Biomedical Engineering Reference
In-Depth Information
and
N
HVC
I
R
HE
=(
E
E
− V
RI
)
g
R
HE
S
(
V
Hj
)
,
(8.28)
j
=1
respectively, which are analogous to (8.21).
Equations (8.22)-(8.28) thus describe a set of interconnected RA excita-
tory neurons which are driven by connections from HVC neurons and are
inhibited by the inhibitory RA neuron. The inhibitory RA neuron, in turn,
is driven by synaptic input from all the RA excitatory neurons, as well as by
projection neurons in HVC.
8.4.3 Qualitative Predictions
In principle, if the purpose of the computational efforts in this field was to
reproduce observed behavior, one could argue against their utility. However,
models are useful when they allow us to go beyond integrating disparate
data. They are useful when they allow us to predict new dynamical regimes,
or behavior in regions of parameter space unexplored experimentally. Ideally,
they could point to situations worth exploring. The paramount complexity
that can in principle be expected in networks of coupled excitable units allows
us to predict that the activity in this field has hardly started.
The authors of [Abarbanel et al. 2004a] explored the dynamics displayed
by this mathematical model of the simple neural circuit used to represent
the motor pathway. In particular, they found that when the syllabic fre-
quency was very high, the average activity of RA (obtained after simulating
the dynamics of individual neurons by means of conductance models) showed
subharmonics. Abarbanel and coworkers described a period-two solution (i.e.,
the patterns of neural activity in the nucleus repeat themselves after twice
the period of the forcing that activates the neural circuit representing HVC).
If the respiratory nuclei and nXIIts nucleus were simply to follow the activity
of the different subpopulations of RA that project onto them, we could link
this result with the observation that in some species there is an alternation
of very similar syllables [Laje and Mindlin 2002]. In fact, this is not neces-
sarily the case. These nuclei are also built from excitable units, and they are
interconnected. But these models have predicted complex dynamic responses
emerging from interaction between simple instructions and a complex con-
nectivity of nonlinear units.
8.5 Sensorimotor Control of Singing
Between the song box that we have discussed throughout this topic and the
forebrain nuclei that we described in the previous sections, there is still a set of
nuclei that constitute the brain-stem respiratory-vocal system [Wild 2004].
