Biomedical Engineering Reference
In-Depth Information
FIGURE 10.10
Output voltage versus core displacement of a typical LVDT transducer.
Consider a blood vessel of diameter,
l,
filled with blood flowing with a uniform velocity,
u
.
If the blood vessel is placed in a uniform magnetic flux,
B
(in weber), that is perpendicular to
the direction of blood flow, the negatively charged anion and positively charged cation parti-
cles in the blood will experience a force,
F
(in newton), which is normal to both the magnetic
field and blood flow directions and is given by
F
¼
q
ð
u
B
Þ
ð
10
:
2
Þ
10
19
C). As a result, these charged particles will be
deflected in opposite directions and will move along the diameter of the blood vessels
according to the direction of the force vector,
F
where
q
is the elementary charge (1.6
. This movement will produce an opposing
force,
Fo
, which is equal to
Fo
¼
q
E
¼
q
V
l
ð
10
:
3
Þ
where
E
is the net electrical field produced by the displacement of the charged particles and
V
is the potential produced across the blood vessel. At equilibrium, these two forces will be
equal. Therefore, the potential difference,
V
, is given by
V
¼
B
l
u
ð
10
:
4
Þ
and is proportional to the velocity of blood through the vessel.
