Biomedical Engineering Reference
In-Depth Information
0
unloaded, non-activated,
l
c
unloaded, activated
F
loaded, activated
Figure 4.6
Different reference and current lengths of a muscle.
F
=
c
c
−
1
.
(4.7)
For this it is assumed that, despite the contraction,
c
does not change. The acti-
vated, but unloaded, length
c
of the muscle may be expressed in terms of the non-
activated length
0
using a so-called activation or contraction stretch
λ
c
defined as:
c
0
.
λ
c
=
(4.8)
Typically
λ
c
<
1 since it represents a contractile action. For simplicity it is
assumed that
λ
c
is known for different degrees of activation of the muscle. Using
the activation stretch
λ
c
, the force-stretch relation for a muscle may be rewritten as
c
λ
1
with
0
.
F
=
λ
c
−
λ
=
(4.9)
Effectively this expression implies that if the muscle is activated, represented by
a certain
λ
c
, and the muscle is not loaded, hence
F
=
0, the muscle will contract
such that
λ
=
λ
c
.
(4.10)
If, on the other hand, the muscle is activated and forced to have constant length
0
, hence
λ
=
1, the force in the muscle equals:
c
1
1
.
F
=
λ
c
−
(4.11)
Rather complicated models have been developed to describe the activation of
the muscle. A large group of models is based on experimental work by Hill [
9
]
and supply a phenomenological description of the non-linear activated muscle.
These models account for the effect of contraction velocity and for the difference
in activated and passive state of the muscle. Later, microstructural models were
developed, based on the sliding filament theories of Huxley [
12
]. These models
