Assessing the sensitivity of a finite-element (FE) model to uncertainties in geometric parameters and material properties is a fundamental step in understanding the reliability of model predictions. However, the computational cost of individual simulations and the large number of required models limits comprehensive quantification of model sensitivity. To quickly assess the sensitivity of an FE model, we built linear and Kriging surrogate models of an FE model of the intact hemipelvis. The percentage of the total sum of squares (%TSS) was used to determine the most influential input parameters and their possible interactions on the median, 95th percentile and maximum equivalent strains. We assessed the surrogate models by comparing their predictions to those of a full factorial design of FE simulations. The Kriging surrogate model accurately predicted all output metrics based on a training set of 30 analyses (R2 = 0.99). There was good agreement between the Kriging surrogate model and the full factorial design in determining the most influential input parameters and interactions. For the median, 95th percentile and maximum equivalent strain, the bone geometry (60%, 52%, and 76%, respectively) was the most influential input parameter. The interactions between bone geometry and cancellous bone modulus (13%) and bone geometry and cortical bone thickness (7%) were also influential terms on the output metrics. This study demonstrates a method with a low time and computational cost to quantify the sensitivity of an FE model. It can be applied to FE models in computational orthopaedic biomechanics in order to understand the reliability of predictions.

References

References
1.
Helgason
,
B.
,
Perilli
,
E.
,
Schileo
,
E.
,
Taddei
,
F.
,
Brynjólfsson
,
S.
, and
Viceconti
,
M.
,
2008
, “
Mathematical Relationships Between Bone Density and Mechanical Properties: A Literature Review
,”
Clin. Biomech.
,
23
(
2
), pp.
135
146
.
2.
Cook
,
D.
,
Julias
,
M.
, and
Nauman
,
E.
,
2014
, “
Biological Variability in Biomechanical Engineering Research: Significance and Meta-Analysis of Current Modeling Practices
,”
ASME J. Biomech.
,
47
(
6
), pp.
1241
1250
.
3.
Viceconti
,
M.
,
Olsen
,
S.
,
Nolte
,
L. P.
, and
Burton
,
K.
,
2005
, “
Extracting Clinically Relevant Data From Finite Element Simulations
,”
Clin. Biomech.
,
20
(
5
), pp.
451
454
.
4.
Anderson
,
A.
,
Ellis
,
B.
, and
Weiss
,
J.
,
2007
, “
Verification, Validation and Sensitivity Studies in Computational Biomechanics
,”
Comput. Methods Biomech. Biomed. Eng.
,
10
(
3
), pp.
171
184
.
5.
ASME
,
2006
, “
Guide for Verification and Validation in Computational Solid Mechanics
,” The American Society of Mechanical Engineers, New York, Standard No. VV10-2006, pp.
1
36
.
6.
Dar
,
F. H.
,
Meakin
,
J. R.
, and
Aspden
,
R. M.
,
2002
, “
Statistical Methods in Finite Element Analysis
,”
ASME J. Biomech.
,
35
(
9
), pp.
1155
1161
.
7.
Clarke
,
S. G.
,
Phillips
,
A. T. M.
,
Bull
,
A. M. J.
, and
Cobb
,
J. P.
,
2012
, “
A Hierarchy of Computationally Derived Surgical and Patient Influences on Metal on Metal Press-Fit Acetabular Cup Failure
,”
ASME J. Biomech.
,
45
(
9
), pp.
1698
1704
.
8.
Isaksson
,
H.
,
van Donkelaar
,
C. C.
,
Huiskes
,
R.
,
Yao
,
J.
, and
Ito
,
K.
,
2008
, “
Determining the Most Important Cellular Characteristics for Fracture Healing Using Design of Experiments Methods
,”
J. Theor. Biol.
,
255
(
1
), pp.
26
39
.
9.
Yao
,
J.
,
Funkenbusch
,
P. D.
,
Snibbe
,
J.
,
Maloney
,
M.
, and
Lerner
,
A. L.
,
2005
, “
Sensitivities of Medial Meniscal Motion and Deformation to Material Properties of Articular Cartilage, Meniscus and Meniscal Attachments Using Design of Experiments Methods
,”
ASME J. Biomech. Eng.
,
128
(
3
), pp.
399
408
.
10.
Malandrino
,
A.
,
Planell
,
J. A.
, and
Lacroix
,
D.
,
2009
, “
Statistical Factorial Analysis on the Poroelastic Material Properties Sensitivity of the Lumbar Intervertebral Disc Under Compression, Flexion and Axial Rotation
,”
ASME J. Biomech.
,
42
(
16
), pp.
2780
2788
.
11.
Mason
,
R. L.
,
Gunst
,
R. F.
, and
Hess
,
J. L.
,
2003
,
Statistical Design and Analysis of Experiments: With Applications to Engineering and Science
,
Wiley
, Hoboken, NJ.
