Biomedical Engineering Reference
In-Depth Information
is related to the spatial distribution of photons within the tissue.
1
For purely
absorbing materials, for instance, the Beer-Lambert law applies, and if a Gaussian beam
profile is additionally assumed, then
Irradiance
f
2
2
Q
L
¼ m
a
*
f
o
exp
ðm
a
z
Þ
exp
ð
2
r
=o
Þ
ð
17
:
50
Þ
where
is radial distance. In the presence of scatter-
ing, one of the scattering models discussed before can be used to describe
f
o
is incident intensity,
z
is depth, and
r
.
Equation (17.48) assumes no other thermal interaction processes such as conduction, con-
vection, or perfusion. If these processes can be ignored, as, for example, for very short laser
pulses, then temperature rise can be estimated as
f
o
D
T
Q
L
D
t
=r
C
ð
17
:
51
Þ
where
is exposure duration. Other thermal effects of laser-tissue interaction will be
considered in more detail in Section 17.5. Equation (17.51) is valid for very short irradiations
during which heat diffusion is negligible. A criteria or an estimate of the upper limit for
validity of Eq. (17.51) is
D
t
1
4m
2
a
p
D
t
MAX
¼
ð
17
:
52
Þ
a
where a is the thermal diffusivity of the material. For water, the value of a is about
1,400 cm
2
/s.
17.3.2 Laser Doppler Velocimetry
In addition to temperature, another physical interaction of light is the Doppler phenom-
enon, which is based on a frequency shift due to the velocity of a moving object. For medi-
cal applications, these objects are typically the moving red blood cells with a diameter of
roughly 7
m. The Doppler approach is used for measuring blood flow velocity for a vari-
ety of medical applications, including heart monitoring, transluminar coronary angioplasty,
coronary arterial stenosis, tissue blood flow on the surface of the body, and monitoring
blood flow on the scalp of a fetus during labor.
When a light wave of frequency
m
impinges on a stationary object, it is
reflected at the same frequency. However, if the object moves with velocity
f
and velocity
c
v
, the reflected
frequency
, from the original
light wave is known as the Doppler effect or Doppler shift and can be described as
d
f
¼
f
f
0
f
' is different from
f
. This difference or shift in frequency,
d
f
ð
17
:
53
Þ
The Doppler shift is described in Eq. (17.54) in terms of the velocity,
v
, of the moving red
blood cells, the refractive index of the medium,
n
, the speed of light in the tissue,
c
o
, the
input frequency,
f
, and the angle between the incident beam and the vessel,
y
:
d
f
=
f
¼
2
vn
cos
y=
c
o
ð
17
:
54
Þ
1
For multiphoton light-tissue interaction processes, the exponent of
f
is increased. For example, for a two-
2
.
photon process
Q
L
¼ m
a
*
f
