• vertebra;
  • bone strength;
  • biomechanics;
  • spinal loading;
  • QCT


  1. Top of page
  2. Abstract
  7. Acknowledgements

We used QCT scans obtained in 687 men and women, 21–97 years of age, to estimate the factor of risk for vertebral fracture, Φvert, defined as the ratio of spinal loading to vertebral strength. With age, vertebral strength declined and Φvert increased significantly more in women than men. Age- and sex-specific differences in Φvert closely resembled previously reported vertebral fracture incidence.

Introduction: Despite the high prevalence of vertebral fractures, little is known about the interaction between spinal loading and vertebral fragility.

Materials and Methods: We assessed the ratio of spinal loading to vertebral strength (i.e., the factor of risk, Φvert) in an age- and sex-stratified population-based sample of 700 women and men 21–97 years of age. We measured volumetric BMD (vBMD, mg/cm3) and cross-sectional area (CSA, cm2) of the midvertebral bodies of L1–L3 using QCT and computed vertebral compressive strength from these data using engineering beam theory. A biomechanical model of the trunk was used to estimate compressive forces applied to the L3 vertebral body during standing, bending forward, and bending forward while lifting 10 kg. The factor of risk for fracture, Φvert, was computed as the ratio of spinal compressive force to vertebral strength for each activity.

Results: Men had a higher vertebral strength at all ages, largely because of their greater CSA. Whereas both sexes exhibited a marked decline in vertebral compressive strength with age (p < 0.001), the decline was greater in women than men (−43% versus −31%, p = 0.008). Compressive forces on L3 were greater in men than women, because of their greater body weight and height. For both sexes, forces during bending and lifting were 8-fold higher than those experienced during upright standing. For all activities, Φvert increased with age, but significantly more so in women than men (p < 0.001). For bending and lifting, Φvert-bending exceeded 1.0 in 30% of women and 12% of men ≥50 years of age, values that are similar to the reported frequency of vertebral fracture.

Conclusion: These findings illustrate potential mechanisms underlying vertebral fractures and provide strong rationale for further evaluation of this QCT-based biomechanical approach for assessment of fracture risk.


  1. Top of page
  2. Abstract
  7. Acknowledgements

The etiology of vertebral fractures remains obscure,(1,2) despite the fact that they are the most common osteoporotic fracture and, moreover, are associated with significant morbidity, increased mortality, and costs approaching $750 million annually in this county.(3) Attention has focused mainly on risk factors related to decreased BMD.(2,4) However, structural failure (i.e., fracture) only occurs when the forces applied to bone exceed its load-bearing capacity.(5,6) Recently, we showed that the ratio of skeletal loading to bone strength indices explains the age- and sex-specific patterns of wrist and hip fractures better than does BMD.(7) Thus, to better understand the mechanisms contributing to vertebral fractures, both the forces applied to the spine and the strength of the vertebrae must be considered. However, in comparison with other fragility fractures, less is known about the relationship between spinal loading and vertebral fragility due to several challenges. First, the definition of a vertebral fracture remains controversial.(8,9) Second, a minority of radiographically evident vertebral deformities come to clinical attention,(10–12) although they are associated with significant morbidity and are strong predictors of future fracture risk.(11,13,14) Finally, compared with limb fractures, relatively few vertebral deformities are of acute onset. Rather, most are believed to develop slowly over time, and therefore the activities associated with vertebral fracture are poorly understood.

Myers and Wilson(15) previously explored relationships between spinal loading and vertebral fragility by computing the “factor of risk” (Φ) for vertebral fracture, defined as the ratio of applied forces to strength,(5) for various activities of daily living. They estimated vertebral strength from an empirically derived relationship between areal BMD (aBMD) and vertebral compressive strength,(16) whereas the forces applied to the vertebrae were estimated from a biomechanical model of the trunk.(17) Their analyses predicted that women with very low aBMD values would be at high risk for vertebral fracture during many routine activities of daily living. Using a similar approach, Duan et al.(18,19) also studied the biomechanics of vertebral fragility in men versus women and in Asians versus whites. Using DXA, they found that vertebral cross-sectional area (CSA) increases more and BMD declines less during aging in men than women, so fewer men are at risk for fracture.(18) Our recent cross-sectional study using QCT(20) also found that women experience greater declines in BMD with age than men; however, in contrast to Duan et al.,(18,19) we found that vertebral CSA increases similarly in men and women with aging.

