Even in a well-functioning total hip replacement, significant peri-implant bone resorption can occur secondary to stress shielding. Stress shielding is caused by an undesired mismatch of elastic modulus between the stiffer implant and the adjacent bone tissue. To address this problem, we present here a microarchitected hip implant that consists of a three-dimensional (3D) graded lattice material with properties that are mechanically biocompatible with those of the femoral bone. Asymptotic homogenization (AH) is used to numerically determine the mechanical and fatigue properties of the implant, and a gradient-free scheme of topology optimization is used to find the optimized relative density distribution of the porous implant under multiple constraints dictated by implant micromotion, pore size, porosity, and minimum manufacturable thickness of the cell elements. Obtained for a 38-year-old patient femur, bone resorption is assessed by the difference in strain energy between the implanted bone and the intact bone in the postoperative conditions. The numerical results suggest that bone loss for the optimized porous implant is only 42% of that of a fully solid implant, here taken as benchmark, and 79% of that of a porous implant with uniform density. The architected hip implant presented in this work shows clinical promise in reducing bone loss while preventing implant micromotion, thereby contributing to reduce the risk of periprosthetic fracture and the probability of revision surgery.

References

1.
Pivec
,
R.
,
Johnson
,
A. J.
,
Mears
,
S. C.
, and
Mont
,
M. A.
,
2012
, “
Hip Arthroplasty
,”
Lancet
,
380
(
9855
), pp.
1768
1777
.
2.
Iolascon
,
G.
,
Di Pietro
,
G.
,
Capaldo
,
A.
,
Gioia
,
C.
,
Gatto
,
S.
, and
Gimigliano
,
F.
,
2010
, “
Periprosthetic Bone Density as Outcome of Therapeutic Response
,”
Clin. Cases Miner. Bone Metabol.
,
7
(
1
), pp.
27
31
.https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2898003/
3.
Dattani
,
R.
,
2007
, “
Femoral Osteolysis Following Total Hip Replacement
,”
Postgrad. Med. J.
,
83
(
979
), pp.
312
316
.
4.
Berry
,
D. J.
,
Harmsen
,
W. S.
,
Cabanela
,
M. E.
, and
Morrey
,
B. F.
,
2002
, “
Twenty-Five-Year Survivorship of Two Thousand Consecutive Primary Charnley Total Hip Replacements
,”
J. Bone Jt. Surg. Am.
,
84
(
2
), pp.
171
177
.
5.
Khanuja
,
H. S.
,
Vakil
,
J. J.
,
Goddard
,
M. S.
, and
Mont
,
M. A.
,
2011
, “
Cementless Femoral Fixation in Total Hip Arthroplasty
,”
J. Bone Jt. Surg. Am.
,
93
(
5
), pp.
500
509
.
6.
Ridzwan, M. I. Z., Shuib, S., Hassan, A. Y., Shokri, A. A., and Mohamad Ibrahim, M. N.,
2007
, “
Problem of Stress Shielding and Improvement to the Hip Implant Designs: A Review
,”
J. Med. Sci.
,
7
(
3
), pp.
460
467
.https://scialert.net/fulltext/?doi=jms.2007.460.467
7.
Mahomed
,
N. N.
,
Barrett
,
J. A.
,
Katz
,
J. N.
,
Phillips
,
C. B.
,
Losina
,
E.
,
Lew
,
R. A.
,
Guadagnoli
,
E.
,
Harris
,
W. H.
,
Poss
,
R.
, and
Baron
,
J. A.
,
2003
, “
Rates and Outcomes of Primary and Revision Total Hip Replacement in the United States Medicare Population
,”
J. Bone Jt. Surg. Am.
,
85
(
1
), pp.
27
32
.
8.
Kurtz
,
S.
,
Ong
,
K.
,
Lau
,
E.
,
Mowat
,
F.
, and
Halpern
,
M.
,
2007
, “
Projections of Primary and Revision Hip and Knee Arthroplasty in the United States From 2005 to 2030
,”
J. Bone Jt. Surg.
,
89
(
4
), pp.
780
785
.https://www.ncbi.nlm.nih.gov/pubmed/17403800
9.
Ulrich
,
S. D.
,
Seyler
,
T. M.
,
Bennett
,
D.
,
Delanois
,
R. E.
,
Saleh
,
K. J.
,
Thongtrangan
,
I.
,
Kuskowski
,
M.
,
Cheng
,
E. Y.
,
Sharkey
,
P. F.
, and
Parvizi
,
J.
