Biomedical Engineering Reference
In-Depth Information
Table 15.1
Parameter values for the lumped parameter Windkessel and coronary models. The unit
of resistance is 10
3
and the unit of capacitance is 10
−
6
dynes s/cm
5
cm
5
/dynes
Windkessel parameters
Coronary parameters
Outlet
R
p
R
d
C
Outlet
R
a
R
a
-
micro
R
v
C
a
C
im
Desc Aorta
0
.
25
2
.
48
500
LAD1
176
287
91
0
.
28
2
.
41
L Subclavian
1
.
88
19
.
0
44
.
7
LAD2
131
214
68
0
.
37
3
.
14
R Subclavian
1
.
88
19
.
0
48
.
3
LAD3
126
206
66
0
.
38
3
.
26
LExtCarotid
4
.
39
44
.
4
15
.
0
LAD4
75
123
39
0
.
61
5
.
19
R Ext Carotid
4
.
39
44
.
4
13
.
9
1 8 8
5
.
07
9
.
17
L Ant Cerebral
11
.
2
113
5
.
23
LCX2
159
260
83
0
.
41
3
.
50
R Ant Cerebral
11
.
2
113
5
.
05
LCX3
213
348
111
0
.
32
2
.
78
LIntCarotid
3
.
18
32
.
1
11
.
0
LCX4
167
272
87
0
.
39
3
.
38
R Int Carotid
3
.
18
32
.
1
10
.
3
RCA1
166
271
86
0
.
59
5
.
07
L Post Cerebral
8
.
29
83
.
8
5
.
41
RCA2
231
377
120
0
.
44
3
.
74
RPostCerebral
8
.
29
83
.
8
6
.
13
RCA3
258
422
134
0
.
39
3
.
38
15.2.3.3 Coronary Model
A lumped parameter model of the coronary vascular bed (Kim et al.,
2010
) was pre-
scribed at the outlets of the large coronary vessels (cf. Fig.
15.2
). In addition to the
resistors and capacitance of the Windkessel model, this model included the venous
circulation and incorporated effects of left ventricular pressure. The latter is criti-
cal since contraction of the heart is one of the main determinants of coronary flow.
The total resistance at each outlet
R
total
was again calculated assuming a MAP of
100 mmHg and that flow through each outlet scaled with cross-sectional area, with
mean coronary flow comprising approximately 4.5 % of cardiac output (Guyton and
Hall,
2006
). The Windkessel portion of the lumped parameter coronary model was
represented by
R
a
,
C
a
, and
R
a
-
micro
. The venous pressure defined the relationship
between
R
a
,
R
a
-
micro
, and
R
v
and was assumed to be 15 mmHg. Two parameters,
C
a
-
total
and
C
im
-
total
, were defined as the sum of all coronary arterial (
C
a
) and intra-
myocardial (
C
im
) compliances. An iterative tuning procedure was used to find val-
ues of
C
a
-
total
and
C
im
-
total
that yielded physiologic coronary flow waveforms. For
the left coronary vessels, the left ventricular pressure found in the lumped parameter
coronary model was equivalent to the pressure derived from the heart model. The
boundary condition for the right coronary artery was based on a scaling of left ven-
tricular pressure that was derived from the heart model, specifically
P
RV
=
0
.
20
P
LV
.
The final parameter values for the heart model and Windkessel models are listed in
Table
15.1
.
