Simulation of The Capacitive Double Layer at The I
Simulation of The Capacitive Double Layer at The I
Simulation of The Capacitive Double Layer at The I
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C=
(2 × 10 )( A)
−11 (1) simple RC circuit agrees with results from
McIntyre, et al., which show that the double
ω
layer capacitance at the interface essentially acts
1000
as a voltage divider. They have found a reduction
in the output voltages in their models by adding
Where A is given in μm2 and ω is the angular this interface capacitor [7]. The effect of the
frequency in rad/s. impedance on our model can therefore be
computed in the frequency domain as:
2.3 The Randles Equivalent Circuit Model
⎛ iωCR ⎞
⎜ ⎟
There has been a great effort to model the
⎜ ω ⎟
capacitance at the electrode-electrolyte interface 1000 ⎟ (2)
Vtissue = VS ⎜
using an equivalent electrical circuit composed ⎜ 1 + iωCR ⎟
of passive elements. These models are discussed ⎜⎜ ω ⎟⎟
⎝ 1000 ⎠
where C is computed according to (1).
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Boston
3. Methods
The approach we have adopted for modeling the Figure 2 - Electrode Shank Geometry.
interface aspects of our system includes the use
of three different software packages – SPICE,
MATLAB, and Comsol Multiphysics. The first
step is modeling the DC behavior of our system
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Boston
Table 1 - Physical Specifications of the Michigan Each of these Fourier components is then scaled
Electrodes used in the FEA simulations. according to the impedance divider calculated in
(2). After computing each scaled Fourier
Shank Length 300 μm Component, we take the Inverse Fast Fourier
Shank Width 30 μm Transform to reconstruct a signal in the time
Shank Thickness 12 μm domain. The results of these computations are
Shank Upper Surface 9000 μm2 then imported into Comsol Multiphysics as the
Area (flat) boundary condition for the electrodes. We used
Shank Lower Surface ~12,800 μm2 Comsol Multiphysics 3.1 for our modeling. The
Area (cylindrical) model consists of 518,497 mesh elements and we
Shank Cross-Sectional ~283 μm2 solved for 606,420 degrees of freedom. We used
Area the built-in library for all of the platinum
Electrode Area ~361 μm2 characteristics and set the conductivity of the
bulk tissue equal to 0.8 S/m, a typical value for
cortical tissue [10]. The shank is 300 μm long
with a base defined by an ellipse with a major
axis of 30 μm and a minor axis of 24 μm. The
platinum electrodes are defined by cylinders with
a radius of 10 μm and a height of 1.5 μm. The
SiO2 layer is modeled as a perfect insulator.
Figure 2 shows the shank geometry and the
dimensions for the shank are summarized in
Table 1.
5. Results
of the tissue. The volume of activation is the Figure 6 - Plot of the input signal (square wave at 10
region of tissue that has a sufficient electric field kHz) along with the constant capacitance and
to incite an action potential within a nerve cell. frequency dependent capacitance models. The
In this paper, we use an electric field of difference between the constant and frequency
dependent models is apparent from this figure.
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Boston
Figure 7 - Final potential and current distributions in the tissue. The blue volumes show the region of tissue that is
activated [14] and the red lines show the current distributions in the volume.
8. Acknowledgements