Biomedical Engineering Reference
In-Depth Information
Before modeling a particular bone tissue
engineering system, several examples of in
silico models at different length scales will be
described. This will give the reader a sense of
what can be (and has been) done, as well as
indicate the inherent limitations of the
approaches described. This will be followed by
a guide to building models. In reviewing in
silico models of bone, emphasis will be placed
on models developed in the author's group over
the past decade.
b
These examples illustrate the
process of developing and analyzing a compu-
tational tissue model. Each of the models pre-
sented below was developed so that it can be
validated experimentally and to achieve
insights across length scales.
pressure, carrying solutes such as nutrients
and waste products to and from the cells. Con-
vective transport (compared to diffusive trans-
port) effi ciently provides bone cells, including
osteocytes, their basic metabolic needs and
removes waste products. In the past
15
years,
advances in endothelial cell research [
22
] and
new computational methods [
] indicated
the need for and possibility of incorporating
convective transport in computational models
of bone with recent work incorporating the
concept for the engineering of functional bone
replacement tissue [
6
,
11
].
The fi rst models of bone as a fl uid-fi lled
structure showed that Piekarski and Munro's
postulate was feasible [
16
,
23
]. The models in
turn led to a series of in vivo, ex vivo, and
in vitro experiments that, although novel in
approach, often raised more questions than
they answered [
6
,
11
10.5 Organ to Tissue Scale In
Silico Models
]. The reason was that the
state of all variables in the biological system
was diffi cult to determine. This underscored
the need for predictive computational models
that would identify the parameters having the
greatest effect on transport into bone. This led
to the development of highly idealized models
of the rat tibia and ulna that would show the
effect of mechanical loading on global fl uid
fl ow, based on specifi c tracer distributions
observed histologically. We now describe two
models designed to increase understanding of
the rationale of the modeling approach.
The end-loading model of the rat ulna (Fig.
9
,
10
Until approximately
years ago, computa-
tional modeling of bones implemented a solid
mechanics approach, to explore structure-
function relationships on the basis of the struc-
tural components of bone, e.g., the trabecular
architecture and mineralized matrix [
40
].
This changed when Maurice Biot adapted the
theory of poroelasticity, originally developed
for fl uid-saturated soil mechanics studies, to
model bone as a stiff, fl uid-saturated “sponge”
[
14
,
29
]. Yet the inclusion of the fl uid component of
bone (
4
10
],
imparts a cyclic compressive load to the distal
and proximal ends of the ulna via a mechanical
testing machine that controls the magnitude
and rate of load. Because of the inherent curva-
ture of bone, compressive loading induces a
combination of compressive and bending loads
within the bone. Interestingly, load transfer is
shared by the ulna and radius through the
interosseous membrane [
.
5
C), fi rst described by Lanyon et al. [
13
% of bone's total volume) in computa-
tional models has only recently become
widespread. Slowly, in the past two decades,
bone physiologists and mechanical engineers
adopted the concepts of poroelasticity to inves-
tigate the interplay between mechanics and
fl uid transport in bones subjected to mechani-
cal loads. Bassett [
25
3
] in
1966
Piekarski and
Munro [
years later postulated
that pressure gradients developing in mechani-
cally loaded, fl uid-saturated bone drive the
fl uid from areas of high pressure to areas of low
19
] more than
10
], the mechanics of
which are only beginning to be understood. We
can predict these loads locally using fi nite
element modeling, in which the bone is meshed
into a fi nite number of elements and the stress
and strain generated through loading are cal-
culated for each element in order to simplify
the complex problem (Fig.
27
b
It should be noted that computational modeling of bone is
a thriving research area and numerous research groups
apply different approaches to the problem; a review of all
previous approaches is beyond the scope of the specifi c
goals addressed in this chapter, but a PubMed search
with the keywords “computational,” “model,” and “bone”
yielded more than
B). Such predic-
tions are validated with the aid of strain gauges
that are glued to the bone prior to loading and
that deform under loads. The deformation
alters the resistive properties of the wire mesh
10
.
5
200
examples at the time of publication.
