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Biomedical Optics Express

Biomedical Optics Express

  • Editor: Joseph A. Izatt
  • Vol. 3, Iss. 3 — Mar. 1, 2012
  • pp: 590–604
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Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy

Sameh Kessentini and Dominique Barchiesi  »View Author Affiliations


Biomedical Optics Express, Vol. 3, Issue 3, pp. 590-604 (2012)
http://dx.doi.org/10.1364/BOE.3.000590


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Abstract

The purpose of this study is to get more efficient gold nanoparticles, for necrosis of cancer cells, in photothermal therapy. Therefore a numerical maximization of the absorption efficiency of a set of nanoparticles (nanorod, nanoshell and hollow nanosphere) is proposed, assuming that all the absorbed light is converted to heat. Two therapeutic cases (shallow and deep cancer) are considered. The numerical tools used in this study are the full Mie theory, the discrete dipole approximation and the particle swarm optimization. The optimization leads to an improved efficiency of the nanoparticles compared with previous studies. For the shallow cancer therapy, the hollow nanosphere seems to be more efficient than the other nanoparticles, whereas the hollow nanosphere and nanorod, offer comparable absorption efficiencies, for deep cancer therapy. Finally, a study of tolerance for the size parameters to guarantee an absorption efficiency threshold is included.

© 2012 OSA

1. Introduction

Photothermal therapy (PTT) is based on the interaction of a suitable light source with gold nanoparticles embedded in cells, which produces a sufficient elevation of temperature to induce their necrosis. The predominating benefits of such treatment are both safety and efficiency as PTT limits the possible damage of healthy cells (unlike microwave ablation, magnetic thermal ablation, and focused ultrasound therapy) [1

1. C. Liu, C. C. Mi, and B. Q. Li, “Energy absorption of gold nanoshells in hyperthermia therapy,” IEEE Trans. Nanobiosci. 7(3), 206–214 (2008). [CrossRef]

]. Moreover, the gold nanoparticles, which are biocompatible and nontoxic, can be easily conjugated to antibodies. Hence, once injected into the body, they get fixed on the cancer cells as represented in Fig. 1(a). Then under suitable illumination they absorb a large amount of light (Fig. 1(b)). Almost all the absorbed light is converted to heat via a series of nonradiative processes [2

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

]. Therefore the cancer cells containing gold nanoparticles receive sufficient heat to induce their necrosis [3

3. V. K. Pustovalov, A. S. Smetannikov, and V. P. Zharov, “Photothermal and accompanied phenomena of selective nanophotothermolysis with gold nanoparticles and laser pulses,” Laser Phys. Lett. 5(11), 775–792 (2008). [CrossRef]

] with minimal damage to their surrounding (localized heat delivery).

Fig. 1 Photothermal therapy using gold nanoparticles.

The choice of the illumination conditions is dictated by the therapeutic application. Two optical windows exist in tissue, as it is mainly transparent within these regions of wavelengths. The main one lies between 600 and 1300 nanometers (nm) and a second one from 1600 to 1850 nm [4

4. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).

]. In these windows, the gold nanoparticles absorb the light millions of times more than the organic molecules [1

1. C. Liu, C. C. Mi, and B. Q. Li, “Energy absorption of gold nanoshells in hyperthermia therapy,” IEEE Trans. Nanobiosci. 7(3), 206–214 (2008). [CrossRef]

]. PTT in the visible region is suitable for shallow cancer (e.g. skin cancer). Whereas for in vivo therapy of tumors deeply seated under skin, Near Infra Red (NIR) light is required because of its deep penetration. In fact, the hemoglobin and water molecules in tissue have minimal absorption and a limited attenuation of scattering in this spectral region. Both the visible (VIS) and NIR regions are therefore investigated (the wavelengths of 633 nm and 800 nm are considered).

The purpose of this study is to compare the efficiencies of nanoparticles for photothermal therapy. Their therapeutic efficiency depends not only on their shape but also on their size. The shape of the gold nanoparticles, commonly used for PTT, are spheres, shells (with silica core), hollow spheres and rods.

In 2003, Hirsch et al. [5

5. 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]

] demonstrated the NIR PTT, both in vitro and in vivo, using gold nanoshells. While in the visible range, nanospheres are of interest only for skin cancer [2

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

]. The advantages of spherical shape were demonstrated. In fact, the non spherical nanostructures can exhibit a broad spectrum absorption. A plasmon tunability and a narrow absorption band are preferred to get a better coupling with the illumination [6

6. A. M. Schwartzberg and J. Z. Zhang, “Novel optical properties and emerging applications of metal nanostructures,” J. Phys. Chem. C 112, 10323–10337 (2008). [CrossRef]

]. Hollow nanospheres and nanoshells can guarantee such tunable behavior at different wavelengths ranging from VIS to NIR, by adjusting their size parameters [7

7. 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. B 110,, 19935–19944 (2006). [CrossRef] [PubMed]

]. Nevertheless, hollow nanospheres are synthesized with great precision and controlled dimensions [7

7. 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. B 110,, 19935–19944 (2006). [CrossRef] [PubMed]

] whereas, forming a uniform shell on the silica core remains challenging [2

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

].

