Biomedical Engineering Reference
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components. This equivalent electric circuit can be represented as a linear system,
and then be solved using Ohm's Law.
Starting from the discretized model, the solution of the system will result in
knowing the electric potential at each vertex of each voxel relative to the model's
ground as well as the current density vector at the center of each voxel. The
method can be applied to 2D or 3D discretized models, formed of either uniform
or different sized cells or voxels. The method for uniform resolution cells can
be found in [32] and it will be briefly summarized here.
The first step is to convert each voxel of the model to its equivalent impedance
network formed of lumped circuital elements. Since the model is linear, each of
the three orthogonal directions (X, Y, and Z) is considered separately, and the
final impedance network for the voxel is obtained combining all the resulting
components.
Considering a single voxel of the discretized model (Figure 15.13), it is
possible for example to approximate the impedance seen by a current flowing
in the X direction by lumping the impedance of each of the sub-volumes into a
circuit element, knowing that the equivalent resistance will be
L
WH
R
=
(8)
and the equivalent capacitance will be
WH
L
C
=
0
r
(9)
where
0
is the permittivity of free space. and
r
are the resistivity and the
relative electric permittivity, respectively, of the voxel's material along the X axis.
W H, and L are the respective width, height, and length of the sub-voxel
volume.
For each voxel, this process is performed in all three orthogonal axes, as
shown in Figure 15.14. Then, the resulting lumped elements are combined to
form the equivalent impedance network that approximates the voxel electrical
Figure 15.13. Voxel sub-volumes used to calculate lumped circuit elements in
X direction. The resistor in parallel with the capacitor will represent the low-frequency
impedance of one sub-volume.
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