Abstract

This study proposes a numerical methodology to minimize the bone mass loss in a femur with a total hip arthroplasty procedure, considering uncertainties in the material parameters and using a reliability-based design optimization (RBDO) procedure. A genetic algorithm (GA) is applied for optimization, and a three-dimensional finite element (FE) model associated with the bone remodeling procedure is proposed and described to account for the internal and external femoral bone behavior. An example of a femoral prosthesis design is presented as a basis for discussion of the proposed methodologies, and the corresponding reliability level is evaluated. Constraints on the strength of all materials and target reliability levels are inputs to the optimization model. The main prosthesis dimensions and Young modulus are the design variables. The proposed methodology is compared with a well-known deterministic optimization (DO) procedure and the results show that it is important to consider the uncertainties in this kind of problem since in this case, the a posteriori reliability may be low.

References

References
1.
Spinelli
,
L. F.
,
Macedo
,
C. A. S.
,
Galia
,
C. R.
,
Rosito
,
R.
,
Schnaid
,
F.
,
Corso
,
L. L.
, and
Iturrioz
,
I.
,
2012
, “
Femoral Stem-Bone Interface Analysis of Logical Uncemented Stem
,”
Braz. J. Bio. Eng.
,
28
(
3
), pp.
238
247
.10.4322/rbeb.2012.031
2.
Prendergast
,
P. J.
,
1997
, “
Finite Element Models in Tissue Mechanics and Orthopaedic Implant Design
,”
Clin. Biomech.
,
12
(
6
), pp.
343
366
.10.1016/S0268-0033(97)00018-1
3.
Huiskes
,
R.
, and
van Rietbergen
,
B.
,
1995
, “
Preclinical Testing of Total Hip Stems: The Effects of Coating Placement
,”
Clin. Orthop. Rel. Res.
,
319
, pp.
64
76
.https://pure.tue.nl/ws/files/1937911/585442.pdf
4.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2010
, “
Computational Simulation of Simultaneous Cortical and Trabecular Bone Change in Human Proximal Femur During Bone Remodeling
,”
J. Biomech.
,
43
(
19
), pp.
294
301
.10.1016/j.jbiomech.2009.08.012
5.
García-Aznar
,
J. M.
,
1999
, “
Modelo de Remodelación Ósea: Análisis Numérico y Aplicaciones al Diseño de Fijaciones de Fracturas Del Fêmur Proximal
,”
Zaragoza
.
6.
Tsangari
,
H.
,
Findlay
,
D. M.
, and
Fazzalari
,
N. L.
,
2007
, “
Structural and Remodeling Indices in the Cancellous Bone of the Proximal Femur Across Adulthood
,”
Bone
,
40
(
1
), pp.
211
217
.10.1016/j.bone.2006.07.007
7.
Jang
,
I. G.
, and
Kim
,
I. Y.
,
2009
, “
Computational Simulation of Simultaneous Cortical and Trabecular Bone Change in Human Proximal Femur During Bone
,”
J. Biomech.
,
42
(
5
), p.
573
.10.1016/j.jbiomech.2008.12.009
8.
Corso
,
L. L.
,
Spinelli
,
L. F.
,
Schnaid
,
F.
,
Zanrosso
,
C. D.
, and
Marczak
,
R. J.
,
2015
, “
Optimization of a Cemented Femoral Prosthesis Considering Bone Remodeling
,”
ASME J. Biomech. Eng.
,
32
(
1
), p.
011002
.10.1115/1.4031938
9.
Belegundu
,
A. D.
, and
Chandrupatla
,
T. R.
,
1999
,
Optimization Concepts and Applications in Engineering
,
Cambridge University Press
,
Cambridge, UK
.
10.
Dickinson
,
A. S.
,
2014
, “
Analogy of Strain Energy Density Based Bone-Remodeling Algorithm and Structural Topology Optimization
,”
ASME J. Biomech. Eng.
,
36
(
4
), pp.
