2.1.

Optical Properties of Gold Nanoshells

The optical response of gold nanoshells can be described by using computed solutions of Mie theory for concentric spherical shells at the boundaries between different mediums.³⁸ For use in the Monte Carlo studies described later, Mie solutions of gold nanoshells were computed with an excitation wavelength of $830\mathrm{nm}$ , within the region of optimal physiological transmissivity best suited for optical bioimaging and biosensing applications. Typically, optical resonances of gold nanoshells are calculated with air $(n=1.0)$ or water $(n=1.33)$ as the embedding medium.^{37, 40} However, it is important that the optical properties of gold nanoshells are calculated with $n=1.4$ , simulating the embedding medium as a physiological environment, as the Monte Carlo studies will use tissue models embedded with nanoshells. Table 1 shows the optical properties of the $\mathrm{R}75∕115$ nanoshell with $n=1.0$ , 1.33, and 1.4. The differences in optical properties must be taken into account as it would subsequently affect the optical properties calculated and used in the Monte Carlo studies.

Table 1

Optical properties calculated from Mie solutions of various particles at a 830-nm excitation wavelength.

To choose different nanoshells with varying optical properties, we first assume independent scattering of the nanoshell particles for simplification. Under independent scattering, the optical cross section per unit volume of the particle becomes more appropriate than the optical efficiency for subsequent calculations of scattering and absorption coefficients^{47, 48} for use in the Monte Carlo studies. Core radius-to-shell thickness space-maps [see Figs. 2(a) and 2(b) ] of volume-normalized optical cross sections are used to select the nanoshells, with a range of sizes and optical properties. The space-maps were computed with an excitation wavelength of $830\mathrm{nm}$ , including sizes that can be fabricated with current laboratory methods. As gold nanoshells possess not just scattering, but also absorbing properties, nanoshells with a variety different scattering and absorbing proportions are also considered for the Monte Carlo studies. A simple relation—the scattering-to-absorption efficiency ratio (Sca/Abs ratio)—can be used to compare how much more scattering a nanoshell is compared to its absorption ability [see Fig. 2(c)].

Fig. 2

Computed optical properties of gold nanoshells as a function of the core radius and the shell thickness (both in nanometers) at an excitation wavelength of $830\mathrm{nm}$ . These diagrams can aid in selecting specific nanoshells with desired optical properties. The graphs describe (a) volume-normalized scattering cross section $(C_{\mathrm{sca}}∕V_p)$ , (b) volume-normalized absorption cross section $(C_{\mathrm{abs}}∕V_p)$ , (c) scattering-to-absorption efficiency ratio (Sca/Abs), and (d) extinction efficiency. These space-maps can aid in determining the desired size and optical properties to be used in subsequent studies.

2.2.

Monte Carlo Modeling

Monte Carlo modeling of photon transport in multilayered tissues by Wang, ⁴⁹ a computational tool written in Standard C, has been widely used to simulate random walk of photons through turbid media and is useful for investigating light propagation in tissue. The fraction of remitted and absorbed photons can be predicted from Monte Carlo computations, and the fraction changes accordingly as the optical parameters of the medium are changed. The theories behind Monte Carlo methods are well described in literature and are not be repeated here.⁴⁹ Simulations were performed on two models (A and B) that will each be differentiated into two sets: a bulk tissue model (models A-1 and A-2) and a multilayered tissue model (models B-1 and B-2). The description of the two sets is provided later. The bulk tissue model was assumed to be an infinitely thick precancerous tissue layer with uniform homogeneous optical properties. The base optical properties before the addition of nanoshells of this precancerous layer was set with the absorption coefficient at ${\mu }_{\mathrm{abs}\left(c\right)}=0.05{\mathrm{cm}}^{-1}$ , and the scattering coefficient, ${\mu }_{\mathrm{sca}\left(c\right)}=50{\mathrm{cm}}^{-1}$ , both within cited literature^{50, 51, 52} values in the NIR. The tissue properties of this layer are then changed, simulating an increasing concentration of nanoparticles added to the tissue.

