Biomedical Engineering Reference
In-Depth Information
80
80
Experiment − Healthy
Simulations − Heal
t
hy
Experiment − Healthy
Simulations − Healthy
60
60
40
40
20
20
0
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0
0.1
0.2
0.3
0.4
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0.8
Pressure (Pa/
m)
Pressure (Pa/
m)
(a)
μ
(b)
μ
Fig. 10.14.
Average velocity of healthy RBCs as a function of pressure gradient and comparison of
simulation and experimental results. Results for converging (a) and diverging geometries (b) (from
[67])
500 DPD points per RBC were sufficient. This is due to the fast dynamic changes
of the RBC membrane as the RBC travels through the narrow constrictions. Param-
eters of the healthy cell model are derived from RBC spectrin network properties
as described in previous sections. In addition, membrane fluctuation measurements
and optical tweezers experiments are used to define simulation parameters. Specifi-
cally, we required that the amplitude of thermal fluctuations of the membrane at rest
to be within the range of experimental observations [12]. We also required that the
characteristic relaxation time of the RBC model in simulations be equal to the ex-
perimentally measured value of 0.18 seconds. The RBC model is immersed into the
DPD fluid. The membrane particles interact with internal and external fluid particles
through the DPD forces. By changing the direction of the body force, the motion of
the cell through channels with converging and diverging pores is simulated using
the same channel geometry.
The DPD model is able to capture the effect of obstacle orientation quite ac-
curately. Quantitative comparison of simulation results with experimental data for
healthy cell velocity as a function of applied pressure gradient is shown in Fig. 10.14.
In order to evaluate contributions of individual mechanical properties of the cell
to overall dynamic behaviour, we run additional simulations. The DPD model pro-
vides a unique opportunity to perform this analysis, since experimental evaluation of
these contributions is laborious or impossible. Larger cells are found to travel with
lower velocities; however, the velocity variation due to cell size is not significant.
Additional simulations were performed in which the membrane shear modulus and
membrane viscosity were varied independently of each other. The results showed
that the RBC velocity in the device is sensitive to shear modulus, while (in contrast
to the device described above) variation of membrane viscosity did not affect the
RBC traversal significantly. This finding may seem to be counter intuitive; when the
membrane viscosity is increased one would expect higher energy dissipation and
therefore lower RBC velocity. Indeed, increased membrane viscosity increases the
time it takes for a RBC to traverse an individual opening between pair of obstacles.
However, it also slows down the recovery of RBC shape when the cell is traveling
