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w3 = wRLD
c1 (t2 )W1 = c1 (t2 )
"
w11
w12
w13
A
#
c1 (t1 )W1 = c1 (t1 )
"
w11
w12
w13
#
c2 (t2 )W2 = c2 (t2 )
c1
w1 = wLLD
(t)
·
w21
w22
w23
#
c2 (t1 )W2 = c2 (t1 )
w
11
"
+
t
c2
(t)
·
w2 = wLRA
w
21
"
=
LR
A
ac
ti
va
tio
w21
w22
w23
#
B
np
att
ern
Figure 1.15 (A) Geometrical representation of two three-dimensional M-modes W1 and W2
(by definition W1 ⊥ W2 ) that are modulated by two independent neural commands C1 and C2
respectively, at two different instants t 1 and t 2 . The direction of the M-modes vectors is fixed,
while their elements are co-vary linearly over time (or over space). (B) Therefore, the LRA
muscle activation pattern over time is the combination of two signals which imply two neural
commands, i.e., at time t 1 is LRA(t 1 ) = c1 (t 1 ) · w11 + c2 (t 1 ) · w21 and at time t 2 is LRA(t 2 ) =
c1 (t 2 ) · w11 + c2 (t 2 ) · w21 . The same happens for the other two muscles. Therefore, it is reduced
the dimension of the neural control task to two commands, less than the number of the muscles.
The orthogonality of the three dimensional muscle space and between M-modes defines their
inter-independence (adapted from Ting, 2007; Ting and Chvatal, 2011).
at higher hierarchical level of motor control. However, by increasing task’s complexity M-modes
composition can change. It was supposed, therefore, that as the task goes more challenging there
are more M-modes to be controlled by the neural controller (Danna-Dos-Santos, Degani, and
Latash, 2008). This was confirmed in many studies of human standing. During voluntary body
sway, where the body is modelled as a single inverted pendulum, M-modes are robust across
subjects stabilizing COP shifts (Danna-Dos-Santos et al., 2007; Klous, Santos, and Latash, 2010).
When trunk or arm segments accelerations are involved during body sway, M-modes are no more
robust accross subjects or trials, however, there are still stibilizing COP shifts (Danna-Dos-Santos,
Degani, and Latash, 2008; Danna-Dos-Santos et al., 2009).
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