Biomedical Engineering Reference
In-Depth Information
A
B
C
11 mm
Lateral
Anterior
23 mm
Proximal
E
D
compression
F
medial
proximal
anterior
tension
Figure 10.6.
Organ-tissue-length scale model of the rat tibia. The finite element (C, D, E) model reveals the interplay between
solid and fluid mechanics. The loading mode used simulated the in vivo four-point bending model [28] where external loading of
the tibia (A). In the area between the distal and proximal junctions with the fibula (B) results in bending loads (F). Fig. 10.6B, C, F
reprinted from
Journal of Theoretical Biology
, Volume 2003, R. Steck, P. Niederer, and M.,L. Knothe Tate, “A finite element analysis
for the prediction of load-induced fluid flow and mechanochemical transduction,” p. 251 (Fig. 10.6B and C), p. 253 (Fig. 10.6F),
2003, with permission from Elsevier.
Table 10.1. Comparison of the continuum and discrete approaches to computational modeling
Continuum approach
Discrete
Properties and variables are averaged over a given
Idealistic or real representation of system to be modeled
volume. This results in effective parameters
Justified when the length over which significant
inhomogeneities occur is small
Advantages
Advantages: a priori examination of system properties including
Utilizes classical engineering approach
Effects of structure
Relatively “lean” computing
Effects of site-specific pore distribution
Disadvantages
Disadvantages
Does not reflect changes in structural
High computational effort
characteristics of the system to be modeled
Gives only average, “effective” results
anisotropic
properties, including elasticity
(which describes the material's deformational
behavior under mechanical load) and permea-
bility. Anisotropy describes properties that
vary as a function of orientation.
In addition to specifying the control volume
and the assumptions underlying the model, the
boundary conditions
of the model need to be
defi ned. For instance, if one is interested in
determining the degree of hypoxia in a volume