Consequently the target is to maximize the absorption efficiency for nanoshell, hollow nanosphere and nanorod in two therapeutic cases: the treatment of shallow cancer under VIS irradiation and of deep cancer under NIR irradiation. For this, numerical methods are required to compute the absorption efficiency Qabs for different shapes. To compute Qabs, we use the Mie theory for nanoshells and hollow nanospheres [14

14. C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, New York, 1998). [CrossRef]

], and the discrete dipole approximation (DDA) for nanorods. Moreover, an optimization algorithm must be used to maximize it. A specific particle swarm optimization (PSO) algorithm is chosen, based on the results of the comparison between different methods of optimization for plasmonic applications [15

15. S. Kessentini, D. Barchiesi, T. Grosges, and M. L. de la Chapelle, “Particle swarm optimization and evolutionary methods for plasmonic biomedical applications,” in IEEE Congress on Evolutionary Computation (CEC 2011) (IEEE, 2011), pp. 2315–2320.

].

The paper is organized as follows: in the second section, the numerical methods used to compute the absorption efficiency and the optimization algorithm are described. In the third section, the different therapeutical cases and the assumptions for simulations are presented, before carrying comparisons and computing the tolerance for the geometrical parameters of the nanoparticles. Finally, concluding remarks are given in the fourth section.

2. Numerical and optimization tools

In this section brief overviews of the numerical methods used to compute the absorption efficiency Qabs and the optimization algorithm are presented. The numerical methods used to compute Qabs are the full Mie theory for nanoshells and hollow nanospheres (as they present spherical symmetry) and the discrete dipole approximation (DDA) for nanorods. Then, Qabs can be maximized using an adequate optimization algorithm [15

15. S. Kessentini, D. Barchiesi, T. Grosges, and M. L. de la Chapelle, “Particle swarm optimization and evolutionary methods for plasmonic biomedical applications,” in IEEE Congress on Evolutionary Computation (CEC 2011) (IEEE, 2011), pp. 2315–2320.

] which is the adaptive particle swarm optimization (APSO).

2.1. Absorption efficiency for spherical nanoparticle

Fig. 2 Spherical nanoparticle: nanoshell or hollow nanosphere (inner radius r1, outer radius r2 and shell thickness e = r2r1)

2.2. The discrete dipole approximation (DDA)

When the analytical solution of Maxwell’s equations is unknown, it is necessary to use numerical methods. Several numerical methods were introduced such as the DDA, the method of moments, the finite difference time domain method and the finite element method. Each of these methods presents some advantages and drawbacks. However the DDA is widely used for absorption and scattering calculations by nanoparticles used in PTT, the computing time (main drawback of DDA) remaining short for small size targets. Moreover, the accuracy of the method was checked by comparison to analytical solutions for spherical nanoparticle [16

16. K. S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption of gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive,” J. Phys. Chem. B 109, 20331–20338 (2005). [CrossRef]

], ellipsoid [16

16. K. S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption of gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive,” J. Phys. Chem. B 109, 20331–20338 (2005). [CrossRef]

] and infinite cylinder [17

17. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for periodic targets: theory and tests,” J. Opt. Soc. Am. A 25, 2693–2703 (2008). [CrossRef]

]. Therefore we use the DDA in this study, for non-spherical particles. In what follows, a brief description of this method and of the numerical tool are given.

The method was firstly developed by Devoe [18

18. H. Devoe, “Optical properties of molecular aggregates. I. classical model of electronic absorption and refraction,” J. Chem. Phys. 41, 393–400 (1964). [CrossRef]

, 19

19. H. Devoe, “Optical properties of molecular aggregates. II. classical theory of the refraction, absorption, and optical activity of solutions and crystals,” J. Chem. Phys. 43, 3199–3208 (1965). [CrossRef]

], and Purcell and Pennypacker [20

20. E. Purcell and C. R. Pennypacker, “Scattering and absorption of light by nonspherical dielectric grains,” Astr. J. 186, 705 (1973). [CrossRef]

]. The main idea is to discretize the geometry of the naoparticle into a set of N elements (j = 1..N) with polarizabilities αj, located at rj. Each dipole has a polarization Pj = αjEj, where Ej is the electric field at rj induced by the incident wave and the sum of the dielectric fields induced by interaction with other dipoles. A system of 3N complex linear equations (see [21

21. B. T. Draine and P. J. Flatau, “Discrete-dipole approximation for scattering calculations,” J. Opt. Soc. Am. A 11, 1491–1499 (1994). [CrossRef]

] for details) must be solved to find polarizations Pj and evaluate the absorption cross section following:
Cabs=4πk|E0|2j=1N{Im[Pj(αj1)*Pj*]23k3|Pj|2}.
(2)

The Fortran code DDSCAT 7.1, developed by Draine and Flatau, is used for calculating scattering and absorption of light by irregular particles based on the DDA [22

22. B. T. Draine and P. J. Flatau, “User guide to the discrete dipole approximation code DDSCAT 7.1,” (2010), http://arXiv.org/abs/1002.1505v1.

