Biomedical Engineering Reference
In-Depth Information
(a)
(b)
250
10
9
200
8
7
150
6
5
100
4
3
50
2
1
0
0
0
500
1000 1500
Radial position (µm)
2000
2500
3000
0
5
10
15 20 25
Radial position (µm)
30
35
40
45
50
FIgurE 17.3
Spatial distribution of forward-propagating and subsequently backscattered SHG photons reaching
the object plane. Monte Carlo simulation was used to model the scattering of initially forward-propagating (
F
i
) and
subsequently backscattered SHG photons in the tissue, to predict the radial distribution of these photons that exit
the tissue interface toward the objective lens. (a) Steady-state radial distribution of the backscattered SHG photons
over a large range of radial position (3 mm) from the initial emission point (i.e., focal volume), demonstrating that
over a large length scale, backscattered SHG photon intensity decays exponentially with the distance from the emis-
sion point. (b) However, the same distribution over a short radial range demonstrates that within ~50 μm from the
emission point, initially forward propagating then backscattered SHG photon intensity remains constant with the
distance from the emission point. (Reprinted from Han, X. and E. Brown. 2010. Measurement of the ratio of forward-
propagating to back-propagating second harmonic signal using a single objective.
Opt Express
,
18
:10538-10550,
Copyright 2010. With permission of Optical Society of America.)
pixel intensity at the largest pinhole size, then the relative pixel intensity as a function of the relative
pinhole size
R
can be expressed as
2
π
R
{
}
∫
∫
d
θ
exp[
−
2
(
r
/
ω
) ]
2
+
(
F B C r dr
/
)
I R
( )
=
0
0
(17.4)
rel
2
π
R
{
}
∫
∫
max
d
θ
exp[
−
2
(
r
/
ω
) ]
2
+
(
F B C r dr
/
)
0
0
where
R
max
is the largest pinhole size [26]. This expression allows relative pixel intensity versus pinhole
size to be plotted and fitted to generate (
F
/
B
)/
C
. To determine
F
/
B
from these data, we must eliminate
C
, that is, the fraction of the signal that originally propagates forward but is then backscattered by the
tissue to reach the pinhole plane. This will vary with the scattering properties of the underlying tissue.
It can be eliminated by including in the sample object plane a fluorescent reference with a known
F
/
B
emission ratio, whose
C
value will be the same (i.e., forward-propagating fluorescent signal emitted
from the reference object in the sample plane will be subject to the same backscattering in the tissue, as
the initially forward-propagating SHG signal). Fluorescent polystyrene beads, for which the
F
/
B
fluo-
rescence emission ratio has been previously measured in buffer alone, are then sprinkled on the sample
surface to serve as this reference standard. Thus, by taking serial images of the collagenous tissue plus
beads through a series of different sized confocal pinholes (Figure 17.4), plotting the epidetected total
collagen SHG intensity of a pixel or small region of interest, as well as the total bead fluorescence inten-
sity versus pinhole size (Figure 17.5), we can fit to Equation 17.4 to obtain (
F
/
B
)/
C
for both the collagen
fibers of interest and the calibration beads [26]. Figure 17.6 further illustrates how the relative pixel
