David L. Kopperdahl

Finite element analysis of the proximal femur and hip fracture risk in older men

Low areal BMD (aBMD) is associated with increased risk of hip fracture, but many hip fractures occur in persons without low aBMD. Finite element (FE) analysis of QCT scans provides a measure of hip strength. We studied the association of FE measures with risk of hip fracture in older men. A prospective case‐cohort study of all first hip fractures (n = 40) and a random sample (n = 210) of nonfracture cases from 3549 community‐dwelling men ≥65 yr of age used baseline QCT scans of the hip (mean follow‐up, 5.6 yr). Analyses included FE measures of strength and load‐to‐strength ratio and BMD by DXA. Hazard ratios (HRs) for hip fracture were estimated with proportional hazards regression. Both femoral strength (HR per SD change = 13.1; 95% CI: 3.9–43.5) and the load‐to‐strength ratio (HR = 4.0; 95% CI: 2.7–6.0) were strongly associated with hip fracture risk, as was aBMD as measured by DXA (HR = 5.1; 95% CI: 2.8–9.2). After adjusting for age, BMI, and study site, the associations remained significant (femoral strength HR = 6.5, 95% CI: 2.3–18.3; load‐to‐strength ratio HR = 4.3, 95% CI: 2.5–7.4; aBMD HR = 4.4, 95% CI: 2.1–9.1). When adjusted additionally for aBMD, the load‐to‐strength ratio remained significantly associated with fracture (HR = 3.1, 95% CI: 1.6–6.1). These results provide insight into hip fracture etiology and demonstrate the ability of FE‐based biomechanical analysis of QCT scans to prospectively predict hip fractures in men.

Quantitative computed tomography estimates of the mechanical properties of human vertebral trabecular bone

The objective of this study was to report our quantitative computed tomography (QCT) density‐mechanical property regressions for trabecular bone for use in biomechanical modelling of the human spine. Cylindrical specimens of human vertebral trabecular bone (from T10 to L4) were cored from 32 cadavers (mean ± SD age = 70.1 ± 16.8; 13 females, 19 males) and scanned using QCT. Mechanical tests were conducted using a protocol that minimized end‐artifacts over the apparent density range tested (0.09–0.38 g/ cm3). To account for the presence of multiple specimens per donor in this data set, donor was treated as a random effect in the regression model. Mean modulus (319 ± 189 MPa) was higher and mean yield strain (0.78 ± 0.06%) was lower than typical values reported previously due to minimization of the end‐artifact errors. QCT density showed a strong positive correlation with modulus (n = 76) and yield stress (r2 = 0.90–0.95, n = 53, p < 0.001). There was a weak positive linear correlation with yield strain (r2 = 0.58, n = 53, p = 0.07). Prediction errors, incurred when estimating modulus or strength for specimens from a new donor, were 30–36% of the mean values of these properties. Direct QCT density‐mechanical property regressions gave more precise predictions of mechanical properties than if physically measured wet apparent density was used as an intermediate variable to predict mechanical properties from QCT density. Use of these QCT density‐mechanical property regressions should improve the fidelity of QCT‐based biomechanical models of the human spine for whole bone and bone‐implant analyses.

Age-dependence of femoral strength in white women and men.

Although age‐related variations in areal bone mineral density (aBMD) and the prevalence of osteoporosis have been well characterized, there is a paucity of data on femoral strength in the population. Addressing this issue, we used finite‐element analysis of quantitative computed tomographic scans to assess femoral strength in an age‐stratified cohort of 362 women and 317 men, aged 21 to 89 years, randomly sampled from the population of Rochester, MN, and compared femoral strength with femoral neck aBMD. Percent reductions over adulthood were much greater for femoral strength (55% in women, 39% in men) than for femoral neck aBMD (26% in women, 21% in men), an effect that was accentuated in women. Notable declines in strength started in the mid‐40s for women and one decade later for men. At advanced age, most of the strength deficit for women compared with men was a result of this decade‐earlier onset of strength loss for women, this factor being more important than sex‐related differences in peak bone strength and annual rates of bone loss. For both sexes, the prevalence of “low femoral strength” (<3000 N) was much higher than the prevalence of osteoporosis (femoral neck aBMD T‐score of −2.5 or less). We conclude that age‐related declines in femoral strength are much greater than suggested by age‐related declines in femoral neck aBMD. Further, far more of the elderly may be at high risk of hip fracture because of low femoral strength than previously assumed based on the traditional classification of osteoporosis.