A three-layered model (models B-1 and B-2) used in our studies (see Fig. 3 ) is similar to the theoretical model used by Quan and Ramanujam,⁵³ which mimics the basic structure of epithelial and stromal tissue. The first layer represents normal surface epithelium with a thickness of $d_1=175\mu \mathrm{m}$ , and optical parameters were kept constant at ${\mu }_{\mathrm{sca}\left(1\right)}=50{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(1\right)}=1.5{\mathrm{cm}}^{-1}$ . The second precancerous layer $(d_2=175\mu \mathrm{m})$ , originates from the basal membrane, occupying space between the stroma and the normal epithelium of the top layer. As the epithelium consists of the most superficial tissue layers, hemoglobin content is negligible. The absorption coefficients of the epithelial layers represent absorption by tissue chromophores such as lipid, water and cytochrome oxidase.^{54, 55, 56} Similar to model A, increasing concentrations of nanoshells were added to this representative precancerous layer and the optical properties of this second layer without any nanoshells was the same as the bulk tissue, where ${\mu }_{\mathrm{sca}\left(c\right)}=50{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(c\right)}=0.05{\mathrm{cm}}^{-1}$ . The stromal layer was modeled as a semi-infinitely thick $(d_3=1.0\times {10}^8\mathrm{cm})$ layer with ${\mu }_{\mathrm{sca}\left(3\right)}=250{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(3\right)}=1.5{\mathrm{cm}}^{-1}$ . The following properties were kept constant for all simulations: the anisotropy factor $\left(g\right)$ was kept constant at 0.9 and $n=1.4$ for the tissue refractive index.

Fig. 3

Schematic showing the multilayered tissue model used in the Monte Carlo studies. The depths of the parameters shown are: normal surface epithelium, $d_1=175\mu \mathrm{m}$ ; precancerous layer, $d_1=175\mu \mathrm{m}$ ; and stromal layer (semi-infinitely thick), $d_3=1.0\times {10}^8\mathrm{cm}$ . The optical parameters of the layers were set as, normal surface epithelium, ${\mu }_{\mathrm{sca}\left(1\right)}=50{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(1\right)}=1.5{\mathrm{cm}}^{-1}$ , and the stromal layer optical properties of ${\mu }_{\mathrm{sca}\left(3\right)}=250{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(3\right)}=1.5{\mathrm{cm}}^{-1}$ . The concentration of nanoparticles was incremented in the precancerous layer, with base optical properties of ${\mu }_{\mathrm{sca}\left(c\right)}=50{\mathrm{cm}}^{-1}$ and ${\mu }_{\mathrm{abs}\left(c\right)}=0.05{\mathrm{cm}}^{-1}$ .

The overall scattering $\left[{\mu }_{\mathrm{sca}\left(t\right)}\right]$ and absorption coefficient $\left[{\mu }_{\mathrm{abs}\left(t\right)}\right]$ of the tissue is altered by the optical properties of the particles added to the models. As a basis of comparison, gold nanoparticles ( $10\mathrm{nm}$ radius) commonly used for biological interrogation such as biomolecular analysis, interactions, and imaging^{34, 57, 58} were used in place of the gold nanoshells. To account for interparticle effects by the nanoparticles on photon scattering, a correction factor is required for volume fractions higher^{59, 60} than $\sim 1\%$ , when the diameter of the particles are much less than the wavelength to account for the reduction of bulk optical cross section as a result of non-independent scattering among subwavelength spheres. As mentioned, for these studies, we impose a limit on the density and size of nanoshells added to the precancerous layers to ensure independent scattering. Each type of nanoparticles is then added separately, so that only one type of particle is added to the models at one time. Using well established light scattering theory, the change in the optical coefficient $\left[\Delta {\mu }_{\left(p\right)}\right]$ due to particles in a medium, is related to the scattering or absorption cross section $\left(C\right)$ and the number of particles per unit volume⁴⁸ $\left(N\right)$ :

In the second set (models A-2 and B-2), the combination of both scattering and absorption by the nanoparticles are taken into consideration. The respective change in absorption coefficient $\left[\Delta {\mu }_{\mathrm{abs}\left(p\right)}\right]$ can then also be calculated using a similar relation. Both the overall scattering $\left[{\mu }_{\mathrm{sca}\left(t\right)}\right]$ and absorption coefficients $\left[{\mu }_{\mathrm{abs}\left(t\right)}\right]$ of tissue are consequently altered by the optical response of the nanoshells. Thus the overall change in optical properties of the precancerous layer is,

3.1.

