Biomedical Engineering Reference
In-Depth Information
Ta b l e 8 . 2
Estimated power-law model parameters (
8.9
) for all the investigated groups, from the
corresponding impulse response. Values are given as mean
±
standard deviation; values in brackets
indicate the 95 % confidence intervals
A
×
10
−
5
10
−
5
−
B
Res
×
Healthy adults
3
.
24
±
0
.
51
0
.
57
±
0
.
10
0
.
54
±
0
.
16
(2.57, 4.93)
(0.52, 0.61)
COPD
9
.
43
±
2
.
62
0
.
43
±
0
.
18
0
.
05
±
0
.
04
(7.65, 9.67)
(0.39, 0.47)
KS
7
.
68
±
5
.
12
0
.
45
±
0
.
26
0
.
09
±
0
.
02
(7.05, 15.9)
(0.41, 0.51)
Healthy children
0
.
70
±
0
.
11
0
.
67
±
0
.
10
0
.
53
±
0
.
15
(0.6, 0.9)
(3.2, 6.2)
Asthma
0
.
60
±
0
.
23
0
.
67
±
0
.
08
0
.
38
±
0
.
12
(0.40, 1.78)
(0.61, 0.73)
CF
1
.
33
±
0
.
45
0
.
61
±
0
.
33
0
.
30
±
0
.
19
(1.08, 1.44)
(0.55, 0.68)
We can therefore conclude that the impulse response can serve as an evaluation tool
for respiratory dynamics and mechanical properties.
The results presented here indicate that both methods provide similar impulse
response data. However, we may suggest that the inverse DFT is a more suitable al-
ternative to the high-order transfer functions obtained using the classical Oustaloup
filter. Additionally, a power-law model is fitted on the impulse response data, em-
phasizing once again the intrinsic fractal dynamics of the respiratory system.
8.2 Mapping the Impedance Values
8.2.1 Multi-dimensional Scaling
Multi-dimensional scaling (MDS) is a family of statistical techniques which attempt
to discover the
hidden structure
in the available data [
22
]. MDS uses a matrix of
proximities among the objects as input and produces an
N
-by-
N
mapping matrix of
the output, given
N
objects for mapping. In other words, the MDS technique pro-
vides a geometric interpretation to (dis)similarity data and is a natural tool for map-
ping data sets in a low-dimensional space. Usually, by minimizing a loss function
calculated for different possible configurations, a set of coordinates can be assigned
to the envisaged objects, providing a functional meaning to the geometry of the map.
The resulting map, or embedding, places objects that have similar attributes close to
each other.