Finite element modeling of the human thoracolumbar spine.

Study Design. Biomechanical properties within cadaveric vertebral bodies were parametrically studied using finite element analysis after calibration to experimental data. Objectives. To develop and validate three-dimensional finite element models of the human thoracolumbar spine based on quantitative computed tomography scans. Specifically, combine finite element modeling together with in vitro biomechanical testing circumventing problems associated with direct measurements of shell properties. Summary of Background Data. Finite element methods can help to understand injury mechanisms and stress distribution patterns within vertebral bodies as an important part in clinical evaluation of spinal injuries. Because of complications in modeling the vertebral shell, it is not clear if quantitative computed tomography-based finite element models of the spine could accurately predict biomechanical properties. Methods. We developed a novel finite element modeling technique based on quantitative computed tomography scans of 19 radiographically normal human vertebra bodies and mechanical property data from empirical studies on cylindrical trabecular bone specimens. Structural properties of the vertebral shell were recognized as parametric variables and were calibrated to provide agreement in whole vertebral body stiffness between model and experiment. The mean value of the shell properties thus obtained was used in all models to provide predictions of whole vertebral strength and stiffness. Results. Calibration of n = 19 computer models to experimental stiffness yielded a mean effective modulus of the vertebral shell of 457 ± 931 MPa ranging from 9 to 3216 MPa. No significant correlation was found between vertebral shell effective modulus and either the experimentally measured stiffness or the average trabecular modulus. Using the effective vertebral shell modulus for all 19 models, the predicted vertebral body stiffness was an excellent predictor of experimental measurements of both stiffness (r2 = 0.81) and strength (r2 = 0.79). Conclusion. These findings indicate that modeling of the vertebral shell using a constant thickness of 0.35 mm and an effective modulus of 457 MPa, combined with quantitative computed tomography-based modeling of trabecular properties and vertebral geometry, can accurately predict whole vertebral biomechanical properties. Use of this modeling technique, therefore, should produce substantial insight into vertebral body biomechanical behavior and may ultimately improve clinical indications of fracture risk of this cohort.

Assessment of Incident Spine and Hip Fractures in Women and Men using Finite Element Analysis of CT Scans

Finite element analysis of computed tomography (CT) scans provides noninvasive estimates of bone strength at the spine and hip. To further validate such estimates clinically, we performed a 5‐year case‐control study of 1110 women and men over age 65 years from the AGES‐Reykjavik cohort (case = incident spine or hip fracture; control = no incident spine or hip fracture). From the baseline CT scans, we measured femoral and vertebral strength, as well as bone mineral density (BMD) at the hip (areal BMD only) and lumbar spine (trabecular volumetric BMD only). We found that for incident radiographically confirmed spine fractures (n = 167), the age‐adjusted odds ratio for vertebral strength was significant for women (2.8, 95% confidence interval [CI] 1.8 to 4.3) and men (2.2, 95% CI 1.5 to 3.2) and for men remained significant (p = 0.01) independent of vertebral trabecular volumetric BMD. For incident hip fractures (n = 171), the age‐adjusted odds ratio for femoral strength was significant for women (4.2, 95% CI 2.6 to 6.9) and men (3.5, 95% CI 2.3 to 5.3) and remained significant after adjusting for femoral neck areal BMD in women and for total hip areal BMD in both sexes; fracture classification improved for women by combining femoral strength with femoral neck areal BMD (p = 0.002). For both sexes, the probabilities of spine and hip fractures were similarly high at the BMD‐based interventional thresholds for osteoporosis and at corresponding preestablished thresholds for “fragile bone strength” (spine: women ≤ 4500 N, men ≤ 6500 N; hip: women ≤ 3000 N, men ≤ 3500 N). Because it is well established that individuals over age 65 years who have osteoporosis at the hip or spine by BMD criteria should be considered at high risk of fracture, these results indicate that individuals who have fragile bone strength at the hip or spine should also be considered at high risk of fracture.

Relation of vertebral deformities to bone density, structure, and strength.