12.
Isaksson
,
H.
,
van Donkelaar
,
C. C.
, and
Ito
,
K.
,
2009
, “
Sensitivity of Tissue Differentiation and Bone Healing Predictions to Tissue Properties
,”
ASME J. Biomech.
,
42
(
5
), pp.
555
564
.
13.
Forrester
,
A.
,
Sobester
,
A.
, and
Keane
,
A.
,
2008
,
Engineering Design Via Surrogate Modelling: A Practical Guide
,
Wiley
, Chichester, UK.
14.
Fitzpatrick
,
C. K.
,
Hemelaar
,
P.
, and
Taylor
,
M.
,
2014
, “
Computationally Efficient Prediction of Bone-Implant Interface Micromotion of a Cementless Tibial Tray During Gait
,”
ASME J. Biomech.
,
47
(
7
), pp.
1718
1726
.
15.
Halloran
,
J. P.
,
Erdemir
,
A.
, and
van den Bogert
,
A. J.
,
2008
, “
Adaptive Surrogate Modeling for Efficient Coupling of Musculoskeletal Control and Tissue Deformation Models
,”
ASME J. Biomech. Eng.
,
131
(
1
), p.
011014
.
16.
Bah
,
M. T.
,
Nair
,
P. B.
,
Taylor
,
M.
, and
Browne
,
M.
,
2011
, “
Efficient Computational Method for Assessing the Effects of Implant Positioning in Cementless Total Hip Replacements
,”
ASME J. Biomech.
,
44
(
7
), pp.
1417
1422
.
17.
Donaldson
,
F. E.
,
Nyman
, Jr,
E.
, and
Coburn
,
J. C.
,
2015
, “
Prediction of Contact Mechanics in Metal-on-Metal Total Hip Replacement for Parametrically Comprehensive Designs and Loads
,”
ASME J. Biomech.
,
48
(
10
), pp.
1828
1835
.
18.
Eskinazi
,
I.
, and
Fregly
,
B. J.
,
2015
, “
Surrogate Modeling of Deformable Joint Contact Using Artificial Neural Networks
,”
Med. Eng. Phys.
,
37
(
9
), pp.
885
891
.
19.
Lin
,
Y.-C.
,
Haftka
,
R. T.
,
Queipo
,
N. V.
, and
Fregly
,
B. J.
,
2010
, “
Surrogate Articular Contact Models for Computationally Efficient Multibody Dynamic Simulations
,”
Med. Eng. Phys.
,
32
(
6
), pp.
584
594
.
20.
Pant
,
S.
,
Limbert
,
G.
,
Curzen
,
N. P.
, and
Bressloff
,
N. W.
,
2011
, “
Multiobjective Design Optimisation of Coronary Stents
,”
Biomaterials
,
32
(
31
), pp.
7755
7773
.
21.
Anderson
,
A. E.
,
Peters
,
C. L.
,
Tuttle
,
B. D.
, and
Weiss
,
J. A.
,
2005
, “
Subject-Specific Finite Element Model of the Pelvis: Development, Validation and Sensitivity Studies
,”
ASME J. Biomech. Eng.
,
127
(
3
), pp.
364
373
.
22.
Daniel
,
M.
,
Iglič
,
A.
, and
Kralj-Iglič
,
V.
,
2005
, “
The Shape of Acetabular Cartilage Optimizes Hip Contact Stress Distribution
,”
J. Anat.
,
207
(
1
), pp.
85
91
.
23.
Ghosh
,
R.
,
Pal
,
B.
,
Ghosh
,
D.
, and
Gupta
,
S.
,
2015
, “
Finite Element Analysis of a Hemi-Pelvis: The Effect of Inclusion of Cartilage Layer on Acetabular Stresses and Strain
,”
Comput. Methods Biomech. Biomed. Eng.
,
18
(
7
), pp.
697
710
.
24.
Bryan
,
R.
,
Surya Mohan
,
P.
,
Hopkins
,
A.
,
Galloway
,
F.
,
Taylor
,
M.
, and
Nair
,
P. B.
,
2010
, “
Statistical Modelling of the Whole Human Femur Incorporating Geometric and Material Properties
,”
Med. Eng. Phys.
,
32
(
1
), pp.
57
65
.
25.
Dalstra
,
M.
,
Huiskes
,
R.
,
Odgaard
,
A.
, and
van Erning
,
L.
,
1993
, “
Mechanical and Textural Properties of Pelvic Trabecular Bone
,”
ASME J. Biomech.
,
26
(
4–5
), pp.
523
535
.
26.
Dalstra
,
M.
, and
Huiskes
,
R.
,
1991
, “
The Pelvic Bone as a Sandwich Construction: A 3-D Finite Element Study
,”
ASME J. Biomech.
,
24
(
6
), p.
