The purpose of this study was to develop an inverse method, coupling imaging techniques with numerical methods, to identify the muscle mechanical behavior. A finite element model updating (FEMU) was developed in three main interdependent steps. First, a 2D FE modeling, parameterized by a Neo-Hookean behavior (C10 and D), was developed from a segmented thigh muscle 1.5T MRI (magnetic resonance imaging). Thus, a displacement field was simulated for different static loadings (contention, compression, and indentation). Subsequently, the optimal mechanical test was determined from a sensitivity analysis. Second, ultrasound parameters (gain, dynamic, and frequency) were optimized on the thigh muscles in order to apply the digital image correlation (DIC), allowing the measurement of an experimental displacement field. Third, an inverse method was developed to identify the Neo-Hookean parameters (C10 and D) by performing a minimization of the distance between the simulated and measured displacement fields. To replace the experimental data and to quantify the identification error, a numerical example was developed. The result of the sensitivity analysis showed that the compression test was more adapted to identify the Neo-Hookean parameters. Ultrasound images were recorded with a frequency, gain, and dynamic of 9 MHz, 34 dB, 42 dB, respectively. In addition, the experimental noise on displacement field measurement was estimated to be 0.2 mm. The identification performed on the numerical example revealed a low error for the C10 (<3%) and D (<7%) parameters with the experimental noise. This methodology could have an impact in the scientific and medical fields. A better knowledge of the muscle behavior will help to follow treatment and to ensure accurate medical procedures during the use of robotic devices.

References

References
1.
Bringard
,
A.
,
Denis
,
R.
,
Belluye
,
N.
, and
Perrey
,
S.
,
2007
, “
Compression élastique externe et fonction musculaire chez l'homme
,”
Sci. Sports
,
22
(
1
), pp.
3
13
.10.1016/j.scispo.2006.11.003
2.
Avril
,
S.
,
Badel
,
P.
,
Dubuis
,
L.
,
Rohan
,
P. Y.
,
Debayle
,
J.
,
Couzan
,
S.
, and
Pouget
,
J. F.
,
2012
, “
Patient-Specific Modeling of Leg Compression in the Treatment of Venous Deficiency
,” Patient-Specific Modeling in Tomorrow's Medicine, Springer Berlin Heidelberg, pp.
217
238
.10.1007/978-3-642-24618-0
3.
Avril
,
S.
,
Bouten
,
L.
,
Dubuis
,
L.
,
Drapier
,
S.
, and
Pouget
,
J. F.
,
2010
, “
Mixed Experimental and Numerical Approach for Characterizing the Biomechanical Response of the Human Leg Under Elastic Compression
,”
ASME J. Biomech. Eng.
,
132
(
3
), p.
31006
.10.1115/1.4000967
4.
Dubuis
,
L.
,
Avril
,
S.
,
Debayle
,
J.
, and
Badel
,
P.
,
2012
, “
Identification of the Material Parameters of Soft Tissues in the Compressed Leg
,”
Comput. Methods Biomech. Biomed. Eng.
,
15
(
1
), pp.
3
11
.10.1080/10255842.2011.560666
5.
Bercoff
,
J.
,
Tanter
,
M.
, and
Fink
,
M.
,
2004
, “
Supersonic Shear Imaging: A New Technique for Soft Tissue Elasticity Mapping
,”
IEEE Trans. Ultrason. Ferroelectri. Freq. Control
,
51
(
4
), pp.
396
409
.10.1109/TUFFC.2004.1295425
6.
Gennisson
,
J. L.
,
Deffieux
,
T.
,
Macé
,
E.
,
Montaldo
,
G.
,
Fink
,
M.
, and
Tanter
,
M.
,
2010
, “
Viscoelastic and Anisotropic Mechanical Properties of In Vivo Muscle Tissue Assessed by Supersonic Shear Imaging
,”
Ultrasound Med. Biol.
,
36
(
5
), pp.
789
801
.10.1016/j.ultrasmedbio.2010.02.013
7.
Bensamoun
,
S. F.
,
Ringleb
,
S. I.
,
Littrell
,
L.
,
Chen
,
Q.
,
Brennan
,
M.