Our objective in this study was to confirm and extend these previous observations by estimating vertebral strength from 3D-QCT data and determining how the factor of risk for vertebral fracture (Φvert) varies with age and sex in a population-based sample. In particular, we asked whether Φvert is higher (i.e., worse) in women than men, whether it increases with age, whether this increase is greater in women than it is in men, and whether the sex-specific age-related changes in Φvert match observed patterns of vertebral fracture incidence. Improved knowledge about the interaction between skeletal loading and bone fragility may improve the identification of those at high risk for fracture.


  1. Top of page
  2. Abstract
  7. Acknowledgements

Study subjects

We studied an age-stratified, random sample of the population of Rochester, MN, as described previously.(20,21) The sample included 325 men (57.2 ± 18.7 years; range, 22–93 years) and 375 women; there were 127 premenopausal women (38.4 ± 9.0 years; range, 21–55 years) and 248 postmenopausal women (67.5 ± 12.0 years; range, 39–97 years). Ninety-eight percent of the sample was white, reflecting the ethnic composition of the Rochester population. Altogether, 368 women and 319 men had valid spine QCT measurements. Of the 687 people with spine measurements, 3 premenopausal and 83 postmenopausal women were receiving estrogen therapy and 11 postmenopausal women and 3 men were receiving bisphosphonate or raloxifene therapy for osteopenia. Because analysis with and without the inclusion of these subjects gave similar results, all were included. The protocol was approved by the Institutional Review Board at Mayo Clinic, and all subjects gave written informed consent before participation.

Vertebral bone density and geometry measurements

As previously described,(20) total volumetric BMD (vBMD, g/cm3, including both cortical and trabecular bone) and CSA (cm2) of the L1–L3 vertebral bodies were assessed from single-energy CT scans (Light Speed QX-I; GE Medical Systems, Wakesha, WI, USA). We analyzed a single slice obtained at the midportion of each vertebral body and used the mean of the three measurements. Analysis of the images was performed using custom software, as previously described.(20,22)

Estimation of vertebral strength

We used the QCT data to estimate vertebral compressive strength using engineering beam theory.(23) Briefly, assuming that bone tissue fails at a constant strain,(24,25) the failure load for a whole bone, or its strength, is proportional to the structural rigidity at its weakest cross-section.(26,27) Structural rigidity measurements combine the intrinsic mechanical behavior of the bone material (i.e., elastic modulus [E] in megapascals [MPa]) with the relevant cross-sectional geometric properties (e.g., CSA for compression). We assumed the vertebral body was primarily loaded in compression and thus estimated vertebral strength (in Newtons [N]) as follows(28):

  • equation image

where Eave is the average elastic modulus in megapascals, derived from vBMD using a previously published, empirically derived relationship between QCT vBMD and the elastic modulus of vertebral bone,(29) and CSA is the cross-sectional area of the midvertebral body (cm2). A prior study using cadaveric lumbar vertebrae showed that this vertebral compressive strength estimate was strongly correlated (r2 = 0.65) to experimentally measured vertebral failure loads.(28)

Estimation of spinal loading

In general, a two-step approach is used to estimate forces on the spine. First, one assumes static equilibrium and uses a linked-segment model of the body to compute the reaction forces and moments at a given spine level for a certain body posture. Then, these forces and moments are balanced by individual muscle forces, along with vertebral compressive and shear forces acting at the cross-section of interest. We estimated the compressive forces applied to the L3 vertebra using a 2D, sagittally symmetric model similar to one previously published by Schultz and Andersson and Schultz et al.(30,31) In this simple model, only the erector spinae muscle force is used to balance the forward flexion moment of the body. The erector spinae moment arm about L3 was assumed to be 51.5 mm for women and 55.4 mm for men.(32) Trunk and limb segment lengths, weights, and centers of mass were derived from each study subject's height, using sex-specific regressions.(33) The proportion of body weight above L3 was taken as 0.569.(34) The reaction forces were resolved as a compressive and shear force acting through the center of the vertebral body. In this study, only the axial compressive force was considered as the force applied to the vertebral body.

