Biomedical Engineering Reference
In-Depth Information
servation angle may result in underprediction of the maximum transverse diameter.
However, the simulation results remain within the experimental error bars.
Next, we compare the MS-RBC versus the LD-RBC models; Fig. 10.7 (right)
presents the axial and transverse RBC deformations for a healthy RBC and for
a RBC at the latest stage (schizont) of intra-erythrocytic parasite development in
malaria disease in comparison with experiments [9]. Simulation results are in excel-
lent agreement with the experiments for both RBC models. The Young's modulus
of a RBC is found to be 18
.
.
N/m for healthy RBC and at the schizont
stage, respectively, in case of the MS-RBC model, while the LD-RBC model yields
the values of 20
9 and 180
0
μ
N/m for the RBC Young's modulus. Note that the low-
dimensional RBC model is able to capture linear as well as non-linear RBC elastic
response.
.
0 and 199
.
5
μ
10.3.2 Membrane rheology from Twisting Torque Cytometry
Twisting torque cytometry (TTC) is the numerical analog of the optical magnetic
twisting cytometry (OMTC) used in the experiments [11, 62], where a ferrimagnetic
microbead is attached to RBC top and is subjected to an oscillating magnetic field.
In simulations a microbead is attached to the modelled membrane, and is subjected
to an oscillating torque as shown in Fig. 10.8 (left). In analogy with the experiments,
the modelled RBC is attached to a solid surface, where the wall-adhesion is mod-
elled by keeping stationary fifteen percent of vertices on the RBC bottom, while
other vertices are free to move. The adhered RBC is filled and surrounded by fluids
having viscosities much smaller than the membrane viscosity, and therefore, only
the membrane viscous contribution is measured. The microbead is simulated by a
set of vertices on the corresponding sphere subject to a rigid body motion. The bead
attachment is modelled by including several RBC vertices next to the microbead
bottom into the rigid motion.
A typical bead response to an oscillating torque measured in simulations is given
in Fig. 10.8 (right). The bead displacement has the same oscillating frequency as the
ω
= 33.1 Hz
oscillating torque
1
300
Torque
Displacement
0.75
200
0.5
displacement
100
0.25
0
0
−0.25
−100
−0.5
φ
−200
−0.75
−1
−300
0
0
2
2
4
4
6
6
8
8
10
10
12
12
Dimensionless time − t
ω
Fig. 10.8. Setup of the TTC (left) and the characteristic response of a microbead subjected to an
oscillating torque (right)
 
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