Biomedical Engineering Reference
In-Depth Information
the conservation of mass and momentum equations for transient, laminar flow
without body forces are given by
∇•
V = 0
(6.3)
ρ f v
∂t
2 V
+ ρ f ( V
•∇
V )=
−∇
P + µ f
(6.4)
where ρ f is the blood density, µ f is the blood viscosity, P is the pressure, V is
the velocity vector, and the subscript f refers to the fluid phase. The influence
of the non-Newtonian properties of blood on flow is approximated using the
Carreau model as
µ )(1 + κ 2 γ 2 ) ( n 1)
µ = µ +( µ o
(6.5)
2
where µ o and µ (used as a reference value for Newtonian case) are the
zero and infinite shear rate viscosities, respectively, γ is the deformation rate,
and κ is a time constant. This model was found to fit well the experimental
data as shown by Cho and Kensey [57] using the following set of parame-
ters: µ o =0 . 056 N
sec / m 2 ,n =0 . 3568 =3 . 313 sec.
To solve the aforementioned equations (6.1-6.4), the boundary conditions of
all computational domains must be formulated. One of the most challenging
problems of modeling biological flow is the specification of the boundary flow
conditions. Physiological velocity and pressure waveforms must be prescribed.
sec / m 2 =0 . 00345 N
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6.6 Construction of Brain Aneurysm Meshes
from CT Scans
Patient-specific geometries or brain aneurysms are essentials for accurate esti-
mation of flow characteristics and wall stresses. Aneurysms can be constructed
using DICOM files obtained from magnetic resonance angiography (MRA),
CTA, or three-dimensional angiograms of living patients. Mimics software
(Materialise, Inc.) is used in this investigation to capture brain aneurysm
geometry from CTA images and to create a three-dimensional model for edit-
ing and numerical modeling. Mimics software has the capability to improve
the quality and speed of finite element analyses through the transformation of
irregularly shaped triangles into more or less equilateral triangles. In addition,
this software can be used to differentiate thrombus and calcium. Another fea-
ture of this software includes the application of assigning variable mechanical
properties (i.e., modulus of elasticity and Poisson's ratio) to different volume
elements. An example of the applicability of this software in Figure 6.2, shows
the geometry of a patient with brain aneurysm.
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