,
2008
, “
Total Hip Arthroplasties: What Are the Reasons for Revision?
,”
Int. Orthop.
,
32
(
5
), pp.
597
604
.
10.
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
.
11.
Bougherara
,
H.
,
Zdero
,
R.
,
Dubov
,
A.
,
Shah
,
S.
,
Khurshid
,
S.
, and
Schemitsch
,
E. H.
,
2011
, “
A Preliminary Biomechanical Study of a Novel Carbon–Fibre Hip Implant Versus Standard Metallic Hip Implants
,”
Med. Eng. Phys.
,
33
(
1
), pp.
121
128
.
12.
Simoes
,
J.
, and
Marques
,
A.
,
2005
, “
Design of a Composite Hip Femoral Prosthesis
,”
Mater. Des.
,
26
(
5
), pp.
391
401
.
13.
Scholz
,
M.-S.
,
Blanchfield
,
J.
,
Bloom
,
L.
,
Coburn
,
B.
,
Elkington
,
M.
,
Fuller
,
J.
,
Gilbert
,
M.
,
Muflahi
,
S.
,
Pernice
,
M.
, and
Rae
,
S.
,
2011
, “
The Use of Composite Materials in Modern Orthopaedic Medicine and Prosthetic Devices: A Review
,”
Compos. Sci. Technol
,
71
(
16
), pp.
1791
1803
.
14.
Evans
,
S.
, and
Gregson
,
P.
,
1998
, “
Composite Technology in Load-Bearing Orthopaedic Implants
,”
Biomaterials
,
19
(
15
), pp.
1329
1342
.
15.
Brandwood
,
A.
,
Noble
,
K. R.
, and
Schindhelm
,
K.
,
1992
, “
Phagocytosis of Carbon Particles by Macrophages In Vitro
,”
Biomaterials
,
13
(
9
), pp.
646
648
.
16.
Wen
,
C.
,
Mabuchi
,
M.
,
Yamada
,
Y.
,
Shimojima
,
K.
,
Chino
,
Y.
, and
Asahina
,
T.
,
2001
, “
Processing of Biocompatible Porous Ti and Mg
,”
Scr. Mater.
,
45
(
10
), pp.
1147
1153
.
17.
Ryan
,
G.
,
Pandit
,
A.
, and
Apatsidis
,
D. P.
,
2006
, “
Fabrication Methods of Porous Metals for Use in Orthopaedic Applications
,”
Biomaterials
,
27
(
13
), pp.
2651
2670
.
18.
Pattanayak
,
D. K.
,
Fukuda
,
A.
,
Matsushita
,
T.
,
Takemoto
,
M.
,
Fujibayashi
,
S.
,
Sasaki
,
K.
,
Nishida
,
N.
,
Nakamura
,
T.
, and
Kokubo
,
T.
,
2011
, “
Bioactive Ti Metal Analogous to Human Cancellous Bone: Fabrication by Selective Laser Melting and Chemical Treatments
,”
Acta Biomater.
,
7
(
5
), pp.
1398
1406
.
19.
Cheng
,
A.
,
Humayun
,
A.
,
Cohen
,
D. J.
,
Boyan
,
B. D.
, and
Schwartz
,
Z.
,
2014
, “
Additively Manufactured 3D Porous Ti–6Al–4V Constructs Mimic Trabecular Bone Structure and Regulate Osteoblast Proliferation, Differentiation and Local Factor Production in a Porosity and Surface Roughness Dependent Manner
,”
Biofabrication
,
6
(
4
), p.
045007
.
20.
Li
,
X.
,
Wang
,
C.
,
Zhang
,
W.
, and
Li
,
Y.
,
2009
, “
Fabrication and Characterization of Porous Ti6Al4V Parts for Biomedical Applications Using Electron Beam Melting Process
,”
Mater. Lett.
,
63
(
3–4
), pp.
403
405
.
21.
Bandyopadhyay
,
A.
,
Espana
,
F.
,
Balla
,
V. K.
,
Bose
,
S.
,
Ohgami
,
Y.
, and
Davies
,
N. M.
,
2010
, “
Influence of Porosity on Mechanical Properties and In Vivo Response of Ti6Al4V Implants
,”
Acta Biomater.
,
6
(
4
), pp.
1640
1648
.
22.
Wang
,
X.
,
Xu
,
S.
,
Zhou
,
S.
,
Xu
,
W.
,
Leary
,
M.
