Biomedical Engineering Reference
In-Depth Information
with
h
1
and
h
2
the homothety factors for the left and right branch, respectively.
The critical value for the lungs is given by
h
0
.
85, corresponding to a low resis-
tance and volume higher than necessary [
164
]. This value is higher than the value
h
=
0
.
79 for the symmetric model [
99
]. The relation (
8.30
) gives the homothety
factor of
h
=
0
.
76, which is close to that given by the symmetrical structure model.
Hence, it follows that the resistance depends on the structure and
not on the degree
of symmetry
. Since the value of 0
.
85
>
0
.
79, it follows that the design of the lungs is
made with a safety margin for breathing in conditions of bronchial constriction [
99
].
The structural changes in the respiratory tree will change the value of the homo-
thety factor
h
and one can analyze the dynamics of the respiratory tree in terms of
pressure and volume variations. If the homothety factor decreases from 'optimal'
then an increase in the pressure drop will occur (higher effort to breath). If the ho-
mothety factor increases from 'optimal', the resistance is small, i.e. the volume will
increase for lower pressure drop values.
In asthma, the inner diameters of the bronchioli, and not their lengths, are re-
duced. In this case, the airway ducts are no longer homothetic and the diameter and
length of the sequential bronchioles are altered. This implies that the pressure drop
is given by
=
R
0
Q
1
N
1
2
i
h
1
(h
d
)
i
P
N
=
+
(8.31)
i
=
1
with
h
1
the length reduction ratio,
h
d
the diameter reduction ratio. The nonlinear
effect of the constriction is more pronounced, since a small reduction in
h
d
will
have a manifold effect in the total tree resistance.
The fractal dimension extracted from the PV and PPP loops is indirectly related
to the structure of the respiratory tree, since it quantifies the work of breathing, a
measure of the combined effect of pressure and volume. This implies that indirectly,
the proposed methods in this paper offer a measure of the degree of homothety in
the lungs. In other words, we indirectly evaluate the degree of optimality in the
respiratory process.
From Table
8.4
, we observe that the values identified from mapping the informa-
tion obtained in the PV loops provide more consistent results than those given by
the PPP plots. Indeed, from Fig.
8.24
, one can observe that the identified values for
(
8.23
) are more dispersed in the context of PV loop, allowing a clearer separation
between the groups. The data for the adults and the children do not overlap, thus
the validity of the results is supported. In terms of the
A
parameter, its value for the
adult group seems to be correlated directly with the airway resistance. Its values are
increasing with COPD and KS, which corresponds to the clinical pathology. For the
children group, its values are close to each other for healthy and asthma. We sus-
pect the reason might be the medication taken by the asthmatic patients, which had
mostly normal-to-the-exam spirometric values (i.e. controlled asthma). The values
for the children with pulmonary cystic fibrosis were lower than in healthy, indicat-
ing a lower resistance, either by means of lower pressure drop, either by means of
higher volume. In terms of the
B
parameter, its value seems to be correlated in-
