Biomedical Engineering Reference
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with the local blood flow after coil embolization of an idealized representa-
tion of the basilar bifurcation with a terminal aneurysm using porous media
theory. The authors assumed circular tubes of the surrounding arteries with
a spherical shape of an aneurysm. The results of that study suggested that
there is a complex interaction between the local hemodynamics and intraa-
neurysmal flow that induces significant forces on the coil mass. Recently, we
developed [50] a numerical model to quantify the reduction in blood veloc-
ity and pressure resulting from the placement of endovascular coils within a
cerebral aneurysm using physiological velocity waveforms. The flow charac-
teristics within the aneurysm sac were modeled using the volume averaged
porous media equations. We studied the effects of narrow and wide aneurys-
mal necks on the velocity fields and pressure within the aneurysmal sac in the
absence of the coils. Within the sac at peak systole, wide-neck aneurysms dis-
played higher velocity and pressure than narrow-neck aneurysms. We showed
that velocity fields are significantly affected by the presence of endovascular
coil within the aneurysm sac. Moreover, we estimated that a volume density
of 20% platinum coil in the aneurysmal sac was sucient to cause sucient
blood flow arrest in the aneurysm to allow for thrombus formation.
6.5 Mathematical Formulations
We chose to explore the application of porous media theory to the modeling of
flow changes in cerebral aneurysms treated by endovascular coils. The conven-
tional CFD technique is not suitable to model flow through a coiled aneurysm
because of the diculties in representing the random geometry of the coils
and the large number of nodal points required to model the coil surface. Even
if the geometry of the coils could be determined, the density and total num-
ber of nodal points required to capture the characteristics of the flow would
represent a major limitation. We thought that a CFD-based porous substrate
approach should result in a more accurate model of the effect of coiling on the
flow and pressure conditions in brain aneurysms. In addition, this technique
is computationally ecient because it results in substantial savings in central
processing unit (CPU) and memory usage and leads faster to grid-independent
solutions. Furthermore, this approach appears to give a more realistic descrip-
tion of the
in vivo
situation since modeling the coils as a porous medium does
not act as a solid region as previously modeled but rather slows down the
flow activity within the aneurysm that should promote thrombus formation.
We modeled the packing of coils in our work as a porous substrate similar
to that reported by Srinivasan et al. [51] in his analysis of heat transfer and
flow through a spirally fluted tube. The main objective of our work was to
model the endovascular coils in the narrow-necked aneurysm sac as a porous
medium of decreasing porosity (decreasing as the number of coils increase)
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