Age- and sex-related regional compressive strength characteristics of human lumbar vertebrae in osteoporosis

Márta Kurutz¹, Judit Donáth³, Miklós Gálos², Péter Varga¹, Béla Fornet⁴

¹Department of Structural Mechanics; ²Department of Construction Materials, Budapest University of Technology and Economics, Budapest, Hungary; ³Department of Reumatology, National Institute for Reumatology, Budapest, Hungary; ⁴Department of Radiology, County Hospital András Jósa, Nyiregyháza, Hungary

Objective: To obtain the compressive load bearing and energy absorption capacity of lumbar vertebrae of osteoporotic elderly for the everyday medical praxis in terms of the simple diagnostic data, like computed tomography (CT), densitometry, age, and sex.

Methods: Compressive test of 54 osteoporotic cadaver vertebrae L1 and L2, 16 males and 38 females (age range 43–93, mean age 71.6 ± 13.3 years, mean bone mineral density (BMD) 0.377 ± 0.089 g/cm², mean T-score −5.57 ± 0.79, Z-score −4.05 ± 0.77) was investigated. Based on the load-displacement diagrams and the measured geometrical parameters of vertebral bodies, proportional, ultimate and yield stresses and strains, Young’s modulus, ductility and energy absorption capacity were determined. Three vertebral regions were distinguished: superior, central and inferior regions, but certain parameters were calculated for the upper/lower intermediate layers, as well. Cross-sectional areas, and certain bone tissue parameters were determined by image analysis of CT pictures of vertebrae. Sex- and age-related decline functions and trends of strength characteristics were determined.

Results: Size-corrected failure load was 15%–25% smaller in women, proportional and ultimate stresses were about 30%–35% smaller for women in any region, and 20%–25% higher in central regions for both sexes. Young’s moduli were about 30% smaller in women in any region, and 20%–25% smaller in the central region for both sexes. Small strains were higher in males, large strains were higher in females, namely, proportional strains were about 25% larger in men, yield and ultimate strains were quasi equal for sexes, break strains were 10% higher in women. Ultimate energy absorption capacity was 10%–20% higher in men; the final ductile energy absorption capacity was quasi equal for sexes in all levels. Age-dependence was stronger for men, mainly in central regions (ultimate load, male: r = −0.66, p < 0.01, female: r = −0.52, p < 0.005; ultimate stress, male: r = −0.69, p < 0.01, female: r = −0.50, p < 0.005; Young’s modulus, male: r = −0.55, p < 0.05, female: r = −0.52, p < 0.005, ultimate stiffness, male: r = −0.58, p < 0.05, female: r = −0.35, p < 0.03, central ultimate absorbed energy density, male: r = −0.59, p < 0.015, female: r = −0.29, p < 0.08).

Conclusions: For the strongly osteoporotic population (BMD < 0.4 g/cm², T-score < −4) the statical variables (loads, stresses) showed significant correlation; mixed variables (stiffness, Young’s modulus, energy) showed moderate correlation; kinematical variables (displacements, strains) showed no correlation with age. The strong correlation of men between BMD and aging (r = −0.82, p < 0.001) and betwen BMD and strength parameters (r = 0.8–0.9, p < 0.001) indicated linear trends in age-related strength loss for men; however, the moderate correlation of women between BMD and aging (r = −0.47, p < 0.005) and between BMD and strength parameters (r = 0.4–0.5, p < 0.005) suggested the need of nonlinear (quadratic) approximation that provided the better fit in age-related strength functions of females modelling postmenopausal disproportionalities.

Keywords: osteoporosis, human lumbar vertebral body, regional compressive strength, load, stress, strain, young’s modulus, energy absorption capacity, age- and sex-dependence