Biomedical Engineering Reference
In-Depth Information
hemodynamic environment, influence of wall modifications on flow patterns and
long-term adaptations of the vascular wall can have useful clinical applications,
especially in view of reconstruction and revascularization operations [
5
,
6
].
Flow visualization techniques and non-invasive medical imaging data acquisition
such as computed tomography, angiography or magnetic resonance imaging, make
feasible to construct three dimensional models of blood vessels. Measuring tech-
niques such as Doppler ultrasound have improved to provide accurate information
on the flow fields. Validated computational fluid dynamics (CFD) models using data
obtained by these currently available measurement techniques [
7
-
9
] can be very
valuable in the early detection of vessels at risk and prediction of future disease
progression.
Hemodynamic finite element simulation studies have been frequently used to
gain a better understanding of functional, diagnostic and therapeutic aspects of
the blood flow. Three different issues are necessary during such study defining the
following methodology:
1. Definition of suitable mathematical models - due to the complexity of the vas-
cular system, a preliminary analysis aiming at introducing suitable simplifying
assumptions in the mathematical modelling process is necessary. Obviously,
different kinds of simplifications are suitable for different vascular problems;
2. Pre-processing of clinical data - the suitable treatment of clinical data is crucial
for the definition of a real geometrical model, taken from a patient. This aspect
demands geometrical reconstruction algorithms in order to achieve simulation in
real vascular morphologies;
3. Development of appropriate numerical techniques - the geometrical complexity
of the vascular system suggests the use of unstructured grids, in particular for
Finite Element Method (FEM), while the strongly unsteady nature of the problem
demands effective time-advancing methods.
The arterial wall is a composite of three layers, each containing different
amounts of elastin, collagen, vascular smooth muscle cells and extracellular matrix.
In diseased vessels which are often the subject of interest, the arteries are less
compliant, wall motion is reduced and in most approximations the assumption of
rigid vessel flow is reasonable.
Blood consists of formed elements suspended in plasma, an aqueous polymer
solution. About 45% volume consists of formed elements and about 55% of plasma.
The majority of formed elements are red blood cells (95%). In large and medium
size vessels, blood is usually modelled as a Newtonian liquid. However in smaller
vessels blood is a complex rheological mixture showing several non-Newtonian
properties, as shear-thinning or viscoelasticity. The temperature and the presence
of pathological conditions may also contribute to non-Newtonian behaviour.
For the steady flow case [
10
] showed that the non-Newtonian effect is small
except for the peak shear stress and that for the pulsatile case the Newtonian
effect in the artery is small and negligible. Perktold and co-workers examined
non-Newtonian viscosity models in carotid artery bifurcation and although the
Newtonian assumption yields no change in the essential flow characteristics they
