Biomedical Engineering Reference
In-Depth Information
while the net impedance increases. Impedance is
primarily provided by the damping of the joint's
relative motion, whereas the damping within a
joint is provided by ligaments. It is assumed that
the ligaments also provide for impedance control.
But the impedance must also meet stability con-
siderations, and the provision of a redundant set
of tendons and ligaments satisfies this require-
ment. Thus, it is not only extremely important to
be able to model the ligament damping, the ten-
don dynamics, and the generation of both forces
by a single muscle but also the moments and the
dynamics of an antagonistic pair of muscles.
Continuously commanded control inputs to
the muscles are assumed to provide neural sig-
nals that make their way into the muscle fiber
via neuromuscular junctions. These signals can
be measured and constitute the
electromyogram
(EMG) signals. The main features of EMG sig-
nals, when used as continuous control command
signals for prostheses, are their nonlinear and
nonstationary characteristics. To develop an
EMG controller for a prosthesis, one approach is
to mimic neuromuscular control models of
human limbs. Modeling of the biological limb
dynamics is expected to result in a more respon-
sive controller for prosthetic limbs. Our objective
is to develop a generic approach to neuromus-
cular modeling of the dynamics of human limbs.
There are four aspects to consider:
and
distal
are anatomical descriptors meaning,
respectively, closer to and farther from the central
reference point of the limb in question.
Connective tissues (collagen), which bind the
parallel fibers that make up skeletal muscles,
join together at the ends of a muscle to form
tendons. For intrinsic muscles, these elastic ten-
dons terminate on the limb component's bones.
In the case of the extrinsic muscles, the tendons
extend from remotely located muscles, spanning
multiple joints in the limb. They are tethered to
intermediate bones by fibrous tunnels that
smoothly guide the tendons to maintain their
relative positions to the neighboring smaller
bones instead of assuming straight paths during
flexion or extension. The organization, network-
ing, and dynamics of connecting tendons pri-
marily determine the range of motion of a limb.
Tendon connections are responsible for the
forces generated by bundles of muscle fibers to
be translated into torques about the joints. If the
resulting moment exceeds an opposing moment
from an antagonistic group of muscles or a dis-
tribution of external loads, then the limb will
rotate about the joint. Because muscles provide
power only during contraction, complementarily
oriented muscles must command tendons to the
bones they are connected to. These muscles are
referred to as
flexors
and
extensors
. A flexor signal
is said to supinate the limb, and an extensor sig-
nal is said to pronate the limb. Control of the
limb is the result of these and other muscles act-
ing together on different sides of a rotational joint
axis. The redundancy of the tendons enables
muscles to contract either antagonistically and/
or synergistically and thereby optimally tune the
loading of articulated joints for different tasks.
Since muscles can pull but not push, to
produce a moment or rotation in both directions
(flexion/extension) one will need a pair of muscles
opposing each other (antagonistic muscles). How-
ever, the stiffness and damping contributions of
the muscles add while the exerted moments sub-
tract. Thus, by carefully coordinating muscle activ-
ities, the net joint torque may be held constant
1. Modeling of the neuromuscular action
potentials,
2. Modeling of the muscle activation dynamics,
3. Modeling of the muscle moment generation,
and
4. Modeling of the tendon length dynamics.
4.3.2.2 Modeling of the Neuromuscular Action
Potentials
Modeling of the neuromuscular action potentials
that mimic the measurements of EMG signals can
be done using either surface-mounted electrodes
or thin-wire electrodes embedded within a mus-
cle. These measurements are aggregate models of
