ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

λ
σ = σ
(8)
act isom f
f 0 ⋅ ⋅ ft ⋅ fl ⋅ fv
λ0
isom where σ 0 is the maximum isometric stress that occurs at the optimum fiber stretch λ 0 .
f t , l f and f v are the activation, the length dependence [8], and the velocity dependence
factors [9]. A plot of the evolution laws of these factors used in the numerical
simulations is shown in Fig. 1.
4. NUMERICAL SIMULATION OF A HUMAN TRICEPS SURAE MUSCLE
4.1 FE-model
The FE model adopted to simulate the isometric contraction of the human triceps surae
muscle is shown in Fig. 2. The 3D geometry was reconstructed from MR images and
the each tissue was manually segmented into gastrocnemius, soleus muscles and
Achilles tendon. The geometry was discretized into 8-node hexahedral elements. The
muscle fiber distributions within the muscles were defined from fascicle arrangement
measured by 2D ultrasound images [10].
Membranes were measured visually based on the anatomical observation from a
cadaver dissection (n = 1). Layers of flat broad with whitish-silvery colour on a part of
the surfaces of the gastrocnemius and soleus muscles can be seen on Fig. 2. The
membrane corresponds to aponeurosis, with similar histological characteristics of
Achilles tendon. The membrane was discretized with 4-nodes quadrilateral membrane
elements fixed on muscle’s surface. A thickness of 0.5 mm was assumed for all
membrane, what was confirmed by recent measurements by optical microscopy. The
constitutive behaviour was considered to be similar to the one of Achilles tendon, and
modelled by an isotropic hyperelastic Mooney-Rivlin model (Eq (5)). The material
constants were identified from experimental measurements of a stress-strain curve of a
cadaveric isolated Achilles tendon [11].
Fig. 2 FE model of the human triceps surae muscle, reconstructed from MR images. (a)
Finite element mesh segmented into Achilles tendon, gastrocnemius and soleus muscles.
Achilles tendon and aponeurosis (membrane element) on the surfaces of (b)
gastrocnemius muscle (green) and (c) soleus muscle (blue).