Biomedical Engineering Reference
In-Depth Information
parameters are shown with the experimental SHG data in Figure 6.7b. The chi-squared test results in
values of 0.13 and 0.29 for the WT and oim, respectively, indicating that, for both tissues at the α = 0.05
level, the experimental and simulated results are not significantly different. This good agreement dem-
onstrates that the combination of 3D imaging, measuring the bulk optical parameters, and then per-
forming simulations combining these aspects provides a robust method of modeling the directional
response and extracting out the emission directionality. As described earlier, this cannot be directly
measured in tissues of thickness >1 MFP, and further cannot be measured reliably in thin sections due
to the unevenness of the tissue slicing.
We now apply the theoretical findings of Section 6.3 to comparing the SHG response in the oim and
normal tissues. Using SEM imaging, we measured the average fibril diameters for these tissues and
found average values of 70 and 100 nm for the oim and WT, respectively. Based solely on size consid-
erations, one might expect that the
F
SHG
/
B
SHG
from the WT should be larger than that of the oim skin.
To explain the observed similar creation ratios, we must also remember that the
F
SHG
/B
SHG
is a function
of Δ
k
as demonstrated in Figure 6.4. To utilize these figures as a descriptive aid, we must consider the
effective domain size
D n
= /
λ
SHG
(i.e., normalized to λ
SHG
), where (
L
) is the average fibril diameter.
Using these domain sizes and assuming Δ
k
f
= Δ
k
1
, we can then estimate effective Δ
k
b
values that pro-
duce 75%
F
SHG
for both oim and WT skin. This results in ~20% higher value for oim over that of WT
(with effective values of 6Δ
k
1
and 5Δ
k
1
, respectively). By this description, one can make the connection
that larger Δ
k
b
values are associated with a higher degree of randomness in the collagen matrix, as is
evidenced in the oim SHG image relative to the WT (Figure 6.5). The increased randomness of the oim
tissue decreases the QPM contribution to the overall SHG; thus, the emission is more forward directed
(although with lower conversion efficiency) compared to the more regularly packed fibrils of the same
size. Thus, the fact that the same
F
SHG
/B
SHG
occurs for the WT and oim is a coincidence that arises from
offsetting contributions from the larger fibril size in the WT and increased randomness in the oim skin.
This example further shows that a treatment based solely on fibril size is insufficient to describe the
emission direction. In this case, the bulk optical parameters were significantly different, resulting in
different measured
F/B
responses for the normal and diseased skin.
6.4.1.3 Depth-Dependent Attenuation of Forward SHG intensity: experiment
and Simulation
The next part of our integrated metric for differentiating normal and diseased tissues is measurement
and simulation of the depth-dependent attenuation of the forward SHG intensity. This axial response
arises from the relative χ
(2)
values, the square of the primary filter effect, SHG creation directionality,
and secondary filter effects governing subsequent propagation. The forward attenuation data were taken
concurrently with the
F/B
data (Figure 6.6) and the resulting averaged data with standard errors are
shown in Figure 6.8 for the oim and WT dermis. As the absolute SHG intensity of the diseased skin is
less than that in WT, the data are normalized to each other by using the maxima in each image stack.
We observe that this method of measuring the SHG attenuation provides clear separation between the
WT and oim skin in terms of the attenuation. Interestingly, despite being characterized by a similar and
smaller μ
s
at the fundamental and SHG wavelengths, respectively, the oim skin displays a more rapid
decrease in intensity with increasing depth than the WT, demonstrating the inadequacies of the use of
bulk optical parameters alone as a quantitative description.
In conventional plane wave scattering experiments, the attenuation can be estimated by fitting the
response to an exponential decay. This is not possible for the SHG case as the attenuation results from
a compounded mechanism composed of the wavelength-dependent bulk optical effects (distinct at the
fundamental and second harmonic frequencies), SHG conversion efficiency (large effect, determined by
simulation), and SHG creation directionality (small effect, determined by simulation), all of which culmi-
nate to produce the measured response. As a consequence, the initial intensity of the SHG at a given depth
is linked to the laser intensity at that point (having been decreased by scattering with increasing depth)