Because they are not reliably discriminated by areal bone mineral density (aBMD) measurements, it is unclear whether minimal vertebral deformities represent early osteoporotic fractures. To address this, we compared 90 postmenopausal women with no deformity (controls) with 142 women with one or more semiquantitative grade 1 (mild) deformities and 51 women with any grade 2–3 (moderate/severe) deformities. aBMD was measured by dual‐energy X‐ray absorptiometry (DXA), lumbar spine volumetric bone mineral density (vBMD) and geometry by quantitative computed tomography (QCT), bone microstructure by high‐resolution peripheral QCT at the radius (HRpQCT), and vertebral compressive strength and load‐to‐strength ratio by finite‐element analysis (FEA) of lumbar spine QCT images. Compared with controls, women with grade 1 deformities had significantly worse values for many bone density, structure, and strength parameters, although deficits all were much worse for the women with grade 2–3 deformities. Likewise, these skeletal parameters were more strongly associated with moderate to severe than with mild deformities by age‐adjusted logistic regression. Nonetheless, grade 1 vertebral deformities were significantly associated with four of the five main variable categories assessed: bone density (lumbar spine vBMD), bone geometry (vertebral apparent cortical thickness), bone strength (overall vertebral compressive strength by FEA), and load‐to‐strength ratio (45‐degree forward bending ÷ vertebral compressive strength). Thus significantly impaired bone density, structure, and strength compared with controls indicate that many grade 1 deformities do represent early osteoporotic fractures, with corresponding implications for clinical decision making.

Femoral strength in osteoporotic women treated with teriparatide or alendronate.

To gain insight into the clinical effect of teriparatide and alendronate on the hip, we performed non-linear finite element analysis of quantitative computed tomography (QCT) scans from 48 women who had participated in a randomized, double-blind clinical trial comparing the effects of 18-month treatment of teriparatide 20 μg/d or alendronate 10mg/d. The QCT scans, obtained at baseline, 6, and 18 months, were analyzed for volumetric bone mineral density (BMD) of trabecular bone, the peripheral bone (defined as all the cortical bone plus any endosteal trabecular bone within 3 mm of the periosteal surface), and the integral bone (both trabecular and peripheral), and for overall femoral strength in response to a simulated sideways fall. At 18 months, we found in the women treated with teriparatide that trabecular volumetric BMD increased versus baseline (+4.6%, p<0.001), peripheral volumetric BMD decreased (-1.1%, p<0.05), integral volumetric BMD (+1.0%, p=0.38) and femoral strength (+5.4%, p=0.06) did not change significantly, but the ratio of strength to integral volumetric BMD ratio increased (+4.0%, p=0.04). An increase in the ratio of strength to integral volumetric BMD indicates that overall femoral strength, compared to baseline, increased more than did integral density. For the women treated with alendronate, there were small (<1.0%) but non-significant changes compared to baseline in all these parameters. The only significant between-treatment difference was in the change in trabecular volumetric BMD (p<0.005); related, we also found that, for a given change in peripheral volumetric BMD, femoral strength increased more for teriparatide than for alendronate (p=0.02). We conclude that, despite different compartmental volumetric BMD responses for these two treatments, we could not detect any overall difference in change in femoral strength between the two treatments, although femoral strength increased more than integral volumetric BMD after treatment with teriparatide.

Once-Monthly Oral Ibandronate Improves Biomechanical Determinants of Bone Strength in Women with Postmenopausal Osteoporosis

