Biomedical Engineering Reference
In-Depth Information
Along the arterial side of the capillary, the net direction of water movement is generally out
of the capillary, with a driving force of approximately 7 mmHg. Along the venous side, the
forces tend to balance to aid in water movement back into the capillary with a driving force
of approximately 3 mmHg. The fluid velocity within the interstitial space is relatively slow,
and the majority of fluid does not have the ability to move freely. This is because there is a
high concentration of charged proteins within the interstitial space which attract water
molecules.
6.7
The hematocrit within capillaries tend to change based on the bifurcation angles and the
splitting of fluid within the microcirculation. Two relationships that can be used to deter-
mine the branch hematocrit and branch velocities are
H
inflow
v
inflow
5
H
branch 1
v
branch 1
1
H
branch 2
v
branch 2
H
branch 1
v
branch 1
1
H
branch 2
v
branch 2
H
inflow
5
v
branch 2
Within the microcirculation, there is a general reduction in the hematocrit, which reduces
the overall effective viscosity of blood. The effective velocity can be used in a modified
Hagen-Poiseuille formulation to calculate the flow rate through a capillary as
v
branch 1
1
Pr
4
5
πΔ
Q
μ
eff
L
8
This reduction in viscosity is primarily caused by a streaming of the blood cellular elements
streaming toward the centerline velocity. Under normal conditions, there is an imbalance of
forces on the cell, which would push the cell toward the lower shearing force. This would
only be balanced when the cell is aligned with the highest fluid velocity.
6.8
In capillaries, red blood cells tend to form packets that act as plugs. Within these red blood
cell packets there is very little plasma, and in fact the plasma normally collects in between
different red blood cell plugs. Due to this plug formation, we can model the mass conserva-
tion of compounds within the fluid by
ð
O
2
Þ
accumlated
5
ð
O
2
Þ
entering
2
ð
O
2
Þ
exiting
1
ð
O
2
Þ
generated
2
ð
O
2
Þ
consumed
which is shown for oxygen. The rate that a species is generated or consumed would depend
on the particular kinetics of that reaction.
6.9
Two-phase flows are flows that have either two phases of matter or one phase of matter
with different material properties. In the microcirculation, the plasma phase and the cellular
phase must be accounted with different methods when analyzing flow conditions. This
would be fairly difficult to do by hand because Newton's Second Law of Motion would
need to be solved independently for each particle within the fluid. In general, these types of
flows are solved using numerical methods.
6.10
In the microcirculation, the effect of cell-wall interactions must also be accounted for
because a cell adhered to the vessel wall may significantly alter the flow profile. Also, it is
likely that white blood cells migrate out of the blood vessels and into the extravascular
space along the capillary wall. To model these interactions, the mechanical properties of the
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