Biomedical Engineering Reference
In-Depth Information
type of analysis. Normal forces can be transmitted by fluids, and these forces can then be
applied to devices within a biological system. For instance, by inserting a catheter into a
patient, there will be some hydrostatic force that the blood transmits onto the device.
While moving the catheter throughout the cardiovascular system, the hydrostatic force
changes, and it may be critical to determine this force or the total force acting on the
device. Imagine undergoing balloon angioplasty (in which a small balloon attached to the
end of a catheter is inflated within the cardiovascular system) and not knowing the hydro-
static pressure that is being applied to the end of the catheter from the fluid. If the physi-
cian does not overcome this pressure, the balloon will not inflate and the procedure will
not be completed to remedy the patient. Therefore, it is critical to understand these princi-
ples (among others) to conduct balloon angioplasty. Hydrostatic pressure is due to the
weight of the fluid itself and the surrounding atmospheric pressure. Therefore, the hydro-
static pressure is different at various heights throughout the body. When a person is
standing upright, the hydrostatic pressure at the top of the head is lower than that at the
heart, and the hydrostatic pressure at the feet is greater than that of the heart. One way to
remember this principle is when you have been standing in the same position for a long
time, without moving your legs, blood pools in your lower extremities. Typically, this
would eventually lead to a “cramping” feeling followed by a “pins and needles” feeling
when blood is re-perfused. The reason that the blood pools in your lower limbs is that the
blood in the leg cannot overcome the hydrostatic pressure to return back to the heart.
Also, after sleeping, if you stand up too fast, the heart cannot overcome the new hydro-
static pressure difference and you may get light-headed. When we discuss venous return
and the heart mechanics, we will show how the body can compensate for these two out-
comes. Another way to recall this phenomenon is that after donating blood, the nurse will
typically tell you to raise your arm. Why is this? This increases the pressure difference
between your heart and your arm and will minimize the blood loss while a clot is forming
at the venipuncture location. In this case, blood would have a hard time overcoming the
new hydrostatic pressure gradient to enter the arm.
As stated in the previous chapter, the primary quantity of interest within fluid statics pro-
blems is the pressure field throughout the fluid. Here we will develop the equations used in
fluid statics analysis. To accomplish this, Newton's second law of motion will be applied to a
differential element of fluid (
Figure 3.1
). Recall that Newton's second law of motion is the
sum of all of the forces acting on an element (body forces and surface forces) is equal to the
element's mass multiplied by the element's acceleration (if density is constant). We will
assume here that the only body force acting on the element is due to gravity. In most biofluid
mechanics problems in this textbook, this will be the only body force that is considered.
However, be cautioned that other body forces can be applied via a magnetic field (blood
flow of a patient within an MRI) or by an electric field. The mass of the differential element,
dm
,
is
equal
to the
fluid density multiplied by the volume of
the
element
(
dm
dxdydz
, in Cartesian coordinates; for other coordinate systems the analysis is
similar, note that
V
5
ρ
dV
5
ρ
volume and
v
velocity ). Therefore, the force due to gravity becomes
dF
-
-
dm
-
ρ
dxdydz
ð
:
Þ
5
5
3
1
where
-
is the gravitational constant.
Search WWH ::
Custom Search