,
Choong
,
P.
,
Qian
,
M.
,
Brandt
,
M.
, and
Xie
,
Y. M.
,
2016
, “
Topological Design and Additive Manufacturing of Porous Metals for Bone Scaffolds and Orthopaedic Implants: A Review
,”
Biomaterials
,
83
, pp.
127
141
.
23.
Kuiper
,
J. H.
, and
Huiskes
,
R.
,
1997
, “
Mathematical Optimization of Elastic Properties: Application to Cementless Hip Stem Design
,”
ASME J. Biomech. Eng.
,
119
(
2
), pp.
166
174
.
24.
Kuiper
,
J. H.
, and
Huiskes
,
R.
,
1992
, “
Numerical Optimization of Hip-Prosthetic Stem Material
,”
Recent Advances in Computer Methods in Biomechanics and Biomedical Engineering
,
J.
Middleton
,
G. N.
Pande
, and
K. R.
Williams
, eds.,
Books and Journals International, Ltd
.,
Swansea, UK
, pp.
76
84
.
25.
Gross
,
S.
, and
Abel
,
E. W.
,
2001
, “
A Finite Element Analysis of Hollow Stemmed Hip Prostheses as a Means of Reducing Stress Shielding of the Femur
,”
J. Biomech.
,
34
(
8
), pp.
995
1003
.
26.
Hedia, H. S., Shabara, M. A. N., EI-Midany, T. T., and Fouda, N.,
2006
, “
Improved Design of Cementless Hip Stems Using Two-Dimensional Functionally Graded Materials
,”
J. Biomed. Mater. Res. B.
,
79
(
1
), pp.
42
49
.
27.
Fraldi
,
M.
,
Esposito
,
L.
,
Perrella
,
G.
,
Cutolo
,
A.
, and
Cowin
,
S. C.
,
2010
, “
Topological Optimization in Hip Prosthesis Design
,”
Biomech. Model. Mech.
,
9
(
4
), pp.
389
402
.
28.
Kayabasi
,
O.
, and
Ekici
,
B.
,
2007
, “
The Effects of Static, Dynamic and Fatigue Behavior on Three-Dimensional Shape Optimization of Hip Prosthesis by Finite Element Method
,”
Mater. Des.
,
28
(
8
), pp.
2269
2277
.
29.
Higa
,
M.
,
Tanino
,
H.
,
Nishimura
,
I.
,
Mitamura
,
Y.
,
Matsuno
,
T.
, and
Ito
,
H.
,
2015
, “
Three-Dimensional Shape Optimization of a Cemented Hip Stem and Experimental Validations
,”
J. Artif. Organs
,
18
(
1
), pp.
79
85
.
30.
Rungsiyakull
,
C.
,
Li
,
Q.
,
Sun
,
G.
,
Li
,
W.
, and
Swain
,
M. V.
,
2010
, “
Surface Morphology Optimization for Osseointegration of Coated Implants
,”
Biomaterials
,
31
(
27
), pp.
7196
7204
.
31.
Lin
,
D.
,
Li
,
Q.
,
Li
,
W.
,
Zhou
,
S.
, and
Swain
,
M. V.
,
2009
, “
Design Optimization of Functionally Graded Dental Implant for Bone Remodeling
,”
Compos. Part B: Eng
,
40
(
7
), pp.
668
675
.
32.
Chen
,
J.
,
Rungsiyakull
,
C.
,
Li
,
W.
,
Chen
,
Y.
,
Swain
,
M.
, and
Li
,
Q.
,
2013
, “
Multiscale Design of Surface Morphological Gradient for Osseointegration
,”
J. Mech. Behav. Biomed. Mater
,
20
, pp.
387
397
.
33.
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
.
34.
Arabnejad
,
S.
,
Johnston
,
R. B.
,
Pura
,
J. A.
,
Singh
,
B.
,
Tanzer
,
M.
, and
Pasini
,
D.
,
2016
, “
High-Strength Porous Biomaterials for Bone Replacement: A Strategy to Assess the Interplay Between Cell Morphology, Mechanical Properties, Bone Ingrowth and Manufacturing Constraints
,”
Acta Biomater.
,
30
, pp.
345
356
.
35.
Melancon
,
D.
,
Bagheri
,
Z.
,
Johnston
,
R.
,
Liu
,
L.
,
Tanzer
,
M.
, and
Pasini
,
D.
