Age trends in proximal femur stresses were evaluated by simulating a fall on the greater trochanter using femur geometry from hip DXA scans of 5334 white men and women in the NHANES III survey. Expansion of femur outer diameter seems to counter net bone loss so that stresses remain similar across age groups, but stresses are higher in older women than in older men.
Introduction: The age decline in hip BMD is caused by both bone loss and expansion of outer diameter that increases the region size over which mass is measured in a DXA scan. Because expansion has an opposing effect on structural strength, it may be a homeostatic adaptation to net bone loss to ensure that load stresses are kept within a narrow range.
Materials and Methods: Age trends in femur stresses were evaluated with an engineering beam simulation of a fall on the greater trochanter. Hip geometry was extracted from hip DXA scans using the Hip Structure Analysis (HSA) software on 2613 non-Hispanic white men and 2721 women from the third National Health and Nutrition Examination Survey (NHANES III). Using body weight as load, stresses were computed on the inferior-medial and superior-lateral femur neck at its narrowest point and the medial and lateral shaft 2 cm distal to the midpoint of the lesser trochanter. Stresses and the underlying geometries in men and women >50 years oaf age were compared with those 20–49 years of age.
Results: Compared with men <50 years of age, stresses in older men were 6% lower on both surfaces of the shaft, 4% lower on the inferior-medial neck, and not different on the superior-lateral neck. In women >50 years of age, stresses on the proximal shaft and inferior-medial neck remained within 3% of young values but were 13% greater on the superior-lateral neck. Neck stresses in young women were lower on the superior-lateral than the inferior-medial neck, but lateral stress increased to the level on the medial surface in older women. Stresses were higher in women than in men, with a greater gender difference in those >50 years of age.
Conclusions: We conclude that femur expansion has a homeostatic effect in men and women that opposes bone loss so that stresses change little with age. Because expansion preserves stresses with progressively less bone mass, the process may reduce structural stability in the femoral neck under fall conditions, especially in the elderly female.
The clinical community and much of the aging public are familiar with the way that BMD changes over the human lifetime. In both men and women, BMD increases during skeletal growth, peaks in young adulthood, and declines gradually thereafter, somewhat more quickly after menopause in women. Because low BMD is firmly linked to osteoporotic fractures, it is broadly believed that the decline in BMD represents a gradual reduction in mechanical strength that ultimately results in fragility. However, a gradual decline in strength through adulthood would suggest that homeostasis was generally deficient in adult bones. However, the biological evidence that bone tissue is self-renewing and that it dynamically adapts to changing loading conditions throughout life is quite compelling. Therefore, how can we reconcile the seemingly inconsistent picture presented by the BMD data and the biological evidence of homeostasis? From a mechanical perspective, bones can weaken by altering the structural geometry so that load stresses increase or by degrading the material so that the tissue fails at a lower level of stress (ultimate stress). The general consensus is that age changes predominately alter the amount and distribution of the bone material within the bone (i.e., structural geometry), with little influence on the ultimate stress.(1,2) (We do not imply that material changes play no role in osteoporotic fragility but that age changes are mainly geometric; see discussion.) If homeostasis is actually effective, it must alter the geometry to keep load stresses relatively constant, but to be consistent with the BMD data, it must do so in a way that permits a decline in BMD and an increase in fracture risk.
The answer to this quandary may be evident in a closer look at the trends in femoral neck BMD data from the third National Health and Nutrition Examination Survey (NHANES III) of the noninstitutionalized U.S. population. Because the length of the neck region normally takes a default value, expansion of region area should be caused by widening of the bone outer margins. We present data that suggest the downward trend with age in femoral neck BMD in both men and women is faster than the trend in bone mass (BMC). These data will suggest that the net bone loss apparent in BMC trends is opposed by expansion of outer diameter. We previously showed the expansion of bone outer margins in a geometric analysis of the same data by the Hip Structure Analysis (HSA) method.(3) The latter effect may be a generalized characteristic of aging long bones.(3–8) It has been speculated to have a homeostatic purpose, because as diameter is increased, bending stiffness requires progressively less material in the cross-section.(4,6,9)
It is not known whether the expansion of diameter is actually sufficient to offset bone loss so that maximum stresses do not increase with age. Because we have previously derived the hip structural geometry on the hip scans from the NHANES III survey by the HSA method,(3) these data can be combined with anthropometry to derive an estimate of mechanical stress so that age trends may be evaluated in adult men and women. We chose to estimate stresses in a simulation of a fall on the greater trochanter because most hip fractures are believed to occur in that mode.(10) Our working hypothesis was that the expansion of femur diameter is sufficient to compensate net bone loss so that stresses change little with age.
