Mathematical Models for Blood Coagulation - Fluid-Structure Interaction and Biomedical Applications - page 525

0.9
0.7
0.5
0.3
0.1
-0.1
-0.3
-0.5
-0.7
-0.9

Y

Z

X

Fig. 7.14 Near-wall velocity magnitude reduction ı at the time 120 s

A longer time evolution of the clot and its effect on blood flow can be seen from
Figs. 7.15 - 7.18 . Besides the fibrin concentration on the deployed vessel surface, 77 a
non-dimensional velocity reduction ı is defined

q.x;0/ q.x;t/
q.x;0/

ı.x;t/D (7.50)

p u 2

Here q.x;t/ is the local velocity magnitude q D C w 2 . The velocity

reduction is evaluated in the first near-wall grid node, because evidently the no-slip
condition is imposed on the vessel wall.
The time evolution of the clot is depicted in Fig. 7.17 . The resulting blood flow
velocity reduction is visualized in Fig. 7.18 .

C v 2

SimplifiedCellBasedCoagulationModel

Another macroscopic coagulation model was recently developed in [ 72 ].
Although it uses the same mathematical basis, i.e., a coupled set of ADR equations
linked to a non-Newtonian blood flow model, as the previously mentioned complex
coagulation model, its biochemical and biomechanical foundations are different.
In comparison with the above described model the model mentioned here differs
notably in several points:

- The biochemistry model follows the cell-basedmodel formalism, rather than the

traditional three-pathway scheme.

- The model is simplified in terms of number of ADR equations being solved (13

equations compared to 23 in the previous model).

77 The dimensions are normalized using the vessel radius (half-diameter) R D 3:1 mm.