Biomedical Engineering Reference
In-Depth Information
Ta b l e 8 . 1
Estimated and derived model parameters and modeling errors for all the investigated
groups. Values are given as mean
±
standard deviation; values in brackets indicate the correspond-
ing 95 % confidence intervals
L
r
1
/C
r
α
r
β
r
Healthy adults
0
.
032
±
0
.
029
1
.
59
±
1
.
10
0
.
42
±
0
.
08
0
.
75
±
0
.
11
(0.019, 0.045)
(1.09, 2.08)
(0.38, 0.47)
(0.70, 0.80)
COPD
0
.
016
±
0
.
007
2
.
81
±
1
.
45
0
.
56
±
0
.
07
0
.
52
±
0
.
10
(0.013, 0.019)
(2.15, 3.47)
(0.53, 0.60)
(0.47, 0.56)
KS
0
.
0173
±
0
.
012
2
.
47
±
0
.
76
0
.
54
±
0
.
05
0
.
55
±
0
.
05
(0.007, 0.02)
(1.85, 3.10)
(0.49, 0.58)
(0.50, 0.59)
Healthy children
0
.
11
±
0
.
08
4
.
73
±
2
.
73
0
.
32
±
0
.
11
0
.
63
±
0
.
16
(0.06, 0.15)
(3.2, 6.2)
(0.26, 0.38)
(0.54, 0.72)
Asthma
0
.
13
±
0
.
17
7
.
96
±
3
.
16
0
.
32
±
0
.
09
0
.
70
±
0
.
13
(0.03, 0.23)
(6.21, 9.7)
(0.27, 0.38)
(0.62, 0.77)
0
.
07
±
0
.
03
8
.
67
±
4
.
63
0
.
38
±
0
.
08
0
.
77
±
0
.
15
CF
(0.05, 0.10)
(5.11, 12.23)
(0.31, 0.44)
(0.66, 0.89)
intervals. These model parameters are then used to calculate the frequency response
in a wide range of frequencies. Statistically significant differences were observed
in adults, between the healthy, COPD, and KS groups (
p<
0
.
01) and, in children,
between healthy, asthma, and CF groups (
p<
0
.
01). There were no significant dif-
ferences between
H
C
and
A
C
groups, due to prior inhaled medication (
p<
0
.
29).
The tuning parameters for the Oustaloup filter were fitted in the frequency range
0-10
6
Hz, with 100 Hz frequency resolution, linearly spaced. The order of the filter
set to
N
pz
=
20 gave good results for all frequency responses. An illustrative ex-
ample is given in Fig.
8.1
by means of the Bode plot, with the corresponding 22nd
order transfer function in the form of (
8.1
) with the gain
K
=
245950
.
9486
(8.10)
the denominator
s
4
s
10
−
8
s
10
−
7
s
10
−
6
s
10
−
5
+
4
.
759
·
+
3
.
369
·
+
2
.
385
·
+
1
.
688
·
×
+
+
+
+
+
(s
0
.
0001195
)(s
0
.
0008463
)(s
0
.
005991
)(s
0
.
04241
)(s
0
.
3003
)
×
(s
+
2
.
126
)(s
+
15
.
05
)(s
+
106
.
5
)(s
+
754
.
2
)(s
+
5339
)(s
+
37800
)
×
s
+
10
−
5
s
+
10
6
s
+
10
7
2676
·
1
.
895
·
1
.
111
·
(8.11)
and the numerator
s
2
s
10
−
8
s
10
−
8
s
10
−
7
s
10
−
6
+
2
.
645
·
+
6
.
3
·
+
1
.
873
·
+
1
.
326
·
×
s
10
−
6
s
10
−
5
(s
+
9
.
386
·
+
6
.
645
·
+
0
.
0004704
)(s
+
0
.
00333
)
