Biomedical Engineering Reference
In-Depth Information
[
183
]. It is based on
Platelet Activation State (PAS)
associated with the kth platelet
at time t:
Ca
"
Z
t
0
#
a
1
Z
t
1=a
k
.t
0
/
C
./
b=a
d C
PAS
. /
b=a
d (7.112)
PAS
k
.t/ D
t
0
Here
PAS
k
.t
0
/ is the value of activation of the platelet at the starting time of
observation t
0
, D .t/ is time-dependent (local, along platelet path) scalar value
of stress.
94
The constants a D 1:3198, b D 0:6256,andC D 10
5
are tuning
parameters of the model obtained from experimental data fitting. This model was
used, e.g., in [
164
] to evaluate shear-induced platelet activation and its relationship
with blood flow in a model of stenosed carotid bifurcation, or in [
177
]topredict
blood damage in prosthetic heart valves.
A different approach to quantify platelet damage and activation in complex flows
was described in [
6
,
8
]. It evaluates a
platelet activation function
A
as an integral
over the platelet stressing history
exp
k
./
c
1
H../
c
/d
Z
t
1
A
0
A
.t/ D
A
.t
0
/ C
(7.113)
t
0
where D .t/ is again a scalar measure of stress with
c
being the critical value
of stress above which the platelets get potentially activated. The integral expresses
the accumulated stress acting on the platelets between the instants t
0
and t.The
Heaviside function H is defined as
n
1 for
c
H.
c
/ D
(7.114)
0 for
<
c
to assure that only supra-critical stresses are taken into consideration, i.e., contribut-
ing to platelet activation. Lower, physiologically standard values have no effect
on activation. The values of the activation function
.t/ are compared against the
platelet activation threshold A
act
and damage threshold A
dam
to decide, whether the
platelet remains resting or gets activated. More details including the full activation
algorithm can be found in [
8
], where a complex blood flow and biochemistry model
is built for thrombus formation and lysis. In the abovementioned implementation,
the model is capable of platelet activation prediction for each separate platelet/fluid-
parcel at the price of Lagrangian tracing and damage integration for every such
particle. This is useful when effects of delayed platelet activation
95
or damage have
to be included, i.e., the values of
A
.t t
act
/ have to be considered when deciding
whether the platelets get activated. For immediate activation, i.e., negligible time t
act
A
94
Usually some kind of norm of the stress tensor. See, e.g., [
214
,
222
].
95
Platelet does not get activated immediately, but only after a certain time t
act
.
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