Three-dimensional finite element modelling of non-invasively assessed trabecular bone structures R. Miiller and P. Riiegsegger Institute for Biomedical Engineering, University of Zurich and Swiss Federal Institute of Technology (ETH), Moussonstrasse 18, CH-8044 Zurich, Switzerland Received 3 February 1994, accepted 5 My 1994 ABSTWCT The three.~i~s~~~uZ ~~~ost~~ture of~unce~~~us bone seems to be one of the kty factors in ihe ~e~i&t~~n of~chan- ical bone properties like bone strength or bone stzff ness. In this paper trabecular bone structure was assessed non- destructively by means of high-resolution computed tomography (CT) with a spatial resolution of 250t~m. Min- eralized bone was separated from bone ma~ow and muscle tissue with ihe help of a three-di~siona~ se~tation algorithm based on the analysis of dirert~onal derivatizles. From the three-di~s~~na~ sta.ck of CT slices a subuohm comparable in size (3.6 x 3.4 x 3.4 mm’) to standard histologic bone sections was selected. We refer to this subvolume as non-invasive bone biopsy. A new automated mesh generator was developed to create a three-dimensional finite e~?lt model of the non-inv~iue bone baby. Four-no~d tetra~dron solid ekments were used to ~arantee a smooth surface representation. The aim of the presented work was to demonstrate the potential of high-resolution, c7‘ imaging in the prediction of the anisotropic material prop&es of cancellous bone. ~elimina~ results of the 3D Jinite etement stress analysis are very promising. The predicted value of the apparent Young’s modulus (564 MPa) is within the range reported for uniaxial compression testings of cancellous bone specimens. Keywords: Finite element method (FEM), quantitative computed tomography (QCT), 3D trabecular bone structure, mechanical bone properties, non-invasive bone biopsy Med. Eng. Phys., 1995, Vol. 17, 126-133, March INTRODUCTION The assessment of the mechanical properties of bone is essential in the determination of the frac- ture risk in osteoporotic subjects. So far, invasive and destructive methods like compression and bending testing had been used to determine dif- ferent mechanical properties like bone strength and bone stiffness. There is strong evidence that mechanical properties significantly depend on the apparent density of bone. Various investigators’.2.” demon- strated that the elastic properties improve with increasing apparent density as a function of power law regressions. This concept could also be sup- ported by an engineering point of view due to the similarity of trabecular bone to porous engineer- ing materials*. Because cancellous bone is inherently anisotropic there is an obvious depen- dence of the material properties on the architec- ture of trabecular bone as noted by Pugh et cd.“. Address for correspondence: Ralph Miiller, Institute for Biomedical Engineering, Moussonstrasse 18, CH-8044 Ziirich, Switzerland Hayes and Snyder’ stressed the importance of studying and quantifying the architecture of tra- becular bone. They developed digital analysis algorithms to correlate mechanical bone proper- ties with trabecular microstructure. The import- ance of trabecular microstructure in relation to fracture incidence was investigated by several groups7.s. In an attempt to analyse bone on a microstruc- tural level different models of the trabecular architecture have been used. McElhaney et aZ.’ presented one of the very early models. Using a porous block model consisting of cubic trabecular bone aggregates they found good agreement between the experimental data and the predic- tions of the modulus and strength based on its density and internal geometry. The primary assumption in the model was that different types of bones have identical microscopic properties but varying microscopic structures. Based on this assumption models of highly idealized trabecular structures have been anal lytical”,” x sed using either an ana- or a numerical’ xl1 approach to predict