Laure-Lise Gras

Viscoelastic properties of the human sternocleidomastoideus muscle of aged women in relaxation.

Improving the numerical models of the head and neck complex requires understanding the mechanical properties of the muscles; however, most of the data in existing literature have been obtained from studies on animal muscles. Muscle is hyper-elastic, but also viscoelastic. The hyper-elastic behaviour of the human sternocleidomastoideus muscle has been previously studied. The aim of this study is to propose a characterization of the viscoelastic properties of the same human muscle in relaxation. Ten muscles were tested in vitro. The viscoelastic behaviour was modelled with a generalized Maxwells model studied at the first and second order, using an inverse approach with a subject-specific, finite-element model of each muscle. Based on these models, relaxation times τ (first order: 103s; second order: 18s and 395s) and ratio moduli γ (first order: 0.33; second order: 0.20 and 0.19) were identified. The first-order model provided a good estimate of the relaxation curve (R(2): 0.82), but the second-order model was more representative of the experimental response (R(2): 0.97). Our results provide evidence that the viscoelastic behaviour of the human sternocleidomastoideus muscle can be described using a second-order Maxwells model and that - combined with the previously identified hyper-elastic properties - the response of the muscle in tension and relaxation is fully characterized.

The non-linear response of a muscle in transverse compression: assessment of geometry influence using a finite element model

Most recent finite element models that represent muscles are generic or subject-specific models that use complex, constitutive laws. Identification of the parameters of such complex, constitutive laws could be an important limit for subject-specific approaches. The aim of this study was to assess the possibility of modelling muscle behaviour in compression with a parametric model and a simple, constitutive law. A quasi-static compression test was performed on the muscles of dogs. A parametric finite element model was designed using a linear, elastic, constitutive law. A multi-variate analysis was performed to assess the effects of geometry on muscle response. An inverse method was used to define Youngs modulus. The non-linear response of the muscles was obtained using a subject-specific geometry and a linear elastic law. Thus, a simple muscle model can be used to have a bio-faithful, biomechanical response.

Influence of muscle-tendon complex geometrical parameters on modeling passive stretch behavior with the Discrete Element Method.

The muscle-tendon complex (MTC) is a multi-scale, anisotropic, non-homogeneous structure. It is composed of fascicles, gathered together in a conjunctive aponeurosis. Fibers are oriented into the MTC with a pennation angle. Many MTC models use the Finite Element Method (FEM) to simulate the behavior of the MTC as a hyper-viscoelastic material. The Discrete Element Method (DEM) could be adapted to model fibrous materials, such as the MTC. DEM could capture the complex behavior of a material with a simple discretization scheme and help in understanding the influence of the orientation of fibers on the MTC׳s behavior. The aims of this study were to model the MTC in DEM at the macroscopic scale and to obtain the force/displacement curve during a non-destructive passive tensile test. Another aim was to highlight the influence of the geometrical parameters of the MTC on the global mechanical behavior. A geometrical construction of the MTC was done using discrete element linked by springs. Young׳s modulus values of the MTC׳s components were retrieved from the literature to model the microscopic stiffness of each spring. Alignment and re-orientation of all of the muscle׳s fibers with the tensile axis were observed numerically. The hyper-elastic behavior of the MTC was pointed out. The structure׳s effects, added to the geometrical parameters, highlight the MTC׳s mechanical behavior. It is also highlighted by the heterogeneity of the strain of the MTC׳s components. DEM seems to be a promising method to model the hyper-elastic macroscopic behavior of the MTC with simple elastic microscopic elements.

Experimental characterization of post rigor mortis human muscle subjected to small tensile strains and application of a simple hyper-viscoelastic model.

In models developed for impact biomechanics, muscles are usually represented with one-dimensional elements having active and passive properties. The passive properties of muscles are most often obtained from experiments performed on animal muscles, because limited data on human muscle are available. The aim of this study is thus to characterize the passive response of a human muscle in tension. Tensile tests at different strain rates (0.0045, 0.045, and 0.45 s−1) were performed on 10 extensor carpi ulnaris muscles. A model composed of a nonlinear element defined with an exponential law in parallel with one or two Maxwell elements and considering basic geometrical features was proposed. The experimental results were used to identify the parameters of the model. The results for the first- and second-order model were similar. For the first-order model, the mean parameters of the exponential law are as follows: Young’s modulus E (6.8 MPa) and curvature parameter α (31.6). The Maxwell element mean values are as follows: viscosity parameter η (1.2 MPa s) and relaxation time τ (0.25 s). Our results provide new data on a human muscle tested in vitro and a simple model with basic geometrical features that represent its behavior in tension under three different strain rates. This approach could be used to assess the behavior of other human muscles.

