Biomedical Engineering Reference
In-Depth Information
estimate the temperature increase of a single cell loaded with
GNPs, one can treat the cell as being loaded with a uniform
distribution of NPs, with a given number density,
N.
he tem-
perature of the cell comes from the superposition of heating in
all GNPs (Keblinski 2006):
(Huettmann 2003, Anderson 1983, Vogel 2003). To treat a
small target area with minimal injury to the surrounding
tissue, the majority of the heat generated needs to be con-
fined in the target area; this is usually called selective photo-
thermolysis (Anderson 1983). There are usually two ways to
achieve this: (1) to use a laser “microbeam” to achieve con-
fined thermal damage; and (2) to use a broad beam but treat
a pigmented or absorber-loaded target. For both methods,
thermal confinement is essential for selective thermal dam-
age. To confine the thermal energy, one has to induce the
damage before the heat diffuses to the surrounding medium.
The diffusion time or the thermal relaxation time for a sphere
is given by
2
Nr
Q
k
cell
nano
T
=
.
(18.12)
micro
2
For example, if one assumes there are 5000 gold nanoshells
in a cell (
r
cell
= 10 µm) and irradiation is with a 35 W/cm
2
laser
as described in Hirsch et al. (Hirsch 2003), the temperature
increase is only about 0.09°C using the previous equation. This
is because we assume that only one cell is present in an infinite
medium. The ability of gold nanoshells to kill cells shown in
this work and many other
in vitro
studies is due to the collective
effect of many GNPs in the cell medium, causing the macro-
scopic heating described next. To selectively kill a single can-
cer cell with GNPs, one needs at least 2~3 orders of magnitude
higher laser irradiance to provide over 10°C of temperature
increase within a cell. This high laser irradiance can be pro-
vided by pulsed lasers as shown in the literature (Zharov 2005b,
Kalambur 2007). However, pulsed laser will induce both ther-
mal and mechanical effects as discussed later in Section 18.6.2.
2
τ=
α
d
27
.
(18.15)
r
The thermal relaxation time scales with the square of the tar-
get size. So the diffusion time scales down rapidly as the size of
the target decreases, shown in Figure 18.6. For example, to con-
duct “nanosurgery” to macromolecules with several K rise at the
nanoparticle surface, nano- to femto-second pulsed lasers have
to be used (Csaki 2007, Huettmann 2003). Note that with the
use of nano absorbers, for example a GNP, “nanosurgery” is pos-
sible and can operate beyond the diffraction limit (i.e., <250 nm)
while not otherwise possible with laser “microbeam.” This pos-
sibility raises the question of whether thermal injury kinetics at
high temperatures and short times will scale from lower tem-
peratures and longer times. This area is not well understood
although some work is beginning to address this interesting
question (Yan 2010).
An important application of thermal confinement is SAR esti-
mation, as discussed next. This is assuming that the heat diffu-
sion during the time of estimation is negligible.
18.5.2.3 Bulk tissue Heating (t
macro
)
As the length scale increases for bulk systems so does the dif-
fusion time. The macroscopic diffusion time for a tumor can be
written as
2
τ =
α
r
tumor
.
(18.13)
macro
This results in a diffusion time
macr
τ
of 7 s and 12 min for a 1 mm
and 1 cm diameter tumor, respectively. Using a modification to
the analysis, the temperature increase at the center of the tumor
can be estimated as (Keblinski 2006, Rabin 2002)
18.5.4 Sar Estimation
In cases when not all the parameters in Equation 18.3 can be
obtained, one can measure SAR experimentally. In principle, SAR
can be measured by two separate methods: (1) characterizing the
laser fluence and absorption; or (2) directly measuring the tem-
perature change within laser NP-heated systems. By obtaining the
optical absorption and local fluence rate, the SAR can be calcu-
lated by the product of the two parameters as shown in Equation
18.3. This requires the measurement of α, the absorption coef-
ficient of the tissue (laden with NPs), and local fluence rate. The
most direct way to measure local fluence is by invasive measure-
ment with an optical fiber, although this can pose some chal-
lenges (Welch 1995).
The second approach to measuring SAR takes advantage of
thermal confinement discussed earlier and uses local tempera-
ture change during short time periods before thermal diffusion
dominates. This approach has the advantage that measuring
2
τ =
NR Q
k
nano
.
(18.14)
macro
2
Again using the typical values for the photothermal therapy
from Hirsch et al., consider tumor size
R
= 5 mm and gold
nanoshell number density
N
=
10
15
m
−
3
(10
9
/ml), the correspond-
ing temperature increase is
macro
=
, which is sufficient for
thermal therapy. One can perform this scaling easily given the
NP's absorption cross section, concentration, and applied laser
intensity as shown in Table 18.7.
T
31
K
18.5.3 the Concept of thermal Confinement
In the discussion of heat diffusion and temperature scaling,
an important underlying concept is
thermal confinement
