Biomedical Engineering Reference
In-Depth Information
TABLE 18.2
Representative GNP Modifications (Size and Shape) and Their Optical
Properties Including Surface Plasmon Resonance Wavelength (
λ
SPR
), Absorption
Cross Section (
C
abs
), and the Ratio of Absorption over Extinction (
C
abs
/
C
ext
)
a
L
1
and L
2
are the width and length of the rod.
b
Au cage L is the outer length of the cubic and t is the thickness of the cage.
medium (Welch 1995). The advantage of the diffusion approxi-
mation is its relative simplicity to solve numerically. In DA, the
absorption (
to calibrate the model parameters that were changing during
the laser photothermal treatment by Feng et al. (Feng 2009).
With the use of supercomputers, real-time predictions are pos-
sible when averaging over 10 runs with 1 million photons in
each run (Feng 2009). In another example, Lin et al. (Lin 2005)
used Monte Carlo to explore the use of light interaction with
gold nanoshells for early cancer detection. Specifically, a small
number of gold nanoshells (<0.05% volume fraction) can induce
measurable change in tissue diffuse reflectance.
To model light transport with the RTE and Monte Carlo method
described here, the optical properties of the NP-laden tissue are
fundamental inputs and need to be described accurately. Under
idealized conditions, for example, the phantom gel used by Elliott
et al. (Elliott 2007), the gold nanoshells are assumed to be uni-
formly distributed. In this case, the optical properties of NP-laden
medium are obtained by the superposition of the NP and medium
properties linearly (Lin 2005, Kirillin 2009). However, GNPs are
known to interact with biological systems, such as cells and tissue,
leading to non-ideal conditions. These include: (1) inhomogeneous
distribution of NPs such as accumulation around blood vessels, as
shown in Perrault et al. (Perrault 2009); and (2) aggregation of NPs
in cells upon internalization (Chithrani 2007). Further studies
to address these non-idealities and possible nonlinear effects on
optical properties are still necessary. Next, the optical properties
of GNPs under idealized conditions are discussed.
µ= ′µ−
, where
g
is
the anisotropy) coefficients are lumped into the optical diffusion
coefficient (
D
):
µ
) and reduced scattering (
(1
g
)
s
s
1
D
=
)
.
(18.6)
3(
µ+µ
s
a
Elliott et al. (Elliott 2007) used DA to model the laser fluence
in phantoms containing different concentrations of NPs and
calculated the temperature distribution within the phantoms
with the finite element method. The calculated temperature was
compared with measurements by magnetic resonance tempera-
ture imaging (MRTI), and showed reasonable agreement at low
gold nanoshell concentrations (1.19 × 10
9
NPs/ml). A follow-up
study by Elliott et al. (Elliott 2009) showed that with higher gold
nanoshell concentration (up to 2.5 × 10
9
NPs/ml), the predic-
tions from DA give unsatisfactory results. Instead, the delta P1
approximation (treat forward-directed and scattered light sepa-
rately) gives a better prediction for both the lower and higher
gold nanoshell concentrations investigated. Modifications to
speed the calculation and increase accuracy of the RTE equation
have also been proposed (Xu 2010). Note that all of these approx-
imations should be used with care, and special attention should
be paid to the applicable conditions and desirable accuracy, for
example, the failure of DA for high gold nanoshell concentration
discussed here (Elliott 2009).
Another approach to evaluate light transport or fluence
involves Monte Carlo ray tracing to directly simulate photon
transport in tissues. Monte Carlo is computationally expensive
as a sufficient number of photons need to be launched and traced
for the technique to be accurate. This method has been used to
estimate laser fluence within the gold nanoshell targeted tumor
(Feng 2009). In addition, an optimization algorithm was used
18.4 Optical properties of GNps
18.4.1 What Is the Ideal absorber?
Most laser-tissue interactions rely upon absorption of laser
energy within the tissue. Thus, being able to modify and con-
trol absorption is important and can be approached through the
addition of exogenous absorbers. Ideally, the absorbing agent
should be biocompatible, stable, easily functionalized using
