Biomedical Engineering Reference
In-Depth Information
Table 9.6. Data used in the elastance model of the right and left halves of the heart
Chambers
Right atrium
Right ventricle
Left atrium
Left ventricle
E A [dyn cm 2
ml 1 ]
79.98
733.15
93.31
3665.75
E B [dyn cm 2
ml 1 ]
93.31
66.65
119.97
106.64
T c [s]
0.17
0.34
0.17
0.34
T r [s]
0.17
0.15
0.17
0.15
t c [s]
0.80
-
0.80
-
t r [s]
0.97
-
0.97
-
V 0 [ml]
4.0
10.0
4.0
5.0
α
0.0005
0.0005
0.0005
0.0005
9.4.7 Non-ideal diode model for the heart valves
The momentum balance in each heart valve is such that we take into account the
non-linear behaviour by which the flow can be inverted when the valve closes. The
model employed is shown in Fig. 9.7 and has been partially inspired by the valve
model presented in [31].
The governing equation for this valve model is the following
L dQ o
dt +
RQ o +
B
|
Q o |
Q o = Ξ (
P i
P o ) ,
(9.72)
where L is the inertance of the fluid, R is the viscous resistance, B accounts for the
flow separation phenomenon and P i and P o are the input and output pressure values
in the compartment. The non-binary state of the valve depends upon the presence of
the coefficient
. This coefficient simulates the behaviour of the orifice of the valve,
and is a function of the opening angle of the valve, denoted by
Ξ
θ
, as follows
4
(
1
cos
θ )
Ξ =
4 ,
(9.73)
(
1
cos
θ max )
Fig. 9.7. Generic chamber-valve element with a non-ideal diode
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