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

analysis of the large-scale human motion, due to the reduced number of degrees of
freedom; however, the lack of volume, internal fibers and pressure distribution limits
the ability to investigate muscles’ biomechanics. To overcome these constraints, a 3D
FE solver to simulate both passive behaviour of biological soft tissues and muscle
contraction has been developed by our team [3].
The 3D FE model is geometrically reconstructed from medical imaging, obtained from
non-invasive scanning techniques, such as CT or MRI. However, depending on the
medical imaging technique, there are some biological tissues that cannot be identified
on medical images, either due to a lack of contrast or due to their small size and/or
thickness. Unlike 1D models of a muscle-tendon system used in the lumped-parameter
model, the accuracy of the mechanical response of a FE simulation is strongly driven by
the accuracy of modelling of tiny details such as muscle membranes, which cannot be
seen and/or identified from the most usual medical imaging techniques.
In conclusion, it is difficult to identify and reconstruct from medical images thin
membranes, such as fascia and aponeurosis. However, these connective tissues play a
paramount role in the biomechanics of muscles and musculo-skeletal systems [4, 5]. In
this study, we aim to investigate the role of membranes during isometric contraction of
a human triceps surae muscle, evaluating mostly the generated forces at Achilles tendon,
with and without considering the existence of membranes.
3. MECHANICAL MODELING
In brief, our FE solver is based on the hyperelastic behaviour of almost incompressible
soft tissues, with a total Lagrangian formulation and a fully implicit time integration
scheme [3]. Due to the incompressibility character of the biological soft tissues, a mixed
type displacement-pressure (u/p) FE formulation was implemented. A muscle has the
ability to develop internal forces and thus to produce internal work as a result of muscle
fibers’ contraction. Therefore, the stress state in a muscle must be seen as the result of a
superposition of passive and active parts [6], i.e.
total pas act
σ = σ + σ , (1)
f f f
total pas
act
where σ f , σ f and σ f are the total, the passive and the active Cauchy stress
component along muscle fiber direction.
3.1 Passive material behaviour
Hyperelastic materials are assumed to be governed by a constitutive law linking the 2 nd
Piola-Kirchhoff stress tensor S and the right Cauchy-Green strain tensor C , by means
of a strain energy potential density W , which plays the role of a stress potential, i.e.,
2 W ∂
S = , (2)
∂C
where the strain energy potential W for almost incompressible materials is given by [7],
k 2 1
2
W = W ( C) + ( J −1) − ( p − pɶ
)
2 2k
. (3)
The first term is related with the hyperelastic constitutive model and is a function of the
2
3
isochoric strain tensor
J −
C = C and the second term represents the strain energy