Because the activities that lead to vertebral fractures are ill-defined,(10) we chose to study several activities of daily living with varying compressive force magnitudes. We computed the compressive force on L3 for (1) upright standing, (2) forward flexion with the trunk at 45°, and (3) forward flexion with the trunk at 90° while lifting 10 kg from the floor. For upright standing, we assumed that the upper body weight is directly over the center of the vertebral column, and therefore there are no bending moments and spinal muscle forces are absent. In the lifting activity, we assumed that the arms hung straight down from the shoulders and that a 10-kg weight was held equally in the right and left hands (i.e., in the center of the body).

Factor of risk for vertebral fracture (Φvert)

Φvert was computed as the ratio of the applied compressive force to vertebral strength for each activity. Theoretically, when Φvert ≥ 1, a fracture is predicted to occur, whereas for when Φvert < 1, no fracture is predicted. Because of possible error in the estimates of both the compressive force and vertebral strength, the absolute fracture threshold is difficult to define. Nonetheless, one can interpret higher values of Φvert to have increased risk of fracture.

Pattern of vertebral fractures

Age- and sex-specific changes in Φvert were compared with incidence rates for vertebral fracture in the local population(24) updated through 1994. Fractures were ascertained using the data resources of the Rochester Epidemiology Project, which incorporates inpatient and outpatient data from the local providers of medical care.(35) Incidence rates for first vertebral fractures were estimated for adults assuming the entire Rochester population to be at risk. Separately, we searched for any clinical mention of a vertebral fracture in the complete (inpatient and outpatient, including radiology reports) community medical records of each study subject.

Statistical analysis

For each sex, the relationships between vertebral BMD, CSA, and compressive strength were studied using Pearson correlation and linear regression, where age was modeled using natural splines. Each model was compared with a linear relationship, and the simplest model was used for analysis. Differences in changes over this age span between men and women were tested using an age–sex interaction term in a regression model. Changes in variables over life (i.e., between 20 and 90 years of age) were based on predicted values from these models. Characteristics of young men and young women, as well as individuals with Φvert ≥ 1.0 and those with Φvert < 1.0, were compared using unpaired Student's t-tests. Differences were considered significant at p < 0.05. A lowess smoother, essentially a type of moving average,(36) was used to explore the data in Fig. 2.


  1. Top of page
  2. Abstract
  7. Acknowledgements

Vertebral BMD, CSA, and strength

The estimated vertebral strength was 22% greater (i.e., better) in young men than women (p < 0.001) and remained higher in men than women throughout life, mainly because of their larger vertebral CSA (Table 1; Fig. 1). With aging, vertebral strength declined significantly in both sexes (p < 0.001). However, this decline was greater in women than men (−43% versus −31%, respectively; p = 0.01). The decline in vertebral strength occurred despite a slight age-related increase in vertebral CSA that was similar in men and women, and therefore the decline was largely caused by a decrease in vBMD, which deteriorated more with age in women than men (−55% versus −39%, respectively; p < 0.001; Table 1).

Table Table 1.. Average Vertebral vBMD, Cross-Sectional Area, Compressive Strength, Compressive Load, and Factor of Risk for Young and Elderly Women and Men, Along With Age-Related Changes
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Figure Figure 1. Sex- and age-related differences in (A) vertebral compressive strength and (B) estimated compressive force applied to the vertebrae during bending and lifting (mean ± SE per decade of age).

