Effects of Cyclic Loading and Binding to Extracellular Matrix on Macromolecular Transport in Soft Biological Tissue - Progress in Organic and Physical Chemistry: Structures and Mechanisms - page 78

environment of the cells [1]. Mass transfer can be accelerated by convection induced
by cyclic loading of the tissue that has boundary with a fluid reservoir and has the
ability to squeeze fluid out of the pores due to deformation. There is experimental evi-
dence that biosynthetic activity of the cells is altered by mechanical stimulation [1, 2,
4, 10], and that the most important stimuli are fluid velocity relative to cells and shear
strain [1]. Studies of articular cartilage repair suggest that the activation of protein
synthesis can partly be triggered by altered molecular transport due to convection [2,
9]. In support of this idea, insulin-like growth factors (IGF) and dynamic compression
applied together showed a synergistic effect on biosynthetic response of chondrocytes
[9, 10]. However, it is poorly understood how the binding of macromolecules to ex-
tracellular matrix influences their transport induce by loading. The factor of binding
seems important because most proteins and signaling molecules have the ability to
interact with matrix components [8].
Recently a number of transport models that consider dynamic loading of biological
tissue have been reported [2, 9-15]. These models are devoted to molecular transport
speci¿ cally in arti¿ cial and native cartilage [2, 10-12], in intervertebral disk [13, 14],
or more generally in soft gels [2, 9, 15]. Soft biological tissue has the structure of a
gel: it consists of polymer matrix and interstitial À uid inside the pores. Therefore, the
predictions of the models for different tissues and gels can be compared. Although
some of these predictions were successfully con¿ rmed by experiments in vitro, many
questions arise. First of all, the authors used continuum mechanics theory of small
deformations to analyze large deformations (up to 20%). Also, many parameters has
been taken into account (such as dependence of diffusivity [11, 15], permeability [2, 9,
11, 14, 15], and porosity [10, 12, 13] on deformation) that made it impossible to under-
stand which of them are minor, and which are of major importance. Finally, there is no
general model even for small deformations that considers solute binding to the matrix,
although it is known that many of the morphogenic proteins, growth factors, and other
regulatory molecules have the ability to speci¿ cally interact with extracellular matrix
components. To date only the molecular transport model by Zhang et al. (2007) [12]
has taken into account both solute binding and cyclic loading, but this model was
developed speci¿ cally to describe transport of IGF in cartilage explants. The results
of this study suggest that the greater increase in solute uptake inside the gel caused
by cyclic loading could be achieved for the free (unbound) IGF and for lower bath
concentrations. This model was modi¿ ed for the application to intervertebral disks by
Travascio (2009) [13].
The main goal of the current study was to develop a mathematical model that ad-
equately describes the response of a gel that has a boundary with bathing solution, to
small strain cyclic deformation. The model predicts the value and time course of À uid
À ow, induced by deformation in the physiological range of frequencies. To explore
the ef¿ ciency of solute transport from the bath to the gel the solute transport equation
was solved. This equation includes diffusion, binding of the solute to the matrix, and
convective À ow of À uid due to cyclic deformation. The aim of the current computa-
tional model is to predict an optimal combination of external deformation and material
parameters of the tissue that would promote solute transport.