Biomedical Engineering Reference
In-Depth Information
Further, it is well known that the wavelength,
l
, is equal to the speed of light divided by
the frequency, so
Þ
A comparable analogy for the Doppler effect with sound waves is a train moving toward an
observer. As the train gets closer, the whistle sounds like a higher pitch.
d f ¼
2
cos
y=l o
ð
17
:
55
vn
EXAMPLE PROBLEM 17.7
Using a laser Doppler system, calculate the velocity of blood given an argon laser (514 nm) at
an angle with the vessel of 30 degrees, an index of refraction of 1.33, and a frequency shift of
60 KHz. Does this make sense physiologically? Does it really matter if you were off in your probe
to vessel measurement angle by 10 degrees?
Solution
Using Eq. (17.55), the velocity can be calculated to be
10 3
10 9
v ¼ðd f
*
lÞ=ð
2
n
cos
ðyÞÞ¼½ð
60
Þð
514
Þ=½
2
ð
cos
ð
30
ÞÞ ð
1
:
33
Þ ¼
1
:
34 cm
=
s
This is reasonable for an average-sized vessel in the human body. If you were off by
10 degrees—for example, if you thought the angle was 40 instead of 30—this would make a pretty
big difference with the newly calculated speed of 1.51 cm/s (a 13 percent error).
Laser Doppler is a good method for monitoring velocities, but one reason it has not
gained wide use clinically is that the flow (cm 3 /sec) of blood or rather the average velocities
of all the particles in the fluid is the physical quantity of diagnostic value, and flow cannot
be directly measured using the Doppler approach. Calculating the flow rate for a rigid tube
filled with water by knowing the velocity is a straightforward problem to solve. However,
determining the absolute flow rate of blood in the body by simply using the Doppler
measured velocity is a much more difficult problem, particularly for narrow vessels. Blood
is thicker than water, and the flow characteristics are more complex. Blood vessels are also
not rigid, straight tubes, and the flow of blood is pulsatile. Finally, a fiber optic probe can be
inserted in the blood vessel and scanned to get a series of velocity measurements to deter-
mine flow, but the probe itself can alter the flow measurement.
Overall, laser Doppler velocimetry is a simple concept that can, with some effort, be used to
measure relative changes in flow, but it is very difficult for this approach to be calibrated for
absolute flow measurements. Thus, the standard for blood mass-flow measurements has been
by thermodilation and is widely used in clinical practice. The thermodilation method is used to
determine flow by inducing a predetermined change in the heat content of the blood at one
point of the circulation and detecting the resultant change in temperature at some point down-
stream, after the flow has caused a controlled degree of mixing across the vessel diameter.
17.3.3 Interferometry
The phenomenon of interference is another method by which physical light interaction
takes place, and it depends on the superposition of two or more individual waves, typically
originating from the same source. Since light consists of oscillatory E and M fields that are
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