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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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Figures

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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. 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. 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. 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. 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. 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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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. 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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