Biomedical Engineering Reference
In-Depth Information
Table 9.4.
Data used in the 0D model of the venous circulation system
Lower body
Upper body
Venules
Veins
Inferior cava Venules
Veins
Superior cava
R
[dyn cm
−
2
sml
−
1
]
53.32
11.997
0.6665
186.62
39.99
0.6665
L
[dyn cm
−
2
s
2
ml
−
1
]
1.333
0.6665
0.6665
1.333
0.6665
0.6665
C
[ml dyn
−
1
cm
2
]
0.00112528
0.05626407
0.01125281
0.00037509
0.01125281
0.00375094
Table 9.5.
Data used in the 0D models for the compartments in the pulmonary circulation
Pulmonary arteries Pulmonary veins
R
[dyn cm
−
2
sml
−
1
]
106.64
13.33
L
[dyn cm
−
2
s
2
ml
−
1
]0.0
0.0
C
[ml dyn
−
1
cm
2
]
0.00309077
0.060015
time-varying function of the elastance which for ventricles is (see [40])
1
cos
⎧
⎨
1
2
t
T
vc
−
π
0
≤
t
≤
T
vc
,
1
cos
1
2
π
(
t
−
T
vc
)
T
vr
e
v
(
t
)=
(9.69)
+
T
vc
<
t
≤
T
vc
+
T
vr
,
⎩
0
T
vc
+
T
vr
<
t
≤
T
,
and for atria is
1
cos
⎧
⎨
π
(
+
−
)
1
2
t
T
t
ar
+
0
≤
t
≤
t
ar
+
T
ar
−
T
,
T
ar
0
t
ar
+
T
arp
−
T
<
t
≤
t
ac
,
1
cos
e
a
(
t
)=
(9.70)
1
2
π
(
t
−
t
ac
)
T
ac
⎩
−
<
≤
+
,
t
ac
t
t
ac
T
ac
1
cos
1
2
π
(
t
−
t
ar
)
T
ar
+
t
ac
+
T
ac
<
t
≤
T
.
Here, the subscript
v
denotes the ventricles and
a
the atria,
T
is the duration of a
cardiac cycle,
T
vc
,
T
ac
,
T
vr
and
T
ar
refer to the times of ventricular/atrial contraction/
relaxation, and
t
ac
,
t
ar
are the instants at which the atria begin to contract and relax,
respectively.
Furthermore, the volume is related to the inflow and outflow as usual
dV
ch
dt
=
−
.
Q
i
Q
o
(9.71)
Table 9.6 shows the data used in the computational implementation of the elastance
model of the right and left halves of the heart.
