Research Papers

Development of an Inverse Approach for the Characterization of In Vivo Mechanical Properties of the Lower Limb Muscles

[+] Author and Article Information
Jean-Sébastien Affagard

Laboratoire de BioMécanique et BioIngénierie,
UMR CNRS 7338,
Centre de recherches de Royallieu,
Université de Technologie de Compiègne (UTC),
Rue Roger Couttolenc CS 60319,
Compiègne 60203, France;
Laboratoire Roberval,
UMR CNRS 7337,
Centre de recherches de Royallieu,
Université de Technologie de Compiègne (UTC),
Rue Roger Couttolenc CS 60319,
Compiègne 60203, France

Sabine F. Bensamoun

Laboratoire de BioMécanique et BioIngénierie,
UMR CNRS 7338,
Centre de recherches de Royallieu,
Université de Technologie de Compiègne (UTC),
Rue Roger Couttolenc CS 60319,
Compiègne 60203, France
e-mail: sabine.bensamoun@utc.fr

Pierre Feissel

Laboratoire Roberval,
UMR CNRS 7337,
Centre de recherches de Royallieu,
Université de Technologie de Compiègne (UTC),
Rue Roger Couttolenc CS 60319,
Compiègne 60203, France
e-mail: pierre.feissel@utc.fr

1Corresponding author.

Manuscript received April 14, 2014; final manuscript received August 15, 2014; accepted manuscript posted September 5, 2014; published online September 24, 2014. Assoc. Editor: Paul Rullkoetter.

J Biomech Eng 136(11), 111012 (Sep 24, 2014) (8 pages) Paper No: BIO-14-1161; doi: 10.1115/1.4028490 History: Received April 14, 2014; Revised August 15, 2014; Accepted September 05, 2014

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.

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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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
Then, C., Vogl, T. J., and Silber, G., 2012, “Method for Characterizing Viscoelasticity of Human Gluteal Tissue,” J. Biomech., 45(7), pp. 1252–1258. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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. [CrossRef]
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. [CrossRef] [PubMed]
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. [CrossRef] [PubMed]
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. [CrossRef]
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.
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. [CrossRef] [PubMed]
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.
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. [CrossRef]
Hild, F., and Roux, S., 2008, CorreliQ4: A Software for Finite Element Displacement Field Measurements by Digital Image Correlation, Internal Report No. 269.
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. [CrossRef]
Grediac, M., and Hild, F., 2011, Mesures de champs et identification en mécanique des solides (Série matériaux et métallurgie, MIM), Lavoisier.
ABAQUS/6.9, 2009, 6.9 Software, User's Manual (6.9), Inc. and Dassault Systemes.
Scan IP, 2010, “3D Image Data Visualisation, Analysis and Model Generation Software,” http://www.simpleware.co.uk
Tarantola, A., 1987, Inverse Problem Theory, Elsevier, Amsterdam, The Netherlands.
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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Fig. 3

Simulation of the different static tests: (a) contention, (b) compression, (c) indentation, and ((d)–(f)) their engineering strain following the direction 1 on the deformed shape. (g) Geometry of the thigh use for the FE simulation.

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Fig. 2

(a) Experimental protocol used for the acquisitions of the successive ultrasound images performed without loading ((b) and (c)). The DIC was applied on these images.

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Fig. 1

Finite element model updating (FEMU) composed of (a) mechanical modeling, (b) numerical example, (c) experimental protocol, and (d) inverse method

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Fig. 4

Ultrasound image obtained with a frequency of 9 MHz (a), 11 MHz (b), and 13 MHz (c)

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Fig. 5

Gray level histograms corresponding to the ultrasound images for three different couples (G: gain and Dyn: dynamic)

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Fig. 7

Standard deviation of the horizontal and vertical displacement fields for a 8 pixels meshsize as a function of the optimal couples

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Fig. 6

Selection of the optimal gain at a fixed dynamic based on the result of the gray level histogram obtained at 9 MHz

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Fig. 8

Cartographies of the displacement sensitivity for the Neo-Hookean parameters of the quadriceps muscle following the contention ((a)–(d)), the indentation ((b)–(e)) test, and the compression ((c))–(f)) loading

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Fig. 9

Identification of the relative error obtained for the C10 and D parameters without (a) and with noise (b). Arrows located on figure (b) indicate the high percentage of error obtained for the D parameters and the arrow figure (d) showed the decrease of the error when the muscles (ischios, gracilis, and sartorius) are grouped ((c) and (d)).



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