455
.
27.
Bergmann
,
G.
,
2001
, “
Hip Contact Forces and Gait Patterns From Routine Activities
,”
ASME J. Biomech.
,
34
(
7
), p.
859
.
28.
Dopico-González
,
C.
,
New
,
A. M.
, and
Browne
,
M.
,
2010
, “
Probabilistic Finite Element Analysis of the Uncemented Hip Replacement-Effect of Femur Characteristics and Implant Design Geometry
,”
ASME J. Biomech.
,
43
(
3
), pp.
512
520
.
29.
Goldstein
,
S. A.
,
1987
, “
The Mechanical Properties of Trabecular Bone: Dependence on Anatomic Location and Function
,”
ASME J. Biomech.
,
20
(
11–12
), pp.
1055
1061
.
30.
Keaveny
,
T. M.
,
Morgan
,
E. F.
,
Niebur
,
G. L.
, and
Yeh
,
O. C.
,
2001
, “
Biomechanics of Trabecular Bone
,”
Ann. Rev. Biomed. Eng.
, pp.
307
333
.
31.
Morgan
,
E. F.
, and
Keaveny
,
T. M.
,
2001
, “
Dependence of Yield Strain of Human Trabecular Bone on Anatomic Site
,”
ASME J. Biomech.
,
34
(
5
), pp.
569
577
.
32.
Dalstra
,
M.
, and
Huiskes
,
R.
,
1995
, “
Load Transfer Across the Pelvic Bone
,”
ASME J. Biomech.
,
28
(
6
), pp.
715
724
.
33.
Taddei
,
F.
,
Martelli
,
S.
,
Reggiani
,
B.
,
Cristofolini
,
L.
, and
Viceconti
,
M.
,
2006
, “
Finite-Element Modeling of Bones From CT Data: Sensitivity to Geometry and Material Uncertainties
,”
IEEE Trans. Biomed. Eng.
,
53
(
11
), pp.
2194
2200
.
34.
Manley
,
M. T.
,
Ong
,
K. L.
, and
Kurtz
,
S. M.
,
2006
, “
The Potential for Bone Loss in Acetabular Structures Following THA
,”
Clin. Orthop. Relat. Res.
,
453
, pp.
246
253
.
35.
Phillips
,
A. T. M.
,
Pankaj
,
P.
,
Howie
,
C. R.
,
Usmani
,
A. S.
, and
Simpson
,
A. H. R. W.
,
2007
, “
Finite Element Modelling of the Pelvis: Inclusion of Muscular and Ligamentous Boundary Conditions
,”
Med. Eng. Phys.
,
29
(
7
), pp.
739
748
.
36.
Zhang
,
Q. H.
,
Wang
,
J. Y.
,
Lupton
,
C.
,
Heaton-Adegbile
,
P.
,
Guo
,
Z. X.
,
Liu
,
Q.
, and
Tong
,
J.
,
2010
, “
A Subject-Specific Pelvic Bone Model and Its Application to Cemented Acetabular Replacements
,”
ASME J. Biomech.
,
43
(
14
), pp.
2722
2727
.
37.
Dalstra
,
M.
,
Huiskes
,
R.
, and
Van Erning
,
L.
,
1995
, “
Development and Validation of a Three-Dimensional Finite Element Model of the Pelvic Bone
,”
ASME J. Biomech. Eng.
,
117
(
3
), pp.
272
278
.
38.
Reilly
,
D. T.
, and
Burstein
,
A. H.
,
1974
, “
The Mechanical Properties of Cortical Bone
,”
J. Bone Joint Surg.—Ser. A
,
56
(
5
), pp.
1001
1022
.
39.
Majumder
,
S.
,
Roychowdhury
,
A.
, and
Pal
,
S.
,
2007
, “
Simulation of Hip Fracture in Sideways Fall Using a 3D Finite Element Model of Pelvis–Femur–Soft Tissue Complex With Simplified Representation of Whole Body
,”
Med. Eng. Phys.
,
29
(
10
), pp.
1167
1178
.
40.
Gorissen
,
D.
,
Couckuyt
,
I.
,
Demeester
,
P.
,
Dhaene
,
T.
, and
Crombecq
,
K.
,
2010
, “
A Surrogate Modeling and Adaptive Sampling Toolbox for Computer Based Design
,”
J. Mach. Learn. Res.
,
11
, pp.
2051
2055
.
41.
Leung
,
A. S. O.
,
Gordon
,
L. M.
,
Skrinskas
,
T.
,
Szwedowski
,
T.
, and
Whyne
,
C. M.
,
2009
, “
Effects of Bone Density Alterations on Strain Patterns in the Pelvis: Application of a Finite Element Model
,”
Proc. Inst. Mech. Eng. Part H
,
223
(
8
), pp.
965
979
.
You do not currently have access to this content.