Biomedical Engineering Reference
In-Depth Information
Start
Set photon packets
Launch focused photon packets
through 0.8 NA objective to depth
z
f
Determine transmittance at
T
ω
at
z
f
Determine fractional
T
within
SHG cross section
σ
Determine relative SHG conversion
W
p
(2
ω
) =
T
ω
2
(
z
,
σ
)
Set SHG emission dircectionality
Determine reflectance
R
(2
ω
)
Detremine transmittance
T
(2
ω
)
based on
µ
s
and
g
at 2
ω
Determine SHG components at tissue
boundaries
%F(SHG) =
T
(2
ω
)/
R
(2
ω
)
%B(SHG) = 1 - %F
F(SHG) = (%f ) *
W
p
(2
ω
)
B(SHG) = (1-%f ) *
W
p
(2
ω
)
Determine SHG attenuation
Y
Another
z
f
N
End
FIgurE 6.1
Flowchart of the algorithm used in the Monte Carlo simulations of the axial dependences of the
measured SHG directionality and attenuation. (Reprinted from
Biophys. J.
94, Lacomb, R., O. Nadiarnykh, and P. J.
Campagnola, Quantitative SHG imaging of the diseased state osteogenesis imperfecta: Experiment and simulation,
4504-4514, Copyright (2008), with permission from Elsevier.)
sectioning, the incident photons are focused by an objective lens to an axial spot within the tissue
at depth
z
f
, where the beam has a width or 1/
e
2
radius of ω
beam
using the experimental NA = 0.8. The
transmission of the laser,
T
ω
, that reaches the focal depth
z
f
is then determined based upon bulk
optical parameters at the fundamental wavelength, and the cone formed by the experimental NA.
This then accounts for the primary filter effect on laser intensity and determines the density of bal-
listic photons that arrive at the focus. To estimate the relative SHG brightness, that is, χ
(2)
values of
the normal and diseased tissues, or different tissues, we next define a two-dimensional scattering
cross-sectional window σ = 2π
r
s
, where
r
s
is the radius in which fundamental photons are converted
to second harmonic photons. This then yields the initial SHG intensity
T z
ω
2
( , ), the initial weight of
which we designate
W
p
(2ω). We next define the SHG emission directionality in terms of the forward
σ
