Chemistry Reference
In-Depth Information
During their physiologic function biological tissues are commonly deformed by
external cyclic loading. The concept of tissue cell activity dependence on mechani-
cal stimulation is accepted in biomechanics, but there is a lack of evidence about the
mechanisms underlying the capacity of cells to sense mechanical stimuli. One of the
hypotheses is that cyclic loading can enhance molecular transport by cyclic convec-
tive À ow. This idea was supported by theoretical and experimental studies on neutral
non-reactive solute transport in avascular tissues such as cartilage. However, the effect
of solute binding to the extracellular matrix has not yet been explored. In the present
study, we develop a transport model for a matrix binding solute using a biphasic model
of biological tissue deformation. A set of non-dimensional parameters was derived.
These parameters characterize the correlation of reaction, material and loading param-
eters and govern the ef¿ ciency of transport. Our results suggest that there is an optimal
loading frequency for a particular matrix and a solute that leads to maximal transport
acceleration. The load-induced uptake of a solute relative to pure diffusion is higher if
this solute can bind to the matrix. Most dramatic effect is seen on uptake of unbound
solute: it can be several times higher as compared to the uptake of non-binding solute
under the same conditions.
Arti¿ cial bone implants are usually connected to soft biological tissue. External
mechanical loading induces À uid À ow in tissue. It is an important stimulus for cells,
which governs the rate of their biosynthetic activity and even differentiation that in
turn promote osseointegration of the implant [1]. It is hypothesized that cyclic loading
can enhance solute transport in biological tissues [2, 3], and through this mechanism
improve tissue nutrition or response to regeneration factors. The existing experimen-
tal data that support this statement are rather limited, and were mainly obtained on
cartilage samples [3-7]. Recently, several theoretical models for solute transport in
loaded gel and tissue were developed [2, 9-15]. These models predict enhancement
of free solute transport induced by cyclic À uid À ow for different ranges of tissue pa-
rameters. Only two studies have taken into consideration the effect of solute binding
to the matrix [12, 13], but their results are limited to protein transport in cartilage and
intervertebral disk.
The objective of this study is to examine the effect of cyclic loading theoreti-
cally and to investigate at what conditions convective transport induced by dynamic
loading might signi¿ cantly alter solute accumulation, taking into account reversible
binding of solute to polymer matrix. Our results could be used to choose the appropri-
ate characteristics of implant coatings, help in selection of effective growth factors
for tissue treatment, and optimize the design and stimulation protocols of controlled
release devices.
7.2 MODEL SYSTEM
The biological tissue undergoing cyclic deformation is modeled by the following sys-
tem (Figure 1): the rectangular piece of a gel of length
h
is placed between two imper-
meable plates. The spacial coordinates (
x
-axis) are associated with the fixed bottom
plate. The upper plate is cyclically loaded. At a point
x
h
the gel has a free surface,
which is the boundary with a bath solution and is perpendicular to the plates. At the
distance
h
from the surface (at point
x
=
0
) there is a symmetry plane, or impermeable
=
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