Biomedical Engineering Reference
In-Depth Information
3.3.3 Identification Algorithm
For the purpose of this example, the model parameters were estimated using a non-
linear least squares optimization algorithm, making use of the
MatLab
function
lsqnonlin
. The optimization algorithm is a subspace trust region method and is
based on the interior-reflective Newton method described in [
21
]. The large-scale
method for
lsqnonlin
requires that the number of equations (i.e., the number
of elements of cost function) is at least as great as the number of variables. Every
iteration involves the approximate solution using the method of preconditioned con-
jugate gradients, for lower and upper bounds. In this application, the lower bounds
were set to 0 (negative values are meaningless) and no upper bounds. The optimiza-
tion stopped either when a high number of iterations reached 100 times the number
of variables (i.e. 500), or a termination tolerance value of 10
e
−
8
. In all cases we
obtained a correlation coefficient between data and model estimates above 80 %.
Along with the corresponding model estimates, the error on the real and imagi-
nary part respectively and the total error between the real patient impedance and the
model estimated impedance are calculated according to the formula:
N
S
1
N
S
−
Re
)
2
E
R
=
(
Re
1
N
S
(3.12)
1
N
S
−
ˆ
Im
)
2
E
X
=
(
Im
1
E
R
+
E
X
E
T
=
with Re denoting the real part of the impedance, Im denoting the imaginary part of
the impedance, and
N
S
the total number of excited frequency points.
3.3.4 Results and Discussion
We apply the input impedance identification methods described initially in [
24
] and
revisitedin[
67
,
69
] on the data measurements from FOT. By using (
3.8
), we obtain
complex input impedances for each group from Table
3.1
from 4-48 Hz frequency
range.
The reported values are given for resistance in cmH
2
O/(l/s); for inertance
in cmH
2
O/(l/s
2
) and for compliance in l/cmH
2
O. The corresponding averaged val-
ues for each model parameter and their standard deviations are reported. The results
were tested using the one way analysis of variance (in Matlab,
anova1
). All re-
ported values were statistically significant (
p<
0
.
001, where
p
is the probability of
obtaining a result at least as extreme as the one that was actually observed, assuming
that the null hypothesis is true).