MATERIALS AND METHODS
Data were taken from NHANES III, conducted by the National Center for Health Statistics, Centers for Disease Control and Prevention, between 1988 and 1994. The survey used a stratified, multistage probability design to select the sample, and collected data through household interviews and by direct standardized physical examinations conducted in specially equipped mobile examination centers. The survey has been described in detail elsewhere.(16) Men and nonpregnant women ≥20 years of age who received the physical examination in the mobile centers were eligible for bone densitometry unless they had fractured both hips previously. Acceptable hip bone mineral measurements were obtained on 14,646 men and women ≥20 years of age. As summarized elsewhere, structural analysis could not be done on 1031 for technical reasons, leaving a total of 13,615 scans.(3) This represents 59% of the eligible selected sample, 72% of the eligible interviewed sample, and 82% of the eligible examined sample. Race and ethnicity were self-reported in NHANES III. This study was restricted to 5334 non-Hispanic whites (2613 men and 2721 women).
Anthropometry and body composition
Upper leg length was measured as the distance between the inguinal crease and anterior surface of the thigh proximal to the patella with the respondent seated and with the right knee bent at a 90° angle.(11)
Bone densitometry and HSA
The left hip was scanned unless there was a history of previous fracture or surgery; only 1% received a scan of the right femur. Because their inclusion did not alter estimates, those who received a scan of the right femur were included. Measurements were obtained with three Hologic QDR 1000 DXA scanners (Hologic, Waltham, MA, USA), located in mobile examination centers. A rigorous quality control (QC) program was used throughout the study to ensure data quality.(12)
The HSA method for extracting cross-sectional geometry from bone mass image data is based on principles first described by Martin and Burr.(13) At a site where the cross-section is to be evaluated, a line of pixel values traversing the bone axis is extracted from the image. The resulting profile is a mass projection of the corresponding cross-section and can be used to describe its geometry relevant to scan plane stresses. Although current HSA algorithms average geometry over five parallel profiles, three profiles were used in the early version on NHANES III. The (blur-corrected) profile width measures bone outer diameter. Average pixel value, calibrated in grams per centimeter squared of hydroxyapatite yields conventional BMD. Dividing profile pixel values by the effective mineral density of fully mineralized bone (1.051 g/cm3)(13) converts them to equivalent linear thickness of bone tissue in centimeters, exclusive of soft tissue (trabecular, vascular, etc.) spaces. The integral of the resulting thickness profile yields the total surface area of (cortical + trabecular) bone in the cross-section (CSA). After determining the profile center of mass, the cross-sectional moment of inertia (CSMI) is derived as the integral of area times the square of distance from the center of mass. Section modulus (Z) is computed by dividing CSMI by the maximum distance from the center of mass to the medial or lateral outer surface. Note that CSMI and Z by this method are only relevant for bending in the image plane unless the cross-section is axially symmetric.
Stresses were computed at two cross-sections in the proximal femur using a formalism described previously for a continuum model of the femur in a simulation of a fall with impact on the greater trochanter.(14) Because of limitations of a 2D image, force vectors were restricted to the DXA image plane; all stresses were computed using body weight as equivalent to the ground reaction force. The ground reaction force was oriented along the bisector of the neck and shaft axes, and the body load was distributed to achieve static equilibrium along antiparallel vectors through the center of the femoral head and the midpoint of the femoral shaft. Measurements of neck-shaft angle and distances between load vectors and section positions were derived from the HSA program; thigh length was incorporated from external anthropometry. Maximum stresses were computed at the medial and lateral margins of two cross-sections: across the narrowest point of the femoral neck and across the proximal femoral shaft at a point 2 cm distal to the midpoint of the lesser trochanter (to eliminate size effects on placement, more recent HSA algorithms place the shaft region at a distance of 1.5 times the minimum neck width distal to the intersection of the neck and shaft axes). The HSA program measured the loci of these sections relative to load vectors within the scan plane.
Using standard engineering beam theory, bending stress was computed at the outer margin of the medial and lateral cortices of the cross-section as equation:
Where M is the bending moment, y is the distance from the center of mass of the cross-section to the medial or lateral margin, and I is the CSMI. The bending moment was computed as the orthogonal component of the load multiplied by distance to the section location, measured parallel to the neck or shaft axis as appropriate. By convention, y in the direction of bending is positive and negative in the opposing direction (lateral and medial, respectively). Axial stress was computed as:
Where Fa is the axial component of the load, and A is bone CSA.
