Identification of hyperelastic properties of passive thigh muscle under compression with an inverse method from a displacement field measurement
Introduction
A deep knowledge of in vivo human soft tissues is necessary (Payne et al., 2015) and has a significant field of investigation with different applications such as surgery where clinicians are more and more assisted by robotic devices and where they need a precise feedback of the mechanical response of tissues to ensure safety interventions.
Currently, several in vivo techniques, from Magnetic Resonance Imaging (MRI) or ultrasound, allow clinicians to assess the elastic behavior, such as Magnetic Resonance Elastography (MRE) (Bensamoun et al., 2006, Muthupillai et al., 1995), SuperSonic Imaging (SSI) or Transient Elastography (TE) (Gennisson et al., 2005, Bercoff et al., 2004, Sandrin et al., 2002a, Sandrin et al., 2002b). These elastography techniques are mainly limited by the dynamic excitation, that only allow us to characterize the viscoelastic behavior (Leclerc et al., 2013, Debernard et al., 2013; Gennisson et al., 2010). These behaviors do not describe correctly tissues at large strains and a hyperelastic behavior could be more appropriated.
Avril et al. (2010) and Tran et al. (2007), proposed to develop an inverse method from quasi-static solicitations, an indentation and a contention, to identify the Neo-Hookean behavior (C10, D) of a group of muscle. In these studies, a Finite Element Model Updating (FEMU) approach was developed where the cost function was built in displacement between the subset outlines of a Finite Element (FE) simulation and of the muscle image under solicitation. It can be noted that a force term was added to the cost function used by Tran et al. (2007). The displacement cost function is built from a few measurement points and an identification of the isolated muscles would probably give results with high uncertainty. As a result, a measurement of displacement fields appears to be beneficial to identify the mechanical properties of muscles.
In comparison to Avril and Tran’s studies, Affagard et al. (2014) has developed a FEMU leading to the displacement fields and the identification (C10, D) of the in vivo isolated thigh muscle. In this study the cost function was also built on the displacement. Similar study had characterized the in vivo Neo-Hookean behavior of soft tissues from a surface displacement field obtained with stereo-correlation (3D DIC) [Moermann et al., 2009]. This approach enables the identification of surface tissues behavior but seems limited for the characterization of deep tissues such as muscles.
A way to measure the displacement and strain fields was developed in the 1990s (Ophir et al., 1991, Ponnekanti et al., 1992, Ponnekanti et al., 1994) and consisted in correlating the B-mode signal (Zhu and Hall, 2002, Hall et al., 2011). Tumors from breast tissue were discerned using the spatial distribution of the hyperelastic material properties, but a full slice member identification was not performed (Goenezen et al., 2011, Gokhale et al., 2008). Moreover, the displacement field measurement performed by coupling Digital Image Correlation and ultrasound techniques was described and validated in Affagard et al., 2015a, Affagard et al., 2015b).
The literature presents a general lack of in vivo hyperelastic characterization of isolated muscle. The challenge of this study is to characterize isolated muscles with a hyperelastic behavior
Section snippets
Materials and methods
This section aims at presenting the FEMU approach developed for the identification of the hyperelastic properties of the thigh muscles. Fig. 1 presents the approach, consisting of three interconnected blocks:
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The experimental protocol (Fig. 1B),
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The modeling (Fig. 1A),
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The identification (Fig. 1C).
Materials properties for undifferentiated muscles
Table 1 presents the Neo-Hookean parameters identified for the undifferentiated muscles. The C10 and D parameters for muscle tissue are respectively 11.6 kPa and 11.9 MPa−1. For the fat tissue, the C10 and D parameters are respectively 0.64 kPa and 29.4 MPa−1.
Comparing with the Avril et al. (2010) study, all the parameters are in the same range (relative discrepancy<14.4%) except the fat tissue D parameter (relative discrepancy<126.4%). In comparison with the Tran et al. (2007) study, which aimed
Experimental protocol
During the experimental mechanical solicitation, a compressive force was imposed. This force was measured by sensors that enable us to characterize the spatial distribution of pressure. In the present study, this force was considered exactly known. Some questions can be raised about the accuracy of the measurements. A way to take into account the force measurement error could be to change the FE modeling and the cost function shape to take into account both the displacement and the force. In
Conclusion
The purpose of this study is to propose a technique for characterizing hyperelastic properties of muscles to increment the in vivo mechanical property databases of muscle. The originality of this study was to couple imaging techniques (Ultrasound, MRI) with numerical methods (DIC, FEMU). This methodology could have an impact in the scientific (sport, ergonomic, etc.) and medical (robotic devices, etc.) fields and will enable a better understanding of diseases and muscle injuries (tear, tensile,
Conflict of Interest Statement
All authors do not have conflict of interest.
Acknowledgements
This project is co-financed by the European Union engaged in Picardie with the European Regional Development Fund and CNRS (grant Collegium UTC CNRS INSIS).
References (25)
- et al.
Measurement of the quadriceps muscle displacement and strain fields with ultrasound and Digital Image Correlation (DIC) techniques
IRBM
(2015) - et al.
Human muscle hardness assessment during incremental isometric contraction using transient elastography
J. Biomech.
(2005) - et al.
Viscoelastic and anisotropic mechanical properties of in vivo muscle tissue assessed by supersonic shear imaging
Ultrasound Med. Biol.
(2010) - et al.
Solution of the nonlinear elasticity imaging inverse problem: the incompressible case
Comput. Methods Appl. Mech. Eng.
(2011) - et al.
Digital image correlation and finite element modelling as a method to determine mechanical properties of human soft tissue in vivo
J. Biomech.
(2009) - et al.
Elastography: a quantitative method for imaging the elasticity of biological tissues
Ultrason. Imaging
(1991) - et al.
The evaluation of new multi-material human soft tissue simulants for sports impact surrogates
J. Mech. Behav. Biomed. Mater.
(2015) - et al.
Axial stress distributions between coaxial compressors in elastography: an analytical model
Ultrasound Med. Biol.
(1992) - et al.
Ultrasonic imaging of the stress distribution in elastic media due to an external compressor
Ultrasound Med. Biol.
(1994) - et al.
Development of an inverse approach for the characterization of in vivo mechanical properties of the lower limb muscles
ASME J. Biomech. Eng.
(2014)
Mixed experimental and numerical approach for characterizing the biomechanical response of the human leg under elastic compression
J. Biomech. Eng.
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