2.1.

Water-Soluble Carbon Nanotubes

MWNTs were synthesized by Dr. David Carrolls group at Wake Forest University,^{1, 3} SWNTs were purchased from SES Research Inc. (Texas) and SWNHs were synthesized by Dr. David Geohegans group at Oak Ridge National Laboratories.^{43, 44} The lengths of MWNTs and SWNTs ranged from 900–1200 nm. Outer diameters of the MWNTs were in the range of 40–60 nm, whereas SWNT outer diameters were <2 nm. Individual SWNHs had diameters of 1–1.5 nm with agglomeration lengths of 50–100 nm. The purity of all CNTs was confirmed to be >95% by thermogravimetric analysis, dynamic light scattering, and transmission electron microscopy (data not included).⁴⁵

MWNTs, SWNTs, and SWNHs are naturally hydrophobic and not soluble in polar solvents, such as water. All types of CNTs were made water soluble by functionalizing their outer surfaces with 1% w/v concentration of Pluronic F-127 purchased from Biotium, Inc. Pluronic at this concentration has been shown to provide desired CNT solubility and is nontoxic in vitro and in vivo. ^{1, 23} CNTs in the pluronic-water solutions were sonicated for 40–50 min to make desired concentrations for measurement of optical properties of water solutions containing CNTs.

2.2.

Tissue Phantom Preparation

Tissue representative phantoms were created with optical properties similar to that of breast tumor tissue. Tissue representative phantoms were produced from sodium alginate Protanal LF 10/60 (FMC Biopolymer, Drammen, Norway), a low-viscosity alginate with a mean guluronate/mannuronate ratio of 70% and mean molecular weight of 180 kDa. Sodium alginate is transparent and does not adequately reflect the intrinsic scattering properties of biological tissues. In order to create phantoms that possess optical properties representative of breast tumor tissue, light scattering and absorbing polystyrene beads and highly light scattering talc-France perfume powder were evenly mixed with sodium alginate.^{46, 47} The final formulation utilized to achieve the optical properties of breast tumor tissue was talc-France perfume powder (40 mg/ml concentration) and polystyrene beads (3 μm diam, 1 mg/ml concentration) in sodium alginate aqueous gel.

Next, the CNT phantom composite tissue structures were created. Three concentrations (0.01, 0.05, and 0.1 mg/ml) of CNTs were suspended in 1% pluronic water. The concentration range was selected based on prior studies showing 0.01–0.1 mg/ml caused minimal toxicity while enabling significant heat generation.^{1, 3, 17, 23} Sodium alginate was stirred vigorously with pluronic water containing CNTs, polystyrene beads, and talc powder to a 3% w/v concentration for 1 h. The final solution was cross-linked with calcium chloride for 1 h.^{48, 49} All samples were approximately 800 μm thickness to permit adequate light transmission necessary for spectrophotometric measurement⁵⁰ [Figs. 1a, 1b, 1c]. The radius (35 mm) of the cylindrical samples was made large enough to completely cover the reflection and transmission ports of the integrating sphere accessory of the spectrophotometer. For each concentration and type of CNT, five experimental samples (N = 5) were made and all results were represented as the mean values of these samples.

Fig. 1

(a) Sodium alginate phantom, (b) phantom with inclusion of polystyrene beads and talc powder, and (c) phantom with polystyrene beads, talc powder, and CNTs.

2.3.

Spectrophotometry

A Cary 5000 Spectrophotometer (Varian Inc., North Carolina) was used to measure transmittance, reflectance, and absorbance of liquid and phantoms with and without CNTs in the wavelength range of 300–1300 nm. A diffuse reflectance accessory (DRA 2500) was mounted in the spectrophotometer to allow measurement of diffuse scattering effects. Ballistic-light intensity was measured for 100% transmission (in the absence of sample, I _0T) and 100% reflection (using a reflectance standard, I _0R) to obtain baseline values. Sample transmittance, reflectance, and absorbance were calculated based on measured light intensity, I _s, at the detector, depending on position of the sample in the DRA [Figs. 2a, 2b, 2c, 2d, 2e].

Fig. 2

Sample position in the DRA in order to measure transmittance, reflectance, and absorbance. Sample position for (a) 100% transmittance and (b) actual sample transmittance. Sample position for measuring (c) 100% reflectance and (d) actual sample reflectance. Sample position for (e) measuring absorbance.

When samples were mounted at the transmission and reflection ports of the integrating sphere, transmittance (T) and reflectance (R) are expressed as T = I _sT/I _0T and R = I _sR/I _0R, respectively. Light attenuation in a sample follows the Beer–Lambert law relationship and is expressed in Eq. 1. The total attenuation coefficient (μ_t) is the summation of absorption (μ_a) and scattering coefficient (μ_s), expressed in Eqs. 2, 3,

In order to determine absorption coefficients (μ_a), CNT solutions were placed in the center of the integrating sphere allowing the spectrophotometer to detect the intensity of light not absorbed by the sample [Fig. 2e]. The absorption coefficient is expressed as follows:

2.4.

Inverse Adding-Doubling Method

The IAD technique was used to calculate the absorption and reduced scattering coefficients for breast cancer phantoms with CNT inclusion. Assumptions can be made such that a soft turbid tissue behaves as an isotropic media and only diffuse transmittance and reflectance are required to measure absorption and reduced scattering coefficients.⁵⁰ According to this assumption, scattering can be expressed in terms of reduced scattering coefficient, [TeX:] $\mu^\prime _{\rm s} = \mu _{\rm s} (1 - g)$ ${\mu }_{\mathrm{s}}^{\prime }={\mu }_{\mathrm{s}}(1-g)$ , where μ_s is the scattering coefficient and g is the anisotropy factor. The IAD method determined optical properties by inverse calculation of the radiative transport equation,⁵⁰ where samples require homogenous optical properties with infinite plane parallel slabs. During computation, this method assumed a set of initial values of albedo (a ^′), optical thickness (b ^′), and sample thickness (δ),^{40, 50} which are expressed in Eqs. 5, 6. These optical properties are expressed in terms of absorption and reduced scattering coefficients in Eqs. 7, 8. Absorption (μ_a) and reduced scattering ( [TeX:] $\mu^\prime _{\rm s}$ ${\mu }_{\mathrm{s}}^{\prime }$ ) coefficients are calculated from albedo and optical thickness in Eqs. 7, 8. The IAD method calculates transmittance and reflectance based on assumed values of optical properties and compares the values of R and T with the corresponding experimentally measured parameters. If the values are not identical, then it assumes a new set of values for optical parameters. The process continues until the calculated reflectance and transmittance values are identical to the experimental values, yielding the most accurate values of optical properties,

2.5.

Optical Coherence Tomography

Optical coherence tomography (OCT) is a ballistic optical imaging technique.^{51, 52} OCT was employed in this study to measure refractive index of phantoms, according to the technique of Sorin and Grey.⁵³ Refractive index was a necessary input parameter to the IAD algorithm. When an optically transparent sample is placed in the incident beam, light is reflected from both the first incident plane (air-to-solid interface) and the second incident plane (solid-to-air interface) of the sample due to the mismatch of refractive index. The optical thickness (OPL) of the sample can be represented as the distance between two reflection peaks of two incident planes. Physical thickness (d) of a sample is represented as the difference between OPL of the sample and optical displacement of a stationary mirror before and after placing the sample in the incident beam. Refractive index is determined by the ratio between optical thickness to the physical thickness (d) of the sample (n _g = OPL/d).

2.6.

Experimental and Computational Validation

In order to validate our experimental measurement technique and IAD algorithm, we determined the optical properties of pig skin and compared our results to previously reported values by Beek ⁵⁴ Fresh pig skin was collected immediately after animal sacrifice with subsequent removal of hair and subcutaneous fat. The optical properties of five samples with a thickness of 1 mm were measured.

3.1.

Total Attenuation and Absorption Coefficients of Carbon Nanotubes in Water

The total attenuation coefficients of MWNTs, SWNTs, and SWNHs of varying concentration (0.01–0.1 mg/ml) in water for the wavelength range of 300–1300 nm are shown in Figs. 3a, 3b, 3c. Inclusion of any of the three CNTs in water caused a significant increase in attenuation across all wavelengths compared to water. The total attenuation coefficient of any of the three CNT solutions increases with higher CNT concentration. The attenuation coefficients of all three CNT types were compared at a concentration of 0.1 mg/ml, as shown in Fig. 3d. Water-containing MWNTs possess the greatest level of attenuation compared to water containing SWNTs and SWNHs. Attenuation coefficients of MWNTs in water are approximately four times higher than SWNTs and two times higher than SWNHs at a concentration of 0.1 mg/ml and wavelength of 1064 nm.

Fig. 3

Total attenuation coefficients (in millimeters⁻¹) of (a) MWNTs, (b) SWNTs, and (c) SWNHs in water for varying concentration (0.01–0.1 mg/ml), (d) attenuation coefficients of MWNTs, SWNHs, and SWNTs in water compared for a concentration of 0.1 mg/ml, absorption and attenuation coefficient of (e) MWNTs, (f) SWNTs, and (g) SWNHs for a CNT concentration of 0.1 mg/ml, and (h) total attenuation coefficient of all three types of CNTs as a function of concentration.

Total attenuation and absorption coefficients of CNTs were measured and compared for a concentration of 0.1 mg/ml in Figs. 3e, 3f, 3g. The comparisons were made to determine the contribution of CNTs to optical scattering and absorption. Total attenuation coefficients were approximately 1.03–1.08 times higher than absorption coefficients for the same range of wavelengths (300–1300 nm) for the above-mentioned CNTs. The curves representing the attenuation and absorption coefficients are nearly identical, implying the contribution of scattering to attenuation is <8%, when CNTs are evenly dispersed in media. The attenuation coefficients of CNTs in water were compared at a wavelength of 1064 nm for varying CNT concentration (0–1.0 mg/ml) and were observed to be linearly correlated with concentration [Fig. 3h], which satisfies Beer's law. Higher CNT concentration produces increased attenuation. However, the linear relationship of attenuation coefficient with MWNT concentration becomes nonlinear for concentrations of 0.5 mg/ml or greater. All results are the mean of five experimental measurements (N = 5) with an average standard deviation of ±0.03–0.08 for the wavelength range of 300–1300 nm.

3.2.

Optical Properties of Tissue Phantoms

Diffuse transmittance and reflectance of sodium alginate phantoms incorporated with polystyrene beads (3 μm diam and 1.0-mg/ml concentration) and talc perfume powder (0–40 mg/ml) were measured with a spectrophotometer. Figure 4a shows the values of diffuse transmittance and reflectance in the wavelength range of 300–1300 nm for phantoms when 1.0 mg/ml polystyrene beads and 40 mg/ml of talc perfume powder were added. The measured transmittance and reflectance were used as inputs to the IAD algorithm and permitted determination of the corresponding absorption and reduced scattering coefficients shown in Figs. 4b and 4c.

Fig. 4

(a)Transmittance and reflectance of phantoms incorporated with talc powder (1 mg/ml) and polystyrene beads (40 mg/ml) measured with a spectrophotometer and computed by IAD. (b,c) Absorption and reduced scattering coefficients of phantoms with varying concentration of polystyrene beads (0 and 1.0 mg/ml) and talc powder (0–40 mg/ml). (d) Reduced scattering coefficient as a function of talc powder concentrations. (e) Absorption and reduced scattering coefficients of sodium alginate phantoms with polystyrene beads (1 mg/ml) and talc (40 mg/ml) computed by the IAD method.

Without incorporating polystyrene beads and talc, the absorption coefficients of sodium alginate phantoms (97% water) were found to have a similar absorption spectra and peaks as water at 970 and 1200 nm [Fig. 4b]^{50, 55} and scattering was found to be negligible [Fig. 4c]. After incorporating polystyrene beads (1.0 mg/ml) in phantoms, both absorption and scattering increased. Inclusion of polystyrene beads alone caused the phantom to possess an absorption coefficient similar to breast cancer tissue; however, the reduced scattering coefficient was not sufficient to mimic actual breast cancer tissue. In order to increase the reduced scattering coefficient for the phantoms, talc powder with concentrations of 0–40 mg/ml was introduced in the phantom in combination with polystyrene beads. For all concentrations of talc, absorption coefficients were unchanged [Fig. 4b]; however, the reduced scattering coefficient increased as a function of talc concentration [Fig. 4c]. The change in scattering coefficent with varying talc concentrations is represented in Fig. 4d, where scattering is linearly related with talc concentration. The final concentration of talc (40 mg/ml) and polystyrene beads (1 mg/ml) in sodium alginate phantoms represent similar optical properties to breast cancer phantoms shown in Fig. 4e. All experiments were conducted with five experimental samples (N = 5), and all results were considered as the mean of five experimental samples with standard deviation of ± 0.02–0.08 for the wavelength range of 400–1300 nm.

Absorption and reduced scattering coefficients of breast cancer phantoms were compared to previously published human breast cancer tissue^{50, 56, 57} at 800 and 900 nm in Table 1. At a wavelength of 800 nm, absorption and reduced scattering coefficients of breast cancer phantoms (μ_a = 0.04–0.05 mm⁻¹ and [TeX:] $\mu^\prime _s $ ${\mu }_s^{\prime }$ = 1.35–1.58 mm⁻¹) were found to correspond closely with human breast cancer tissue (μ_a = 0.02–0.07 mm⁻¹ and [TeX:] $\mu^\prime _s $ ${\mu }_s^{\prime }$ = 0.7–1.4 mm⁻¹). The phantom optical properties were also found to be similar to breast tissue for a wavelength of 900 nm, where the absorption and reduced scattering coefficients of breast cancer phantom are μ_a = 0.04–0.06 mm⁻¹ and [TeX:] $\mu^\prime _s $ ${\mu }_s^{\prime }$ = 1.22–1.5 mm⁻¹ and those for human breast cancer tissue are μ_a = 0.05–0.07 mm⁻¹ and [TeX:] $\mu^\prime _s $ ${\mu }_s^{\prime }$ = 0.8–1.2 mm⁻¹.

Table 1

Optical properties of actual breast cancer tissue and breast cancer phantom.

3.3.

Model Validation

Prior to measuring optical properties of tissue representative phantoms and their CNT composites, optical properties of pig skin were determined in order to validate our experimental measurement technique and IAD algorithm. Figure 5 shows absorption and reduced scattering coefficients of pig skin computed by the IAD method for the wavelength range of 400–1300 nm. Our measured absorption and reduced scattering coefficients of pig skin correspond closely with the experimental results of Beek ⁵⁴ at wavelengths of 632.8, 790, and 850 nm, confirming the accuracy of our measurement and computational techniques.

Fig. 5

Absorption and reduced scattering coefficients of pig skin measured by our group and compared to the experimental results of Beek (Ref. 54).

3.4.

Refractive Index

The refractive indices (n) of phantoms, in combination with polystyrene beads, talc powder, and CNTs, were measured with OCT at a wavelength of 1310 nm. The values were found to vary between 1.39 and 1.41 and used as input parameters to the IAD model. Refractive index (1.37) of sodium alginate phantoms without polystyrene beads, talc, and CNTs was measured by Esteban ⁵⁸ Our measured values (refractive index) of breast cancer representative phantoms was higher than Esteban,⁵⁸ due to the presence of talc (40 mg/ml) with refractive index,⁵⁹ n = 1.586 and polystyrene beads (1 mg/ml) with refractive index,⁶⁰ n = 1.592.

3.5.

Breast Cancer Phantom–Carbon-Nanotube Composites

The diffuse transmittance and reflectance of breast cancer phantoms incorporated with MWNTs of varying concentration are shown in Figs. 6a and 6b, respectively. Both transmittance and reflectance decreased with increasing MWNT concentration due to the significant degree of absorption by MWNTs. Absorption and reduced scattering coefficients of phantoms containing MWNTs are shown in Figs. 6c and 6d. These properties were computed by IAD based on measured transmittance and reflectance shown in Figs. 6a and 6b. Absorption and reduced scattering coefficients of phantoms containing SWNTs and SWNHs were computed in a similar manner and are shown in Figs. 6e, 6f, 6g, 6h.

Fig. 6

(a) Measured transmittance and (b) reflectance of breast cancer phantoms containing MWNTs of varying concentration (0.01, 0.05, and 0.10 mg/ml) for the wavelength range of 400–1300 nm. Absorption coefficient and reduced scattering coefficient of breast cancer phantoms containing (c,d) MWNTs, (e,f) SWNTs, and (g,h) SWNHs of varying concentration determined with the IAD method for the wavelength range of 400–1300 nm.

For all types of CNTs, absorption coefficient increased with greater CNT concentration. Inclusion of MWNTs caused the absorption coefficients of phantoms (0.1 mg/ml) to increase by 21 times compared to phantoms without MWNTs [Fig. 6c] at a wavelength of 1064 nm. Absorption coefficients of phantoms containing SWNTs and SWNHs increased by five and nine times, respectively, for the same CNT concentration (0.1 mg/ml) and wavelength (1064 nm) compared to phantoms without CNTs [Figs. 6e and 6g]. Reduced scattering coefficients of phantoms with 0.1 mg/ml CNTs increased with values of 1.2–1.3 times greater compared to phantoms without CNTs [Figs. 6d, 6f, 6h]. Trends described for a wavelength of 1064 nm were observed for all wavelengths considered. These results suggest that CNTs are predominantly absorbing particles with little contribution to scattering.

The absorption coefficient of phantoms containing varying types of CNTs were compared for an equal concentration 0.1 mg/ml [Fig. 7a]. Phantoms containing MWNTs have the largest absorption coefficients. Absorption of phantoms containing MWNTs is about four times higher than phantoms containing SWNTs and approximately two times higher than phantoms containing SWNHs at the wavelength of 1064 nm. The absorption coefficient of phantoms with SWNHs is about two times higher than phantoms with SWNTs at the same wavelength. The variation in reduced scattering coefficient was at most 10% for all CNTs at the same concentration and wavelength [Fig. 7b].

Fig. 7

(a) Absorption and (b) reduced scattering coefficients of phantoms containing MWNTs, SWNTs, and SWNHs for an identical concentration of 0.1 mg/ml.

The absorption coefficients of breast cancer phantoms with CNT inclusion for a range of concentrations (0.0–0.1 mg/ml) of CNTs were found to be linearly related to concentrations (Fig. 8) at a wavelength of 1064 nm. Figure 8 can be used for determining the absorption coefficients of breast cancer tissue for CNTs of varying types and concentrations up to 0.1 mg/ml.

Fig. 8

Absorption coefficients of phantoms containing varying CNT types as a function of CNT concentration at a wavelength of 1064 nm.

4.1.

Optical Properties of Carbon Nanotubes in Water

The total attenuation coefficient was measured for three types of CNTs in water. Inclusion of all types of CNTs in water for the concentration range (0.01–0.1 mg/ml) significantly increased the light attenuation. We demonstrated that absorption and total attenuation coefficient were nearly identical, indicating the scattering effect of CNTs to be minor (<8%) over the wavelength range of 300–1300 nm [Figs. 3e, 3f, 3g]. In our experiments with liquid samples, we found the absorbance of MWNTs to be approximately four fold higher than SWNTs at a concentration of 0.1 mg/ml and wavelength of 1064 nm [Fig. 3d]. Previous literature has predicted that the absorbance of MWNTs should be superior to SWNTs, which coincides with our experimental results.^{3, 61} The absorption of MWNTs is twofold higher than SWNHs and SWNHs possess approximately twofold higher absorption than SWNTs at the same concentration in water with identical wavelength.

The linear relationship of attenuation coefficient with CNT concentration in water [Fig. 3h] satisfies Beer's law,⁵⁰ which will enable determination of unknown attenuation or absorption coefficient at concentrations up to 0.1 mg/ml at a wavelength of 1064 nm. The linear relationship of attenuation and absorption coefficients is similar to the absorbance study of Kam,⁸ where absorbance of noncovalently functionalized SWNTs in water had a linear relationship with SWNT concentration. However, for MWNTs at a concentration of 0.5 mg/ml or greater, the absorption curve became nonlinear, no longer complying with Beer's law. At and beyond this concentration, the sample sufficiently diminishes light transmission, preventing measurement and prohibiting use of this relation for concentration or absorption coefficient determination.

4.2.

Breast Cancer Phantom with Carbon Nanotubes

Prior to determining the optical properties of phantoms, we confirmed the accuracy of our technique by comparing the absorption and reduced scattering coefficients of pig skin determined by our method with the well-known results of Beek ⁵⁴ (Fig. 5). Because tissue is composed of nearly 70% water, its absorption coefficient is similar, but slightly higher than water due to the presence of hemoglobin and protein.⁵⁰ The absorption profile of all types of phantoms exhibited relative maxima at 970 and 1200 nm, which are the characteristics of well-known water absorption peaks.² However, the light-scattering properties vary significantly for different types of tissue due to variation of collagen fibers and blood vessels.^{62, 63} Sodium alginate, which formed the basis for the breast tumor phantom structure, is highly transparent with optical properties similar to water. Therefore, in order to mimic breast cancer tissue, we incorporated varying concentrations of highly light-scattering particles, including polystyrene beads and talc perfume powder in the sodium alginate to increase the scattering coefficient to more effectively match the actual breast tumor scattering properties [Fig. 4c]. The final composition of the breast tumor phantom utilized 1 mg/ml polystyrene beads (3 μm diam) and 40 mg/ml talc powder in alginate, providing a tissue-representative phantom with absorption and reduced scattering coefficients very close to actual breast cancer tumors^{47, 50} at wavelengths of 800 and 900 nm, as shown in Fig. 4e and Table 1.

Inclusion of CNTs in breast cancer phantoms caused the absorption to increase significantly. Absorption coefficients of MWNTs, SWNHs, and SWNTs in phantoms were increased by 21-fold, 9-fold, and 5-fold compared to phantoms without CNTs, respectively [Figs. 6c, 6e, 6g] for an identical concentration of 0.1 mg/ml and wavelength of 1064 nm. For the same concentration and wavelength, the change in reduced scattering coefficient is relatively minor with a 1.2- to 1.3-fold increase compared to phantoms without CNTs [Figure 6d, 6f, 6h].

4.3.

Comparison of Multiwalled Carbon Nanotubes, Single-Walled Carbon Nanotubes, and Single-Walled Carbon Nanohorns

Phantoms containing MWNTs possess the highest absorption coefficient. MWNTs absorb light approximately four times greater than SWNTs and 2 times greater than SWNHs for a CNT concentration of 0.1 mg/ml in phantoms at the wavelength of 1064 nm [Fig. 7a]. A similar phenomenon was observed for CNTs in water, where MWNTs possessed approximately four and two times higher absorption than SWNTs and SWNHs, respectively, at a concentration of 0.1 mg/ml [Fig. 3d]. Previous literature predicted that MWNTs may possess superior light-absorbing capacity compared to SWNTs,^{3, 61, 64} which was confirmed by our study. CNTs in water and phantoms exhibit similar, but not identical absorption and scattering coefficients, which may be due to the absorption by beads and talc powder in phantoms and difference of interfacial contact for CNTs with solids and liquids.

Variation in scattering effects among different types of CNTs is <1% for an identical concentration confirming inclusion of various types of CNTs has minimal effect on the scattering properties of a media. The measured optical properties of breast cancer representative phantoms with inclusion of CNTs provide an estimate of the effects CNTs may have on the overall optical properties of real tumor tissue. Similar to CNTs in water [Fig. 3h], the absorption coefficient of solid breast cancer phantoms containing CNTs increase linearly with rising CNT concentrations (Fig. 8).