In Silico Biofluid Mechanics - Biofluidmechanics: An Introduction to Fluid Mechanics Macrocirculation and Microcirculation - page 346

dynamics, these simulations are useful in describing cardiovascular disease conditions and
the flow around cardiovascular devices.
Briefly, one of the major areas for FSI research is the interaction of blood cells with the
blood vessel wall. As discussed previously, platelets and white blood cells can adhere to
endothelial cells under stress conditions. It is thought that this adhesion can mediate many
cardiovascular disease conditions. To accurately portray this interaction, the movement of
the blood vessel wall must be included because the wall is not rigid and there may be some
rebound/recoil after impact. From these research projects, many fundamental biological
events have been described and have been validated with experimental methods.

Example
Figure 13.9 demonstrates the drainage route of aqueous human based on John and Kamm's
model. Trabecular mesh was modeled as a porous elastic body, shown in the figure as springs.
Schlemm's canal is modeled in two dimensions, with the outer wall (top) and the inner wall
(bottom) being parallel to each other. The inner wall is permeable (so aqueous humor leaks
through), and it deforms as the trabecular mesh work stretches. The local height of the canal is a
function of position x and intraocular pressure (IOP). Under certain disease conditions (such as
glaucoma), the size of Schlemm's canal may decrease due to the increase in IOP; therefore, aque-
ous humor drainage resistance increases. We can use FSI to model the interface of the moving
inner wall and aqueous humor.

Collector
channel

Collector
channel

X

Schlemm's canal

Trabecular
mesh

Intraocular pressure (IOP)

FIGURE 13.9 Model of Schlemm's canal for in-text example. Adapted from John and Kamm.

Solution
First of all, we need to develop the mesh motion for our model. According to Newton's sec-
ond law, the acceleration of the inner wall is proportional to the net force acting on it. In differ-
ential form, the equation to describe the motion of the inner wall is
m dv

dt 5F flow 2F spring