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Compressive loading on the vertebrae

Because of their greater body weight and height, young men had 36–45% higher compressive forces on their vertebral bodies than did women for all activities (Table 1). In either sex, compared with upright standing, predicted compressive forces were ∼5-fold higher for forward flexion to 45° and 8-fold higher for bending forward to 90° while lifting 10 kg. In men, estimated vertebral compressive forces did not change before age 50 (−2%), but declined steadily thereafter (−19%, p < 0.001). In women, estimated vertebral compressive forces increased from 20 to 50 years of age (18%, p < 0.001) and declined thereafter (−26%, p < 0.001; Fig. 1). The net decline in vertebral compressive forces between 20 and 90 years of age, as judged from these cross-sectional data, was similar in men and women (6% to 24% depending on the activity).

Factor of risk for vertebral fracture (Φvert)

For upright standing, the average Φvert-standing was very low at all ages in both sexes (i.e., <0.12), even though it increased significantly with age in both men and women (Table 1). For forward bending to 45°, the average Φvert-bending was 0.39 ± 0.09 in young individuals, with men having a slightly higher value than women. Over life, Φvert-bending increased significantly in both sexes, but markedly more so in women than men (88% versus 25%; p < 0.001). Yet, few individuals had Φvert-bending values that would put them at high risk for fracture, because only 4/246 women and 2/194 men over age 50 had values >0.9, and only one woman exceeded 1.0 (the presumptive fracture threshold). For bending forward while lifting 10 kg, Φvert-lifting was much higher at all ages, with mean values of 0.64 ± 0.12 in young adults and 0.91 ± 0.28 in those >80 years of age. As before, Φvert-lifting increased in both sexes with age, but more so in women than men (92% versus 29%, respectively; p < 0.001) from 20 to 90 years of age (Table 1; Fig. 2).

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Figure Figure 2. Factor of risk for bending and lifting (Φvert-lifting) as a function of age in (A) men and (B) women. The dotted line represents Φvert = 1.0, the level at which fractures are expected to occur.

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Altogether, 97 subjects ≥50 years of age had Φvert-lifting values ≥1.0 (mean, 1.18 ± 0.15), whereas the remaining 343 subjects had lower values (0.76 ± 0.13). Compared with individuals with Φvert-lifting that was <1.0, those with Φvert-lifting ≥ 1.0 were older, heavier, had lower vBMD, had lower predicted vertebral strength, and had higher estimated compressive forces applied to the L3 vertebra during bending and lifting (Table 2). In addition, men with Φvert-lifting ≥ 1.0 were taller and had increased vertebral CSA. The proportion of subjects ≥50 years of age with Φvert-lifting ≥ 1.0 who had a history of vertebral fracture mentioned in their community medical records was 39% compared with just 21% in those with values <1.0.

Table Table 2.. Characteristics of Individuals ≥50 Years of Age With Φvert-lifting ≥ 1 vs. Those With Φvert-lifting < 1
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Comparison of factor of risk for bending and lifting with observed fracture patterns

For bending and lifting, a number of individuals were predicted to be at high risk for fracture, such that 74/246 women (30%) and 23/194 men (12%) over age 50 had Φvert-lifting that was ≥1.0. By decade, the proportion of women with Φvert-lifting that was ≥1.0 increased from 4% to 27% to 53% at 40–49, 60–69, and 80+ years of age, respectively (Fig. 3A). The proportion of men with Φvert-lifting that was ≥1.0 increased from 4% to 11% to 21% at 40–49, 60–69, and 80+ years of age, respectively (Fig. 3A). These age- and sex-specific differences in Φvert-lifting were strikingly similar to the age- and sex-specific incidence of vertebral fracture in this population (Fig. 3B).

