Biomedical Engineering Reference
In-Depth Information
M
i
O
i
P
j
=
×
F
j
i
where P
j
i
is the insertion point of muscle j on body segment i and F
j
stands for the
force applied by this muscle. Let us consider that the norm of F
j
is denoted T
j
.Using
the superposition theorem we can express M
i
as the product of Tj and I
i
where I
i
is
the theoretical Momentum associated with a unit force vector Fj (
F
j
=
1
N
):
M
j
i
I
j
i
=
∗
T
j
and
m
I
j
i
i
ext
∀
i
∈
[1
,
n
]
∗
T
j
=−
τ
j
=
1
which can be rewritten in a matrix form:
.
T
musc
=−
τ
ext
m matrix containing I
j
×
where
i
for all i (body segment) and j (action
line), T
musc
is the m-vector containing the forces of all the action lines and
is the n
τ
ext
is the
n-vector of the external torques and moment applied to all the body segments.
This linear system is not invertible because n is not equal to m. In general m is
greater than n leading to redundancy of the actuators (the action lines). It consequently
leads to an optimization problemwith a space of solutions. In addition to this equality
constraint, it is possible to add inequality constraints such as:
•
A muscle force is positive and its maximum value is equal to K(l)*K
0
*PCSA as
shown previously,
People naturally tend to minimize energy and torques (
j
=
1
F
i
•
in many motions
(
j
=
1
F
i
2
[
32
] (or the normalized effort
)
[
18
]),
F
max
i
•
Taking some EMG signals into account in the solving process [
1
]
This domain is very active in biomechanics and many researchers try to improve
the quality and to validate the results. One of the most important problems is to be
able to take contraction of antagonist into account. Using EMG signals to check if
the antagonist muscles are active is a very promising approach.
The approach presented in this section is named inverse dynamics but there exist
two other approaches to solve this type of problem using direct dynamics within
an optimization loop or directly exploiting EMG signals. Whatever the method, it is
still difficult to validate the results. However, it is a promising contribution to analyse
more accurately the actions performed by the user in a virtual environment, as it has
been shown in ergonomics [
27
]. VR is more and more used to evaluate and train
disable people as it provides a safe and reproducible environment. In this type of
application EMG and muscle contraction feedbacks are very important.
