impact energies E p in the range of 0.24 joule to 0.36 joule never resulted in failure of the specimen 共partial or complete兲. For E p ⫽0.3 joule, which did not FEBRUARY 2005, Vol. 127 Õ 201 break femora with intact trabecular tissue, our strain measurements consistently resulted in a peak strain of ⬃0.18% 共1800 microstrain兲 and strain rate of ⬃10%/s 共100 000 microstrain/s兲. The outcomes of fracture tests conducted with 107 additional femora, of which 95 were manipulated to reduce the trabecular content in the proximal epiphysis, were plotted as a function of the amount of core trabecular tissue that was extracted in each trial 关Fig. 3共b兲兴. The mean weight of the complete trabecular contents of the proximal epiphysis (W T ) was 0.7⫾0.08 g (mean ⫾standard deviation兲. Removal of over 0.05 g (⬃7% weight fraction兲 of trabecular tissue caused partial or complete failures in 37 of the 93 trials conducted with impact energies of 0.36 joule or less. Measurements of geometry and structural mechanical properties verified the uniformity of the test specimens. Specifically, cortical thickness of femoral specimens 共mean: 1.2 mm兲 showed only small variation 共standard deviation: 8%兲. Likewise, volume of specimens 共mean 11.7 ml兲 showed small variation 共standard deviation: 7%兲. Structural strength and structural stiffness were 210⫾12 共6%兲 N and 100⫾17 共17%兲 N/mm, respectively (mean ⫾standard deviation). The ANOVA tests showed that the removed trabecular weight (W), the energy (E p ) and the interaction term (W⫻E p ) were all significantly different (p⬍0.01) among the three fracture groups 共NB, P, C兲. Specifically, Tukey-Kramer analyses showed that 共i兲 The ‘‘complete break’’ and ‘‘partial break’’ groups were statistically indistinguishable 共i.e., all three parameters, W, E p , and W ⫻E p , were statistically similar between these two groups兲. 共ii兲 The complete break and nonbreak groups differed significantly in both E p (pⰆ0.01) and W (p⬍0.05). 共iii兲 Importantly, the interaction term W⫻E p was significantly different between the complete break and nonbreak groups (pⰆ0.01) and between the partial break and non-break groups (p⬍0.01), thus indicating that the effect of energy (E p ) on the fracture outcome 共NB, P, or C兲 depended on the value of extracted trabecular weight (W). 4 Discussion The results of this study support the hypothesis that trabecular tissue in epiphyses of long bones contributes to resisting and distributing impact loads that induce tension in the lateral aspect of the proximal femur. Relatively small variations in geometry and structural properties across femoral specimens were measured, and so we concluded that our femoral specimens were sufficiently uniform for the impact studies. Unaltered proximal femora 共with intact trabecular tissue兲 never broke 共fully or partially兲 when tested under impact energies E p of 0.36 joule or less 关Fig. 3共a兲兴. We concluded that the lowest impact energy that can fracture a normal proximal femur of an adult chicken is 0.37 joule. Accordingly, we designed the subsequent experiments with specimens that underwent extraction of trabecular tissue, so that 93 of the 95 specimens were impacted with E p levels of 0.36 joule or less. It is evident from Fig. 3共b兲 that lower impact energies are required to fracture the proximal femora of chickens after more than 0.05 grams (⬃7% weight fraction兲 of core trabecular tissue were extracted from the epiphysis. For example, when a substantial amount 关over 0.50 grams (⬃71% weight fraction兲兴 of trabecular tissue was removed, partial fractures were caused by energies of less than 0.20 joule, which were clearly insufficient to fracture control specimens, or specimens from which less than 0.25 grams (⬃36% weight fraction兲 of trabecular tissue was extracted 共Fig. 3兲. We concluded that trabecular tissue contributes to strength of avian epiphyses under impact loading. An energy-weight curve describing a no-break region was obtained by fitting a hyperbolic function to the ‘‘partial fracture’’ cases that occurred when W⫻E p was minimal 关Fig. 3共b兲兴. This curve, which satisfies the hyperbolic relation E p ⬍ ␣ /W  , defines a distinct no-break zone where ␣ ⫽0.122 关joule兴 and  ⫽0.279 were calculated using a least-squares fit 共EXCEL, Microsoft Co.兲. 202 Õ Vol. 127, FEBRUARY 2005 Similarly, E p values that always produced a ‘‘break’’ outcome 共partial or complete兲 were characterized using the linear relation E p ⬎⫺ ␥ W⫹ ␦ 共for W⬎0) where the constants are ␥ ⫽0.44 关joule/g兴 and ␦ ⫽0.47 关joule兴 关Fig. 3共b兲, dashed line兴. This linear boundary for the break region was plotted so that all nonbreak cases were contained under it. The distribution of experimental points determines the uniqueness of this linear break boundary. The area bounded between these no-break and break functions shows a transition from a greater number of no-break cases in proximity to the no-break zone to a majority of break cases in proximity to the break threshold 关Fig. 3共b兲兴. In early stages of osteoporosis, the dominant changes in bone architecture are thinning of trabeculae and increased intertrabecular spaces. However, in progressive osteoporosis, substantial voids may appear in the proximal femur due to coupled accumulative mechanical failure of abnormally thin trabeculae and accelerated bone mass resorption 关23兴. In these progressive stages, resorption of all trabecular groups 共except some of the trabecular paths in the ‘‘principal compressive’’ group兲 occurs 关24兴. In the most severe forms of osteoporosis, even these latter ‘‘principal compression’’ trabecular paths may be obliterated partially or completely, so that the femoral head and neck become nearly void 关24兴. Our protocol of removing core trabecular tissue best represents partial or complete resorption of the secondary compressive and tensile groups 关which are the first to meet the driller, Fig. 