Relation between vertebral compressive strength and trabecular architecture is presented in terms of aging and sex. Complex in vitro medical-engineering analysis of cadaver human lumbar L1 and L2 vertebrae was executed: densitometry, CT, MRI, mechanical test and histology, in aspect of osteoporosis. In this paper the results of the mechanical test are detailed only. The compressive mechanical parameters, like limit stress and strain, proportional stress and strain, Young modulus, ductility, energy absorption capacity were determined. Morphometry analysis was based on the CT pictures. Density and diameter of trabeculae were measured. Correlation between morphometric and mechanical properties was evaluated in terms of aging, sex and bone mineral density

Fornet, B.

Gálos, M.

Kurutzné Kovács, Márta

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COMPRESSIVE LOAD-BEARING AND BONE ARCHITECTURE OFLUMBAR VERTEBRAE IN TERMS OF SEX AND AGINGM. Kurutz1, M. Gálos2 and B. Fornet31. ABSTRACTRelation between vertebral compressive strength and trabecular architecture is presentedin terms of aging and sex. Complex in vitro medical-engineering analysis of cadaverhuman lumbar L1 and L2 vertebrae was executed: densitometry, CT, MRI, mechanicaltest and histology, in aspect of osteoporosis. In this paper the results of the mechanicaltest are detailed only. The compressive mechanical parameters, like limit stress andstrain, proportional stress and strain, Young modulus, ductility, energy absorption ca-pacity were determined. Morphometry analysis was based on the CT pictures. Densityand diameter of trabeculae were measured. Correlation between morphometric and me-chanical properties was evaluated in terms of aging, sex and bone mineral density.2. INTRODUCTIONCompressive strength of cadaver lumbar vertebrae was determined by mechanical tests,and compared with the morphometry of the trabecular bone of vertebrae. One-waycompressive test was carefully performed on each vertebra up to the collapse. Theautomatically plotted load-displacement diagrams were evaluated. Age- and sex-relatedfunctions and trends of both strength characteristics and vertebral architecture were ob-tained. Limit stresses and strains, Young's elastic moduli, proportional stresses andstrains, ductility and energy absorption capacity were calculated for the human lumbarvertebrae L1 and L2, in terms of aging and sex. The relations with bone architecturewere based on CT pictures.This paper aims to obtain the trends of age- and sex-related change of compres-sive strength characteristics, in terms of bone mineral density and trabecular architec-ture. The results can be used in numerical simulation of osteoporotic processes.3. METHODS54 cadaver lumbar L1 and L2 vertebrae without posterior elements were ob-tained from the spine of 16 males and 38 females. The age of males was between 47-87years (mean age 65,6 year); of females was between 43-93 years (mean age 74,2 year).Keywords: lumbar vertebrae, compressive test, morphometry, BMD                                                1 Professor, Head of Department, Department of Structural Mechanics, Research Centre of Biomechanics,Budapest University of Technology and Economics, H-1521 Budapest, Hungary2Professor, Department of Building Materials and Engineering Geology,Budapest University of Technology and Economics, H-1521 Budapest, Hungary3Head Physician, International Medical Center, Budapest, HungaryBefore mechanical testing, areal bone mineral density (aBMD), CT and MRIanalysis were made for each vertebra. The CT pictures have been used for bone archi-tecture analysis. The CT pictures have been improved by an image analyzer to measurethe diameters, the distribution and density of trabeculae in 2D. The measurements havebeen repeated in the coronal and sagittal plane and in the horizontal cross sectionalplane of vertebrae. For mechanical testing, the two end-plates of vertebrae were clearedaway, so that the upper and lower planes of vertebrae be parallel and smooth. In thisway, the original height of vertebrae decreased. The reduced height and the upper andlower cross-sectional areas were measured and registered.One-way compressive test was carefully performed on each vertebra up to thecollapse. No cyclic loading and no unloading were performed. The measuring limit ofthe tester was 12,5 kN with accuracy of 3%. The compressive deformations were meas-ured in three points, by angle of 120 degree from each other, with 0-5 mm measuringlimit.Loading forces and the occurred displacements between the two end-plates wereregistered and plotted to a load-displacement