In Silico Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 343

[ms ∧ − 1]

Platelet velocity
Platelet trajectory

x

0 0.003 0.006 (m)

z

y

0.0015 0.0045

FIGURE 13.7 A discrete phase model can be used to estimate platelet trajectories after they pass an 80% steno-

sis in the left descending artery. This image shows the trajectories of every particle seeded at the inlet and we can
see that a significant proportion of these become trapped in the recirculation zone downstream of the stenosis.

instantaneous velocities in the carrier phase (blood) are used to solve for the particle veloc-
ity. The instantaneous characteristics will be calculated by adding random fluctuations
obtained from the k-ω

simulation, using the equation

r

2 k
3

u N 5u1λ ð 13 : 18 Þ

where 1 to 1 sampled from a normal distribution.

Furthermore, the stress that one platelet experiences along its trajectory can also be esti-
mated. For example, we can use the Boussinesq approximation to compute the total stress
(laminar plus turbulent stresses) applied to a single platelet, as

λ is a random number between 2

X

t max

ðε i 2ε i 1 1 Þ
2

i Þ 1KE i 3ρ

3 ðμ i 1μ 3Δt i ð 13 : 19 Þ

t5t 0

i

where ε i is the strain rate, μ i is the viscosity, μ is the turbulent viscosity, ρ is the density,

KE i Δt is the time step.

Figure 13.7 shows platelet trajectories calculated using the method discussed above. In
Figure 13.8 , the shear stress history of one platelet with an interesting trajectory was

is the turbulent kinetic energy, and