Tensile response of the muscle–tendon complex using discrete element model

Tear of the muscle–tendon complex (MTC) is one of the main causes of sports injury (De Labareyre et al. 2005). However, the mechanisms leading to such injury are still unclear (Uchiyama et al. 2011). Before modelling the tear of the MTC, its behaviour in tensile test will be first studied. The MTC is a multi-scale, non-isotropic and noncontinuous structure that is composed of numerous fascicles gathered together in a conjunctive sheath (epimysium). Many MTC models use the finite element method (FEM) (Bosboom et al. 2001) to simulate MTC’s behaviour as a hyper-viscoelastic material. The discrete element method (DEM) used for modelling composite materials (Iliescu et al. 2010) could be adapted to fibrous materials as the MTC. Compared to the FEM, the DEM could allow to capture the complex behaviour of a material with a simple discretisation scheme in terms of concept and implementation as well as to understand the influence of fibres’ orientation on MTC behaviour. The aim of this study was to obtain the force/displacement relationship during a numerical tensile test of a pennate muscle model with the DEM.

Modelling of human muscle behaviour with a hyper-elastic constitutive law

Even though numerous studies have been performed assessing muscle mechanical properties, knowledge about this living material is still limited. Many authors have focused on the longitudinal behaviour of muscle by performing tension tests (Anderson et al. 2001; Dresner and Ehman 2001). Muscles tested were mainly animal muscles and muscle behaviour was modelled with rheological elements involving springs and dampers. In order to complete these results, the aim of this study was to assess human muscle behaviour in tension and to derive a hyper-elastic law from the experiments.

Evaluation of 6 and 10 Year-Old Child Human Body Models in Emergency Events

Emergency events can influence a child’s kinematics prior to a car-crash, and thus its interaction with the restraint system. Numerical Human Body Models (HBMs) can help understand the behaviour of children in emergency events. The kinematic responses of two child HBMs–MADYMO 6 and 10 year-old models–were evaluated and compared with child volunteers’ data during emergency events–braking and steering–with a focus on the forehead and sternum displacements. The response of the 6 year-old HBM was similar to the response of the 10 year-old HBM, however both models had a different response compared with the volunteers. The forward and lateral displacements were within the range of volunteer data up to approximately 0.3 s; but then, the HBMs head and sternum moved significantly downwards, while the volunteers experienced smaller displacement and tended to come back to their initial posture. Therefore, these HBMs, originally intended for crash simulations, are not too stiff and could be able to reproduce properly emergency events thanks, for instance, to postural control.

Modelling of fascia lata rupture during tensile tests via the discrete element method

Musculoskeletal models are often used to better understand the behaviour of the many components of the body, to predict injuries and design safety devices. These models become increasingly more detailed by including connective tissues. However, their implementation is often challenging due to the small amount of data regarding their mechanical properties. Fascia lata is a connective tissue wrapped around the muscles of the thigh. Histological studies on goat fascia lata (Pancheri et al. 2014) have shown its heterogeneous structure composed of two layers of collagen fibres connected by a proteoglycan matrix. Both layers have a specific fibre orientation, and are not orthogonal. The discrete element method (DEM) makes it possible to model complex structures by discretizing them into simple elements, associated to a mass, and cohesive bonds, such as springs. This allows for a better understanding of the relationship between micro and macroscale properties of materials. While this method is usually used to model composite materials, it has been adapted to model biological materials, such as the muscle-tendon complex (Roux et al. 2016). The aim of this study is thus to reproduce numerically the macroscopic behaviour of the fascia lata submitted to a tensile test using DEM.

Quasi-static compression on dog muscles at high strain

The knowledge about passive mechanical properties of muscles is quite limited. Even if a lot of studies have been done on longitudinal muscle properties (Davis et al. 2003; Bensamoun et al. 2006), different authors have tested whole muscles or muscle fibres to identify the mechanical properties. However, few studies only tested muscle’s transversal properties (Aimedieu et al. 2003), and they considered pieces of muscles. Moreover, the strain levels studied were very low. The aim of the presented study is to evaluate mechanical properties of whole muscles in their transversal directions for high level of strain.