Biomedical Engineering Reference
In-Depth Information
5.8.
At bifurcations, the flow will also be separated based on the geometry of bifurcation. By
minimizing the work that the branches conduct, a set of formulas have been developed to
describe the most ideal branch angles. These formulas are
r
1
5
r
2
1
r
3
r
1
1
r
2
2
r
3
cos
θ
5
2
r
1
r
2
r
1
2
r
2
1
r
3
cos
φ
5
2
r
1
r
3
r
1
2
r
2
2
r
3
cos
ðθ
1
φÞ
5
2
r
2
r
3
Flow separation occurs at bifurcations because the wall pressure gradient becomes positive,
and therefore, the flow would tend to move upstream along the wall. Another occurrence
at bifurcations is that the flow tends to skew toward the inner walls of the bifurcation. This
means that the maximal velocity is no longer along the centerline of the blood vessel.
5.9.
Most blood vessels experience a significant taper along their length. This can be modeled
with the exact formulation for the wall geometry or can be simplified with steps at speci-
fied distances along the vessel length. Regardless of the choice, it would need to be consid-
ered within the formulations.
5.10.
In most of the arterial circulation, the velocity and pressure waveforms change with time.
This is directly related to the contraction (and hence the pressure pulse) of the left ventricle.
Due to the pulsatile nature of the blood velocity, temporal changes in the fluid parameters
must be considered. It is also possible for turbulence to develop within the arterial system.
Turbulent flows are modeled with statistical methods, where the time averaged fluctua-
tions in fluid properties must be considered. For a general fluid property, the formulation
would be
t
0
ð
T
1
1
T
x
xdt
5
t
0
x
0
x
x
5
2
5.11.
Arteriosclerosis, stroke, and high blood pressure are common diseases that affect the vascu-
lar tree. Arteriosclerosis is characterized by a decrease in the cross-sectional area of arterial
blood vessels. If a blood vessel that supplies the brain becomes arteriosclerotic, it is possi-
ble for stroke to develop. High blood pressure is linked to arteriosclerosis because the heart
would need to develop a high pressure head to force blood through the vascular tree.
Platelets can activate in the presence of high shear stress, which can be generated when the
cross-sectional area of the blood vessels decrease. If platelets begin to aggregate, there is
the potential for emboli to form, which can occlude other regions of the vascular system.
Aneurysm occurs when there is a thinning of the vascular wall that eventually leads to a
distention of the blood vessel because it cannot maintain the high pressure within the arte-
rial circulation.
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