We present a new approach to designing three-dimensional, physically realizable porous femoral implants with spatially varying microstructures and effective material properties. We optimize over a simplified design domain to reduce shear stress at the bone-prosthetic interface with a constraint on the bone resorption measured using strain energy. This combination of objective and constraint aims to reduce implant failure and allows a detailed study of the implant designs obtained with a range of microstructure sets and parameters. The microstructure sets are either specified directly or constructed using shape interpolation between a finite number of microstructures optimized for multifunctional characteristics. We demonstrate that designs using varying microstructures outperform designs with a homogeneous microstructure for this femoral implant problem. Further, the choice of microstructure set has an impact on the objective values achieved and on the optimized implant designs. A proof-of-concept metal prototype fabricated via selective laser melting (SLM) demonstrates the manufacturability of designs obtained with our approach.
Issue Section:
Research Papers
Topics:
Bone,
Design,
Optimization,
Prostheses,
Shear stress,
Artificial limbs,
Stress,
Materials properties
References
1.
Zheng
, X.
, Lee
, H.
, Weisgraber
, T. H.
, Shusteff
, M.
, Deotte
, J.
, Duoss
, E. B.
, Kuntz
, J. D.
, Biener
, M. M.
, Ge
, Q.
, Jackson
, J. A.
, Kucheyev
, S. O.
, Fang
, N. X.
, and Spadaccini
, C. M.
, 2014
, “Ultralight, Ultrastiff Mechanical Metamaterials
,” Science
, 344
(6190
), pp. 1373
–1377
.2.
Bendsøe
, M. P.
, and Sigmund
, O.
, 2003
, Topology Optimization: Theory, Methods, and Applications
, Springer Verlag
, Berlin.3.
Rodrigues
, H.
, Guedes
, J. M.
, and Bendsoe
, M.
, 2002
, “Hierarchical Optimization of Material and Structure
,” Struct. Multidiscip. Optim.
, 24
(1
), pp. 1
–10
.4.
Coelho
, P.
, Fernandes
, P.
, Guedes
, J.
, and Rodrigues
, H.
, 2008
, “A Hierarchical Model for Concurrent Material and Topology Optimisation of Three-Dimensional Structures
,” Struct. Multidiscip. Optim.
, 35
(2
), pp. 107
–115
.5.
Cramer
, A. D.
, Challis
, V. J.
, and Roberts
, A. P.
, 2016
, “Microstructure Interpolation for Macroscopic Design
,” Struct. Multidiscip. Optim.
, 53
(3
), pp. 489
–500
.6.
Khanoki
, S. A.
, and Pasini
, D.
, 2012
, “Multiscale Design and Multiobjective Optimization of Orthopedic Hip Implants With Functionally Graded Cellular Material
,” ASME J. Biomech. Eng.
, 134
(3
), p. 031004
.7.
Malchau
, H.
, Herberts
, P.
, Eisler
, T.
, Garellick
, G.
, and Söderman
, P.
, 2002
, “The Swedish Total Hip Replacement Register
,” J. Bone Joint Surg.
, 84
(Suppl 2
), pp. S2
–S20
.8.
Kuiper
, J.
, and Huiskes
, R.
, 1997
, “Mathematical Optimization of Elastic Properties: Application to Cementless Hip Stem Design
,” ASME J. Biomech. Eng.
, 119
(2
), pp. 166
–174
.9.
Chanda
, S.
, Gupta
, S.
, and Pratihar
, D. K.
, 2015
, “A Genetic Algorithm-Based Multi-Objective Shape Optimization Scheme for Cementless Femoral Implant
,” ASME J. Biomech. Eng.
, 137
(3
), p. 034502
.10.
Engh
, C. A.
, McGovern
, T.
, Bobyn
, J.
, and Harris
, W. H.
, 1992
, “A Quantitative Evaluation of Periprosthetic Bone-Remodeling After Cementless Total Hip Arthroplasty
,” J. Bone Joint Surg. Am.
, 74
(7
), pp. 1009
–1020
.11.