Gold Nanoshells

Figures 2(a), 2(b), 2(c), 2(d) shows various optical properties of gold nanoshells compared to core radius and shell thicknesses up to an overall radius of $280\mathrm{nm}$ at an excitation wavelength of $830\mathrm{nm}$ . The figures show the volume normalized scattering cross section [Fig. 2(a)], volume normalized absorption cross section [Fig. 2(b)], and the scattering-to-absorption efficiency ratio [Fig. 2(c)]. Figure 2(d) shows the extinction efficiency of the nanoshells. Using these space-maps of optical properties, nanoshells of different sizes and properties (also see Table 1) were chosen and their effect on tissue diffuse reflectance investigated. The table shows that the particles with the highest scattering and absorption efficiencies do not necessarily show the highest optical cross sections per unit volume of the particle, and this becomes important and are described later. To further describe the optical versatility of gold nanoshells, Fig. 4 shows representative optical extinction profiles of some of the nanoshells ( $\mathrm{R}75∕115$ , $\mathrm{R}50∕60$ , and $\mathrm{R}55∕80$ ) used in these studies showing very different responses across wavelengths. Figure 5 shows volume-normalized absorption, scattering and extinction of the $\mathrm{R}75∕115$ nanoshell.

Fig. 4

Representative extinction efficiencies of three different nanoshells, $\mathrm{R}75∕115$ , $\mathrm{R}50∕60,$ and $\mathrm{R}55∕80$ , used in the Monte Carlo experiments. The different extinction profiles are plotted against a broad wavelength range, showing optical activity well into the NIR. Nanoshells of different sizes produce unique and different optical responses.

Fig. 5

Volume normalized cross sections of the $\mathrm{R}75∕115$ gold nanoshell $(n=1.4)$ . Although the scattering property of the nanoshell generally dominates the absorption, it is expected that the diffuse reflectance of tissue with nanoshells will decrease across wavelength.

3.2.

Monte Carlo Studies

The Monte Carlo studies show that the addition of gold nanoshells to tissue causes a significant change in tissue reflectance. It is also possible to detect the change in reflectance due to a buried layer of tissue containing nanoshells. Between Monte Carlo modeling sets 1 and 2, the absorption properties of nanoshells are an important factor for predicting the tissue reflectance and cannot be neglected, even if the optical properties of the particle is dominated by scattering. The gold nanoshells were observed to scatter or absorb light far more efficiently than the gold nanoparticles. A large change in reflectance was observed with only a very small amount of nanoshells, while the gold nanoparticle caused little change in reflectance.

In set 1 of the Monte Carlo studies, the diffuse reflectance generally increased as the amount of nanoshells added increased. Figures 6(a) and 6(b) shows the diffuse reflectance results from the bulk (model A-1) and multilayered (model B-1) tissue models after gold nanoshells of a variety of scattering properties and the $10\text{-}\mathrm{nm}$ gold nanoparticles were added to the tissue with increasing concentration. The reflectance increases after the addition of gold nanoshells, while the results from the gold colloid particle remain relatively unchanged. The photon reflectance, before adding any nanoparticles, is approximately 0.6 from model A-1 and 0.3 from model B-1. With the same concentration of particles added, the particle with the greater volume-normalized scattering cross sections shows higher reflectance. For example, the $\mathrm{R}55∕80$ nanoshell exhibits the highest reflectance, while the $\mathrm{R}40∕45$ shows the lowest of all the nanoshells. This corresponds to the volume-normalized scattering cross-section values as shown in Table 1. The $\mathrm{R}55∕80$ nanoshell exhibits the highest volume-normalized scattering cross section (Abs $\mathrm{XS}∕\mathrm{Vol}=3.15\times {10}^7{\mathrm{m}}^{-1}$ ) and the $\mathrm{R}40∕45$ nanoshell had the lowest value among the gold nanoshells used, with Abs $\mathrm{XS}∕\mathrm{Vol}=1.50\times {10}^6{\mathrm{m}}^{-1}$ . The $10\mathrm{nm}$ radius gold colloid particle (R10-Au) with the lowest volume-normalized scattering cross section correspondingly shows very little change in both models A-1 and B-1.

Fig. 6

Diffuse reflectance from the (a) bulk (model A-1) and (b) multilayered (model B-1) models with ${\mu }_{\mathrm{abs}\left(c\right)}=0.05{\mathrm{cm}}^{-1}$ , using different types of nanoparticles. The higher the volume-normalized scattering cross section, the more the diffuse reflectance increases with the same volume fraction of nanoshells added. The results show the studies that neglected absorption from the nanoparticles, assuming the particles as simple scatterers.

