A Model of Electromechanical Coupling in the Small Intestine - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 181

(iii) ''sheet-normal'', which was orthogonal to both the ''fiber'' and ''sheet''
directions, and therefore orthogonal to the plane of the muscle layer. The orien-
tations of the fibers in this case were aligned with the local n 1 and n 2 directions,
i.e., no fiber was aligned in the transmural direction (Fig. 1 c). Application of the
anatomical model in electrical and electromechanical modeling process are dis-
cussed in the following two sections.

3 Electrophysiological Modeling

This section presents an overview of the mathematical models we used to simulate
the intestinal slow wave activity, i.e., the electrical activity generated by the
interstitial cells of Cajal and smooth muscle cells. The slow wave activity was then
integrated in a continuum setting, i.e., across multiple cells in a spatially averaged
electrical syncytium. The electrical control of the intestinal tissue is somewhat
unique with respect to its involvement of two separate levels of control by these
two different types of cell models. Earlier intestinal cell models utilized coupled
oscillators to phenomenologically reproduce the periodicity of slow waves [ 2 ].
Even though these phenomenological models offer a computationally efficient way
of simulating slow waves, they lack the sophistication required to link the elec-
trical activity to mechanical activity. More recently biophysically-based models of
these two types of cells have been developed. These models are generally based on
the gated ion conductance approach pioneered by Hodgkin and Huxley [ 30 ]. These
biophysically-based cell models have the advantage of relating physically mean-
ingful parameters, e.g., ion concentrations, to physiologically realistic processes,
e.g., voltage-dependent ion transport. In this section, we use a biophysically-based
smooth muscle cell model as an example of how slow waves can be simulated
using a system of ordinary differential equations.
A biophysically-based model of gastrointestinal smooth muscle cell was
developed in 2007 [ 14 ]. This model adopts the Hodgkin and Huxley formulation to
describe the eight types of commonly known ion channels in the smooth muscle
cell membrane. These eight ion channels, also referred to as conductances, in
combination with a pacemaking current term (i.e., the pacemaking current from
the interstitial cells of Cajal), specify depolarization of the smooth muscle cell,
through,

o V m

ot ¼ 1

ð I ion I ICC Þ ; ð 3 Þ

C m

where

I ion ¼ I CaL þ I LVA þ I Kr þ I Ka þ I BK þ I Kb þ I Na þ I NSCC ; ð 4 Þ

specifically, I CaL represents Ca 2 þ

current through voltage-dependent, dihydro-

pyridine (DHP)-sensitive, L-type channels which are expressed in all