Fraldi
, M.
, Esposito
, L.
, Perrella
, G.
, Cutolo
, A.
, and Cowin
, S.
, 2010
, “Topological Optimization in Hip Prosthesis Design
,” Biomech. Model. Mechanobiol.
, 9
(4
), pp. 389
–402
.12.
Hoffman
, O.
, 1967
, “The Brittle Strength of Orthotropic Materials
,” J. Compos. Mater.
, 1
(2
), pp. 200
–206
.13.
Challis
, V.
, Roberts
, A.
, and Wilkins
, A.
, 2008
, “Design of Three Dimensional Isotropic Microstructures for Maximized Stiffness and Conductivity
,” Int. J. Solids Struct.
, 45
(14
), pp. 4130
–4146
.14.
Kang
, H.
, Lin
, C.-Y.
, and Hollister
, S. J.
, 2010
, “Topology Optimization of Three Dimensional Tissue Engineering Scaffold Architectures for Prescribed Bulk Modulus and Diffusivity
,” Struct. Multidiscip. Optim.
, 42
(4
), pp. 633
–644
.15.
Torquato
, S.
, and Donev
, A.
, 2004
, “Minimal Surfaces and Multifunctionality
,” Proc. R. Soc. London, Ser. A
, 460
(2047
), pp. 1849
–1856
.16.
Head
, W. C.
, Bauk
, D. J.
, and Emerson
, R. H.
, Jr., 1995
, “Titanium as the Material of Choice for Cementless Femoral Components in Total Hip Arthroplasty
,” Clin. Orthop. Relat. Res.
, 311
, pp. 85
–90
.17.
Zhang
, L.
, Klemm
, D.
, Eckert
, J.
, Hao
, Y.
, and Sercombe
, T.
, 2011
, “Manufacture by Selective Laser Melting and Mechanical Behavior of a Biomedical Ti–24Nb–4Zr–8Sn Alloy
,” Scr. Mater.
, 65
(1
), pp. 21
–24
.18.
Challis
, V. J.
, Xu
, X.
, Zhang
, L. C.
, Roberts
, A. P.
, Grotowski
, J. F.
, and Sercombe
, T. B.
, 2014
, “High Specific Strength and Stiffness Structures Produced Using Selective Laser Melting
,” Mater. Des.
, 63
, pp. 783
–788
.19.
Williams
, M.
, 1952
, “Stress Singularities Resulting From Various Boundary Conditions
,” ASME J. Appl. Mech.
, 19
(4
), pp. 526
–528
.20.
Bendsøe
, M. P.
, and Kikuchi
, N.
, 1988
, “Generating Optimal Topologies in Structural Design Using a Homogenization Method
,” Comput. Methods Appl. Mech. Eng.
, 71
(2
), pp. 197
–224
.21.
Svanberg
, K.
, 1987
, “The Method of Moving Asymptotes—A New Method for Structural Optimization
,” Int. J. Numer. Methods Eng.
, 24
(2
), pp. 359
–373
.22.
Svanberg
, K.
, 2002
, “A Class of Globally Convergent Optimization Methods Based on Conservative Convex Seperable Approximations
,” SIAM J. Optim.
, 12
(2), pp. 555–573.23.
Camron
, H.
, Pilliar
, R.
, and Macnab
, I.
, 1976
, “The Rate of Bone Ingrowth Into Porous Metal
,” J. Biomed. Mater. Res.
, 10
(2
), pp. 295
–302
.24.
Boyan
, B. D.
, Hummert
, T. W.
, Dean
, D. D.
, and Schwartz
, Z.
, 1996
, “Role of Material Surfaces in Regulating Bone and Cartilage Cell Response
,” Biomaterials
, 17
(2
), pp. 137
–146
.25.
Khanoki
, S. A.
, and Pasini
, D.
, 2013
, “Fatigue Design of a Mechanically Biocompatible Lattice for a Proof-of-Concept Femoral Stem
,” J. Mech. Behav. Biomed. Mater.
, 22
, pp. 65
–83
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