A Model of Electromechanical Coupling in the Small Intestine - Multiscale Computer Modeling in Biomechanics and Biomedical Engineering - page 194

0.0 s 0.5 s 1.0 s

1.5 s 2.0 s 2.5 s

3.0 s 3.5 s 4.0 s

4.5 s 5.0 s 5.5 s

6.0 s 6.5 s 7.0 s

7.5 s 8.0 s

-7 0 -30

V m (mV)

Fig. 6 Simulated intestinal electromechanical activity. Mechanical deformation is seen as
occlusion of the intestinal lumen. Visualization of slow wave membrane potential at regular
intervals in an idealized intestinal model, from 0 to 8 s. The color bar indicates membrane
potential values in mV, ranging from 70 (blue)to 30 mV (red)

degrees of freedom in total. The solution procedure for the electromechanically
coupling model involved solving for deformed geometric coordinates, which were
then used to update the model geometry, including the coordinates of the electrical
solution points, before the next solution step. At each mechanical solution point
i.e., gauss point, the following variables were defined as outputs: (i) deformed
nodal coordinates, (ii) Lagrangian strains, (iii) active Piola-Kirchhoff stresses, and
(iv) total Piola-Kirchhoff stresses.
More specifically in this example, the electromechanically coupled model was
solved for a simulated period of 8 s, and solutions output at time steps of 0.5 s
(Fig. 6 ). The electrical component was solved first. The [Ca 2 þ ] i values from the
grid points were interpolated and used to update the Ca 2 þ variable at each
mechanical gauss point. A trilinear interpolation scheme was used for this update
step. These [Ca 2 þ ] i values were subsequently input into the active mechanics
model. For the mechanical component, the nonlinear finite deformation equations
were linearized using the Newton-Raphson method, then numerically solved using
UMFPACK. The solution converged within five iterations in most cases, with each
iteration taking between 50 and 80 s to solve. Within each mechanical solution