Advanced Topics and Future Trends - Computational Hemodynamics: Theory, Modelling and Applications - page 309

boundary methods and with the Lagrangian method is to avoid instability occurring
from mesh distortion with large deformation. Another advantage is that mass is
strictly conserved, and the full Eulerian approach can be easily parallelized for high
level supercomputing facilities.
The multiphysics, and multiscales related to blood flow requires numerical
methods for fluid-structure and fluid-membrane interactions to be accounted for.
Matsumoto et al. (2014) presented a multiscale framework for modelling a deform-
able vesicle problem dealing with red blood cells and platelets. A supercomputer of
10 Peta flops speed under the Next-Generation Supercomputer Project in Japan was
used. The researchers developed a full Eulerian Fluid-Structure Interaction solver
without mesh generation, to allow simulations to be conducted directly from medi-
cal images.
The conventional FSI method has been to define the fluid domain in the Eule-
rian approach, while the structure domain is described in the Lagrangian approach,
which makes up the Arbitrary-Lagrangian-Eulerian, or the Immersed Boundary
method, based on how the kinematic and dynamic interactions are coupled on
the moving interface. However, for a system involving complex geometry of a
large number of bodies, it requires extreme computational resources to generate
the mesh and to reconstruct the mesh topology for the moving bodies. Matsumoto
et al. (2014) formulated an efficient numerical scheme to account for geometrical
flexibility and avoids a breakdown in a large deformation owing to the absence of
the mesh distortion. The equations of the system consist of a Newtonian fluid and
hyperelastic structure/membrane and are applied to three-dimensional blood flows
including blood cells in a capillary vessel and in a microchannel, and the relevance
of the red blood cells thrombus formation.
This method allows a fully coupled approach between the red blood cells, plate-
lets and vessel. Figure 9.2 shows the multiphase blood flow at three time instants,
where the red blood cells rotate and mix. Its deformed shape takes the form of a
parachute, and migrates towards the vessel wall. Matsumoto et al. (2014) work
showed that the cell-free layer (in which the number density of the red blood cell is
very low) is confirmed to form near the wall and to be thicker over time.
Rahimian et al. (2010) presented a fast, petaflop-scalable algorithm for direct
simulation of blood, modelling a mixture of a Stokesian fluid (plasma) and red
blood cells. Their work simulated up to 260 million deformable red blood cells
while preserving the physics related to nonlinear solid mechanics to capture the
Fig. 9.2 Results from the work by Matsumoto et al. (2014) showing snapshots of the red blood
cells (in red ) and platelets (in yellow )