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1476 JOURNAL OF COMPUTERS, VOL. 8, NO. 6, JUNE 2013
Loop 7: H
7
− H9
− H10
+ H11
= 0 ,
Loop 8: H
8
− H10
+ H11
− H12
− H13
+ H14
− H15
= 0 .
We knew l , d
1
, ρ of the cerebral circulation network
from paper [1], it is shown in table I.
TABLE I.
THE ARTERIAL GEOMETRY PARAMETERS OF THE CIRCLE OF WILLIS
artery number length(cm) diameter(cm)
internal carotid a. 7,1 25 0.4
basilar a. 9 3 0.4
Posterior communicating 11,15 2 0.12
a.
posterior cerebral a.Ⅰ 10,8 2 0.3
anterior cerebral a.Ⅰ 12,14 2 0.25
anterior communicating a. 13 0.5 0.15
middle cerebral a. 5,2 7 0.35
posterior cerebral a.Ⅱ 6,16 7 0.3
Figure 5. The network equivalent plane diagram of cerebral circulation
(16 branches).
The network of the cerebral circulation has 16
branches, 8 nodes and 1 generator branch. Choose
branches 9 to 16 and generator as the tree of the network.
The node equations can be expressed as:
Node 1: Q in
− Q1 − Q7
− Q9
= 0 ;
Node 2: Q
8
+ Q10
− Q9
= 0 ;
Node 3: Q
6
− Q10
− Q11
= 0 ;
Node 4: Q
5
− Q7
+ Q11
+ Q12
= 0 ;
Node 5: Q
4
− Q12
+ Q13
= 0 ;
Node 6: Q
3
− Q13
− Q14
= 0 ;
Node 7: Q
2
+ Q14
+ Q15
− Q1
= 0 ;
Node 8: Q
16
− Q8
− Q15
= 0 ;
After transformation:
Q in
= Q1 + Q7
+ Q9
Q in
= Q1 + Q7
+ Q8
+ Q10
Q in
= Q1 + Q6
+ Q7
+ Q8
− Q11
Q in
= Q1 + Q5
+ Q6
+ Q8
+ Q12
Q in
= Q1 + Q4
+ Q5
+ Q6
+ Q8
+ Q13
Q in
= Q1 + Q3
+ Q4
+ Q5
+ Q6
+ Q8
− Q14
Q in
= Q2 + Q3
+ Q4
+ Q5
+ Q6
+ Q8
+ Q15
Q in
= Q2 + Q3
+ Q4
+ Q5
+ Q6
+ Q16
The loop equations can be expressed as:
Loop 1: H
1
− H
9
− H10
− H11
+ H12
− H13
− H14
= 0 ;
Loop 2: H
2
− H15
− H16
= 0 ;
Loop 3: H
3
+ H14
− H15
− H16
= 0 ;
Loop 4: H
4
− H13
+ H14
− H15
− H16
= 0 ,
Loop 5: H
5
− H12
− H13
+ H14
− H15
− H16
= 0 ,
Loop 6: H + H − H − H + H − H − H 0 ,
6 11 12 13 14 15 16
=
anterior cerebral a.Ⅱ 4,3 5 0.25
ρl
1.63l
We can obtain T from T = and R from R = .
4
S
D
We may obtain Q c0 equation set from type (19), this
equation only has numerical solution, but does not have
the exact solution, uses the genetic algorithm to get the
iterative solution. We can get H from Q , H is equal to
P .
First, we solve the cerebral circulation blood flow Q
with the normal person, and we can get H from (2), that
is P in (1), its computing simulation result is shown in
figure 6.
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