ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

3.3 Surface and solid mesh reconstruction
The superficial and solid mesh was obtained using the Simpleware (v4.3 - Scan IP
module) image processing software. The superficial mesh was constructed using
triangle elements to obtain the geometry in STL format, then the solid mesh of
tetrahedral elements was obtained using the +FE Grid algorithm trying to conserve all
the possible contacts to apply then the boundary conditions.
3.4 CFD Analysis
Once the mesh was obtained the CFD analysis was performed using the commercial
software Fluent 12.1 (Ansys-United States). The steady-state Navier-Stokes equations
were solved to calculate the velocity profile and the WSS of each network. The blood
properties that were used to simulate the fluid within the different vascular networks are
given in Table 1. Taking into account the rheological behavior of the blood and the
vascular network size, a Non-Newtonian fluid was simulated (Eq. 1). The non-
Newtonian molecular viscosity model used in this study was the non-Newtonian power
law where the viscosity is calculated as [12].
Where , , , and are input parameters. is a measure of the average viscosity
of the fluid (the consistency index); is a measure of the deviation of the fluid from
Newtonian (the power–law index), is the reference temperature; and and are
respectively, the lower and upper limits of Newtonian viscosity used in the power law.
The fluid shear stress, denoted by is calculated as
Given the low Reynolds numbers under the applied flow rates, fluid was assumed to be
incompressible and laminar. The mass and momentum conservation equations for
laminar flow were solved.
Table 1 Blood properties and non-Newtonian power law parameters
Blood properties
Density (Kg.m -3 ) 1060
Power-law index (n) 0.7
Consistency index (kg s n−2 /m) 0.01691
References temperature (ºK) 310
Minimum viscosity limit nmin(kg/ms) 0.0001
Maximum viscosity limit nmin(kg/ms) 0.1
The boundary conditions were defined in Fluent to simulate blood movement from the
superior to inferior position. A constant velocity equal to 0.001 ms -1 was applied in the
superior region and null pressure outlet was applied in the inferior region of the
networks. Blood walls were set to zero diffusive flux. To perform the CFD analysis we
have used Window Server 2008 R2 Enterprise with two processors Intel (R) Xeon(R)
3GHz and 48GB of memory RAM
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