Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 8

a b

Fig. 1.5 ( a ) A cell adherent to a substratum and subjected to a fluid shearing action. ( b )An
analysis of the forces on a cell of Fig. 1.5 (a), the cell adherent to a substratum and subjected to a
fluid shearing action

model is adequate for determining the trajectory of the skier, it is an inadequate
model for the transition of the skier's position from the crouch of the downhill run
to the erect and forward leaning body posture adopted for flight, and inadequate to
deal with the question of impact upon landing.
This traditional method of analysis of macroscopic force systems is also applied
at the microscopic level. For example, one method of studying the response of cells
to mechanical loading situations is to culture or grow the cells on a surface such as
glass and subject the surface to fluid shear stresses as illustrated in Fig. 1.5a .
Some of the forces that act on the cell in this flow situation are shown in
Fig. 1.5b . The forces that act on a cell include the weight of the cell, W cell , the
buoyant force on the cell due to its aqueous environment, W buoyant ; the adhesive
force of the cell to its substrata, F , the fluid pressure on the cell, the shear force due
to fluid flowing over the surface of the cell, forces due to electrical charge or
magnetic fields, and self generated forces by the cell. The same forces act on these
cells in vivo, but the forces are illustrated in vitro because it is an easier situation to
visualize and to draw. The weight of the cell, W cell, is about 1 piconewton. The cell
is subjected to a buoyancy force as a consequence of its immersion in an aqueous
environment. The buoyant force on the osteocyte is equal to the weight of the water
it displaces, W buoyant ¼ 0.9 piconewton, nine-tenths of a piconewton. The processes

of cell adhesion to substrata, as well as the influence of substratum surface
properties on cell adhesion, have been studied in recent years by subjecting cells,
in vitro, to fluid shear stress. Adhesion of cells to solid substrata is influenced by
several substratum surface properties including substratum wettability, surface
roughness, and surface charge. The force F of adhesion for a single cell is the
surface area A that the cell presents to the flow times the shear stress when the cell is
removed from the surface by the fluid shear stress. The shear stress at which cells
capable of adhesion detach from a glass substratum is about 400 dyn/cm 2 . Assum-
ing an appropriate surface area,

the adhesive force on the cell F is about

6,000 piconewtons. Since W cell ¼ 6,000 W cell . Thus a cell can

express adhesive forces that are three to four orders of magnitude larger than the
cell weight. For man on the surface of the earth, the largest forces with which we

1 piconewton, F ¼