,
Ehman
,
R. L.
, and
An
,
K. N.
,
2006
, “
Determination of Thigh Muscle Stiffness Using Magnetic Resonance Elastography
,”
J. Magn. Reson. Imaging
,
23
(
2
), pp.
242
247
.10.1002/jmri.20487
8.
Leclerc
,
G. E.
,
Charleux
,
F.
,
Robert
,
L.
,
Ho-Ba-Tho
,
M. C.
,
Rhein
,
C.
,
Latrive
,
J. P.
, and
Bensamoun
,
S. F.
,
2013
, “
Analysis of Liver Viscosity Behavior as a Function of Multifrequency Magnetic Resonance Elastography (MMRE) Postprocessing
,”
J. Magn. Reson. Imaging
,
38
(
2
), pp.
952
957
.10.1002/jmri.23986
9.
Debernard
,
L.
,
Leclerc
,
G. E.
,
Robert
,
L.
,
Charleux
,
F.
, and
Bensamoun
,
S. F.
,
2013
, “
In Vivo Characterization of the Muscle Viscoelasticity in Passive and Active Conditions Using Multifrequency MR Elastography
,”
J. Musculoskeletal Res.
,
16
(
2
), pp.
397
401
.10.1142/S0218957713500085
10.
Linder-Ganz
,
E.
,
Shabshin
,
N.
,
Itzchak
,
Y.
, and
Gefen
,
A.
,
2007
, “
Assessment of Mechanical Conditions in Sub-Dermal Tissues During Sitting: A Combined Experimental-MRI and Finite Element Approach
,”
J. Biomech.
,
40
(
7
), pp.
1443
1454
.10.1016/j.jbiomech.2006.06.020
11.
Then
,
C.
,
Vogl
,
T. J.
, and
Silber
,
G.
,
2012
, “
Method for Characterizing Viscoelasticity of Human Gluteal Tissue
,”
J. Biomech.
,
45
(
7
), pp.
1252
1258
.10.1016/j.jbiomech.2012.01.037
12.
Vogl
,
T. J.
,
Then
,
C.
,
Naguib
,
N. N.
,
Nour-Eldin
,
N. E. A.
,
Larson
,
M.
,
Zangos
,
S.
, and
Silber
,
G.
,
2010
, “
Mechanical Soft Tissue Property Validation in Tissue Engineering Using Magnetic Resonance Imaging: Experimental Research
,”
Acad. Radiol.
,
17
(
12
), pp.
1486
1491
.10.1016/j.acra.2010.08.010
13.
Hendriks
,
F. M.
,
Brokken
,
D.
,
Oomens
,
C. W. J.
,
Bader
,
D. L.
, and
Baaijens
,
F. P. T.
,
2006
, “
The Relative Contributions of Different Skin Layers to the Mechanical Behavior of Human Skin In Vivo Using Suction Experiments
,”
Med. Eng. Phys.
,
28
(
3
), pp.
259
266
.10.1016/j.medengphy.2005.07.001
14.
Hendriks
,
F. M.
,
Brokken
,
D.
,
Van Eemeren
,
J.
,
Oomens
,
C. W. J.
,
Baaijens
,
F. P. T.
, and
Horsten
,
J.
,
2003
, “
A Numerical-Experimental Method to Characterize the Non-Linear Mechanical Behaviour of Human Skin
,”
Skin Res. Technol.
,
9
(
3
), pp.
274
283
.10.1034/j.1600-0846.2003.00019.x
15.
Tran
,
H. V.
,
Charleux
,
F.
,
Rachik
,
M.
,
Ehrlacher
,
A.
, and
Ho-Ba-Tho
,
M. C.
,
2007
, “
In Vivo Characterization of the Mechanical Properties of Human Skin Derived From MRI and Indentation Techniques
,”
Comput. Methods Biomech. Biomed. Eng.
,
10
(
6
), pp.
401
407
.10.1080/10255840701550287
16.
Gokhale
,
N. H.
,
Barbone
,
P. E.
, and
Oberai
,
A. A.
,
2008
, “
Solution of the Nonlinear Elasticity Imaging Problem: The Compressible Case
,”
Inverse Probl.
,
24
(
4
), p.