To determine whether age has an effect on stresses, mean values were compared between 20–49 and 50+ years of age for men and women separately. To examine gender differences, mean values were compared between sexes for the younger (20–49 years) and older (50+ years) age groups. The same group comparisons were done for conventional femoral neck BMD, BMC, and bone area, as well as BMD and geometric properties at the two proximal femur regions for HSA variables. All group differences were evaluated with p < 0.05 as significant using an unpaired two-tailed t-test. Analyses were performed using SUDAAN,(15) a family of statistical procedures for analysis of data from complex sample surveys.
Trends in femur neck BMC, BMD, bone area, and outer diameter
Figures 1A and 1B shows femur neck BMC data by decade in non-Hispanic white men and women, respectively, after normalizing values to those of young adults so that cross-sectional patterns by age are easily seen. For comparison purposes, Fig. 1 also shows data for BMD, bone area, and outer diameter (width); the BMD and outer diameter data have been published previously.(4) Means for these variables are compared between young and old age groups in Table 1. It can be seen that the apparent age decline in bone mass (BMC) is smaller than that in BMD and that this is caused by higher values for bone area with increasing age. The expansion of the Hologic neck bone area (FNBA) is likely explained by the expansion of the outer diameter of the neck with age as documented by the HSA method.
Table Table 1.. Mean Values of Body Weight, BMD, and Geometric Properties of the Femoral Neck and Proximal Shaft in Young and Old Men and Women
Mean values by decade of medial and lateral stresses are plotted at the neck (Fig. 2A) and proximal shaft (Fig. 2B) for men and women. To evaluate age and gender effects, the mean stresses for young (<50 years) and old (≥50 years) men and women are compared in Table 2. Stresses appear lower in men than in women at both neck and shaft; differences were significant (Table 2). At the neck in both men and women, stresses are lower on the superior-lateral surface than on the inferior-medial surface, and these differences disappear with age. Medial and lateral stresses are comparable (within 3% in women and 1% in men) in the shaft in both genders through the age span. Inferior-medial neck stresses in women vary little with age (Fig. 2A), and differences between young and old women are not significant. However, superior-lateral neck stresses in women do increase substantially by ∼13% between young and old age groups. Shaft stresses in women are significantly, albeit slightly, higher in older women on both surfaces. At the femur neck in men, inferior-medial stresses are on average 4% lower than in younger individuals. At both shaft surfaces in men, the apparent decline with age is more evident, so that stresses in older men are 6% less than in younger counterparts.
Table Table 2.. Mean Stresses (MPa) at the Medial and Lateral Surfaces of the Femoral Neck and Proximal Shaft for Oold and Young Age Groups in Non-Hispanic White Men and Women*
Table 1 shows gender and age group differences in body weight, conventional DXA parameters at the femoral neck, and geometry at the femoral neck and proximal shaft. The men were, of course, heavier than women, but within gender, there was little difference in weight between younger and older groups. The well-known age differences in conventional BMD in both men and women are evident as are the opposing age differences in BMC and in FNBA. The age group BMD differences from the HSA analysis are consistent with their conventional counterparts at the neck and are smaller in both genders at the shaft. Note that the age group difference in bone width is similar at the neck and shaft and across genders. The effects of the apparent expansion of diameter on BMD and geometry are complex; they differ between shaft and neck and across genders. At the shaft in men, greater width essentially explains why BMD is lower in the older group; the apparent decline in the amount of bone (CSA) in the cross-section does not reach significance. In older women, however, expansion of diameter is responsible for approximately one third of the 15% lower BMD. At the neck in both men and women, roughly one third of the age difference in BMD is caused by an expanded diameter. The effects of diameter differences on CSMI are nonlinear, because this parameter varies as the fourth power of the outer radius. In older men and women, CSMIs in the femoral shaft were significantly larger by 10% and 6% respectively, compared with the younger group. At the femoral neck, the CSMI in older men and women was within 3% of the young value, although an increase was apparent in men and a decline in women. The strong dependence of CSMI on outer diameter explains the rather large gender difference in this bending property; and like most other parameters, the gender difference was greater in the older age group. At the neck, the center of mass (centroid position) shifted medially with age in both genders but significantly more so in women. No shift was apparent in the shafts of men, and only a slight medial shift was seen in women.
