Page 276 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

FINITE-ELEMENT ANALYSIS 253

current research. Of particular interest are the idealizations that must be made to keep both compu-
tational and general modeling times within reason. In many cases, these idealizations have been
shown to present findings very close to those seen clinically.
Arterial Studies. Numerous recent papers have sought to evaluate the behavior of blood in arteries
utilizing computational fluid dynamics (CFD). Analogous to solid finite element modeling, these
codes evaluate the local fluid velocities along with particulate motion and wall shear profiles. High
and low wall shear are of concern in the evaluation of atherogenesis (the beginning of plaque for-
mation), and for blood platelet activation. A second area of concern is boundary layer separation and
fluid recirculation, where by-products can build up and platelets can attach to the vessel wall. Of par-
ticular interest are the carotid artery (which feeds the brain), the coronary arteries (to the heart), and
arterial aneurysms (widening of the artery, culminating in leakage or rupture). The major areas at
issue in these evaluations are how to model the vessel walls and how to evaluate the blood. Blood
vessel walls have nonlinear material properties, both as pertaining to radius changes at a given
location and as one moves along the vessel axially.
As will be noted below, the first (and often reasonable) assumption is that the vessel is isotropic.
The difficulty in determining the actual mechanical properties are, in part, related to the difficulty in
determining the properties. If bench tested, one does not account for the extensive tethering that
exists in the body. If testing in the body, it is difficult to determine all the orientational properties.
The other, perhaps more significant, issue is that blood is non-Newtonian and pulsatile. The red
cells are relatively large when considering small vessels, and they themselves are deformable. This
makes the blood behave as a power-law-based viscosity fluid and a Bingham material, with a finite
shear stress required for initial motion. Once in motion, the red cells may become elongated, with
the surface membrane “tank-treading” in the flow. In larger vessels, such as the carotid or aorta, the
vessel diameter is large enough that the red cells do not interact significantly, and the flows can gen-
erally be assumed (at least initially) as being Newtonian. The fact that blood flow in most instances
is pulsatile (although some new heart assist devices utilize steady flow with no apparent ill effects)
makes computer modeling difficult. On the other hand, it should be pointed out that the elasticity of
the arterial walls partially damps out the effects of the pulsatile flow.
Carotid Artery. First, it should be noted that “old” averaged models remain valid. Many recent
studies utilize subject-specific 3D geometries. Bressloff (2007) recently utilized an averaged carotid
geometry developed in the 1980s to evaluate the need for using an entire pulse cycle.
Most recent studies have utilized rigid walls in their studies. Birchall et al. (2006) evaluated wall
shear in stenosed (narrowed) carotid vessels, with atherosclerotic plaque geometries derived from
magnetic resonance images. Glor et al. (2004) compared MRI to ultrasound for 3D imaging for com-
putational fluid dynamics, and suggested (while using Newtonian pulsatile flow) that MRI is more
accurate, although more expensive. Tambasco and Sreinman (2003) utilized deformable red cell
equivalents and pulsatile conditions to simulate stenosed vessel bifurcations (branches). Box et al.
(2005) utilized a carotid model averaged from 49 healthy subjects and non-Newtonian blood flow to
evaluate wall shear (it should be noted that a cell-free layer clinically exists adjacent to the wall).
Coronary Artery. Giannoglou et al. (2005) averaged 83 3D geometries for their CFD model of
the left coronary artery tree, using rigid walls and non-Newtonian averaged flow conditions, noted
adverse pressure and shear gradients near bifurcations. Papafaklis et al. (2007) utilized biplane
angiography and ultrasound of atherosclerotic coronaries to produce their models, which noted the
correlation of low shear to plaque thickness.
The author has not touched upon the realm of heart valve replacement. This is an area where the
solid and fluid computer models intersect. Utilizing similar techniques to those noted above for arte-
rial studies (Birchall et al., 2006; Box et al., 2005; Bressloff, 2007; Glor et al., 2004; Giannoglou
et al., 2005; Papafaklis et al., 2007; Tambasco and Sreinman, 2003), it is convenient to model new
valve designs prior to initial bench testing, and to compare them to earlier valves as well as native
(intact) valves.
Grafts. Many studies utilize CFD to evaluate the replacement of arteries. As a transition from
the coronary flow models above to graft analysis, an example of this work is the study by
Frauenfelder et al. (2007a). This study utilized a pulsatile Newtonian flow with rigid walls, based on
two subjects with coronary bypass grafts, and evaluated flow velocities and wall shear near the