Biomedical Engineering Reference
In-Depth Information
Fig. 5.3
General scheme of a ladder network in gamma-cell configuration; here
N
denotes the
total number of cells
In this chapter we make use of the theoretical basis available in the literature
for similar structures, but tailored upon the conditions and the characteristics of the
respiratory system.
Consider the generalized case depicted in Fig.
5.3
. The longitudinal and transver-
sal impedances can be defined irrespective of their elements, in function of voltage
and current:
U
m
−
1
(s)
U
m
(s)
I
m
−
1
(s)
−
Zl
m
(s)
=
(5.5)
and
U
m
(s)
I
m
−
1
(s)
−
I
m
(s)
Zt
m
(s)
=
(5.6)
from which we can further write
U
m
(s)
−
U
m
+
1
(s)
=
Zl
m
+
1
(s)I
m
(s)
(5.7)
or, equivalently,
I
m
(s)
U
m
(s)
=
1
/Zl
m
+
1
(s)
(5.8)
U
m
+
1
(s)
I
m
(s)Zl
m
+
1
(s)
1
+
and
U
m
+
1
(s)
Zt
m
+
1
(s)
I
m
(s)
−
I
m
+
1
(s)
=
(5.9)
or, equivalently
U
m
+
1
(s)
I
m
(s)
Zt
m
+
1
(s)
=
(5.10)
+
Zt
m
+
1
(s)
I
m
+
1
(s)
1
U
m
+
1
(s)
From (
5.8
)-(
5.10
), the total admittance of the ladder at level
m
=
0 is given by
I
0
(s)
U
0
(s)
=
1
/Zl
1
(s)
Y
1
(s)
=
(5.11)
U
1
(s)
I
0
(s)Zl
1
(s)
1
+
or, equivalently, by
1
/Zl
1
(s)
Y
1
(s)
=
(5.12)
Zt
1
(s)/Zl
1
(s)
1
1
+
Zt
1
(s)
I
1
(s)
U
1
(s)
+