We hypothesized that the expansion of femur diameter with age represents a homeostatic adaptation that opposes the effects of bone loss so that load stresses remain constant. Our results are generally consistent with this hypothesis, with one exception: superior-lateral neck stress was 13% higher in older women than in younger women. However, stresses on the inferior-medial neck and both surfaces of the shaft in women remained within 3% of young values. Among men, stresses on the medial neck and both surfaces of the shaft were actually slightly lower in older men relative to younger men. Like the pattern in women, stresses on the lateral neck surface in men were greater in the older group, but unlike women, the difference did not reach significance. In both younger men and women, femoral neck stresses were lower on the superior-lateral than on the inferior-medial surface, and magnitudes converged after age 50. The apparent age increase in superior-lateral stress that produced convergence is only significant in females and seems to be caused by an inferior-medial shift in the femoral neck center of mass (i.e., centroid position; also apparent to a lesser extent in males). Together with the increase in neck diameter, the shift increases the value of y in Eq. 1, with a greater effect in females. It is interesting that, whereas the superior-lateral neck stress shows an apparent increase with age in women, the magnitude only rises to the higher level seen on the inferior-medial neck surface. Overall, these findings suggest that, in a fall on the greater trochanter, the resulting stresses would differ little between younger and older individuals, and the only substantial age difference is on the superior-lateral neck in women.
In contrast to the general lack of differences by age, we found gender differences worthy of comment. Stresses generated in a fall are higher in women than in men, and this effect is greater in older individuals. The changes in cross-sectional geometry that explain the stress differences with age and gender are quite clear. The expansion of diameter does seem to offset bone loss, but there are subtle consequences of the process that may not be advantageous under the conditions of a fall. In normal upright ambulation, the femur is bent in the opposite direction than in the fall mode. This means that in normal ambulatory activity, bending stresses on the superior-lateral neck surface are in tension and the thicker inferior-medial cortex is in compression. The reverse is true in the fall mode, where the thinner superior-lateral surface is in compression. Physiologic loads add axial forces that subtract from the tensile stresses caused by bending on the superior-lateral surface and that add to the compressive stress on the inferior-medial neck. Effectively, the lateral neck is relatively unloaded during normal ambulation(16); thus, peak stresses that drive adaptation are concentrated on the medial surface where cortices seem not to thin with age.(17) The resulting redistribution of material in the aging neck shifts the center of mass toward the medial surface. Bending stresses (Eq. 1) are inversely dependent on I/y, where y is the distance from the center of mass to the medial or lateral surface for the respective stresses. In long bones, y generally increases with age because of expansion of diameter that displaces the cortical surface farther from the center of mass. This age-dependent increase in y is greater on the lateral neck because of the additional effect of the inferior-medial shift in the center of mass. The larger medial shift in women is likely the main reason why superior-lateral neck stresses are higher in older women, whereas inferior-medial stresses are not. Mayhew et al.(17) recently described the age shift in femoral neck center-of-mass in a study that analyzed CT scans of the femoral neck in a cross-sectional sample of 77 adult cadaver specimens. They conjectured that the shift is caused by adaptation to habitual patterns of ambulatory stresses that are less varied in modern inactive populations than in more primitive ones.
The finding that load stresses vary little with age contrasts starkly with the epidemiological evidence of increasing hip fracture rates in old age and with age patterns in BMD. They are, however, remarkably consistent with the geometric findings of Russo et al.(18) based on quantitative CT scans of the tibia in a cross-sectional sample of Italian adults. In both men and women, they showed an upward trend in the external dimensions of tibial cross-sections that seemed to preserve resistance to bending stress.(18) If the geometric adaptation that underlies declining areal BMD ensures that stresses remain relatively constant with age, why do bones become fragile in old age? One explanation might be that changes in the material strength may reduce the stress capacity of old bones or at least in those who suffer fractures.(19) There is a great deal of semantic confusion regarding material properties in the literature because of differences in their definition. Strictly speaking, material properties refer to the mechanical behavior of bone tissue under load and are a function of the tissue composition (i.e., properties of the organic matrix, osteon substructure, mineralization, accumulated microdamage). There are no reliable methods for noninvasive measurement of bone tissue material properties in vivo, and specialized methods such as nanoindentation are required for their evaluation from biopsies.