Biomedical Engineering Reference
In-Depth Information
The consequent propagation phase is described by Eqs. (
7.53
)-(
7.56
):
k
2
ŒWŒII
K
2M
C ŒII
R
II
D
(7.53)
R
IIa
DR
II
h
2
ŒIIaŒATIII
(7.54)
k
1
ŒIIaŒI
K
1M
C ŒI
R
I
D
(7.55)
h
1a
ŒPLAŒIa
H
1M
C ŒIa
R
Ia
DR
I
(7.56)
The termination of clotting is described by (
7.57
)-(
7.60
):
R
ATIII
Dh
2
ŒIIaŒATIII h
2W
ŒWŒATIII
(7.57)
k
PC
ŒIIaŒI
K
PCM
C ŒI
R
PC
D
(7.58)
R
APC
DR
PC
h
PC
ŒAPCŒǛ
1
AT h
1W
ŒAPCŒW
(7.59)
R
Ǜ
1
AT
Dh
PC
ŒAPCŒǛ
1
AT
(7.60)
while the clot lysis is modeled by (
7.61
)-(
7.64
)
R
tPA
D 0
(7.61)
k
PLA
ŒtPAŒPLS
K
PLAM
C ŒPLS
R
PLS
D
(7.62)
R
PLA
DR
PLS
h
PLA
ŒPLAŒǛ
2
AT
(7.63)
R
Ǜ
2
AT
Dh
PLA
ŒPLAŒǛ
2
AT
(7.64)
For the full description of the biochemistry model, see the original paper [
72
]and
the references therein.
Flow Model
.
The flow is simulated using the generalized Newtonian model
similar to the one described in Sect.
7.7.2
using Eqs. (
7.118
), (
7.119
). With
respect to the classical Newtonian fluid case the model is altered to account for
shear rate P and fibrin concentration ŒIa dependence in both, viscosity and
density . The corresponding modified momentum equations can be written as:
.ŒIa/
@
u
@t
C
u
r
u
h
. P ;ŒIa/
r
u
Cr
u
T
i
(7.65)
Drp Cr
The shear-rate P dependent (shear-thinning) fluid viscosity . P /can be defined,
e.g., using the generalized Cross model (
7.119
). The change in values of and
depending on the fibrin concentration ŒIa is governed by a Heaviside jump
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