A Model of Electromechanical Coupling in the Small Intestine - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 182

gastrointestinal smooth muscle cells, and have therefore been referred to as the
backbone of electromechanical coupling in the gut [ 49 ]. I LVA describes a low
voltage-activated, DHP-insensitive, T-type calcium current. I Kr and I Ka represent
potassium currents through outward delayed rectifier channels and through out-
ward fast-inactivating, Ca 2 þ -independent channels respectively. I BK represents
Ca 2 þ -activated potassium conductance, and I Kb , an experimentally-determined,
background potassium current. I Na is a sodium conductance and I NSCC is current
through non-selective cation channels, which have been found in the gastroin-
testinal tract of several species. The stimulus current, I ICC , represents the slow
wave from the interstitial cells of Cajal which depolarizes the surrounding smooth
muscle cells.
A generic expression of the conductance of ion x is in the form,

I x ¼ G x ð V m E x Þ g ð 5 Þ

where I x is the ionic current of an arbitrary ion species, G x is the maximum
channel conductance, and E x is the Nernst potential of x. The voltage dependency
of the ion conductance comes from the gating variable, g, which has a generic
form,

dg

dt ¼ g 1 g

ð 6 Þ

s 1

Equation ( 6 ) specifies the rate of change of the gating variable, g, as a function of
voltage-dependent variables, g 1 and s 1 , both of which can be fitted to experi-
mental measurements.
Another important cellular process which contributes to the behavior of these
ion channels, and which is of particular interest to the intestinal electromechanics,
is the regulation of intracellular calcium during the depolarization of the smooth
muscle cells. In this cell model, the increase in [Ca 2 þ ] i is balanced by a calcium
extrusion current (I CaEXT ), which includes re-uptake by the sarcoplasmic reticulum
and mitochondria, as well as extrusion from the cell through Ca 2 þ pumps. These
processes were combined and modeled using the following expression,

;

1 : 34
i

Ca 2 þ

I CaExt ¼ 0 : 317 ð 7 Þ

based on observation of normal Ca 2 þ levels after each slow wave activity. The
smooth muscle cell model was applied to successfully simulate slow wave
membrane potential traces which have been validated against experimental
recordings. Activity of the individual ion conductance was also simulated (Fig. 2 ).
Most important to the electromechanical model, the corresponding Ca 2 þ transient
had an amplitude of 300 pM (Fig. 2 top), as contractions of the smooth muscle
cells are related to the amplitudes of Ca 2 þ transients [ 44 ].