A Model of Electromechanical Coupling in the Small Intestine - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 191

and E 11 and E 22 are the strains in the circumferential and longitudinal directions
respectively; C, a 1 , a 2 and a 3 are parameters fitted from the experimental data. It
was found that the direction of maximum stiffness at different location in the small
intestine is not consistent across all the tissue samples from that location [ 6 ]. Not
all, but a majority of the duodenal and ileum samples are stiffer in the circum-
ferential direction, while a majority of the jejunal samples are stiffer in the lon-
gitudinal direction [ 6 ]. A lumped model was therefore developed in order to
average out some of the anisotropic behaviors in the tissue.
4.2.1 Measurement of Passive Tension
Passive tension should technically be measurable between contractions when the
muscle is at rest. However, this is challenging in practice, due to the spontaneous
contractile nature of the muscle cells, as well as the presence of specific tone in the
tissue, which is difficult to isolate from pure passive properties [ 26 ]. In their efforts to
obtain the passive tension-length relationship in arterial smooth muscle, Herlihy and
Murphy developed a protocol which involves reversibly stretching muscle strips
[ 29 ]. Their results closely match measurements obtained from muscle strips which
were irreversibly equilibrated in Ca 2 þ -free solution, a process which they believed
inactivates the contractile apparatus. However, although various mechanisms have
been found to arrest spontaneous contractions, the mechanical behavior of the
''resting'' smooth muscle varies with the type of mechanism used [ 24 ]. This means
that there is an additional active component in the smooth muscle, i.e., tonic tension,
which is still present, but to varying degrees depending on experimental conditions,
even when the phasic behavior has been inactivated.
Assuming a relatively inert intestinal tissue sample can be obtained, passive
stiffness in the material can be investigated using planar biaxial tests. The tissue
sample is loaded simultaneously in the longitudinal and circumferential directions.
By tracking the movement of markers on the surface of the sample, one can
observe the dependence of the response in one direction on the material properties
of the other direction. Assuming the material is incompressible, the response in the
third direction, i.e., the transmural direction, can be approximated. The stress-
strain responses are incorporated into a constitutive law, which can then be used to
predict the behavior of the tissue under any general loading state. The review by
Sacks provides a detailed explanation of the biaxial testing technique [ 48 ].
Another commonly used technique for measuring passive tension in tubular
organs is balloon manometry. A probe is inserted into the intestine and a balloon
attached to the probe is inflated to apply an outward pressure onto the intestinal
wall [ 46 ]. The radius of the tube is measured using imaging techniques. The
tension in the wall is then approximated from applied pressure, radius and wall
thickness. This method has the advantage of being able to directly test on the intact
intestinal tissue, rather than on muscle strips. However, this is essentially a uni-
axial method, which is limited by the stiffness data that assumes isotropic material