1
10
.
11.
Agarwal
,
H.
,
2004
,
Reliability Based Design Optimization: Formulation and Methodologies
,
University of Notre Dame
,
Notre Dame, IN
.
12.
Zhang
,
Y.
,
Putnam
,
A. W.
,
Heiner
,
A. D.
,
Callaghan
,
J. J.
, and
Brown
,
T. D.
,
2002
, “
Reliability of Detecting Prosthesis/Cement Interface Radiolucencies in Total Hip Arthroplasty
,”
J. Orthop. Res.
,
20
(
4
), pp.
683
687
.10.1016/S0736-0266(02)00005-0
13.
Kayabasi
,
O.
, and
Ekici
,
B.
,
2008
, “
Probabilistic Design of a Newly Designed Cemented Hip Prosthesis Using Finite Element Method
,”
Mater. Des.
,
29
(
5
), pp.
963
971
.10.1016/j.matdes.2007.03.024
14.
Agarwal
,
H.
,
Renaud
,
J. E.
,
Preston
,
E. L.
, and
Padmanabhan
,
D.
,
2004
, “
Uncertainty Quantification Using Evidence Theory in Multidisciplinary Design Optimization
,”
Reliab. Eng. Syst. Saf.
,
85
(
1–3
), pp.
281
294
.10.1016/j.ress.2004.03.017
15.
Gomes
,
H. M.
, and
Corso
,
L. L.
,
2017
, “
A Hybrid Method for Truss Mass Minimization Considering Uncertainties
,”
Math. Probl. Eng.
,
3
, pp.
1
14
.10.1155/2017/2324316
16.
Ho-Huu
,
V.
,
Duong-Gia
,
D.
,
Vo-Duy
,
T.
,
Le-Duc
,
T.
, and
Nguyen-Thoi
,
T.
,
2018
, “
An Efficient Combination of Multi-Objective Evolutionary Optimization and Reliability Analysis for Reliability-Based Design Optimization of Truss Structures
,”
Expert Syst. Appl.
,
102
, p.
262
10.1016/j.eswa.2018.02.040
17.
Lago
,
M. A.
,
Rupérez
,
M. J.
,
Martínez-Martínez
,
F.
,
Martínez-Sanchis
,
S.
,
Bakic
,
P. R.
, and
Monserrat
,
C.
,
2015
, “
Methodology Based on Genetic Heuristics for In-Vivo Characterizing the Patient-Specific Biomechanical Behavior of the Breast Tissues
,”
Expert Syst. Appl.
,
41
(
21
), pp.
7942
7950
.10.1016/j.eswa.2015.05.058
18.
Buroni
,
F. C.
, and
Comisso
,
P. E.
,
2004
, “
Modelado Numérico Computacional de Estruturas Óseas – Desarrollo de Uma Metodologia y Aplicación a Uma Prótesis de Reemplazo de Cúpula Radial
,” Instituto Facultad de Ingeniería Universidad Nacional de Mar del Plata., Mar del Plata, Argentina.
19.
Colloca
,
M.
,
Ito
,
K.
, and
Rietbergen
,
B. V.
,
2014
, “
An Analytical Approach to Investigate the Evolution of Bone Volume Fraction in Bone Remodeling Simulation at the Tissue and Cell Level
,”
ASME J. Biomech. Eng.
,
136
(
3
), p.
031004
.10.1115/1.4026227
20.
Beaupré
,
G. S.
,
Orr
,
T. E.
, and
Carter
,
D. R.
,
1990
, “
An Approach for Time Dependent Bone Modeling and Remodeling*Application: A Preliminary Remodeling Simulation
,”
J. Orthop. Res.
,
8
(
5
), pp.
662
670
.10.1002/jor.1100080507
21.
Moreo
,
P.
,
Pérez
,
M. A.
,
García-Aznar
,
J. M.
, and
Doblaré
,
M.
