Biomedical Engineering Reference
In-Depth Information
Longitudinal bone sections demonstrate this
effect well; in the unloaded ulna, the contents
of the medullary canal are highly fl uorescent,
and isolated blood vessels in the cortex show
the fl uorescent tracer as well; the periosteum
shows
nized around a central Haversian canal that
contains a blood vessel. Haversian canals,
which run along the length of the long bone,
are connected to one another by Volkmann's
canals, which run orthogonal to the long bone
axis. Each cell is connected to a blood vessel
(within a Haversian or Volkmann canal) via
the pericellular space or lacunocanalicular
system, which constitutes the cell's “circulatory
system.” In this way, the nutritional needs of
every cell can be met in large bones.
In smaller bones the transport network is
simpler, in that blood vessels are dispersed in
the cortex. Because the cortex is relatively thin
and the blood vessels are quite close, no cell in
the cortex, the periosteum, or the medullary
cavity is more than
F). In
contrast, in the loaded ulna, the medullary
cavity is much less fl uorescent, the blood
vessels of the cortex show fl uorescence, and
many periosteocytic spaces also exhibit fl uo-
rescence, as does the periosteum. Qualitatively,
the effect of mechanical loading is clear.
However, to understand the interplay between
loading and transport in bone, loading magni-
tudes and durations must be correlated with
tracer concentrations locally and throughout
the skeleton.
little
or
no
tracer
(Fig.
10
.
5
m away from a blood
vessel. In this way, nutrients are distributed to
the cells through the lacunocanalicular system,
and no branching transport system is needed.
Having shown by modeling and experimen-
tation [
200
µ
10.6 On Choosing Models and
Relationships Appropriate for
Length Scale
] that load-induced fl uid fl ow
involves convective transport, we then studied
how magnitude, mode (e.g., compression versus
tension), and duration of loading affected con-
vective transport in bone. We used the four-
point-bending model of the rat tibia (Fig.
7
,
10
We chose the rat ulna model to understand the
problem in terms of organ and tissue distribu-
tion of fl uids. However, the length of the rat
ulna (
10
.
6
A)
for this purpose [
]. Our virtual model was
based on three-dimensional data obtained
from microcomputed tomographic (
28
cm) is almost an order of magnitude
less than that of the human ulna (
∼
3
cm). Dif-
ferences in scale between a model and the bio-
logical system of interest may present challenges
to carrying out experiments and to interpret-
ing the model results for the human situation.
Experimental challenges typically involve the
inherent diffi culties in achieving spatial resolu-
tion (in strain gauge measurements or bone
structure imaging) in such tiny bones. Even
more confounding may be the fact that rat and
mouse bones (like those of other small animals
with high metabolic rates) do not have the
osteonal structure of human bone [
∼
25
µ
CT)
images of a rat tibia (Fig.
B). The model
volume was that of the tibial cortex, without the
distal and proximal joint surfaces or the fi bula
(Fig.
10
.
6
B and C). The tibia model was loaded
with a four-point approach similar to what had
been applied experimentally. The model was
meshed into
10
.
6
7200
elements (pieces), comprising
20
node pore pressure elements. This allowed
for suffi cient computational sensitivity to cal-
culate pressure fi elds and the resulting fl uid
velocities within the poroelastic material that
had been chosen to simulate the solid-fl uid
material properties of bone. In the model we
represented bone as a
continuum
. This means
that bone is a stiff, fl uid-fi lled sponge or poro-
elastic material. In a
discrete
model (see Table
10
].
Recent studies point to the role the mean trans-
port path distance plays in the organization of
bone. Mammals with thick cortices (up to
several centimeters in humans and more than
10
16, 17
cm in elephants) require a two-tiered trans-
port structure for long-distance fl uid trans-
port, just as a circulatory system is needed once
organisms reach a size that can no longer be
served by diffusional transport alone.
In osteonal bone, two systems assure distri-
bution of fl uid and solutes locally and in the
organ as a whole. The osteonal layers are orga-
for a comparison of the two approaches),
the bone structure would be represented with a
specifi c microarchitecture and defi ned porosi-
ties. Applying the continuum assumption effec-
tively “smears” local properties to effective
tissue values and does not account for micro-
scopic detail. Furthermore, we defi ned the
material of our virtual model to have limited
.
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