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

[9]. Stenosis of 25, 45, 65 and 85 mm in length were tested. The position
of the stenosis is measured from the bottom of the trachea to the middle of the stenoting
zone; therefore, is included in the interval [( ) , ( ) ,].
The chosen levels were 56.5, 62.5, 68.5 and 73.5 mm. The tracheal inclination ( )
that is, the angle between the tracheal mean axis and the vertical direction (Z) was
chosen equal to 12º, 17º, 22º and 27º [10]. The prosthesis penetration , defined as the
difference between and , was supposed to be always within the interval ]0, 1[
mm. Thus levels were taken equal to 0.2, 0.4, 0.6 and 0.8 mm.
With the chosen independent factors and with 4 levels each, the appropriate orthogonal
Taguchi's array is the .
3.2 Mathematical approaches
In this work, a quadratic regression is used but formulated in a multiple linear matrix
regression formulation, where the product and squares of factors are considered as
variables. To analyze a model which pretends to explain the behavior of a variable y,
information provided by some values of the independent variables , ,..., , is used
[11]. The multiple linear regression is written as:
where (
( ) design matrix, (
), is a ( ) vector of dependent variable observations, an
vector of regression parameters, and (
(1)
( )
( )
( )
), (
( )
) a ( )
) the ( ) vector of additive errors.
Quadratic equation was used to determine and linking the independent variables
with and :
Least-Squares was used to fit a regression line to estimate the coefficient . Two robust
design procedures were applied: Stepwise and Best Subsets Regression.
( ) (3)
where is the FEM output variable and , ..N}, N: number of tests.
(
)
3.3 Models and simulations
For each experiment to run, a new finite element model based on a simplified geometry
(2)