In set 2, the results, when absorption from gold nanoshells and gold colloid $\left[\Delta {\mu }_{\mathrm{abs}\left(p\right)}\right]$ was considered together with the scattering, are shown in Figs. 7(a) and 7(b) . The results also show an immediate decrease in reflectance after the nanoparticles were included. When the concentration of the particles was increased, the diffuse reflectance decreased, and this occurred for all the particle configurations used in the simulations. Furthermore, the diffuse reflectance from model A-2 decreases more rapidly compared to model B-2 and eventually shows higher reflectance for the same amount of nanoshells added, as shown in the inset of Fig. 7(a). The graph shows that at a volume fraction of 0.00005, the reflectance with the $\mathrm{R}75∕115$ gold nanoshell is approximately 0.15 in model A-2, and about 0.28 from model B-2. Compared to when no particles were added to the tissue, the reflectances are approximately 0.3 (model B-2) and 0.6 (model A-2). Further increases in concentration diminish the reflectance close to zero. The uniform change in the optical properties of the bulk model (model A-2), leads to a higher probability that photons will be absorbed in the topmost regions, whereas in model B-2, as the precancerous layer is buried away from the surface, there are greater chances of scattering when the photons first travel through the surface epithelium.

Fig. 7

Diffuse reflectance from the (a) bulk (model A-2) and (b) multilayered (model B-2) tissue when both scattering and absorption from the nanoparticles were considered. As the volume-normalized absorption cross section of the particle increases, the reflectance decreases. Model B-2 shows a more gradual decrease in reflectance compared to model A-2, and eventually shows higher reflectance as more particles were added, even though model A-2 showed higher reflectance before any nanoparticles were added. To describe this, the insert shown in (a) shows comparison of the diffuse reflectance fraction from the bulk (solid line) and multilayered (dotted line) models with increasing volume fractions of the $\mathrm{R}75∕115$ nanoshell.

Even as it is useful to use the scattering-to-absorption ratio (Abs/Sca ratio) of the optical properties to describe how much more scattering the particle is compared to absorption, the volume-normalized absorption cross section of the particles is a more adequate description of how the optical properties of the particles influences tissue reflectance in our studies. The comparison of the scattering and absorbing properties of each particle is shown in Table 1 under Abs/Sca Ratio. For example, the $\mathrm{R}75∕115$ nanoshell shows a scattering cross section of almost 9 times over the absorption cross section, while the scattering of the $\mathrm{R}40∕45$ nanoshell is about 5.9% that of its absorption. Comparing this to the reflectance, the $\mathrm{R}75∕115$ and $\mathrm{R}40∕45$ nanoshells, however, do not show the highest and lowest reflectances, respectively. Thus, we can infer that absorption from the particles has a far greater effect on reflectance and cannot be neglected, even if the particle possess scattering cross section several times larger than its absorption. When we consider only scattering from the nanoparticles in models A-1 and B-1, it is obvious that higher scattering cross section per unit volume of the particle shows higher reflectance with the limitation of independent scattering. However, with different configurations of scattering and absorption from the gold nanoshells, the reflectance is more dependent on the volume-normalized absorption cross section than the combination of scattering and absorption. Figure 8 shows the relationship between diffuse reflectance and volume-normalized absorption cross sections of gold nanoshells. The diffuse reflectance decreases correspondingly (volume fraction, $V_f=0.0002$ and 0.0005) as the absorption of gold nanoshells increase. This reemphasizes the importance of absorption from the particles and suggests that gold nanoshells can more efficiently lower the photon reflectance compared to gold colloid. This can be potentially useful for enhancing reflectance signatures through absorption for spectroscopic detection modalities. Furthermore, only a very small number of nanoshells are required to produce an observable change in the remitted signal. The volume-normalized absorption cross section of the $\mathrm{R}75∕115$ nanoshell shown in Fig. 5 range from $1.6\times {10}^7{\mathrm{m}}^{-1}$ at $520\mathrm{nm}\text{to}3.74\times {10}^6{\mathrm{m}}^{-1}$ at $1000\mathrm{nm}$ $(n=1.4)$ . As spectroscopic methods typically use a range of wavelengths, comparing these values to the R10-Au gold nanoparticle, these values are still considerably larger. Thus, when comparing normal tissue and nanoshell targeted tissue, the spectra of the diseased tissue would likely show a much reduced spectral intensity with the presence of nanoshells, which would provide an indication of the presence of targeted cells.

Fig. 8

The diffuse reflectance as a function of the volume normalized absorption cross section of different gold nanoshells used in the multilayered Monte Carlo studies (refer to Table 1). As the volume normalized absorption increases, the reflectance correspondingly decreases. Volume fractions $\left(V_f\right)$ of 0.0002 and 0.0005 are shown, within the constraints for independent scattering.

Throughout the Monte Carlo simulations, the anisotropy $\left(g\right)$ of the tissue was assumed to remain constant with the addition of the particles. From Mie solutions of the gold nanoshells, the $g$ values for the nanoshells can be calculated, and the overall effect on the anisotropy of the tissue is related by,