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

For the numerical simulation of the isometric contraction, the degrees of freedom at the
insertions with bones were fixed. A 100% maximal voluntary contraction (MVC),
whose time history is shown in Fig. 1a, was applied to all muscles. The maximum
isometric stress of the muscle contraction model was considered to be of 0.3 MPa [4].
4.2 Results
The displacement-field and nodal force vectors resultant from the isometric contraction
of the human triceps surae muscle is shown in Fig. 3. The outer surface of the
gastrocnemius muscle was moved distally during the contraction. Their surface was
displaced by around 30.2 mm without and 12.4 mm with the membrane. Almost all
muscle fibers were shortened during the contraction. The average fiber strain
( ε = λ − 1)
of gastrocnemius muscle at the initial configuration was 0.176. At the end of
f f
the activation, the fiber strains were -0.389 without and -0.067 with the membrane. The
aponeurosis, located in between the gastrocnemius and soleus muscles, was moved
proximally during the contraction, indicating that Achilles tendon is stretched along
proximo-distal axis. The nominal strains of the external Achilles tendon were 0.061 and
0.074 without and with membrane, respectively. The total force at Achilles tendon at
the end of the activation can be observed at the insertion with the calcaneus (Fig. 3c).
This force was greater with (1080.8 N) than without (645.6 N) the membrane.
Fig.3 Simulation results of the isometric contraction of the human triceps surae muscle.
Distributions of the displacement in the longitudinal direction at the end of the
activation (a) without and (b) with membrane. (c) The nodal force vectors at the end of
the activation. The circle indicates the forces at the insertion with the calcaneus.
5. DISSCUSSION AND CONCLUSIONS
The membrane tissue plays a very important role on the generated force at the Achilles
tendon. In fact, the numerical results show that the force developed at Achilles tendon
with membranes is 1.67 times the force attained without membranes. The absolute value
of the generated force at the Achilles tendon with the membrane came close to our
experimental observation in planter flexor’s force (1354.0 N).
The membrane connects muscle fibers with tendons and ligaments, and thus with bones.