(20) Certain practical issues have resulted in an alternative definition, which is more properly termed apparent material properties. Traditional engineering tests of material properties use specimens machined to standardized geometric dimensions so that and any differences in load behavior are caused by material properties and not differences in stress. Bone specimens machined to typical test sizes, however, vary in porosity, especially in aging cortical bone and trabecular specimens. Stresses are really not constant because applied loads are supported by varying amounts and arrangements of material hence measurements reflect only “apparent” material properties. Work by several investigators showed that age dependence and osteoporotic differences in apparent properties are mainly caused by porosity,(1,2,21) with little systematic change at the tissue level. If bone microstructure is measured with sufficient resolution, apparent material properties are unnecessary, and μCT methods capable of doing so in vivo at certain extremity sites(22) have become available. Finite element analysis (FEA) models evaluate irregular structures by breaking them into small box-like elements. Models with millions of microelements small enough to evaluate the fine trabecular structure have been developed from μCT data. Because computational demands scale with numbers of elements, such high-resolution models require massively parallel supercomputers and hundreds of hours of computation time (see van Rietbergen et al.(23) and Eswaran et al.(22) for examples). FEA models with element sizes of a few millimeters are far more manageable and correspond better to resolution capabilities of high-end total body CT scanners. However, because the fine structure cannot actually be resolved, the concept of apparent material properties is a convenient method way of handling their effects. Apparent material properties are also unnecessary in analyses derived from DXA, not because the microstructure is imaged, but because porosity effects are eliminated. Only the mineral mass is projected into the DXA image plane; the surrounding or internal soft tissues are subtracted out by the dual-energy mathematics. Effectively, pores within cortical or trabecular bone are collapsed out and are thus not present in the cross-sectional geometry measured from the mineral mass profiles. Although it does not seem to be a general effect of age or osteoporosis, degraded material strength may play a role in some osteoporotic fractures, although current noninvasive imaging methods are not yet capable of quantifying it.
Age-related loss of bone strength can only be caused by increased stresses (degraded geometry) or reduced stress capacity of the material. Here we argue that age-related strength loss is probably not in the (actual) material properties and doesn't seem to be in the geometry according to our calculations. Macroscopic properties such as CSA and CSMI are integrated over the whole cross-section; however, under compressive loads, thin-walled structures can exhibit local failure of a portion of the cross-section, and in such cases, stresses are underestimated by the CSA and CSMI.(24) There is little doubt that the aging femoral neck cross-sections exhibit cortical thinning with age, albeit preferentially on surfaces that are not heavily loaded in normal ambulation.(17) Together with expansion of outer diameter and bending the thinning surface in a fall, these geometric changes should cause strength loss caused by the contribution of local buckling as speculated by Mayhew et al.(17) Further work will be needed to determine if this is theoretically likely with geometries that are achieved in osteoporotic bones.
There are a number of methodological limitations to this work. The DXA-based geometry method restricts cross-sectional moments of inertia and thus the stress analysis to the 2D image plane; conclusions cannot be drawn regarding out-of-plane stresses. Because DXA methods cannot evaluate material effects, the entire analysis assumes that all differences are geometric, although this is actually true of most engineering analyses of bone to date. As we have pointed out, it is possible that some age changes alter material strength at the tissue level, although such effects can only be reliably evaluated by biopsy methods at present. It is also important to recognize that the apparent changes in geometry that are responsible for keeping stresses relatively constant with age are an adaptive response to loading conditions experienced in normal activity; bones certainly don't adapt to remain strong under the conditions of a fall on the hip as evaluated here. Ultimately a stress analysis should be repeated on a data set that has sufficient information to simulate physiologic loading configurations and magnitudes (which are probably not best characterized by body weight) so that adaptive changes across the age span can be better evaluated.
Because the NHANES sample is cross-sectional, cohort effects could confound the age trends described in this study. Cross-sectional age patterns in femur BMD have been shown to differ from longitudinally determined age patterns,(25) so those observed here need to be confirmed prospectively. Other limitations of the NHANES data include the exclusion of institutionalized persons from the sampling frame; they may have lower BMD and potentially different geometry. Finally, some individuals who were selected for the survey did not participate. However, a previous analysis suggested that nonrespondents did not differ importantly from respondents.(4)
We conclude that the expansion of diameter that partially explains the reduction in BMD of the aging proximal femur represents a homeostatic adaptation that offsets the apparent net loss of bone mass observed in aging men and women participating in the NHANES survey. Despite significantly lower BMD levels in older men and women, proximal femur stresses generated in a simulation of a fall on the greater trochanter were similar in older versus younger persons. A modestly higher stress on the superior-lateral surface in older women seems to be caused by a shift in the center of mass, so that in a fall configuration, the cortex may experience higher stresses in compression. When combined with greater cortical thinning with age in an expanded diameter, that surface may be more susceptible to fractures initiated by buckling instability in elderly women if they fall with impact on the greater trochanter.
This work was supported by research Grant AR44655 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institutes of Health.