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

pathological swallowing trajectories, the meshing process, the constitutive behavior of
the trachea composing tissues and finally the clinical validation of the results [4- 6]. For
that reason, FEM results, based on a set of virtual experiments, are collected and used
for a statistical study to provide thoracic surgeons a tool capable to predict in an optimal
time, the consequences of the tracheal endoprosthesis implantation. This could be
helpful to take decisions during pre-operative planning of tracheal interventions.
3. MATERIAL AND METHOD
To obtain numerical models that fit the real behavior of the human trachea, results of
experimental studies were used [7] to perform a complete human trachea finite element
model and highlight the effect of a tracheal implant on the stress response of the trachea
and on its physiological capacity to swallow, comparing real cases of patients before
and after the implantation of Dumon prostheses. The tracheal intolerance to the
endoprosthesis and the damage that suffer the trachea once in contact with a stent were
analyzed and the physiological force to swallow was estimated and fixed to 10.5N [5].
Due to the huge time-cost that takes making simulations, a statistical study was made
based on the Taguchi's method and the analysis of variance (ANOVA) with clinical
verification, to help the thoracic surgeon to choose the position and appropriate
dimensions of the Dumon prosthesis depending on each patient, trying in this way to
optimize the outcomes of the prosthetic insertion.
3.1 Robust design of experiments
Design of experiments is based on Taguchi’s method which imposes a selection of the
factor levels to do the fewest possible runs. This methodology is used to analyze
swallowing movement with Dumon prosthesis and to study the parameters with highest
influence on the stress state of the trachea and on the ability to swallow (maximal
vertical displacement) considered as a direct consequence of prosthesis implantation
[4,5]. Information about quantitative analysis as the percentage of influence of each
factor (ANOVA) on the output variables which are the maximal tracheal displacement
in (Z), , and the maximum principal stress , and qualitative analysis as
interactions between factors were obtained. In collaboration with the surgeons and
based on the results of [5], several experimental designs were made. In those
experiments, several variables are taken as fixed:
The tracheal length from the vocal cords to the carina [8].
The thickness of the trachea was fixed to .
The stenosis diameter ( is the tracheal diameter) traduces the
surgical intervention made on the stenosis to use it as a support for the stent.
The prosthesis length = + 2, exceeds one millimeter each border of the
stenosis which has as length. It is supposed that cannot exceed the interval
[ , ]. The upper and lower 10% are taken as a margin from the
carina and the vocal cords.
Factors with higher influence on the output variables were identified the diameter of the
prosthesis ( ), the length of the stenosis ( ), the position of stenosis ( ), the tracheal
inclination ( ) and the penetration of the prosthesis in the trachea ( ) (see Figure 1).
The level of each of these variables was selected based on anatomical, physiological and
commercial references. The value of is defined by the manufacturers, being
available generally between 12 and 18 mm. The chosen levels were 14, 15, 16 and 17
mm. belongs to the interval [( ) , ( ) ] with a minimum of