ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

is generated. The real tracheal section [5] is preserved and a program is implemented to
replicate elements in the vertical direction (Z) until getting the total length and a
hexahedral structured mesh. In the areas of stenosis, the x and y coordinates are scaled
to reduce the tracheal diameter 2 mm and narrowing the trachea at any position and with
any extension necessary for the design of experiments.
The 16 models to run were simulated with the cartilagenous structure considered as
elastic material with Young Modulus E = 3.33 MPa and Poison coefficient = 0.49 [7].
Smooth muscle, and annular ligaments were approximated as isotropic hyperelastic
materials with a stiffness C = 32.7 KPa and = 0.3, whereas Dumon stent was
simulated as an elastic material with E = 1 Mpa and = 0.28 [7].
Boundary conditions used for the tracheal ascending movement during swallowing are:
Null displacements at the bottom layer of the trachea, at the level of bifurcation.
Radial displacement of 1 mm is imposed to the prosthesis driving to the
stenosis/prosthesis contact.
Swallowing force of 10.5 N inclined -18.43º.
All simulations were made in the same way and using the same contact option.
3. RESULTS
The analysis of the statistical data resulting from the robust design of experiments
showed that the stenosis length, and the prosthesis diameter are the only factors that
have influence on the patient swallowing capacity (percentage of influence >5%),
whereas all factors have almost a similar effect on (see Figure 2). The Figure 3
shows that decreases, non-linearly when increases and linearly when
increases, and has a non-monotonic behavior when and vary. In the chosen range,
seems to have no influence on . Regarding , non-monotonic relations were
obtained when , , , and vary. The interactions of the different factors on
and are considered synergic. The best regression corresponds to the lowest
standard deviation (S), while the quadratic correlation (R-Sq) should tend to 100%.
The following regression equations were finally chosen:
, (R-Sq=90.69%, S=2.56%) (3)
, (R-Sq=72.5%, S=0.18%) (4)
The absolute error found between FEA results and those with the regression varies
from 0.32% to 39%. The absolute error between found with FEA and the one found
with the regression equations, fluctuates between 0.04% and 30.6%.
The same process used to found and was also used to find the equations that fit
and in each node of the tracheal model mesh.
To make a clinical validation, a comparison of the statistical results to those of real
patient simulations made with his real tracheal geometry and real pathological
swallowing trajectory, was made. For , the regression results presented a value of
23.3 mm, whereas the FEA results was 23.8 mm.