Abstract

Despite much research efforts being devoted to the design optimization of metallic nanoshells, no account is taken of the fact that the number of the nanoshells that can be delivered to a given cancerous site vary with their size. In this paper, we study the effect of the nanoshell number density on the absorption and scattering properties of a gold-nanoshell ensemble exposed to a broadband near-infrared radiation, and optimize the nanoshells’ dimensions for efficient cancer treatment by analyzing a wide range of human tissues. We first consider the general situation in which the number of the delivered nanoshells decreases with their mean radius R as ∝ Rβ, and demonstrate that the optimal design of nanoshells required to treat cancer most efficiently depends critically on β. In the case of β = 2, the maximal energy absorbed (scattered) by the ensemble is achieved for the same dimensions that maximize the absorption (scattering) efficiency of a single nanoshell. We thoroughly study this special case by the example of gold nanoshells with silica core. To ensure that minimal thermal injury is caused to the healthy tissue surrounding a cancerous site, we estimate the optimal dimensions that minimize scattering by the nanoshells for a desired value of the absorption efficiency. The comparison of gold nanoshells with different cores shows that hollow nanoshells exhibiting relatively low absorption efficiency are less harmful to the healthy tissue and, hence, are preferred over the strongly absorbing nanoshells. For each of the cases analyzed, we provide approximate analytical expressions for the optimal nanoshell dimensions, which may be used as design guidelines by experimentalists, in order to optimize the synthesis of gold nanoshells for treating different types of human cancer at their various growth stages.

© 2012 OSA

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2012 (6)

V. P. Pattani and J. W. Tunnell, “Nanoparticle-mediated photothermal therapy: A comparative study of heating for different particle types,” Lasers Surg. Med.44, 675–684 (2012).
[CrossRef] [PubMed]

P. Puvanakrishnan, J. Park, D. Chatterjee, S. Krishnan, and J. W. Tunnell, “In vivo tumor targeting of gold nanoparticles: Effect of particle type and dosing strategy,” Int. J. Nanomed.7, 1251–1258 (2012).
[CrossRef]

S. Kessentini and D. Barchiesi, “Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy,” Biomed. Opt. Express3, 590–604 (2012).
[CrossRef] [PubMed]

M. L. Marasinghe, M. Premaratne, D. M. Paganin, and M. A. Alonso, “Coherence vortices in Mie scattered nonparaxial partially coherent beams,” Opt. Express20, 2858–2875 (2012).
[CrossRef] [PubMed]

R. Fiolka, K. Si, and M. Cui, “Complex wavefront corrections for deep tissue focusing using low coherence backscattered light,” Opt. Express20, 16532–16543 (2012).
[CrossRef]

H. Trabelsi, M. Gantri, T. Sghaier, and E. Sediki, “Computational study of a possible improvement of cancer detection by diffuse optical tomography,” Adv. Stud. Biol.4, 195–206 (2012).

2011 (8)

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Complex-ω approach versus complex-k approach in description of gain-assisted surface plasmon-polariton propagation along linear chains of metallic nanospheres,” Phys. Rev. B83, 115451 (2011).
[CrossRef]

I. B. Udagedara, I. D. Rukhlenko, and M. Premaratne, “Surface plasmon-polariton propagation in piecewise linear chains of composite nanospheres: The role of optical gain and chain layout,” Opt. Express19, 19973–19986 (2011).
[CrossRef] [PubMed]

S. N. Il’chenko, Y. O. Kostin, I. A. Kukushkin, M. A. Ladugin, P. I. Lapin, A. A. Lobintsov, A. A. Marmalyuk, and S. D. Yakubovich, “Broadband superluminescent diodes and semiconductor optical amplifiers for the spectral range 750–800 nm,” Quantum Electron.41, 677–680 (2011).
[CrossRef]

T. Grosges, D. Barchiesi, S. Kessentini, G. Grehan, and M. L. de la Chapelle, “Nanoshells for photothermal therapy: A Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express2, 1584–1596 (2011).
[CrossRef] [PubMed]

J. F. Lovell, C. S. Jin, E. Huynh, H. Jin, C. Kim, J. L. Rubinstein, W. C. W. Chan, W. Cao, L. V. Wang, and G. Zheng, “Porphysome nanovesicles generated by porphyrin bilayers for use as multimodal biophotonic contrast agents,” Nat. Mater.10, 324–332 (2011).
[CrossRef] [PubMed]

S. J. Tan, M. J. Campolongo, D. Luo, and W. Cheng, “Building plasmonic nanostructures with DNA,” Nat. Nanotechnol.6, 268–276 (2011).
[CrossRef] [PubMed]

X. Zheng and F. Zhou, “Noncovalent functionalization of single-walled carbon nanotubes by indocyanine green: Potential nanocomplexes for photothermal therapy,” J. X-Ray Sci. Tech.19, 275–284 (2011).

L. C. Kennedy, L. R. Bickford, N. A. Lewinski, A. J. Coughlin, Y. Hu, E. S. Day, J. L. West, and R. A. Drezek, “A new era for cancer treatment: Gold-nanoparticle-mediated thermal therapies,” Small7, 169–183 (2011).
[CrossRef] [PubMed]

2010 (5)

J. Chen, C. Glaus, R. Laforest, Q. Zhang, M. Yang, M. Gidding, M. J. Welch, and Y. Xia, “Gold nanocages as photothermal transducers for cancer treatment,” Small6, 811–817 (2010).
[CrossRef] [PubMed]

S. Y. Liu, Z. S. Liang, F. Gao, S. F. Luo, and G. Q. Lu, “In vitro photothermal study of gold nanoshells functionalized with small targeting peptides to liver cancer cells,” J. Mater. Sci. Mater. Med.21, 665–674 (2010).
[CrossRef]

J. Z. Zhang, “Biomedical applications of shape-controlled plasmonic nanostructures: A case study of hollow gold nanospheres for photothermal ablation therapy of cancer,” J. Phys. Chem. Lett.1, 686–695 (2010).
[CrossRef]

X. Huang and M. A. El-Sayed, “Gold nanoparticles: Optical properties and implementations in cancer diagnosis and photothermal therapy,” J. Adv. Res.1, 13–28 (2010).
[CrossRef]

M. L. Marasinghe, M. Premaratne, and D. M. Paganin, “Coherence vortices in Mie scattering of statistically stationary partially coherent fields,” Opt. Express18, 6628–6641 (2010).
[CrossRef] [PubMed]

2009 (5)

C. E. Dimas, C. L. Tan, H. S. Djie, and B. S. Ooi, “Coherence length characteristics from broadband semiconductor emitters: superluminescent diodes versus broadband laser diodes,” Proc. SPIE7230, 72300B (2009).
[CrossRef]

F. Y. Cheng, C. T. Chen, and C. S. Yeh, “Comparative efficiencies of photothermal destruction of malignant cells using antibody-coated silica@Au nanoshells, hollow Au/Ag nanospheres and Au nanorods,” Nanotechnol.20, 425104 (2009).
[CrossRef]

J. Park, A. Estrada, J. A. Schwartz, P. Diagaradjane, S. Krishnan, C. Coleman, J. D. Payne, A. K. Dunn, and J. W. Tunnell, “Two-photon-induced photoluminescence imaging of gold nanoshell’s tumor biodistribution,” Proc. SPIE7192, 71920T (2009).
[CrossRef]

P. Cimalla, J. Walther, M. Mehner, M. Cuevas, and E. Koch, “Simultaneous dual-band optical coherence tomography in the spectral domain for high resolution in vivo imaging,” Opt. Express17, 19486–19500 (2009).
[CrossRef] [PubMed]

G. Wu, A. Mikhailovsky, H. A. Khant, and J. A. Zasadzinski, “Synthesis, characterization, and optical response of gold nanoshells used to trigger release from liposomes,” Methods Enzymol.464, 279–307 (2009).
[CrossRef] [PubMed]

2008 (8)

C. Liu, C. C. Mi, and B. Q. Li, “Energy absorption of gold nanoshells in hyperthermia therapy,” IEEE Trans. Nanobiosci.7, 206–214 (2008).
[CrossRef]

C. C. Handapangoda, M. Premaratne, D. M. Paganin, and P. R. D. S. Hendahewa, “Technique for handling wave propagation specific effects in biological tissue: mapping of the photon transport equation to Maxwell’s equations,” Opt. Express16, 17792–17807 (2008).
[CrossRef] [PubMed]

O. Pena, U. Pal, L. Rodriguez-Fernandez, and A. Crespo-Sosa, “Linear optical response of metallic nanoshells in different dielectric media,” J. Opt. Soc. Am. B25, 1371–1379 (2008).
[CrossRef]

R. J. Bernardi, A. R. Lowery, P. A. Thompson, S. M. Blaney, and J. L. West, “Immunonanoshells for targeted photothermal ablation in medulloblastoma and glioma: an in vitro evaluation using human cell lines,” J. Neurooncol.86, 165–172 (2008).
[CrossRef]

A. M. Gobin, J. J. Moon, and J. L. West, “EphrinAl-targeted nanoshells for photothermal ablation of prostate cancer cells,” Int. J. Nanomed.3, 351–358 (2008).

S. Lal, S. E. Clare, and N. J. Halas, “Nanoshell-enabled photothermal cancer therapy: Impending clinical impact,” Acc. Chem. Res.41, 1842–1851 (2008).
[CrossRef] [PubMed]

M. P. Melancon, W. Lu, Z. Yang, R. Zhang, Z. Cheng, A. M. Elliot, J. Stafford, T. Olson, J. Z. Zhang, and C. Li, “In vitro and in vivo targeting of hollow gold nanoshells directed at epidermal growth factor receptor for photothermal ablation therapy,” Mol. Cancer Ther.7, 1730–1739 (2008).
[CrossRef] [PubMed]

X. Huang, P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Plasmonic photothermal therapy (PPTT) using gold nanoparticles,” Lasers Med. Sci.23, 217–228 (2008).
[CrossRef]

2007 (1)

J. M. Stern, J. Stanfield, Y. Lotan, S. Park, J. T. Hsieh, and J. A. Cadeddu, “Efficacy of laser-activated gold nanoshells in ablating prostate cancer cells in vitro,” J. Endourol.21, 939–943 (2007).
[CrossRef] [PubMed]

2006 (4)

A. R. Lowery, A. M. Gobin, E. S. Day, N. J. Halas, and J. L. West, “Immunonanoshells for targeted photothermal ablation of tumor cells,” Int. J. Nanomed.1, 149–154 (2006).
[CrossRef]

P. K. Jain, K. S. Lee, I. H. El-Sayed, and M. A. El-Sayed, “Calculated absorption and scattering properties of gold nanoparticles of different size, shape, and composition: Applications in biological imaging and biomedicine,” J. Phys. Chem. B110, 7238–7248 (2006).
[CrossRef] [PubMed]

A. M. Schwartzberg, T. Y. Olson, C. E. Talley, and J. Z. Zhang, “Synthesis, characterization, and tunable optical properties of hollow gold nanospheres,” J. Phys. Chem. B110, 19935–19944 (2006).
[CrossRef] [PubMed]

J. Li, G. Sun, and C. T. Chan, “Optical properties of photonic crystals composed of metal-coated spheres,” Phys. Rev. B73, 075117 (2006).
[CrossRef]

2005 (3)

V. V. Tuchin, “Optical clearing of tissues and blood using the immersion method,” J. Phys. D: Appl. Phys.38, 2497–2518 (2005).
[CrossRef]

M. Premaratne, E. Premaratne, and A. Lowery, “The photon transport equation for turbid biological media with spatially varying isotropic refractive index,” Opt. Express13, 389–399 (2005).
[CrossRef] [PubMed]

A. N. Rubinov and A. A. Afanas’ev, “Nonresonance mechanisms of biological effects of coherent and incoherent light,” Opt. Spectrosc.98, 943–948 (2005).
[CrossRef]

2004 (2)

C. Loo, A. Lin, L. Hirsch, M. H. Lee, J. Barton, N. Halas, J. West, and R. Drezek, “Nanoshell-enabled photonics-based imaging and therapy of cancer,” Technol. Cancer Res. Treat.3, 33–40 (2004).
[PubMed]

D. D. Evanoff and G. Chumanov, “Size-controlled synthesis of nanoparticles. 2. Measurement of extinction, scattering, and absorption cross sections,” J. Phys. Chem. B108, 13957–13962 (2004).
[CrossRef]

2003 (2)

E. Prodan, C. Radloff, N. J. Halas, and P. Nordlander, “A hybridization model for the plasmon response of complex nanostructures,” Science302, 419–422 (2003).
[CrossRef] [PubMed]

L. R. Hirsch, R. J. Stafford, J. A. Bankson, S. R. Sershen, B. Rivera, R. E. Price, J. D. Hazle, N. J. Halas, and J. L. West, “Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance,” Proc. Natl. Acad. Sci. U.S.A.100, 13549–13554 (2003).
[CrossRef] [PubMed]

2001 (2)

V. U. Fiedler, H. J. Schwarzmaier, F. Eickmeyer, F. P. Muller, C. Schoepp, and P. R. Verreet, “Laser-induced interstitial thermotherapy of liver metastases in an interventional 0.5 Tesla MRI system: Technique and first clinical experiences,” J. Magn. Reson. Imaging13, 729–737 (2001).
[CrossRef] [PubMed]

B. Choi and A. J. Welch, “Analysis of thermal relaxation during laser irradiation of tissue,” Lasers Surg. Med.29, 351–359 (2001).
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1999 (3)

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C. Loo, A. Lin, L. Hirsch, M. H. Lee, J. Barton, N. Halas, J. West, and R. Drezek, “Nanoshell-enabled photonics-based imaging and therapy of cancer,” Technol. Cancer Res. Treat.3, 33–40 (2004).
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S. Lal, S. E. Clare, and N. J. Halas, “Nanoshell-enabled photothermal cancer therapy: Impending clinical impact,” Acc. Chem. Res.41, 1842–1851 (2008).
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L. C. Kennedy, L. R. Bickford, N. A. Lewinski, A. J. Coughlin, Y. Hu, E. S. Day, J. L. West, and R. A. Drezek, “A new era for cancer treatment: Gold-nanoparticle-mediated thermal therapies,” Small7, 169–183 (2011).
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X. Huang and M. A. El-Sayed, “Gold nanoparticles: Optical properties and implementations in cancer diagnosis and photothermal therapy,” J. Adv. Res.1, 13–28 (2010).
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[CrossRef]

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X. Huang, P. K. Jain, I. H. El-Sayed, and M. A. El-Sayed, “Plasmonic photothermal therapy (PPTT) using gold nanoparticles,” Lasers Med. Sci.23, 217–228 (2008).
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P. Puvanakrishnan, J. Park, D. Chatterjee, S. Krishnan, and J. W. Tunnell, “In vivo tumor targeting of gold nanoparticles: Effect of particle type and dosing strategy,” Int. J. Nanomed.7, 1251–1258 (2012).
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Figures (5)

Fig. 1
Fig. 1

Normalized average powers absorbed (left panels) and scattered (right panels) by three Si@Au nanoshell ensembles. The total number N of the nanoshells in the ensembles vary as N ( R 2 ) R 2 β, where β = 1 in (a) and (b), β = 2 in (c) and (d), and β = 3 in (e) and (f). In all cases, nanoshells were assumed to be embedded in cancerous tissue with n0 = 1.44; the refractive index of silica was taken from Ref. [49].

Fig. 2
Fig. 2

Average [(a) and (b)] absorption and (c) scattering efficiencies of gold nanoshells with silica core [(b) is the magnified part of (a)]; the nanoshells were assumed to be surrounded by cancerous tissue with n0 = 1.44. Solid line (of slope 1.17) and dashed curve show the optimal nanoshell dimensions predicted with the quasistatic approximation using Eqs. (11) and (13), respectively. (d) Ratio of average absorption efficiency to average scattering efficiency in logarithmic scale. Density index β = 2 in all cases.

Fig. 3
Fig. 3

Variation of (a) minimal Ssca, (b) maximal Sabs/Ssca, (c) optimal R1, and (d) optimal R2 with refractive index of cancerous tissue for different absorption thresholds S abs ( th ) of SiO2@Au nanoshell. The exact values are shown by filled circles, which are joined together by lines serving as guides for eyes.

Fig. 4
Fig. 4

Average absorption (left panels) and scattering (right panels) efficiencies of [(a) and (b)] Si@Au nanoshells, [(c) and (d)] SiO2@Au nanoshells, and [(e) and (f)] hollow gold nanoshells. The nanoshells were assumed to be embedded in cancerous tissue with n0 = 1.35; the refractive index of silicon was taken from Ref. [61].

Fig. 5
Fig. 5

Same as in Fig. 3 for hollow gold nanoshells. The exact values shown by filled circles are joined together by lines serving as guides for eyes.

Tables (1)

Tables Icon

Table 1 Optimal dimensions of gold nanoshells for three types of cancerous tissues and two types of core material. The values of ratio Sabs/Ssca are rounded up to one decimal point. For more detail, see Fig. 5.

Equations (23)

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Q abs ( R 1 , R 2 , λ ) = 1 2 ( λ π n 0 R 2 ) 2 n = 1 ( 2 n + 1 ) [ Re ( a n + b n ) | a n | 2 | b n | 2 ] ,
Q sca ( R 1 , R 2 , λ ) = 1 2 ( λ π n 0 R 2 ) 2 n = 1 ( 2 n + 1 ) ( | a n | 2 + | b n | 2 ) ,
S abs ( R 1 , R 2 ) = 0 Q abs ( R 1 , R 2 , λ ) f ( λ ) d λ ,
S sca ( R 1 , R 2 ) = 0 Q sca ( R 1 , R 2 , λ ) f ( λ ) d λ .
0 f ( λ ) d λ = 1 ,
P abs N ( R ¯ 1 , R ¯ 2 ) = 0 0 P abs ( R 1 , R 2 , λ ) g ( R 1 , R 2 , R ¯ 1 , R ¯ 2 ) d R 1 d R 2 ,
P sca N ( R ¯ 1 , R ¯ 2 ) = 0 0 P sca ( R 1 , R 2 , λ ) g ( R 1 , R 2 , R ¯ 1 , R ¯ 2 ) d R 1 d R 2 ,
0 0 g ( R 1 , R 2 , R ¯ 1 , R ¯ 2 ) d R 1 d R 2 = N ( R ¯ 1 , R ¯ 2 ) .
ε 2 ( R 1 , R 2 , ω ) = ε 2 ( ω ) + ω p 2 ω 2 + i ω γ ω p 2 ω 2 + i ω Γ ( R 1 , R 2 ) ,
f ( λ ) = H ( λ λ 1 ) H ( λ λ 2 ) λ 2 λ 1 ,
g ( R 1 , R 2 , R ¯ 1 , R ¯ 2 ) = A R ¯ 2 β δ ( R 1 R ¯ 1 ) δ ( R 2 R ¯ 2 ) ,
P abs N ( R ¯ 1 , R ¯ 2 ) = π A I 0 R ¯ 2 2 β S abs ( R ¯ 1 , R ¯ 2 ) , P sca N ( R ¯ 1 , R ¯ 2 ) = π A I 0 R ¯ 2 2 β S sca ( R ¯ 1 , R ¯ 2 ) .
β = ln ( ρ ( a ) / ρ ( b ) ) ln ( R ¯ 2 ( b ) / R ¯ 2 ( a ) ) .
g ( R 2 , h , μ R 2 , σ R 2 , μ h , σ h ) = N 2 π R 2 h σ R 2 σ h exp ( ( ln R 2 μ R 2 ) 2 2 σ R 2 2 ( ln h μ h ) 2 2 σ h 2 ) ,
α = ε 2 ε a ε 3 ε b ε 2 ε a + 2 ε 3 ε b R 2 3 ,
x 3 = 1 + 3 ε 2 ( ε 3 + ε 1 / 2 ) ( ε 2 ) 2 ( ε 2 ) 2 ε 2 ( ε 1 + ε 3 ) + ε 1 ε 3 .
α ^ = α 1 α k 3 2 / R 2 ( 2 i / 3 ) α k 3 3 ,
R 1 opt 35 n 0 2 149 n 0 + 185 ,
R 2 opt 40 n 0 2 165 n 0 + 208 .
R 1 opt { 19 n 0 2 81 n 0 + 96 for S abs ( th ) = 1 , 14 n 0 2 79 n 0 + 110 for S abs ( th ) = 1.5 , 36 n 0 2 144 n 0 + 162 for S abs ( th ) = 2 ,
R 2 opt R 1 opt + { 5 for S abs ( th ) = 1 , 6 for S abs ( th ) = 1.5 , 7 for S abs ( th ) = 2 ,
R 1 opt { 19 n 0 2 75 n 0 + 87 for S abs ( th ) = 1 , 19 n 0 2 81 n 0 + 101 for S abs ( th ) = 1.5 , 29 n 0 2 116 n 0 + 136 for S abs ( th ) = 2 ,
R 2 opt R 1 opt + { 4 for S abs ( th ) = 1 , 5 for S abs ( th ) = 1.5 , 6 for S abs ( th ) = 2 ,

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