Tonic Finite Element Model of the Lower Limb

Abstract

It is widely admitted that muscle bracing influences the result of an impact, facilitating fractures by enhancing load transmission and reducing energy dissipation. However, human numerical models used to identify injury mechanisms involved in car crashes hardly take into account this particular mechanical behavior of muscles. In this context, in this work we aim to develop a numerical model, including muscle architecture and bracing capability, focusing on lower limbs. The three-dimensional (3-D) geometry of the musculoskeletal system was extracted from MRI images, where muscular heads were separated into individual entities. Muscle mechanical behavior is based on a phenomenological approach, and depends on a reduced number of input parameters, i.e., the muscle optimal length and its corresponding maximal force. In terms of geometry, muscles are modeled with 3-D viscoelastic solids, guided in the direction of fibers with a set of contractile springs. Validation was first achieved on an isolated bundle and then by comparing emergency braking forces resulting from both numerical simulations and experimental tests on volunteers. Frontal impact simulation showed that the inclusion of muscle bracing in modeling dynamic impact situations can alter bone stresses to potentially injury-inducing levels.

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

“…L.-L. Gras et al 14 An elastic, linear, constitutive law was used. It was defined with density, Young's modulus and Poisson's ratio fixed at 0.495 to preserve the quasi-incompressibility of the muscle (Weiss et al 1996;Johansson et al 2000;Bosboom et al 2001;Blemker et al 2005;Behr et al 2006;Blemker and Delp 2006). The superior plate was modelled with four-node shell elements (thickness: 1 mm) and was placed 1 mm above the muscle.…”

“…Knowledge of the mechanical properties of muscle tissue in compression is necessary in many fields, such as impact biomechanics (Behr et al 2006;Soni et al 2009) and clinical diagnosis (Linder-Ganz and Gefen 2004; Jolivet et al 2008). …”

“…Most of the recent finite element models to represent muscles are generic (Johansson et al 2000;Bol and Reese 2008;Hedenstierna et al 2008;Tang et al 2009) or subject specific (Bosboom et al 2001;Oomens et al 2003;Blemker et al 2005;Behr et al 2006;Jolivet et al 2008). They are designed to understand muscle behaviour in tension and compression, and use complex, constitutive laws with hyper-elastic and visco-elastic characteristics.…”

Hyper-elastic properties of the human sternocleidomastoideus muscle in tension

“…Since the muscle is considered to be incompressible (Behr et al, 2006;Blemker et al, 2005;Blemker and Delp, 2006;Bosboom et al, 2001;Johansson et al, 2000;Weiss et al, 1996), Poisson's ratio is 0.5. Then, the parameter m (Pa) represents the shear modulus.…”

“…Moreover regarding transverse strains, elasticity that appeared in compression was really small in comparison with tension. The material was considered to be almost incompressible, and Poisson's ratio was fixed at 0.495 (Behr et al, 2006;Blemker et al, 2005;Blemker and Delp, 2006;Bosboom et al, 2001;Johansson et al, 2000;Weiss et al, 1996). The m and a parameters of the constitutive law were identified using an iterative and dichotomous process.…”