**10. Conclusions**

This chapter presents some important findings for Functionally Graded Material (FGM) dental implant design in a power law configuration. This is vital for maintaining the overall health of the bone tissues. The research clearly suggests that, a better performance in bone turnover can be achieved by lowering the FGM dental implant material gradient. However, this will at the same time reduce the stiffness of implantation, consequently placing the bone-implant interface at higher risk of damage during the early healing stage.

Optimum Functionally Gradient Materials for Dental Implant Using Simulated Annealing 237

Chu, C.L., Xue, X.Y., Zhu, J.C. & Yin, Z.D. (2006). In vivo study on biocompatibility and bonding strength of hydroxyapatite-20 vol%Ti composite with bone tissues in the

Davidson, R. & Harel, D. (1996). Drawing graphs nicely using simulated annealing. ACM

Fleischer, M. (1995). Simulated annealing: past, present, and future, *Simulation Conference* 

Hedia, H.S. & Mahmoud, N.A. (2004). Design optimization of functionally graded dental

Hedia, H.S. (2005). Design of functionally graded dental implant in the presence of cancellous bone. *Journal of Biomedical Materials Research-Part B Applied Biomaterials*, Vol.

Hedia, H.S., Shabara, M.A.N., El-midany, T.T. & Fouda, N. (2006). Improved design of cementless hip stems using two-dimensional functionally graded materials. *Journal of* 

Huiskes, R., Dalstra, M., Vondervenne, R., Grootenboer, H. & Slooff, T.J. (1987). A hypothesis concerning the effect of implant rigidity on adaptive cortical bone

Kirkpatrick, S., C.D. Gellat, Jr. & Vecchi, M.P. (1983). Optimization by simulated annealing.

Lin, D., Li, Q., Li, W. & Swain, M.V. (2008a). Dental implant induced bone remodeling and associated algorithms. *Journal of Mechanical Behavior of Biomedical Materials*, Vol. 2, No. 5,

Lin, D., Li, Q., Li, W. & Swain, M.V. (2008b). Functionally graded implant and its effect on

Lin, D., Li, Q., Li, W., Zhou, S. & Swain, M.V. (2009). Design optimization of functionally graded dental implant for bone remodeling. *Composites Part B: Engineering*, Vol. 40, pp.

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M., Teller, A.H. & Teller, E. (1953). Equation of state calculations by fast computing machines. *Journal of Chemistry and Physics*, Vol.

O'Mahony, A.M., Williams, J.L. & Spencer, P. (2001). Anisotropic elasticity of cortical and cancellous bone in the posterior mandible increases peri-implant stress and strain under

Parks, G. T. (1990). An intelligent stochastic optimization routine for nuclear fuel cycle

Rho, J.Y., Hobatho, M.C. & Ashman, R.B. (1995). Relations of mechanical-properties to density and Ct numbers in human bone. *Medical Engineering & Physics*, Vol. 17, No. 5,

Suman, B. (2004). Study of simulated annealing based algorithms for multi-objective optimization of a constrained problem. *Computers & Chemical Engineering*, Vol. 28, pp.

*Biomedical Materials Research - Part B Applied Biomaterials*, Vol. 79, pp. 42-49.

remodeling in the femur. *Journal of Biomechanics*, Vol. 20, No. 8, pp. 808-809.

bone remodeling. *Advance Materials Research*, Vol. 47-50, pp. 1035-1038.

oblique loading. *Clinic Oral Implants Research*, Vol. 12, No. 6, pp. 648-657.

Rouge, F. (1896). *V. Pareto, Cours D'Economie Politique*. volume I and II, Laussane.

design. *Nuclear Technology,* Vol. 89(2), pp. 233-246.

rabbit. *Biomedical Materials and Engineering*, Vol.16, No. 3, pp. 203-213.

*Proceedings IEEE*, pp. 155-161, Arlington, VA, USA, Aug., 2002.

implant. *Biomedical Materials and Engineering*, Vol. 14, pp. 133-143.

Transactions on Graphics, Vol. 15, pp. 301-331.

75, pp. 74-80.

pp. 410-432.

668-675.

21, pp. 1087-1092.

pp. 347-355.

1849-1871.

*Science*, Vol. 220, pp. 671-680.

The problem may be solved by the multi-objective optimization method. The Pareto front was determined using the Suppapitnarm Multi-Objective Simulated Annealing (SMOSA) optimization procedure. The results obtained from the SMOSA confirm the results obtained by the Response Surface Methodology (RSM), in addition to offering further improvements. The SMOSA optimized the objective functions on a wider data range than RSM and offered better results with respect to the cortical density function (almost 33% more than RSM). SMOSA optimization in this case, gives more selection of material gradient (*m*) for designing FGM dental implant compared to RSM. The material gradient varies from 0.1 to 0.65 given by SMOSA.

By considering the point that the scale in the FGM dental implant is in micro, the importance of accuracy in optimization of the FGM implant is understood. The design of FGM gradient parameter is expected to maximize the densities (cortical and cancellous) and minimize the displacement and plays a more important role in the design methodology. However, sacrifice may be made when the third criterion of displacement is introduced, which means that an optimal gradient *m* for bone remodeling may not be the best for stiffness. It is expected that the design methodology can produce more favorably patient specific implant, better improving the immediate and long-term restorative outcomes.
