Biomedical Engineering Reference
In-Depth Information
Solution
Given scattering coefficients
m s 0 ,
r o , and
f
(
r o )/
f o , an algebraic equation for
m a based on the dif-
fusion approximation is required.
r
Þ¼f o exp
ð
r
=dÞ=ð
4
p
Dr
Þ
ð
ex
:
1
Þ
Þ=f o ¼
r
=d ½
log 4
þ
log p
þ
log D
þ
log r
log
½fð
r
D
¼
1
=
3
m t 0
p
D
d ¼
=m a
The left-hand side of Eq. (ex.1) is a known value—say,
k 1 :
k 1 ¼
r
=d ½
log 4
þ
log
p þ
log D
þ
log r
ð
ex
:
2
Þ
k 1 þ
log 4
þ
log
p þ
log r
¼
r
=d
log D
The left-hand side of Eq. (ex.2) is again a known value—say, k 2 :
p
D
k 2 ¼
r
=m a
Þ
log D
p
m a =
k 2 ¼
r
ð
D
Þ
log D
p
m a =
m t 0 ÞÞ
m t 0 Þ
ð
ex
:
3
Þ
k 2 ¼
r
ð
1
3
log
ð
1
=
3
p
3
m t 0 Þ
k 2 ¼
r
ð
m a m t 0
Þ
log
ð
1
=
3
p
3
ðm a þ m s 0 ÞÞ
m a ðm a þm s 0 Þ
k 2 ¼
r
ð
Þ
log
ð
1
=
3
Solving Eq. (ex.3), the value of the coefficient of absorption can be found.
17.2.3 Measurement of Optical Properties
The measurement of optical properties—namely, absorption coefficient (
m a
), scattering coef-
ficient (
)—of biological tissues is an important problem in the
field of biomedical optics. Knowledge of these parameters is important in both therapeutic
and diagnostic applications of light in medicine. For example, optical properties are required
to predict fluence distributions for irradiation procedures such as photodynamic therapy, pho-
tocoagulation, and tissue ablation. Also, in addition to having a profound impact on in vivo
diagnostics such as fluorescence spectroscopy and optical imaging, the optical properties
themselves can potentially be used to provide metabolic information and diagnose diseases.
To date, a number of methods have been developed to measure tissue optical properties.
The collimated transmission technique can be used to measure the total interaction coeffi-
cient (
m s
), and scattering anisotropy (
g
). In this technique, a collimated light beam illuminates a thin piece of tissue.
Unscattered transmitted light is detected, while the scattered light is rejected by use of
a small aperture. The unscattered transmitted light can be calculated based on the Beer-
Lambert law, which is an extension of Eq. (17.30). The Beer-Lambert law for absorbing
and scattering media is
m a þ m s
) is the unscattered transmitted
light intensity after penetrating a depth of z. In collimated transmission measurements,
I
(
z
)
¼
I 0 exp[-(
m a þ m s )
z
], where
I
(
z
I 0 ,
(
), and
are measured. Therefore,
m a þ m s can be deduced.
I
z
z
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