Biomedical Engineering Reference
In-Depth Information
6.6 The myogenic theory is not widely accepted as the only regulator for blood flow through
microvascular networks. Prepare a statement that is for the myogenic theory and one that is
against the myogenic theory.
6.7 The endothelial cell nucleus protrudes into the bloodstream within the capillary beds. Does
this affect blood flow and cellular transport through the microvascular network? Why is the
capillary not “smooth”?
6.8 How does the intercellular cleft restrict the diffusion of small uncharged molecules through
the capillary wall? How does the intercellular cleft restrict the diffusion of larger charged
molecules? Why is there a difference between the diffusion of these two types of molecules?
6.9 List the major differences between vascular smooth muscle cells and skeletal muscle cells.
Is mechanical work generated in a similar way between these two cell types?
6.10 Calculate the apparent viscosity for a capillary that has a pressure difference of 4 mmHg,
a diameter of 10
m.
6.11 Calculate the apparent viscosity for the same conditions as in problem 6.10 if the mean
velocity reduces to 0.2 mm/s, due to the precapillary sphincter constriction.
6.12 Determine the velocity profile within a 12
μ
m, and a mean velocity of 12 mm/s, with a length of 100
μ
μ
m diameter capillary, with a viscosity of 4 cP,
m. Assume that gravitational effects can be
ignored and that the blood vessel is perfectly cylindrical.
*6.13 Determine the velocity profile within a 12
and a pressure gradient of
5 mmHg/500
μ
2
μ
m diameter capillary that has a red blood cell
(8
m diameter) flowing down the centerline of the blood vessel. Assume that the center-
line velocity is 10 mm/s, that the pressure gradient is
μ
m, and that the
viscosity is 4 cP. The capillary is vertical, so gravitational effects cannot be ignored.
*6.14 Calculate the drag coefficient and viscous forces on the surface of the red blood cell in
problem 6.13, assuming that the only force which acts on the blood cell is shear stress due
to the flowing blood. Also, simplify the geometry of the red blood cell so that the area of
interest can be considered a perfect sphere. What is the Reynolds number in this flow
scenario?
6.15 Calculate the volumetric flow rate of water out of the capillary under normal conditions
where the permeability constant is 0.25 mL/(min * mmHg). How much fluid leaks out of
the capillary within one day? Is this reasonable?
6.16 A patient is experiencing edema and the permeability constant increases to 1 mL/(min *
mmHg). Assuming that the capillary hydrostatic pressure reduces to 23 mmHg and the
interstitial pressure increases to
2
5 mmHg/500
μ
2 mmHg, and that the osmotic pressures have not changed,
howmuch fluid leaks out of the capillary within one day?
6.17 What is the hematocrit in each of the daughter branches for a simple one-parent-to-two-
daughter-branch network, if the inflow velocity is 50 mm/s (in a tube with a diameter of
60
2
μ
m) and the velocity in the first branch is 75 mm/s (in a tube with a diameter of 40
μ
m)?
The diameter of the second branch is 30
μ
m. The feed hematocrit is 40% and the hematocrit
in the second branch is 24%.
6.18 Calculate the concentration of carbon dioxide within a capillary assuming that all reactions
can be modeled with first-order kinetics. In this scenario, the blood vessel is 300
min
length, with a mean blood velocity of 15 mm/s. The kinetic rate constants for carbon diox-
ide formation and consumption is 1.17 mol/s and
μ
0.2 mol/s, respectively. Assume that
the initial concentration of carbon dioxide within the blood vessel is 100 mL.
2
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