Printed in Great Britain M21-9290193 $6_W+.oO Pergamon Press Ltd DO BONE INGROWTH PROCESSES PRODUCE A GLOBALLY OPTIMIZED STRUCTURE?

Abstract-A topology optimization program was applied to test the hypothesis that bone adaptation to porous coated implants produces a structure which minimizes the global strain energy density. The program was used to predict the optimal material layout around a porous coated tibia1 component with multiple cones [Goldstein et al., Trans. 37th ORS, p. 92 (1991)]. The sensitivity of the predicted adaptation to analysis assumptions was assessed and the predicted bone ingrowth and apposition were compared with the experimental findings of Goldstein et al. The results showed that apposition occurred consistently at the cone tips regardless of analysis assumptions. The specific topology of apposition at the cone tips was most sensitive to the assumed loading conditions. A comparison with the experimental results for 11 subdivisions showed that the general predicted location of material agreed with the experimental results (R *>0.59). However, the program predicted a consolidated bone greater than 1000 pm in thickness at the cone tips, which differed from the porous bone structure found experimentally. This discrepancy was reflected in a refined comparison over 31 subdivisions which did not produce a significant correlation (R2 GO.3). The program also predicted little ingrowth (< 6-7%). indicating that ingrowth past the first bead layer contributed little to the overall bone-implant interface layer stiffness. Based on these results, we conclude, within limitations of a two-dimensional analysis. that bone adaptation to porous coated implants does not produce a structure solely optimized to minimize the global strain energy density. We hypothesize that the final bone structure reflects the need to meet both mechanical and nutritional demands