Page 270 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

FINITE-ELEMENT ANALYSIS 247

In the cardiovascular realm, due to symmetry, the evaluation of single aortic valve leaflets may
be considered 2D for a first approximation (de Hart et al., 2000). The full pattern of valve motion or
flow in the proximal aorta would require a 3D analysis (de Hart et al., 1998; Grande et al., 2000).
Fluid boundary layer separation at vascular bifurcations or curves (as found in the carotid and
coronary arteries) may be considered 2D if evaluating centerline flow (Steinman and Ethier, 1994).
Along this plane, the secondary flows brought on by the vessel cross-sectional curvature will not
affect the flow patterns. These models may be used to evaluate boundary layer separation in the
carotid artery, the coronaries, and graft anastomoses.

10.2.2 Model Detail

In addition to the number of dimensions is the detail of the model. As with 2D versus 3D models,
detail varies with area of interest. If you are examining a plate along a long bone, the bone surface
may be considered smooth. If you are assuming complete integration of the screw threads into the
bone, this interface may not include the screw teeth (but rather a “welded” interface). Braces and
orthotics (if precast) may also be considered smooth and of uniform thickness. Thermoformed mate-
rials (such as ankle-foot orthotics) may be considered of a uniform thickness to start, although the
heavily curved sections are generally thinner. Large joints, such as the knee, hip, and shoulder may
also be considered smooth, although they may have a complex 2D shape.
Bones such as the spine require varying levels of detail, depending on the analysis of interest.
A general model examining fixation of the spine via a rod or clamps would not require fine detail
of vertebral geometries. A fracture model of the spinous processes would require a greater level of
detail.
Joints such as the ankle and wrist consist of many small bones, and their surfaces must be deter-
mined accurately. This may be done via cadaveric examination or noninvasive means. The cadaveric
system generally consists of the following (or a modification): The ligaments and tendons are stained
to display the attachments (insertions) into the bones; the construct is then embedded in Plexiglas,
and sequential pictures or scans are taken as the construct is either sliced or milled. Slices on the
order of a fraction of a millimeter are needed to fully describe the surfaces of wrist carpal bones.
Noninvasive measures, such as modern high-sensitivity computed tomographic (CT) scans, may also
be able to record geometries at the required level of detail.
Internal bone and soft tissue structures may generally be considered uniform. A separation should
be made with bone to distinguish the hard cortical layer from the spongier cancellous material, but
it is generally not required to model the cell structure of bone. If one is interested in specifically
modeling the head of the femur in great detail, the trabecular architecture may be required. These
arches provide a function similar to that of buttresses and flying buttresses in churches. While work
continues in detailed FEA studies of these structural alignments down to the micron level, this is not
required if one only seeks to determine the general behavior of the entire structure.
Similar approximations may be made in the biofluids realm. Since the size and orientation of
vessels vary from person to person, a simple geometry is a good first step. The evaluation of
bifurcations can be taken to the next level of complexity by varying the angle of the outlet sides.
Cadaveric studies are helpful in determining general population data. As mentioned earlier, CT studies
lend exact data for a single subject or a small group of subjects [such as the abdominal aortic
aneurysm work of Raghavan et al. (2000)].

10.3 MATERIAL PROPERTIES

Hard tissue should be modeled as orthotropic, even when using 2D analysis. The differences in prop-
erties are on the order of those seen in wood, with the parallel-to-the-grain direction (vertical along
the tree trunk) being the stiffest. Basic mechanical properties can be found in Fung’s text on bio-
mechanics (1996). As can be seen, isotropic modeling will produce significant deviation from expected