045010
.10.1088/0266-5611/24/4/045010
17.
Oberai
,
A. A.
,
Gokhale
,
N. H.
,
Goenezen
,
S.
,
Barbone
,
P. E.
,
Hall
,
T. J.
,
Sommer
,
A. M.
, and
Jiang
,
J.
, “
Linear and Nonlinear Elasticity Imaging of Soft Tissue In Vivo: Demonstration of Feasibility
,”
Phys. Med. Biol.
,
54
(
5
), pp.
1191
1207
.10.1088/0031-9155/54/5/006
18.
Hall
,
T. J.
,
Barbone
,
P. E.
,
Oberai
,
A. A.
,
Jiang
,
J.
,
Dord
,
J. F.
,
Goenezen
,
S.
, and
Fisher
,
T. G.
,
2011
, “
Recent Results in Nonlinear Strain and Modulus Imaging
,”
Curr. Med. Imaging Rev.
,
7
(
4
), pp.
313
327
.10.2174/157340511798038639
19.
Zhu
,
Y.
, and
Hall
,
T. J.
,
2002
, “
A Modified Block Matching Method for Real-Time Freehand Strain Imaging
,”
Ultrasound Imaging
,
24
(
3
), pp.
161
176
.10.1177/016173460202400303
20.
Fu
,
Y.
,
Chui
,
C.
,
Teo
,
C.
, and
Kobayashi
,
E.
,
2011
, “
Motion Tracking and Strain Map Computation for Quasi-Static Magnetic Resonance Elastography
,”
Medical Image Computing and Computer-Assisted Interventional MICCAI 2011
, Toronto, ON, Sept. 18–22, pp.
428
435
.
21.
Moerman
,
K. M.
,
Sprengers
,
A. M. J.
,
Nederveen
,
A. K.
, and
Simms
,
C. K.
, “
A Novel MRI Compatible Soft Tissue Indentor and Fibre Bragg Grating Force Sensor
,”
Med. Eng. Phys.
,
35
(
4
), pp.
486
499
.10.1016/j.medengphy.2012.06.014
22.
Affagard
,
J. S.
,
Feissel
,
P.
, and
Bensamoun
,
S. F.
, 2013 “
Characterization of Muscle Displacement Field Using Ultrasound Technique
,” 19th Congress of European Society of Biomechanics, Patras, Greece, Aug. 25–28.
23.
Hild
,
F.
, and
Roux
,
S.
,
2006
, “
Digital Image Correlation: From Displacement Measurement to Identification of Elastic Properties: A Review
,”
Strain
,
42
(
2
), pp.
69
80
.10.1111/j.1475-1305.2006.00258.x
24.
Hild
,
F.
, and
Roux
,
S.
,
2008
,
CorreliQ4: A Software for Finite Element Displacement Field Measurements by Digital Image Correlation
, Internal Report No. 269.
25.
Chevalier
,
L.
,
Calloch
,
S.
,
Hild
,
F.
, and
Marco
,
Y.
,
2005
, “
Digital Image Correlation Used to Analyze the Multiaxial Behavior of Rubber-Like Materials
,”
Eur. J. Mech. A
,
20
(
2
), pp.
169
187
.10.1016/S0997-7538(00)01135-9
26.
Grediac
,
M.
, and
Hild
,
F.
,
2011
,
Mesures de champs et identification en mécanique des solides
(Série matériaux et métallurgie, MIM), Lavoisier.
27.
ABAQUS/6.9, 2009, 6.9 Software, User's Manual (6.9), Inc. and Dassault Systemes.
28.
Scan IP,
2010
, “
3D Image Data Visualisation, Analysis and Model Generation Software
,” http://www.simpleware.co.uk
29.
Tarantola
,
A.
,
1987
,
Inverse Problem Theory
,
Elsevier
,
Amsterdam, The Netherlands
.
30.
Affagard
,
J. S.
,
Bensamoun
,
S. F.
, and
Feissel
,
P.
,
2012
, “
Inverse Method to Identify the Muscle Mechanical Properties,” Euromech Colloquium 534, Advanced Experimental Approaches and Inverse Problems in Tissue Biomechanics
, Saint-Etienne, France, May 29–May31.
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