A Model of Electromechanical Coupling in the Small Intestine - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 192

behavior in all three orthogonal material directions [ 48 ]. Recent adaption of the
fiber optic technology also allowed intraluminal pressure to be measured at high-
resolution using a pressure-sensing catheter placed in the colon [ 16 , 18 ]. This
method has the potential to resolve movements and pressure developments in
multiple directions.

4.3 Modeling Active Tension

Active tension is generated by the contractile apparatus in the smooth muscle cells
in response to the increase in [Ca 2 þ ] i caused by slow wave depolarization of the
cell. Smooth muscles are capable of generating longer sustained contractions than
striated muscle with the similar level of myosin phosphorylation, because of the
ability of smooth muscle to form latch-bridges. There are several models of the
active behavior of the intestinal smooth muscle [ 25 , 27 , 47 ]. Many of these models
describe detailed mechanisms of the cross-bridge cycling in the smooth muscle
cells. Another simplified approach is to adapt the steady-state tension-length-
calcium relationship (SS-T-L-Ca 2 þ ) relationship developed by Hunter et al. [ 32 ],
and use it to describe the active tension generated in response to the increase in
[Ca 2 þ ] i following electrical activation. The model assumes cardiac-specific
kinetics of Ca 2 þ , including binding of Ca 2 þ to Troponin-C in cardiac cells. The
Ca 2 þ -Troponin-C complex binds to tropomyosin and unblocks the binding sites,
and the model provides a phenomenological description for the steady-state pro-
portion of available binding sites (z ss ), as follows,

h
i

Ca 2 þ

z ss ¼ ð 26 Þ

:

h
i þ C 50

Ca 2 þ

where C 50 is the value of [Ca 2 þ ] i required to achieve 50 % availability of actin
binding sites and h determines the steepness of the sigmoidal curve. The tension
developed by the muscle fiber at steady-state length is directly proportional to z ss ,
and was fitted to cardiac isometric tension data using the following expression,

T ¼ T ref 1 þ b O k 1 ð ½ Þ z ss ; ð 27 Þ

where k is the extension ratio of the muscle fiber, T ref is the tension recorded at an
extension ratio of 1, and b O relates to myofilament cooperativity, a phenomenon
which describes how activation of a single cardiac muscle cell facilitates activation
of neighboring cells [ 53 ].
Although originally specified from cardiac muscle data, the parameters of the
SS-T-L-Ca 2 þ model can be readily adjusted to simulate smooth muscle behavior.
Figure 5 shows the tension-[Ca 2 þ ] i relationship with parameters b O = 1.45,
C 50 = 0.65, and h = 2.5 to match a set of normalized tension over a range of strains.