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Figure Figure 3. (A) Proportion of men and women with Φvert-lifting ≥ 1.0, by decade of age, and (B) age-specific vertebral fracture incidence (per 100,000 person-years) in men and women from Rochester, MN.(24)

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  1. Top of page
  2. Abstract
  7. Acknowledgements

We explored the age- and sex-specific differences in vertebral fracture incidence using a biomechanical approach to fracture risk assessment in a population-based study. Specifically, we computed the factor of risk for vertebral fracture, Φvert, by comparing the compressive forces applied to the lumbar vertebrae to vertebral strengths derived from QCT-based structural rigidity analyses in 687 persons 21–97 years of age. A strength of our approach is that we were able to compare the age- and sex-specific differences in Φvert to vertebral fracture incidence that was assessed in the same population from which our sample was selected. As expected, we found that the forces applied to the vertebra, and therefore the risk for vertebral fracture, vary with the activity.(37) Few individuals of either sex, or any age, were predicted to be at risk for fracture during upright standing or forward bending. However, forces applied to the lumbar vertebrae during bending while lifting 10 kg from the floor were 8- to 9-fold higher than those during standing and, with aging, a substantial proportion of individuals were predicted to be at high risk for fracture during this activity.

However, consistent with the low incidence of vertebral fracture among young persons, even for bending and lifting, Φvert was very low below age 50 years. Moreover, Φvert-lifting did not differ among young men and women, despite significant differences in compressive forces, CSA, and vBMD. Because of their larger body size, spine compressive forces in young men were 35% higher than in women. However, in accordance with the notion that the skeleton adapts to habitual mechanical loading, young men also had higher vertebral compressive strength due largely to a greater vertebral CSA. This similarity of Φvert among men and women disappeared with aging, because Φvert-liting increased (i.e., worsened) nearly 3-fold more in women than in men over life. Thus, in individuals >70 years of age, 47% of women but only 16% of men had a Φvert-bending ≥ 1.0. Because vertebral compressive forces actually declined slightly and CSA increased slightly with age, this marked increase in Φvert-lifting (and predicted fracture risk) was caused by the decline in vertebral vBMD, which was greater in women than in men (−55% versus −39%).

Most of these findings are consistent with those previously reported by Duan et al.,(18) including the observation that Φvert did not differ markedly among young persons and that the dramatic increase in Φvert with age in women versus men was attributable to a greater decline in BMD. However, in contrast to Duan et al., who reported that men had a greater increase in CSA over life than women, we found that vertebral CSA increased with age to a similar extent in both men and women.(20) This difference in findings is likely because of the fact that different methodologies were used to measure vertebral CSA.

Unlike previous clinical studies of vertebral biomechanics,(18,37) we estimated vertebral compressive strengths using engineering structural rigidity analyses(26,27) combined with empirical studies of human cadaveric vertebrae.(28,29) Theoretically, a noninvasive imaging technique that integrates information about bone geometry and material properties should provide better estimates of bone strength than aBMD. Whereas QCT can assess 3D bone geometry, it does not measure material properties such as elastic modulus, directly, but rather relies on empirical relationships between vBMD and biomechanical properties derived from cadaver studies. In the absence of substantial alterations in bone tissue mineralization, such as seen in osteomalacia or fluoride treatment, these empirical relations are likely to be reasonably robust. In support of this notion, QCT-based structural rigidity measurements were shown to be strongly correlated to vertebral strength in human cadavers.(26,28) Our estimated vertebral compressive strengths averaged 5033 N (range: 1650–10,620 N), values that are consistent with those measured in human lumbar vertebrae.(16,38,39) Moreover, Snyder et al.(27) recently showed that QCT-based structural rigidity analyses have high sensitivity and specificity for prediction of pathologic fractures in children with benign bone lesions. One limitation to our approach is that we used only a single QCT slice through the midvertebral body for estimating vertebral strength. Using either a multislice approach to identify the weakest cross-section(26) or QCT-based finite element analysis(28) may further improve predictions of vertebral strength. Also, whereas the QCT-based axial rigidity measurement reflects BMD and bone geometry, the main contributors to vertebral strength, it does not reflect alterations in collagen content or cross-linking that may also impact bone strength.

