Biomedical Engineering Reference
In-Depth Information
and velocity profile of blood flow in tissue, which attracted a number of biomedical
applications, for example, determination of the depth of burns and determining
tissue perfusion to ensure adequate oxygenation of the tissue after injury, wound
closure, grafting, etc. Other applications include distinguishing between arterial and
venous blockages in tissue after injury or monitoring the effect of pharmaceuticals
on blood transport in the tissues.
The Doppler effect describes the shift in frequency of waves reflected from
moving objects. This frequency shift can be used to determine object-moving
velocity. For electromagnetic waves such as light, derivation of the Doppler shifted
frequency from a moving object requires the application of special relativity. The
result for a Doppler shifted frequency f d is
r c C u
c u f 0 ;
f d D
(5.46)
where f 0 is the initial frequency of the electromagnetic wave, c the speed of light,
and u is the speed of the moving object. Here, it is assumed that u is positive when
the object is moving toward the observer. In this case, it is seen that the Doppler
shifted frequency, f , must be greater than the initial frequency:
f
D f d f 0 :
(5.47)
It can be shown that when u is much less than c, the velocity of the moving
sample is given by
u
c f d :
f
D
(5.48)
In the practical DOCT system, Fig. 5.16 , the interferometer sample arm is angled
relative to the direction of flow by an amount . Detected light is scattered from a
moving particle in the sample, undergoing a double Doppler shift—once from the
source to the particle and once again from the particle back to the objective. These
two factors are taken into account by expressing Eq. 5.48 in terms of initial source
and scattered wavevectors k 0 and k d , respectively. The Doppler shift can then be
written as
1
2 .k d k 0 / u :
D
f
(5.49)
Therefore, the velocity of moving particles can be determined from the measure-
ment of the Doppler shift and knowledge of the relative angle between the optical
signal and the flow [ 112 ]:
f
2 cos. / :
u D 0
(5.50)
Structural information about the sample is obtained by either conventional TD-
OCT or more recently FD-OCT [ 111 ]. However, to retrieve data regarding the flow
of particles within submerged capillary, extra measurements of the Doppler shifted
frequency must be made. To do this in the time domain, the reference mirror of
 
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