Biomedical Engineering Reference
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voxel size produced from clinical imaging does not permit the accurate differentia-
tion of different degrees of aqueductal stenosis. Finally, inlets and outlet boundaries
were created using CFD-VisCART (ESI Group, Paris France), which was also used
to generate non-conforming computational grids. The final smoothed STL file for
an open aqueduct (i.e. no applied stenosis) is seen in Fig. 22.2 , along with a clearer
labeling technique.
22.3.4 Solution Method
The governing multicompartmental poroelastic equations are solved with an im-
plicit second-order central finite differences scheme on the midpoints and for-
ward/backward Euler used on the boundary nodes. The quasi-steady time discretiza-
tion (for the temporally dependent terms in the boundary conditions) is performed
via a first-order Euler approach.
Flow through the multidimensional aqueducts is solved using the multiphysics
software CFD-ACE+ (ESI Group, Paris France) which is based on the finite vol-
ume approach, along with central spatial differentiating, algebraic multigrid scheme
(Webster, 1994 ; Khandelwal and Visaria, 2006 ;Tuetal., 2008 ) and the SIMPLEC
pressure-velocity coupling. The coupling between the poroelastic solver and the
flow solver is achieved through the CFD-ACE+ user-defined subroutines (UDS's).
This approach allows for the embedding of the patient-specific aqueduct of Sylvius
into the model.
22.4 Results and Discussion for Aqueductal Stenosis
TheresultsshowninFig. 22.4 show the first application of the MPET model to
acute HCP. The transfer of water between the four networks to mimic the cerebral
environment reveals interesting features. The plots in Fig. 22.4 show the results
of the ventricular displacement along with the corresponding CSF pressure for the
three cases of stenosed aqueduct. The greatest displacement was witnessed for the
severely stenosed case, which was 1 . 93
10 4 m. The severe case also exhibited the
highest ventricular CSF pressure, that being 1096 Pa.
The CSF pressure converges to 1089 Pa on the skull, for all cases, as expected
since that value is connected with the venal absorption boundary condition. The
ventricular displacement decreases to 0 m at the skull, since this is imposed as a
rigid, adult skull boundary condition (skull radius of 10 cm).
The Reynolds number, defined as R e =
·
ρ e D h ν p e , where ν p is the peak ve-
locity flowing through the aqueduct, varied from 15 in the open case, 112 for the
mild and 135 for the severely stenosed aqueduct. The peak velocities associated
with these Reynolds numbers correspond to 4 . 4, 80 and 152 mm / s, respectively.
The hydraulic diameter D h is given by D h =
4 A/P , where A is the cross sectional
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