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 85

proportionally to the bound solute concentration. This relationship is expressed in the
following Equation [19]:

dc s
dt

c F ( N s c s ) c s = k f ⋅ − − k r ⋅

(14)

where c s is the concentration of the bound solute with respect to the solid phase
volume, N s is the concentration of the binding sites with respect to the solid phase
volume. (The values of parameters k f and k r are taken from literature considering
this notation).
Let us transform Equation (14) so that all variables attribute to the same volume
that is volume of the À uid phase. The bound solute and the binding sites contain in
the solid phase, so their concentrations with respect to the solid phase volume can be
presented as:

φ

c s = c B

1 − φ

And

φ

N s = N

1 − φ

where c B and N are concentrations with respect to the fluid phase volume. Then,
Equation (14) takes the form:

φ dc B

dt

φ φ

= k f ⋅ c F ( N − c B ) − k r

− φ ⋅

c B

1 − φ 1 − φ 1

that is equal to

∂ c B

∂

= k f ⋅ c F ( N − c B ) − k r ⋅ c B

(15)

t

which is the expression for the net rate of change of bound concentration.

7.3.4 Boundary Conditions
The dynamic loading to the upper plate (see Figure 1) is applied under displacement
control. The deformation is set to be sinusoidal and comprise compression and tension
phases that is: