Biomedical Engineering Reference
In-Depth Information
I
1
=
tr(
M
)
2
(tr(
M
))
2
−
tr(
M
·
M
)
1
I
2
=
I
3
=
det(
M
) .
(7.46)
Exercises
7.1
A drug is administered to the blood via an intravenous drug delivery sys-
tem. In the figure a two-dimensional schematic is given of the blood vessel
(in a fixed
xy
-coordinate system). The stationary concentration field
c
(
x
,
y
)
of the drug in the blood is sketched by means of iso-concentration lines. It
may be assumed that the concentration is constant in the
z
-direction. The
coordinates
x
and
y
are defined in the unit [mm], the concentration is in
[mMol per litre].
y
10
30
70
60
50
30
40
40
x
10
20
Give an estimate of the gradient
∼
c
of the concentration field in the point
with coordinates
x
=
20 [mm],
y
=
5 [mm].
7.2
A cube ABCDEFGH (with edge
a
) rotates with angular velocity
ω
around
the straight line
, coinciding with the body diagonal CE. The points C
and E, and consequently the rotation axis
, have a fixed position in the
xyz
-coordinate system.
z
E
H
F
G
y
A
D
B
x
C
ω
