Biomedical Engineering Reference
In-Depth Information
TABLE 18.4
Thermal Properties of Water and Gold Including the Thermal Conductivity, Density,
Specific Heat, Thermal Diffusivity, and Mean Free Path
Properties
Liquid Water (H
2
O)
Solid Gold (Au)
Tissue
a
Thermal conductivity (k, W/m·K)
0.613
317
0.567
Density (ρ, kg/m
3
)
0.997 × 10
3
19.3 × 10
3
1.05 × 10
3
Specific heat (c
p
, kJ/kg·K)
4.179
0.129
1.5
Thermal diffusivity (α, m
2
/s)
1.47 × 10
−7
1.27 × 10
−4
1.5 × 10
−7
Mean free path (λ, nm)
<1 nm, 0.2 nm
31
b
Note:
All properties are at room temperature except noted.
a
Human liver, data from Cooper et al. (1972)
b
Tissue mean free path should be similar to water
many GNPs (Keblinski 2006, Richardson 2009). Another pos-
sibility of generating larger temperature increase is to increase
the laser fluence with CW or pulsed laser. Figure 18.5b shows
several degrees of temperature increase for spherical GNP and
gold nanoshell with a laser fluence of 10
4
W/cm
2
. Note that this
is three orders of magnitude higher than the laser fluence used
for
in vivo
photothermal therapy as shown and discussed later
in Table 18.7.
where
Q
nano
is the heat generated by or in the GNP, and
k
is the
thermal conductivity of the medium. The maximum tempera-
ture occurs at the NP surface, given by
Q
nano
p
T
=
.
(18.10)
nano
4
π
kr
One can use the typical laser parameters for GNP photother-
mal therapy to calculate this nanoscale temperature increase,
T
nano
. For example, Hirsch et al. (Hirsch 2003) designed
a gold nanoshell with
r
18.5.2.2 Microscale Heating (t
micro
)
The same methodology presented for single NP heating can be
applied to the heating of a cell. The time for a heated cell to reach
equilibrium with the surrounding medium can be written as
p
=
65
nm
absorption cross section
C
=×
−
3.810
14
m
2
and CW laser fluence
I
=
4/
2
Wcm
. This
abs
yields
nano
=
in water using properties in Table 18.4.
The reason for this extremely small temperature increase is
because of the large surface-to-volume ratio of the NP, which
yields rapid heat dissipation. While a single GNP doesn't pro-
vide enough temperature increase for photothermal therapy
at the nanoscale, the macroscopic temperature increase is sig-
nificant as shown later, due to the collective heating effect of
T
0.003
k
2
τ=
α
r
cell
.
(18 .11)
micro
cell
=µ
and using the dif-
fusivity of water, the characteristic time is around 0.7 ms. To
Considering a cell with radius
r
5
m
Pulse length (s)
Pulsed
CW
10
-15
10
-12
10
-9
10
-6
10
-3
10
0
10
3
10
-9
Macromolecule
Membranes
10
-8
10
-7
Organelle
10
-6
Object laden with
nanoscale
absorbers
Single cell
10
-5
10
-4
Small cell clusters
10
-3
ermal confinement
10
-2
Tumor
10
-1
FIGURE 18.6
The concept of thermal confinement. To confine the heat within the object shown, one needs to work with the parameters at the
lower left regime below the dashed line. (Adapted from Huettman, G. et al.
Proceedings of SPIE
, 5142, 2003.)