,
2017
, “
Mechanical Characterization of Structurally Porous Biomaterials Built Via Additive Manufacturing: Experiments, Predictive Models, and Design Maps for Load-Bearing Bone Replacement Implants
,”
Acta Biomater.
,
63
, pp.
350
368
.
36.
Deb
,
K.
,
Pratap
,
A.
,
Agarwal
,
S.
, and
Meyarivan
,
T.
,
2002
, “
A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II
,”
IEEE T. Evolut. Comput.
,
6
(
2
), pp.
182
197
.
37.
Biyikli
,
E.
, and
To
,
A. C.
,
2015
, “
Proportional Topology Optimization: A New Non-Sensitivity Method for Solving Stress Constrained and Minimum Compliance Problems and Its Implementation in MATLAB
,”
PloS One
,
10
(
12
), p.
e0145041
.
38.
Rozvany
,
G. I.
,
Zhou
,
M.
, and
Birker
,
T.
,
1992
, “
Generalized Shape Optimization Without Homogenization
,”
Struct. Optim
,
4
(
3-4
), pp.
250
252
.
39.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
1999
, “
Material Interpolation Schemes in Topology Optimization
,”
Arch. Appl. Mech.
,
69
(
9–10
), pp.
635
654
.
40.
Bendsøe
,
M. P.
, and
Sigmund
,
O.
,
2003
,
Topology Optimization: Theory, Methods, and Applications
,
Springer
,
Berlin
.
41.
Jensen
,
K. E.
,
2016
, “
Anisotropic Mesh Adaptation and Topology Optimization in Three Dimensions
,”
ASME J. Mech. Des.
,
138
(
6
), p.
061401
.
42.
Allaire
,
G.
,
Jouve
,
F.
, and
Toader
,
A.-M.
,
2004
, “
Structural Optimization Using Sensitivity Analysis and a Level-Set Method
,”
J. Comput. Phys
,
194
(
1
), pp.
363
393
.
43.
Wang
,
M. Y.
,
Wang
,
X.
, and
Guo
,
D.
,
2003
, “
A Level Set Method for Structural Topology Optimization
,”
Comput. Methods Appl. Mech. Eng
,
192
(
1–2
), pp.
227
246
.
44.
Deng
,
X.
,
Wang
,
Y.
,
Yan
,
J.
,
Liu
,
T.
, and
Wang
,
S.
,
2016
, “
Topology Optimization of Total Femur Structure: Application of Parameterized Level Set Method Under Geometric Constraints
,”
ASME J. Mech. Des.
,
138
(
1
), p.
011402
.
45.
Liu
,
J.
, and
Ma
,
Y.
,
2017
, “
Sustainable Design-Oriented Level Set Topology Optimization
,”
ASME J. Mech. Des.
,
139
(
1
), p.
011403
.
46.
Svanberg
,
K.
,
1987
, “
The Method of Moving Asymptotes—A New Method for Structural Optimization
,”
Int. J. Numer. Methods Eng.
,
24
(
2
), pp.
359
373
.
47.
Egan
,
P. F.
,
Ferguson
,
S. J.
, and
Shea
,
K.
,
2017
, “
Design of Hierarchical Three-Dimensional Printed Scaffolds Considering Mechanical and Biological Factors for Bone Tissue Engineering
,”
ASME J. Mech. Des.
,
139
(
6
), p.
061401
.
48.
Arabnejad
,
S.
,
Johnston
,
B.
,
Tanzer
,
M.
, and
Pasini
,
D.
,
2017
, “
Fully Porous 3D Printed Titanium Femoral Stem to Reduce Stress-Shielding Following Total Hip Arthroplasty
,”
J. Orthop. Res.
,
35
(
8
), pp.
1774
1783
.
49.
Bagheri
,
Z. S.
,
Melancon
,
D.
,
Liu
,
L.
,
Johnston
,
R. B.
, and
Pasini
,
D.
,
2017
, “
Compensation Strategy to Reduce Geometry and Mechanics Mismatches in Porous Biomaterials Built With Selective Laser Melting
,”
J. Mech. Behav. Biomed. Mater
,
70
, pp.
17
27
.
50.
Shan
,
Z.
, and
Gokhale
,
A. M.
,
2002
, “
Representative Volume Element for Non-Uniform Micro-Structure
,”
Comput. Mater. Sci.
,
24
(
3
), pp.
361
379
.
51.
Arabnejad
,
S.
, and
Pasini
,
D.
,
2013
, “
Mechanical Properties of Lattice Materials Via Asymptotic Homogenization and Comparison With Alternative Homogenization Methods
,”
Int. J. Mech. Sci.