diagram. The compressive stresses wereobtained as the quotient of the loading force and the cross sectional area. The compres-sive strains were calculated as the quotient of the shortened and the original height ofvertebra. The automatically plotted load-displacement diagrams were linearized, and therelated stress-strain diagrams were classified.3. RESULTSTable 1 and 2 contains the mean values of measured and calculated mechanicalcharacteristics of vertebrae L1 and L2, respectively, by distinguishing the sexes.Mean mechanical characteristicsof lumbar vertebrae L1in compression Malesn=10Femalesn=21Totaln=31Proportional stress pσ MPa 2,0 1,4 1,6Proportional strain  pε % 3,6 2,9 3,2Young modulus E MPa 92 74 80Limit stress uσ MPa 2,8 2,1 2,3Limit strain, ductility uε % 5,3 5,1 5,2Energy absorption capacity Joule 1,58 1,03 1,21Table 1: Mechanical characteristics of lumbar vertebrae L1 in compressionMean mechanical characteristicsof lumbar vertebrae L2 in compression Malesn=6Femalesn=17Totaln=23Proportional stress pσ MPa 1,9 1,0 1,3Proportional strain  pε % 2,8 2,5 2,7Young modulus E MPa 89 57 65Limit stress uσ MPa 2,7 1,6 1,9Limit strain, ductility uε % 4,6 4,7 4,7Energy absorption capacity Joule 1,71 0,95 1,15Table 2: Mechanical characteristics of lumbar vertebrae L2 in compressionIn Table 1 and 2, the proportional stresses and strains, Young's moduli, limitstresses and strains and energy absorption capacity are illustrated.In Fig. 1 the linearized stress-strain diagrams of unified vertebrae L1-L2 are seenwith the relating characteristic points and values, for males and females together.Figure 1: Linearized stress-strain diagrams of vertebrae L1-L2Figs 2 and 3 illustrate the linear approximation of the age-related decline of measuredbreak loads and calculated limit stresses of vertebrae L1-L2, between 43-93 years, bydistinguishing the sexes. The decrease trends are also given numerically.Figure 2: Linear age- and sex-related decline of break load of vertebrae L1-L2Figure 3: Linear age- and sex-related decline of limit stresses of vertebrae L1-L2In Figs 4 and 5 the Young's moduli and the energy absorption capacity are illustrated interms of aging, by distinguishing sexes. The decrease trends are also given numerically.Linearized stress-strain diagram of L1-L2, total 71,7 year, A=1436 mm2, h=19,9 mm, BMD=0,376 1,78; 0,75E=73,7 Mpaσp=1,5 Mpaσu=2,1 MPa3,98; 2,11 4,93; 2,1401234560 2 4 6 8 10ε [%]σ [σ [σ [σ [Mpa] ]]]Break load versus aging and sexmale: -91 N/yearfemale:-56 N/year020004000600080001000040 50 60 70 80 90 100Age, yearLoad, Nmale femaleLimit stress versus aging and sexmale: -0,07 MPa/yearfemale: -0,05 MPa/year0123456740 50 60 70 80 90 100Age, yearStrength, MPamale femaleFigure 4: Linear age-related decline of Young's moduli of vertebrae L1-L2Figure 5: Linear age-related decline of energy absorption capacity of vertebrae L1-L26: Linear age-related decline of areal bone mineral density of vertebrae L1-L2Fig. 6 illustrates the age-related decrease of the areal bone mineral density(aBMD) of the measured vertebrae. Linear approximation is supposed to obtain thebone loss per a year.In Fig. 7 the age-related decrease of parameters of the trabecular architecture isillustrated. Linear approximation of age-dependence of trabecular diameters, the ratio oftrabecular bone area over total area of vertebral cross section are illustrated.In Fig. 8 the linear approximation of the increase of limit stress in terms of thediamater and areal ratio of trabeculae can be seen.Young's modulus versus aging and sexmale: -2,8 MPa/yearfemale: -1,7 MPa/year05010015020025040 50 60 70 80 90 100Age, sexYoung mod, MPamale femaleEnergy absorption capacity versus aBMDmale: -0,03 Joule/yearfemale: -0,02 Joule/year01234540 50 60 70 80 90 100Age, yearsEnergy, Joulemale femaleBone mineral density versus aging and sexmale: -0,0050 g/cm2/yearfemale: -0,0025 g/cm2/year0,00,10,20,30,40,50,60,740 50 60 70 80 90 100Age, yearsBMD g/cm2male female7: Linear age-related decrease of trabecular architecture of vertebrae L1-L28: Linear increase of limit stress vs trabecular architecture of vertebrae L1-L24. DISCUSSION AND CONCLUSIONAs a result of the compression tests, there is a 15-18% decrease in the compressive loadbearing properties, in stress and strain moduli in distal direction. There is a significantdifference in the load bearing properties of males and females, namely, the compressiveload bearing capacity of women is about 30% smaller than that of the men. The breakload of women is 40-50% smaller. Moreover, since the cross sectional areas of womenare only 15% smaller, consequently, both the