CONTEXT Bone strength and fracture resistance are determined by bone mineral density (BMD) and structural, mechanical, and geometric properties of bone. DESIGN, SETTING, AND OBJECTIVES: This randomized, double-blind, placebo-controlled outpatient study evaluated effects of once-monthly oral ibandronate on hip and lumbar spine BMD and calculated strength using quantitative computed tomography (QCT) with finite element analysis (FEA) and dual-energy x-ray absorptiometry (DXA) with hip structural analysis (HSA). PARTICIPANTS Participants were women aged 55-80 yr with BMD T-scores -2.0 or less to -5.0 or greater (n = 93). INTERVENTION Oral ibandronate 150 mg/month (n = 47) or placebo (n = 46) was administered for 12 months. OUTCOME MEASURES The primary end point was total hip QCT BMD change from baseline; secondary end points included other QCT BMD sites, FEA, DXA, areal BMD, and HSA. All analyses were exploratory, with post hoc P values. RESULTS Ibandronate increased integral total hip QCT BMD and DXA areal BMD more than placebo at 12 months (treatment differences: 2.2%, P = 0.005; 2.0%, P = 0.003). FEA-derived hip strength to density ratio and femoral, peripheral, and trabecular strength increased with ibandronate vs. placebo (treatment differences: 4.1%, P < 0.001; 5.9%, P < 0.001; 2.5%, P = 0.011; 3.5%, P = 0.003, respectively). Ibandronate improved vertebral, peripheral, and trabecular strength and anteroposterior bending stiffness vs. placebo [7.1% (P < 0.001), 7.8% (P < 0.001), 5.6% (P = 0.023), and 6.3% (P < 0.001), respectively]. HSA-estimated femoral narrow neck cross-sectional area and moment of inertia and outer diameter increased with ibandronate vs. placebo (respectively 3.6%, P = 0.003; 4.0%, P = 0.052; 2.2%, P = 0.049). CONCLUSIONS Once-monthly oral Ibandronate for 12 months improved hip and spine BMD measured by QCT and DXA and strength estimated by FEA of QCT scans.

Mechanical contributions of the cortical and trabecular compartments contribute to differences in age‐related changes in vertebral body strength in men and women assessed by QCT‐based finite element analysis

The biomechanical mechanisms underlying sex‐specific differences in age‐related vertebral fracture rates are ill defined. To gain insight into this issue, we used finite element analysis of clinical computed tomography (CT) scans of the vertebral bodies of L3 and T10 of young and old men and women to assess age‐ and sex‐related differences in the strength of the whole vertebra, the trabecular compartment, and the peripheral compartment (the outer 2 mm of vertebral bone, including the thin cortical shell). We sought to determine whether structural and geometric changes with age differ in men and women, making women more susceptible to vertebral fractures. As expected, we found that vertebral strength decreased with age 2‐fold more in women than in men. The strength of the trabecular compartment declined significantly with age for both sexes, whereas the strength of the peripheral compartment decreased with age in women but was largely maintained in men. The proportion of mechanical strength attributable to the peripheral compartment increased with age in both sexes and at both vertebral levels. Taken together, these results indicate that men and women lose vertebral bone differently with age, particularly in the peripheral (cortical) compartment. This differential bone loss explains, in part, a greater decline in bone strength in women and may contribute to the higher incidence of vertebral fractures among women than men.

Femoral and Vertebral Strength Improvements in Postmenopausal Women With Osteoporosis Treated With Denosumab

In the randomized, placebo‐controlled FREEDOM study of women aged 60 to 90 years with postmenopausal osteoporosis, treatment with denosumab once every 6 months for 36 months significantly reduced hip and new vertebral fracture risk by 40% and 68%, respectively. To gain further insight into this efficacy, we performed a nonlinear finite element analysis (FEA) of hip and spine quantitative computed tomography (QCT) scans to estimate hip and spine strength in a subset of FREEDOM subjects (n = 48 placebo; n = 51 denosumab) at baseline, 12, 24, and 36 months. We found that, compared with baseline, the finite element estimates of hip strength increased from 12 months (5.3%; p < 0.0001) and through 36 months (8.6%; p < 0.0001) in the denosumab group. For the placebo group, hip strength did not change at 12 months and decreased at 36 months (–5.6%; p < 0.0001). Similar changes were observed at the spine: strength increased by 18.2% at 36 months for the denosumab group (p < 0.0001) and decreased by –4.2% for the placebo group (p = 0.002). At 36 months, hip and spine strength increased for the denosumab group compared with the placebo group by 14.3% (p < 0.0001) and 22.4% (p < 0.0001), respectively. Further analysis of the finite element models indicated that strength associated with the trabecular bone was lost at the hip and spine in the placebo group, whereas strength associated with both the trabecular and cortical bone improved in the denosumab group. In conclusion, treatment with denosumab increased hip and spine strength as estimated by FEA of QCT scans compared with both baseline and placebo owing to positive treatment effects in both the trabecular and cortical bone compartments. These findings provide insight into the mechanism by which denosumab reduces fracture risk for postmenopausal women with osteoporosis.