,
77
, pp.
249
262
.
52.
Hollister
,
S. J.
, and
Kikuchi
,
N.
,
1992
, “
A Comparison of Homogenization and Standard Mechanics Analyses for Periodic Porous Composites
,”
Comput. Mech.
,
10
(
2
), pp.
73
95
.
53.
Cameron
,
A. C.
, and
Windmeijer
,
F. A.
,
1997
, “
An R-Squared Measure of Goodness of Fit for Some Common Nonlinear Regression Models
,”
J. Econom.
,
77
(
2
), pp.
329
342
.
54.
Pidaparti
,
R.
, and
Turner
,
C.
,
1997
, “
Cancellous Bone Architecture: Advantages of Nonorthogonal Trabecular Alignment Under Multidirectional Joint Loading
,”
J. Biomech.
,
30
(
9
), pp.
979
983
.
55.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2009
, “
Computational Simulation of Trabecular Adaptation Progress in Human Proximal Femur During Growth
,”
J. Biomech.
,
42
(
5
), pp.
573
580
.
56.
Tsai
,
S. W.
, and
Wu
,
E. M.
,
1971
, “
A General Theory of Strength for Anisotropic Materials
,”
J. Compos. Mater.
,
5
(
1
), pp.
58
80
.
57.
Austman
,
R. L.
,
Milner
,
J. S.
,
Holdsworth
,
D. W.
, and
Dunning
,
C. E.
,
2008
, “
The Effect of the Density–Modulus Relationship Selected to Apply Material Properties in a Finite Element Model of Long Bone
,”
J. Biomech.
,
41
(
15
), pp.
3171
3176
.
58.
Wirtz
,
D. C.
,
Schiffers
,
N.
,
Pandorf
,
T.
,
Radermacher
,
K.
,
Weichert
,
D.
, and
Forst
,
R.
,
2000
, “
Critical Evaluation of Known Bone Material Properties to Realize Anisotropic FE-Simulation of the Proximal Femur
,”
J. Biomech.
,
33
(
10
), pp.
1325
1330
.
59.
Heller
,
M.
,
Bergmann
,
G.
,
Kassi
,
J.-P.
,
Claes
,
L.
,
Haas
,
N.
, and
Duda
,
G.
,
2005
, “
Determination of Muscle Loading at the Hip Joint for Use in Pre-Clinical Testing
,”
J. Biomech.
,
38
(
5
), pp.
1155
1163
.
60.
Speirs
,
A. D.
,
Heller
,
M. O.
,
Duda
,
G. N.
, and
Taylor
,
W. R.
,
2007
, “
Physiologically Based Boundary Conditions in Finite Element Modelling
,”
J. Biomech.
,
40
(
10
), pp.
2318
2323
.
61.
Sperati
,
G.
, and
Ceri
,
L.
,
2014
, “
Total Hip Arthroplasty Using TRI-LOCK® DePuy Bone Preservation Femoral Stem: Our Experience
,”
Acta Biomed.
,
85
(
2
), pp.
66
70
.https://www.ncbi.nlm.nih.gov/pubmed/25409721
62.
Burt
,
C. F.
,
Garvin
,
K. L.
,
Otterberg
,
E. T.
, and
Jardon
,
O. M.
,
1998
, “
A Femoral Component Inserted Without Cement in Total Hip Arthroplasty. A Study of the Tri-Lock Component With an Average Ten-Year Duration of Follow-Up*
,”
J. Bone Jt. Surg.
,
80
(
7
), pp.
952
960
.
63.
Cuppone
,
M.
,
Seedhom
,
B. B.
,
Berry
,
E.
, and
Ostell
,
A. E.
,
2004
, “
The Longitudinal Young's Modulus of Cortical Bone in the Midshaft of Human Femur and Its Correlation With CT Scanning Data
,”
Calcif. Tissue Int.
,
74
(
3
), pp.
302
309
.https://www.ncbi.nlm.nih.gov/pubmed/14517712
64.
Sigmund
,
O.
,
2001
, “
A 99 Line Topology Optimization Code Written in Matlab
,”
Struct. Multidiscip. Optim.
,
21
(
2
), pp.
120
127
.
65.
Eschenauer
,
H. A.
, and
Olhoff
,
N.
,
2001
, “
Topology Optimization of Continuum Structures: A Review*
,”
ASME Appl. Mech. Rev.
