Biomedical Engineering Reference
In-Depth Information
where
Δp is the pressure difference across the fluid surface, and r is the radius of curva-
ture in the x- and y-directions. This can be normalized to a force by considering the area
of contact between the two surfaces, where A C is the contact area:
1
r 1 1
1
r 2
F ST 5 γA C
ð
7
:
19
Þ
The surface tension of water is approximately 71 kPa/m, which can be used to approxi-
mate the forces or pressures associated with cells coming into contact with other struc-
tures. In fact, the surface tension of biomaterials is a common property to alter, in order to
promote cell adhesion or inhibit cell adhesion. For instance, for cardiovascular devices, it
has become common to make the surface tension very large, so that platelets will not
adhere to the device. The reverse is true: if the device was designed to become endothelia-
lized, the surface tension would be reduced to promote endothelial cell adhesion.
Adhesion occurs when two different molecules tend to stick together, due to some
attractive force between the molecules. Adhesion is typically quantified by the amount of
work that is required to separate the two materials and this is dependent on the surface
tension of the materials, as follows:
W 12 δ
A
1
δ
2
δ
12
5 γ
1 γ
2 γ
ð
7
:
20
Þ
where
,
within which the materials are bathed. The force associated with adhesion can be calcu-
lated from the distance that is required to separate the materials and the work that is input
into the system to separate the materials. Cohesion arises due to the interaction of the
same molecules within the material. This attraction is caused by intermolecular forces,
such as the common hydrogen bonding that occurs between individual water molecules.
Dipole interactions can also lead to a cohesive interaction between molecules. Cohesion is
also quantified through the surface tension of the material, as follows:
γ
is the surface tension generated between materials 1 and 2 or the medium,
δ
W 1
1
2
γ
ð
7
:
21
Þ
C 5
where
is the surface tension between the material phase of material 1 and its equilibrium
vapor phase. Again, the force associated with cohesion can be calculated from the distance
required to separate two molecules in solution.
Cellular adhesion can be divided into three basic categories, which include cell contact,
cell adhesion/attachment, and cell separation. Cell contact is based on random connec-
tions that occur due to cells coming into contact with each other. These connections can
act over varying ranges and may have a large force associated with them. Cell adhesion/
attachment is based on chemical bonds which can be sub-divided into the different molec-
ular forces that we have described previously. These typically act over a range of no more
than 0.5 nm and are typically in the nano-Newton range. Cell separation is based on the
same attachment forces, when there are other forces that are acting to pull the cells apart.
Initial adhesion and separation are based on the cell surface properties and geometries.
We have hinted at this before: to model these interactions, many simplifying assumptions
on these relationships would need to be made because cells are neither homogenous in the
expression of surface molecules nor in contact geometry. Furthermore, both of these prop-
erties are time varying.
γ
Search WWH ::




Custom Search