Our study had several limitations. First, we used a cross-sectional study design to infer age-related changes. Second, the activities that cause vertebral fractures are largely unknown. Therefore, it is not clear whether bending and lifting are the loading conditions that are relevant for studying vertebral fracture etiology. However, as the relevant activities are identified through epidemiologic studies, they can be tested using this approach. Third, we used a relatively simply model of the trunk to estimate vertebral compressive forces. Thus, we computed the compressive forces applied to the vertebrae using a 2D, sagittally symmetric, static model of the spine. Our model did not incorporate inertial forces, which can increase spinal loading during lifting by up to 50%.(40) Our model also did not account for forces imposed on the vertebral body during lateral bending or twisting, activities that may contribute to vertebral fractures. We assumed that the erector spinae was the only muscle that contributed to balancing forces in the cross-section. Depending on the activity, this may have led to either an over- or underestimation of the vertebral compressive forces. Use of a more sophisticated model that incorporates additional muscles in the cross-section and uses optimization schemes to partition the muscle forces amongst the various muscle groups may improve estimates of vertebral compressive forces.(17,41–43) We also assumed a constant erector spinae moment arm in men and women. Because the prediction of spinal loads is sensitive to trunk muscle geometry, accounting for individual differences in trunk muscle geometry may enhance the accuracy of spinal load prediction.(44–46) Nonetheless, despite these shortcomings, the predictions of spinal compression forces obtained using a variety of techniques show reasonable agreement, lending validity to our overall approach.(41,47)

Another limitation relates to the absence of vertebral fracture assessment to further evaluate our approach. Although we noted which subjects had a history of vertebral fracture recorded in their community medical records, we did not have lateral thoracic and lumbar radiographs available. We did have images from the QCT scan, but neither morphometric nor expert assessment for vertebral deformity has been standardized for this technique, and the proper basis for diagnosing vertebral fractures remains controversial.(8,9) As a consequence, the value for Φvert that would provide optimal discrimination of fracture subjects from controls is unknown. Here, we assumed that fracture would occur when Φvert exceeded 1.0. Given the possible errors in assessing both compressive forces and vertebral strengths, the value for Φvert that provides the best sensitivity and specificity for fracture risk prediction can only be identified in a subsequent case-control or prospective fracture study.

However, Duan et al.(48) recently reported that their fracture risk index (FRI) was no better than aBMD at discriminating vertebral fracture cases from controls. They performed a case-control study, comparing 89 postmenopausal women with prevalent vertebral fractures to 306 unfractured controls, and a prospective study, comparing 30 women with incident vertebral fractures to 150 controls. FRI measurements were made at the L3, whereas fractures occurred mainly in the midthoracic and upper lumbar regions; one can speculate that the factor of risk approach may perform better if measurements are made at vertebral levels adjacent to fracture sites. Moreover, their study assessed only a single loading condition, namely bending forward. One interpretation of their findings, consistent with this study, is that this loading condition is not associated with vertebral fractures. Perhaps another loading condition, such as lifting or lateral bending, would better differentiate fracture subjects from controls. Nonetheless, their findings further emphasize the need for additional studies to test the ability of our biomechanical approach to differentiate subjects with vertebral fractures.

These limitations notwithstanding, we found that the age- and sex-specific differences in Φvert were remarkably similar to observed patterns of vertebral fracture incidence in this population. Similarly, we previously showed that factor of risk estimates at the hip and distal forearm more closely resembled age- and sex-specific patterns of hip fracture and wrist fracture incidence than did BMD measures.(7) Altogether, these findings show potential mechanisms underlying fracture risk and provide strong rationale for further evaluation of this QCT-based biomechanical approach for fracture risk assessment. Ultimately, improved knowledge about the interaction between skeletal loading and bone fragility may improve identification and treatment of those at high risk for fracture.


  1. Top of page
  2. Abstract
  7. Acknowledgements

The authors thank Lisa McDaniel, RN, and Louise McCready, RN, for assistance in recruitment and management of the study subjects, James M Peterson for assistance with data management and file storage, and Sara J Achenbach for statistical assistance. Ronald A Karwoski and Mahlon C Stacy of the Biomedical Imaging Center provided valuable assistance in analysis of the spiral QCT scans. This study was supported in part by NIH Grants AR27065 and M01 RR00585.


  1. Top of page
  2. Abstract
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