Biomedical Engineering Reference
In-Depth Information
refractive index as well as step changes of index if the interfaces are sharper in terms of refractive index
change.
The index of refraction of the scattering medium
n
s
can be described as the sum of the average back-
ground index
n
0
and the mean index variation, <Δ
n
>:
n = n
s
+ <
n
>
(8.1)
s
As explained by Tuchin [23], the average background index
n
0
is merely the weighted average of indi-
ces of the cytoplasm (
n
cp
= 1.367), and the interstitial fluid (
n
is
= 1.355) taken at their respective volume
fractions
f
using the law of Dale and Gladstone
n
=
f n
+
(
1
−
f n
)
(8.2)
0
cp cp
cp
is
where we arrive at
n
0
= 1.362 if we assume about 60% of the total fluid is retained in the intracellular
compartment. To estimate the mean index variation within the tissue, we consider the average weighted
differences between the respective pairs of refractive indexes (fibers
n
ib
and interstitial liquid
n
is
, nucleus
n
nucl
and cytoplasm
n
cp
, organelles
n
org
, and cytoplasm) as follows:
<
∆
n
> =
f
(
n
−
n
)
+
f
(
n
−
n
)
+
f
(
n
−
n
)
(8.3)
fib
fib
is
nucl
nucl
cp
org
org
cp
In fibrous tissues, collagen has a considerably higher refractive index from 1.411 in the human cornea
to 1.47 in tendon, depending on the degree of hydration. Taking into account the different contents of
collagen in various tissue types (from 3% in nonmuscular internal organs to 70% of fat-free dermis),
Equation 8.3 estimates the mean index variation <Δ
n
> to range between 0.04 and 0.09.
The effect of the refractive indices mismatch on tissue scattering properties; hence, optical transmit-
tance and reflectance can be examined applying Mie theory, as described by Tuchin [23]. Strictly speak-
ing, Mie theory holds for spherical particles, but its results are still useful for cumulative properties of
the tissue composed of irregularly shaped obstacles. For a simplified monodisperse model of dielectric
spheres, the reduced scattering coefficient
μ
s
is given by
0 37
.
2
π
λ
a
µ
′ =
3 28
.
π ρ
a
2
(
m
−
1
)
2 09
.
(8.4)
s
s
where
a
is the sphere radius,
ρ
s
is the sphere volume density, and
m
=
n
s
/
n
0
is the ratio of the refractive
index between the scattering particle and the background. This equation shows that
μ
s
′ is a steep func-
tion of the magnitude of this mismatch, and it can be reduced considerably if index variation is lowered,
and approaches zero for the index-matched case (
n
s
=
n
0
).
Index matching has been argued as the main mechanism of optical clearing [7,24]. However, due to
complexity of interactions between OCAs and tissue components, other mechanisms have been offered,
including reversible collagen dissociation [25], tissue dehydration by OCAs [7,26,27], and two studies even
claimed no correlation between OCA's refractive index, osmolarity, and optical clearing potential [28,29].
For SHG, in particular, additional consideration of any changes in local packing of molecular sources
is important [24]. Since SHG arises from the polarization induced over the noncentrosymmetrically
arranged dipoles, the emission is coherent and extremely sensitive to local molecular organization below
the optical resolution, where the relevant structure size scales from ~λ
SHG
/10 to λ
SHG
. Owing to second-
order nonsymmetry constraints, SHG is not possible in centrosymmetric environment, whereas the SHG
conversion efficiency increases for well-ordered nonsymmetric structures. The efficiency is given by
sin
∆
∆
(
kL
kL
/
2
)
E
∝
E
2
2
ω
ω
/
2
