A HOMOGENIZATION SAMPLING PROCEDURE FOR CALCULATING TRABECULAR BONE EFFECTIVE STIFFNESS AND TISSUE-LEVEL STRESS

A homogenization sampling procedure is introduced which allows computa tion of effective trabecular bone stiffness and individual trabecula l evel stress based on precise models of trabecular bone architecture. T hree-dimensional digitized images of 53 trabecular bone specimens with a resolution of 50 mum per voxel were directly converted into three-d imensional finite element meshes by making each voxel an 8-node isopar ametric brick element. Owing to the large mesh of 8000 elements, an el ement-by-element preconditioned conjugate gradient (EBEPCG) program wa s written to solve the local homogenization finite element equations. Predicted effective stiffness measures correlated well with experiment al results (R2 > 0.73). The predicted effective stiffnesses tended to under estimate the experimental values. Average absolute errors in eff ective stiffness estimates ranged between 31 and 38% for the sampling procedure compared to a range 49-150% for a regression fit to volume f raction squared. Trabecula level stress ranged between - 200 and + 300 times that predicted by analyzing trabecular bone as a continuum. Bot h tensile and compressive tissue stresses were engendered by a continu um compressive stress. Trabecula level strain energy density (SED) ran ged between 0 and 100 times the continuum SED value for two trabecular specimens. In conclusion, the homogenization sampling procedure consi stently predicted the influence of trabecular bone architecture on eff ective stiffness. It can also provide trabecular tissue stress and str ain estimates for arbitrary global loading of whole bones. Tissue stre sses and strains showed large variations compared to corresponding con tinuum level quantities.