,
54
(
4
), pp.
331
390
.
66.
Harrysson
,
O. L.
,
Cansizoglu
,
O.
,
Marcellin-Little
,
D. J.
,
Cormier
,
D. R.
, and
West
,
H. A.
,
2008
, “
Direct Metal Fabrication of Titanium Implants With Tailored Materials and Mechanical Properties Using Electron Beam Melting Technology
,”
Mater. Sci. Eng. C: Mater.
,
28
(
3
), pp.
366
373
.
67.
de Wild
,
M.
,
Schumacher
,
R.
,
Mayer
,
K.
,
Schkommodau
,
E.
,
Thoma
,
D.
,
Bredell
,
M.
,
Kruse Gujer
,
A.
,
Grätz
,
K. W.
, and
Weber
,
F. E.
,
2013
, “
Bone Regeneration by the Osteoconductivity of Porous Titanium Implants Manufactured by Selective Laser Melting: A Histological and Micro Computed Tomography Study in the Rabbit
,”
Tissue Eng. Part A
,
19
(
23–24
), pp.
2645
2654
.
68.
Kowalczyk
,
P.
,
2001
, “
Design Optimization of Cementless Femoral Hip Prostheses Using Finite Element Analysis
,”
ASME J. Biomech. Eng.
,
123
(
5
), pp.
396
402
.
69.
Harvey
,
E.
,
Bobyn
,
J.
,
Tanzer
,
M.
,
Stackpool
,
G.
,
Krygier
,
J.
, and
Hacking
,
S.
,
1999
, “
Effect of Flexibility of the Femoral Stem on Bone-Remodeling and Fixation of the Stem in a Canine Total Hip Arthroplasty Model Without Cement
,”
J. Bone Jt. Surg. Am.
,
81
(
1
), pp.
93
107
.
70.
Weinans
,
H.
,
Huiskes
,
R.
, and
Grootenboer
,
H. J.
,
1992
, “
Effects of Material Properties of Femoral Hip Components on Bone Remodeling
,”
J. Orthop. Res
,
10
(
6
), pp.
845
853
.
71.
Huang
,
X.
, and
Xie
,
Y.
,
2007
, “
Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method
,”
Finite Elem. Anal. Des
,
43
(
14
), pp.
1039
1049
.
72.
Murr
,
L.
,
Gaytan
,
S.
,
Medina
,
F.
,
Lopez
,
H.
,
Martinez
,
E.
,
Machado
,
B.
,
Hernandez
,
D.
,
Martinez
,
L.
,
Lopez
,
M.
, and
Wicker
,
R.
,
2010
, “
Next-Generation Biomedical Implants Using Additive Manufacturing of Complex, Cellular and Functional Mesh Arrays
,”
Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci.
,
368
(
1917
), pp.
1999
2032
.
73.
Heinl
,
P.
,
Müller
,
L.
,
Körner
,
C.
,
Singer
,
R. F.
, and
Müller
,
F. A.
,
2008
, “
Cellular Ti–6Al–4V Structures With Interconnected Macro Porosity for Bone Implants Fabricated by Selective Electron Beam Melting
,”
Acta Biomater.
,
4
(
5
), pp.
1536
1544
.
74.
Liu
,
L.
,
Kamm
,
P.
,
García-Moreno
,
F.
,
Banhart
,
J.
, and
Pasini
,
D.
,
2017
, “
Elastic and Failure Response of Imperfect Three-Dimensional Metallic Lattices: The Role of Geometric Defects Induced by Selective Laser Melting
,”
J. Mech. Phys. Solids
,
107
, pp.
160
184
.
75.
Babic
,
B.
,
Nesic
,
N.
, and
Miljkovic
,
Z.
,
2008
, “
A Review of Automated Feature Recognition With Rule-Based Pattern Recognition
,”
Comput. Ind.
,
59
(
4
), pp.
321
337
.
76.
Sigmund
,
O.
,
2007
, “
Morphology-Based Black and White Filters for Topology Optimization
,”
Struct. Multidiscip. Optim.
,
33
(
4–5
), pp.
401
424
.
77.
Andreassen
,
E.
,
Clausen
,
A.
,
Schevenels
,
M.
,
Lazarov
,
B. S.
, and
Sigmund
,
O.
,
2011
, “
Efficient Topology Optimization in MATLAB Using 88 Lines of Code
,”
Struct. Multidiscip. Optim.
,
43
(
1
), pp.
1
16
.
You do not currently have access to this content.