Biomedical Engineering Reference
In-Depth Information
B
2
2
F
0
=
B
1
v
1
+
F
1
;
F
1
=
v
2
+
F
2
(6.10)
1
K
1
F
1
;
2
K
2
F
2
v
1
=
v
2
+
v
2
=
The values of resistors and capacitors are calculated with the model from Fig.
6.5
and relations (
4.62
)-(
4.64
):
R
e
16
=
10
−
6
1
.
57 kPa/(l/s) and
C
e
16
=
3
.
06
·
l/kPa.
From these values one can calculate the equivalent
B
m
and
K
m
values, taking into
R
em
/
2
m
−
1
2
m
−
1
C
em
, respectively, from (
5.1
) and
account that
R
em
=
and
C
em
=
(
5.3
). The superscript
∗
denotes a single branch in the respiratory level represented
by the subscript
m
:
F
m
v
m
=
P
m
B
m
=
Q
m
A
2
m
=
R
em
A
2
m
(6.11)
A
2
m
C
em
F
m
x
m
=
P
m
V
m
K
m
=
A
2
m
=
with
P
the pressure,
Q
the flow,
V
the volume,
A
m
=
πR
m
the area,
R
m
the radius
of a tube at level
m
, and
x
the axial displacement.
Figure
6.6
-left depicts the evolution of the parameters in a single tube at a cer-
tain level
m
, whereas Fig.
6.6
-right depicts their evolution in the entire level. One
Fig. 6.5
An illustrating example of the first two levels in the electrical and the mechanical net-
works
Ta b l e 6 . 1
The
electro-mechanical analogy
Electrical
Mechanical
Voltage
e
[V]
Force
F
[N]
Current
i
[A]
Velocity
v
[m/s]
Resistance
R
e
[
]
Damping constant
B
[N s/m]
Capacitance
C
e
[F]
Spring constant 1
/K
[m/N]
Inductance
L
e
[H]
Mass
M
[kg]
