Biomedical Engineering Reference
In-Depth Information
7.7
White blood cells express many adhesion molecules that allow them to adhere to the endo-
thelium and roll along the endothelium. Once a more stable adhesion occurs, the white blood
cells can stay in one location and transmigrate into the extravascular space. Most of these
adhesions are modulated through the actions of selectins that have an average bond strength
of 20 pN or integrins that have an average bond strength of 50 pN. Most of these adhesion
properties occur during inflammatory reactions, although white blood cells always express a
low quantity of adhesion molecules.
HOMEWORK PROBLEMS
7.1
Discuss the steps necessary for red blood cells to become oxygenated. What are the rate-
limiting steps of this process?
7.2
Make a mathematical prediction of the changes in oxygen diffusion with either an
increased hematocrit or a decreased hematocrit.
7.3
Determine the permeability coefficient (barrier
plasma) for oxygen assuming that the
1
thickness of
the barrier increases to 5
μ
m and the diffusion coefficient decreases to
5cm
2
/s (e.g., the patient has edema). Assume that the hematocrit is 38% and that
there are no changes in the rate of diffusion characteristics for plasma.
0.8
E
7.4
What is the Biot number and effectiveness factor for homework problem 7.3 (assuming
that no changes occur in the kinetics of oxygen saturation)? What does this suggest?
7.5
What is the maximum capillary spacing (using the Krogh model) for a capillary with a
radius of 4.5
10
2
8
mol/cm
3
? The oxygen
μ
m and a plasma oxygen concentration of 5
3
10
2
8
mol/cm
3
s. Assume that at maximum spacing the oxygen concen-
tration at the Krogh radius will be 3
reaction rate is 4
3
10
2
8
mol/cm
3
.
3
*7.6
In the previous example, we used a standard Krogh model to determine the oxygen
concentration as a function of distance from the capillary. Extend this model and consider a
scenario where there is a differential oxygen usage (as measured by a different oxygen reac-
tion rate) in the extravascular space. Assume that the oxygen reaction rate is 4
10
2
8
mol/
3
cm
3
s for 4.5
μ
m
,
r
,
12
μ
m. For
r
greater than 12
μ
m, the oxygen reaction rate decreases
10
2
8
mol/cm
3
s. Calculate the maximal spacing under these conditions.
to 1.5
3
7.7
Under tumorgenic conditions, oxygen usage increases significantly. Assume a two-cylinder
Krogh model (as in homework problem 7.6) with an oxygen reaction rate of 2
10
2
7
3
mol/cm
3
s for a radius between 4.5
μ
m and 10
μ
m. For radii greater than 10
μ
m, the oxygen
10
2
8
mol/cm
3
s. What is the maximal capillary spacing under these
conditions? Do new blood vessels need to grow to meet this need?
reaction rate is 4
3
7.8
(Modeling) Make a model for glucose transport considering the discussion of permeability
and transporters needed to move glucose across the vascular wall. Test this model with
empirical data.
7.9
A charged element is moving through a protein channel in the microvasculature. The
charged element has an excess charge of 50 pC and the protein has an excess charge of
200 pC. If the channel has a mean radius of 100 nm, what is the force associated with these
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