proportional and limit stresses are 30-40%smaller in women than in men. The Young's moduli of women are about 20-30%smaller than that of the man. At the same time, there is no significant sex-difference inthe proportional or limit strains and in the duclility. However, there is a significant dif-ference again in the energy absorption capacity of men and women: women have about35-45% smaller absorption capacity than men. This comes partly from the smaller limitstresses and partly from the smaller volume of vertebrae of females.The results of Lindahl (1976) and Hansson et al. (1987) concern the cancellouscore of vertebrae, proving that due to the high ductility, there is the trabecular bone thatis responsible for the energy absorption ability of vertebrae to avoid the injury in thecase of an accidental dynamical load. Mosekilde (2000) emphasized that a basic under-standing of age-related changes in the quality and strength of vertebral bone is crucial.Based on his combinative study he demonstrated that the age is the major determinantof vertebral bone strength, mass, and microarchitecture. There is, after the age of 50years, a higher tendency for disconnection of trabecular network in women than in men.By applying linear approximation for the age-related behaviour of all strengthcharacteristics, it can be observed that the decrease trends of women are smaller thanthat of men, seen in Fig. 2 for break load, in Fig. 3 for limit stress, in Fig. 4 for Young'smodulus and in Fig. 5 for energy absorption capacity.As a conclusion of our experiments, during the age period between 40-90 years,the strength properties decrease by 60-70% for both sexes. According to the linear re-gression analysis of McCaldren et al (1997), the compressive strength decrease yields8,5% in each decade of aging. This means that the 80 years long decrease period yields68% of total strength decrease. Mosekilde (1998) also mentioned that the decline instrength of the whole vertebral body during normal aging for both men and women is70-80%. These results are in agreement with our results.As seen in Fig. 6, the analyzed vertebrae belong to the strongly osteoporoticclass. It can be concluded that the areal bone minearal density decrease significanly withaging. The decrease trend can be numerically verified by applying linear approximation.All compressive strength parameters increase significantly with bone mineral density,or, inversely, decrease significantly with the age-related decrease of aBMD. Fig. 7 il-lustrates the age-related weakening of trabecular architecture, namely, the loss of trab-ecular diameter and the parameters of several trabecular areal ratio.  Fig 8 verifies nu-merically the effect of trabecular architecture on the compressive strength of vertebraein osteoporosis.In this study the compressive strength of osteoporotic lumbar vertebrae has beennumerically verified in terms of aging, sex and bone structure, based on mechanicaltests.5. REFERENCES1. Hansson, T.H., Keller, T.S., Panjabi, M.M.: A study of the compressive propertiesof lumbar vertebral trabeculae: effects of tissue characteristics, Spine, 1987, 2:56.2. Lindahl, O.: Mechanical properties of dried defatted spongy bone, Acta Orthop.Scand., 1976, 47:11.3. McCaldren, R.W., McGeough, J.A., Court-Brown, C.M.: Age-related changes in thecompressive strength of cancellous bone. The relative importance of changes in den-sity and trabecular architecture, Bone Joint Surg. Am., 1997, 79(3):421-427.4. Mosekilde, L.: The effect of modelling and remodelling on human vertebral bodyarchitecture, Technol. Health Care, 1998, 6(5-6):287-297.5. Mosekilde, L.: Age-related changes in bone mass, structure, and strength effects ofloading, Z. Rheumatol., 2000, 59(Suppl.1):1-9.ACKNOWLEDGEMENTSThe study has been supported by the projects ETT- 257/2000 and OTKA T033020,T025256, T046755,

Age-related changes in bone mass, structure, and strength effects of loading,

C.M.: Age-related changes in the compressive strength of cancellous bone. The relative importance of changes in density and trabecular architecture, Bone Joint Surg. Am.,

M.M.: A study of the compressive properties of lumbar vertebral trabeculae: effects of tissue characteristics,

Mechanical properties of dried defatted spongy bone, Acta Orthop. Scand.,

The effect of modelling and remodelling on human vertebral body architecture, Technol. Health Care,

Compressive load bearing and bone architecture of lumbar vertebrae in terms of sex and aging

Compressive load bearing and bone architecture of lumbar vertebrae in terms of sex and aging

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