2共b兲兴. This condition is analogous to an osteoporotic femur with a Singh index of severity that is 4 or over 关24兴. Our experimental procedure of removing core trabecular tissue therefore limits the interpretation of the results to progressive human osteoporosis 共Singh index ⭓4). In weight-bearing human and chicken femora, the proximal lateral aspect of the femur is subjected to tensile stress due to bending by the hip joint load and due to tension by the abductor muscles 关Fig. 1共b兲兴. Since whole bones resist compression better than they resist tension 关25兴, we theorized that fractures in bending initiate at regions subjected to tension. Hence, we chose to induce tension on a bone surface that is physiologically adapted to bear 共bending-related兲 tensile stress. Although this loading configuration does not represent a specific injury scenario in humans, it may simulate some aspects of stumbling during which rapid bending-related tension acts on the lateral proximal femur. However, loading of the femur during the ground-contact phase of falling is not represented by the present experimental design. Loading from a fall usually induces opposing compressive forces to the greater trochanter and femoral head, and the distal aspect of the femur is loaded mainly through the inertial effects of the limb 关26兴. The lateral aspect of the proximal femur just distal to the region of impact is subjected to considerable amount of torsion 关26兴, which could not be produced with the present experimental apparatus. However, it is reasonable to assume that sudden torsional loading of the lateral proximal femur may produce similar experimental results to the ones presented herein for sudden tensile loading, since bone tissue is not well-suited to withstand either tension or torsion 关25兴. An interesting application of this study, which utilized chicken femora, is in investigating the effects of osteoporosis in laying hens. Osteoporosis in laying hens is a major problem in poultry science 关27,28兴. Similar to human osteoporosis associated with immobilization, osteoporosis in egg-laying hens housed densely in cages is a condition that involves progressive loss of bone structure during the laying period. Administration of steroids to increase muscle mass 共in order to increase revenue from meat兲 is also likely to play a role in bone degradation 关27兴. Tibial bones of mature 共22-week-old兲 turkeys that were treated with dexamethasone 共a synthetic steroid similar to steroid hormones produced naturally in the adrenal gland兲 had significantly decreased strength and stiffness with respect to controls, and in immature turkeys 共7-week-old兲, steroid administration stunted bone growth 关27兴. Transactions of the ASME The mechanism for these changes was suggested to be inhibition of recruitment of osteoblasts by the steroid, which prevents normal bone formation 关27兴. The bone loss due to immobilization 共and possibly, steroid administration兲 results in increased bone fragility and susceptibility to fracture in hens, with fracture incidences of over 30% during a laying period due to traumatic loads caused throughout routine handling such as during depopulation, transport to a processing factory, or hanging the chicken on shackles. Surprisingly, 98% of chicken carcasses are found to contain broken bones when reaching the end of the evisceration line during processing 关27兴. Production losses due to hen osteoporosis have directed substantial research efforts to minimize this problem, e.g., administration of higher calcium diet, chicken growth hormone, or selective breeding 关28,29兴. The contribution of the present study to these efforts is in indicating that the quality of trabecular bone in laying hens should be considered 共in addition to cortical thickness兲 and be compared across preventive interventions to help minimizing the scale of this problem. In closure, quantification of the load sharing between cortical and trabecular bone during impact is essential for understanding the risk for hip fractures. In sites of dominant trabecular content 共such as in the femoral neck or vertebrae兲, trabeculae were shown to provide a substantial portion of the mechanical integrity of the structure during static or slow loading 关30,31兴. The present study is the first to provide experimental evidence for the importance of trabecular tissue for withstanding impact loads. These results are consistent with those from studies that were conducted using static or slow loading velocities 关30,31兴: trabecular tissue is a significant contributor to whole bone strength. Acknowledgments This study was supported by the Ela Kodesz Institute for Medical Engineering and Physical Sciences and by the Internal Fund of Tel Aviv University, Israel. Mr. Arie Dar from Ammo Engineering Co., Israel, is thanked for his technical assistance with the LIPTM. Mr. Tal Raich from the Musculoskeletal Biomechanics Laboratory of the Department of Biomedical Engineering at Tel Aviv University is appreciated for designing and building the jigs for impact testing of chicken bones. Ms. Ronit Twaig and Mr. Josh Levine from the Musculoskeletal Biomechanics Laboratory are thanked for their technical assistance. References 关1兴 Ray, N. F., Chan, J. K., Thamer, M., and Melton, L. J., 1997, ‘‘Medical Expenditures for Treatment of Osteoporotic Fractures in the United States in 1995: Report from the National Osteoporosis Foundation,’’ J. Bone Miner. Res., 12, pp. 24 –35. 关2兴 National Osteoporosis Foundation, Disease Statistics, www.nof.org 关3兴 Seeman, E., 2003, ‘‘Pathogenesis of Osteoporosis,’’ J. Appl. Physiol., 95, pp. 2142–2151. 关4兴 Riggs, B. L., Wahner, H. W., Seeman, E., Offord, K. P., Dunn, W. L., Mazess, R. B., Johnson, K. A.; and Melton, III, L. J., 1982, ‘‘Changes in Bone Mineral Density of the Proximal Femur and Spine with Aging. 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