Biomedical Engineering Reference
In-Depth Information
Most of the algorithms for solving the inverse problem seek a solution in
which the conductivity distribution is such that when it is used to solve the
forward
problem the electric potential obtained is close to the measured volt-
age on the electrodes (Cheney et al. 1990). The search for this conductivity
distribution can be performed iteratively, in a single step or using search tech-
niques such as genetic algorithms, simulated annealing, and even exhaustive
search (Olmi et al. 2000; Lionheart 2004). Regardless of the search method,
once an acceptable solution has been reached, the conductivity distribution
depicts the structure of the tissue, or, in our case, the location of electropo-
rated regions. In Figure 2.7, we show an example of a common reconstructed
two-dimensional image of simulated electroporation. A homogeneous tissue
with two needles that are used for electroporation serves as a model. Addi-
tional electrodes are placed around the tissue and are used for the EIT current
injections and voltage measurements. The final results of the entire simulation
procedure described earlier are shown in Figure 2.7.
2.5 Mass Transfer in Tissue with Reversible
Electroporation
A mathematical model for mass transfer of drug molecules in tissue is an
important tool for
in vivo
reversible electroporation applications even with
monitoring techniques such as real-time imaging using EIT. Such a model
can serve as a basic design tool for piecing together a treatment protocol on
one hand and for real-time adjustments of the treatment using information
supplied by feedback mechanisms such as EIT. Here we describe the basic
design of a class of multiscale models that may be used for these purposes.
From the large-scale perspective, looking at the tissue, the model describes
the generally nonuniform electric field in the treated region. The electric field
is affected by the tissue geometry, the local conductivity at different regions
of the tissue if the tissue is not homogenous, and by the electroporation elec-
trodes configuration, both in terms of the electrodes' location and the applied
voltages. The diffusion of drug molecules across the tissue is also modeled at
large scale to track how the initial concentration changes as the drug enters
the electroporated cells. From the small-scale perspective, looking at individ-
ual cells, the model describes the electroporation effects on the cell membrane.
We need to consider the membrane's permeability due to the creation of pores,
their expansion and the resealing process as well as the mass transfer of drug
molecules across the membrane.
Beginning with the microscale part of the model we examine a single cell
in a uniform electric field and study the effects of electroporation on its mem-
brane. This model is a simplified view for two main reasons, but may be
extended to a more realistic model following similar arguments. The first
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