Biomedical Engineering Reference
In-Depth Information
delayed weighted summations of neural signals
in the form of action potentials emerging from
the nerve cells embedded in each muscle fiber
within a pool of muscle fibers. It is these weight
summations of several single fiber action poten-
tials that constitute a typical EMG measurement.
The EMG signal is assumed to be an amplitude-
modulated
carrier
with multiplicative noise (to
model the firing and recruitment of motor units
near the sensors when there is change in the mus-
cle force level) and additive noise (arising from
distal motor units) of the activation inputs to a
neuromuscular model of the limb dynamics. It is
assumed that the activation signals are extracted
following several steps that include pattern rec-
ognition and/or blind signal analysis.
the order of 10 ms for fast twitch fibers and 60 ms
for slow tonic fibers.
4.3.2.4 Modeling of the Muscle Moment
Generation
To model the forces within a muscle, it is essen-
tial to consider several recruitment schemes of
multiple motor units for different fibers. The
sudden recruitment of a motor unit at its initial
firing rate causes a step increase of muscle force;
the size of that step is determined by the frac-
tional physiological cross-sectional area of that
unit, which is a function of the number of motor
units. Upon recruitment, the lumped motor unit
modulates its frequency according to an effec-
tive recruitment signal that is proportional to
the amount of muscle recruited. The effective
recruitment signal is characterized by a rise
and fall time constant that is determined by the
first-order dynamics of the exchange of calcium
between the nerve cells and muscle fiber within
the motor unit
[77]
. The level of effective activa-
tion of each fiber results from a linear combina-
tion of multiple motor unit activations weighted
by their respective fractional physiological cross-
sectional area. The differences between tonic (or
slow) and twitch (or fast) fiber types are reflected
in rise and fall time constants of the excitation
dynamics that model the sagging or yielding
properties, the activation frequency that rep-
resents the calcium dynamics, and the muscle
force-length and muscle force-velocity proper-
ties. Thus, the muscle force is represented as
4.3.2.3 Modeling of the Muscle Activation
Dynamics
Sensory and motor nerve fibers enter the muscle
in one or two nerve branches. Most muscle fibers
are supplied by alpha motoneurons
[1; see Sec-
tion 4.2.4.5]
, while gamma motoneurons
[1; see
Section 4.2.4.5]
supply the muscle fibers within
the muscle spindle. The nerve fiber enters the
muscle at the motor endplate, and the whole of
the neuromuscular junction at the nerve fiber
constitutes a motor unit. Depolarization of the
nerve fiber activates the muscle fiber at the
motor unit and is responsible for the activation
that in turn increases the concentration of cal-
cium ions, which in turn switches on the muscle
contraction. The activation state is a function of
calcium ion concentration.
Concentration dynamics can be modeled by
the Nernst equation, but a simplified model is
used for the gating function of the calcium ions.
Zajac
[76]
defined it by
J
F
=
F
0
W
I
×
A
FI
×
F
IV
(
V
)
F
IL
(
L
)
Q
I
+
F
PI
(
L
)
,
I
=1
(4.7)
where
F
0
is the maximum force generated,
which could itself be dynamic and could be
modeled by a first-order dynamic model,
although it is assumed constant here;
W
i
are
a set of weights;
A
i
is the frequency of activa-
tion, which primarily depends on the dynam-
ics of calcium ion concentration;
F
iV
is the
DQ
DT
=
[β + (1 − β)
U
]
1
τ
ACT
U
,
Q
+
(4.6)
τ
ACT
where
u
is the depolarizing input from a motor
unit,
q
is the activating state,
β
is the fraction of
the activating state that is not influenced by the
external control, and
τ
act
is the time constant of
