Biomedical Engineering Reference
In-Depth Information
transmitted intensities were measured by placing the specimen (~100 micron thickness) between a
three- and a two-port dual integrating sphere setup. This setup yields the absorption coefficient, μ
a
, and
the reduced scattering coefficient,
µ
s
, where
′
µ
′ =
µ
(1
−
g
)
(6.1)
s
s
The refractive indices necessary for the extraction of the scattering and absorption coefficients [25]
were obtained using the method of Li [26], where the specimen is placed on a cylindrical lens and the
critical angle for total internal reflection is measured. To experimentally determine the anisotropy fac-
tor,
g
, the Henyey-Greenstein function was fitted to experimental data following a similar technique as
demonstrated by Marchesini et al. [27]. We recorded the angular scattering profile by rotating a photon
detector with a slit-aperture about a fixed central specimen. The intensity of the scattered light from the
tissues was measured from 5 to 45 degrees and the normalized values were fit to the following expression:
p
(cos
θ
)
=
(
1
−
g
2
) (
/
1
+
g
2
−
2
g
cos
θ
)
/
3 2
(6.2)
Utilizing the diffuse reflectance, transmittance, index of refraction, and anisotropy,
g
, we performed
a multilayer inverse Monte Carlo simulation [28,29] and calculated the absorption coefficient μ
a
and
scattering coefficient μ
s
.
6.2.4 Monte carlo Simulations
Monte Carlo simulations based on photon diffusion using the bulk optical parameters were performed to
analyze the measured depth-dependent
F/B
ratio and forward intensity attenuation in terms of decoupling
the contributing factors to the total response, which cannot be achieved directly. This allows the isolation of
the most sensitive factors that can discriminate normal and diseased tissue. Our approach is based on the
MCML framework of Wang and Jacques [30], where we added the necessary modifications to simulate the
3D SHG response [18]. The Monte Carlo technique is a stochastic approach that utilizes probability distribu-
tion functions to perform a three-dimensional random walk to estimate the transport equation [30] given by
dJ r s
ds
( , )
α
π
∫
= −
α
J r s
( , )
+
s
p s s
( ,
′
) ( ,
J r s d
′
)
ω
(6.3)
t
4
4
π
where
p
(
s
,
s
′) is the phase function of a scattered photon from direction
s
′ into
s
,
ds
is the incremental
path length, and
d
ω is the incremental solid angle about direction
s
. If the scattering is symmetric about
the optical axis, the phase function can be written as the form of Equation 6.3. The radiance
J
(
r,s
) relates
to the observable quantity, intensity
I
, through the relation
=
∫
I
J r s d
( , )
ω
(6.4)
4
π
The six principle operations that influence an individual photons trajectory are the launch of
the laser, excitation pathway generation, absorption, scattering, elimination, and detection. As the
MCML framework is well documented, we only present our modifications to the basic approach
required to simulate the SHG directional and attenuation responses as a function of focal depth.
In terms of creation attributes, these are based upon an assumed initial
F
SHG
/B
SHG
creation ratio
and scattering cross-sectional window σ, which represents the relative value of the χ
(2)
susceptibil-
ity tensor [31]. We also account for the primary and secondary filter effects on the laser and SHG
signal, respectively. A flowchart for the simulations is shown in Figure 6.1. First, to simulate optical