,
2006
, “
Modelling the Mixed-Mode Failure of Cement–Bone Interfaces
,”
Eng. Fract. Mech.
,
73
(
10
), pp.
1379
1395
.10.1016/j.engfracmech.2006.01.005
22.
Martin
,
R. B.
,
2007
, “
Targeted Bone Remodeling Involves BMU Steering as Well as Activation
,”
Bone
,
40
(
6
), pp.
1574
1580
.10.1016/j.bone.2007.02.023
23.
Pivonka
,
P.
,
Zimak
,
J.
,
Smith
,
D. W.
,
Gardiner
,
B. S.
,
Dunstan
,
C. R.
,
Sims
,
N. A.
,
Martin
,
T. J.
, and
Mundy
,
G. R.
,
2008
, “
Model Structure and Control of Bone Remodeling: A Theoretical Study
,”
Bone
,
43
(
2
), pp.
249
263
.10.1016/j.bone.2008.03.025
24.
Holland
,
J. H.
,
1975
,
Adaptation in Natural and Artificial Systems
,
University of Michigan Press
,
Ann Arbor, MI
.
25.
Ardestani
,
M. M.
,
Moazen
,
M.
, and
Jin
,
Z.
,
2014
, “
Gait Modification and Optimization Using Neural Network–Genetic Algorithm Approach: Application to Knee Rehabilitation
,”
Expert Syst. Appl.
,
16
, p.
41
.10.1016/j.eswa.2014.06.034
26.
Ang
,
A. H.-S.
, and
Tang
,
W. H.
,
2006
,
Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering
, 2nd ed.,
Wiley
,
Danvers, MA
.
27.
Hasofer
,
A. M.
, and
Lind
,
D.
,
1974
, “
An Exact and Invariant First-Order Reliability Format
,”
J. Eng. Mech.
,
100
, pp.
111
121
.10.1080/03601217408907258
28.
Tu
,
J.
,
Choi
,
K. K.
, and
Park
,
Y. H.
,
1999
, “
A New Study on Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
121
(
4
), pp.
557
564
.10.1115/1.2829499
29.
Macedo
,
C. A. S.
,
2007
,
Desenvolvimento de Haste Femoral Não Cimentada Nacional, Validade Por Normas Internacioais
,
Universidade Federal Do Rio Grande Do Sul
,
Porto Alegre, Brazil
.
30.
Goldberg
,
D. E.
,
1989
,
Genetic Algorithms in Search, Optimization and Machine Learning
,
Reading Addison-Wesley Publishing
,
Boston, MA
.
31.
Garcia
,
J. M.
,
Doblaré
,
M.
, and
Cegoñino
,
J.
,
2002
, “
Bone Remodeling Simulation: A Tool for Implant Design
,”
Comput. Mater. Sci.
,
25
(
1–2
), pp.
100
114
.10.1016/S0927-0256(02)00254-9
32.
Stucinskas
,
J.
,
Clauss
,
M.
,
Tarasevicius
,
S.
,
Wingstrand
,
H.
, and
Ilchmann
,
T.
,
2012
, “
Long-Term Femoral Bone Remodeling After Cemented Hip Arthroplasty With the Müller Straight Stem in the Operated and Nonoperated Femora
,”
J. Arthroplasty
,
27
(
6
), pp.
927
933
.10.1016/j.arth.2011.09.011
33.
Bennet
,
D.
, and
Goswami
,
T.
,
2008
, “
Finite Element Analysis of Hip Stem Designs
,”
Mater. Des.
,
29
, pp.
45
60
.10.1016/j.matdes.2006.12.014
34.
Pérez
,
M. A.
,
Vendittoli
,
P.-A.
,
Lavigne
,
M.
, and
Nuno
,
N.
,
2014
, “
Bone Remodeling in the Resurfaced Femoral Head: Effect of Cement Mantle Thickness and Interface Characteristics
,”
Med. Eng. Phys.
,
36
, pp.
185
195
.10.1016/j.medengphy.2013.10.013
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