Biomedical Engineering Reference
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Fig. 8 Equivalent circuit models for the CNT neuron. A biophysical mathematical model combin-
ing voltage-dependent cell excitability with the interfacing of the neuronal membrane to CNT-
based electrodes, as implemented in NEURON. Two versions of the same model were defi ned. The
fi rst ( a ) assumes that an extracellular coupling always occurs between the neuronal membrane and
the CNTs, as in metal microelectrodes. As expected, simulations of this model predict a much
larger signal-to-noise ratio, compared to a metal microelectrode ( c ). The second model hypothe-
sized that bundles of CNTs penetrate the lipid double layer and become exposed to the cytosolic
environment ( b ). Under these conditions, the model predicts a response amplitude two orders of
magnitude larger and anticipates a qualitatively different signal shape, intriguingly similar to the
intracellular membrane potential ( d ). C cnt , CNT equivalent capacitance; C sh , amplifi er shunt capaci-
tance; R in , amplifi er input resistance; R s , seal resistance; R sp , spread resistance; R cnt , CNT equiva-
lent resistance; R s , seal resistance; V cnt , CNT potential; V m , membrane potential
“spread” resistance. These components describe the ease of ion currents to couple
the extracellular space to the CNT and quantify the electrical shunt to the bulk elec-
trolyte. In Fig. 8a-b , R s is the sealing resistance between the neuronal membrane
and the surface of the CNT layer, and it accounts for how much the neuronal mem-
brane is in proximity with the CNT electrode. Depending on the size of the electro-
lyte cleft between the neuronal membrane and the nanotubes, this resistance assumes
distinct values, increasing with decreasing distance. R s depends, therefore, only on
the resistivity r s of the electrolyte (i.e., r s = 70 W cm) and on geometrical parameters
(Fromherz 2002 ) ; thus,
is surface overlapping coeffi cient and d is
thickness of the electrolyte cleft. Because at a mesoscopic scale the surface of the
CNT substrate appears as a fractal landscape (Fig. 3a ), the thickness d of the cleft of
electrolyte and the surface overlapping coeffi cient
d (Grattarola and Martinoia 1993 )
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