Biomedical Engineering Reference
In-Depth Information
same and is 10
m, that the incident pressure within each branch is 50 mmHg (for wave
propagation), and that the Young's Modulus of each vessel
μ
is 15 kPa. Calculate the
reflected pressure and the pressure within each daughter branch.
5.14
Calculate the radius of the parent branch knowing that the radii of the two daughter
branches are 400
μ
m and 435
μ
m. Determine the bifurcation angles and draw an accurate
figure of this branch.
*5.15
Calculate the radius of the daughter branches and the angles of bifurcation if the parent
branch has a radius of 500
m.
*5.16
Can Murray's Law be extended to a more complicated branching pattern (i.e., two daugh-
ter branches that branch in three dimensions or three daughter branches)? If so, derive
the applicable relationships.
5.17
The velocity through a tapering channel can be estimated as
-
5
μ
e
2
L
i
. Calculate the
acceleration of any particle along the centerline and the position of a particle that is
located at
x
v
i
1
2
0 at time zero, where
L
is the vessel length and
v
i
is the inflow centerline
5
velocity.
*5.18
The radius of a continuously tapering blood vessel can be modeled as
r
.
2
L
ð
x
Þ
5
r
i
e
2
Determine the velocity and the acceleration of the fluid within this blood vessel.
5.19
Under atherosclerotic conditions, the aorta can reduce in cross-sectional area. Is it more
likely for the blood flow to remain laminar or become turbulent? What would happen to
the blood flow if there is an aneurysm present within the aorta?
*5.20
Show that the volumetric flow rate for a Casson model of blood flow is
"
#
0
:
5
0
:
5
4
2
2
3
R
4
8
2
τ
y
R
2
τ
y
R
5
π
dp
dx
2
16
7
dp
dx
4
3
dp
dx
Q
2
2
1
η
*5.21
If the elastic deformation of the blood vessel wall is relatively small, what happens to the
pressure-flow relationship? Show the approximate function and describe the physiology
behind this.
5.22
If the diameter of a person's aorta is abnormally large, would the flow through the aorta
more likely be laminar or turbulent? What if the heart rate is increased, but flow rate is
maintained the same?
5.23
In a Casson model of
flow,
the yield shear
stress varies with hematocrit as
(0.325*Hct)
3
, where Hct is the hematocrit (e.g., 0.4). Plot and describe this relationship
for various cardiovascular diseases.
τ
y
5
References
[1] J.W. Adamson, Regulation of red blood cell production, Am. J. Med. 101 (8-26-1996) 4S.
[2] R.K. Andrews, J.A. Lopez, M.C. Berndt, Molecular mechanisms of platelet adhesion and activation, Int.
J. Biochem. Cell Biol. 29 (1997) 91.
[3] M. Anliker, M.B. Histand, E. Ogden, Dispersion and attenuation of small artificial pressure waves in the
canine aorta, Circ. Res. 23 (1968) 539.
[4] T. Aoki, D.N. Ku, Collapse of diseased arteries with eccentric cross section, J. Biomech. 26 (1993) 133.
[5] E.O. Attinger, Wall properties of veins, IEEE Trans. Biomed. Eng. 16 (1969) 253.
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