]. DDSCAT enables to deal with many shapes such as cylinder, ellipsoid or cylinder with capped ends. It also offers the possibility of editing new shapes. We edit some shapes to ensure flexible orientation of the nanoparticle relative to the incident polarization of light. Then the inter-dipole distance should be chosen. For this, the DDA results are compared to those of Mie theory for a sphere of radius 40 nm. The results are reported in Fig. 3 and show that an inter-dipole distance d equal to 1 nm is sufficient to achieve reasonable accuracy in this size range.

Fig. 3 Comparison of DDA with Mie theory for different values of the inter-dipole distance d for a sphere of radius 40 nm.

2.3. The optimization algorithm: the adaptive PSO

3. Assumptions, results and discussion

3.1. Assumptions and therapeutic cases

Fig. 4 Different shapes for modeling nanorods.

The diffusion and the depolarization of light in tissue can be another important issue, mainly for medical diagnosis [35

35. V. V. Tuchin, Tissue optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE, Bellingham, Washington, 2007).

]. This parameter would be critical if the power of the incoming light should be determined. However, the computed Qabs is relative to a unity incoming field, which is supposed to be the reference in the vicinity of the nanoparticle embedded in the cells. Therefore the optimization of sizes and shapes does not depend on the depolarization of light. For instance, the nanorods are more sensitive to longitudinal polarization and the contributions of the other polarization would increase Qabs only slightly (Tab. 1).

Table 1. Optimized shape parameters (Figs. 2 and 4) of gold nanoparticles in the two therapeutic cases: case 1, the nanoparticles are embedded in skin dermis, using 633 nm illumination wavelength; case 2, the nanoparticles are embedded in subcutaneous fat, using 800 nm illumination wavelength.

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Finally, regarding the therapeutic cases, we choose to consider the two followings cases:
  • case 1: treatment of shallow cancer assuming the skin dermis as surrounding tissue (refractive index 1.55 [4

    4. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).

    ]) under illumination λ = 633 nm (VIS)
  • case 2: treatment of deep cancer assuming subcutaneous fat as surrounding tissue (refractive index 1.44 [4

    4. F. A. Duck, Physical Properties of Tissue: A Comprehensive Reference Book (Academic, London, 1990).

    ]) under illumination λ = 800 nm (NIR)

3.2. Results and discussion

Optimized results

The optimal size parameters, that ensure the maximum absorption efficiency Qabs, are reported in Tab. 1. For optimized nanoshell and hollow nanosphere under linear polarization, and nanorod under circular polarization, the extinction, absorption and scattering efficiency spectra are displayed in Fig.5. As expected, they present maxima for the illumination used for the corresponding therapeutic case.

Nanoshell v.s. hollow nanosphere

For both the therapeutic cases, the optimized hollow nanospheres are slightly smaller than the optimized nanoshells (silica core coated with gold) and exhibit higher absorption efficiency (Tab. 1). The improvement is by 11% in the first therapeutic case and by 14 % in the second one. This improvement may be considered slight however, the hollow nanosphere should be preferred, especially as getting a uniform shell on the silica core remains challenging [2

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

, 37

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

].

Choice of nanorod shape

Lee and El-Sayed [16

16. K. S. Lee and M. A. El-Sayed, “Dependence of the enhanced optical scattering efficiency relative to that of absorption of gold metal nanorods on aspect ratio, size, end-cap shape, and medium refractive,” J. Phys. Chem. B 109, 20331–20338 (2005). [CrossRef]

] suggested that capped cylinder would better describe nanorods. However Ungureanu et al. [32

32. C. Ungureanu, R. G. Rayavarapu, S. Manohar, and T. V. Leeuwen, “Discrete dipole approximation simulations of gold nanorod optical properties: Choice of input parameters and comparison with experiment,” J. Appl. Phys. 105, 102032–102039 (2009). [CrossRef]

] found that, in some cases, ellipsoids or cylinders have spectral extinction closer to experiments. On the other side, when comparing the optimized three shapes, we find that in two cases, the optimized spheroid, capped cylinder and cylinder have different total length (D1 for spheroid, D + L for capped cylinder and L for cylinder). However they have similar absorption efficiencies (difference less than 13%). Therefore we suggest for each therapeutic case, the fabrication of optimized samples with the optimal length and width (Tab. 1) and the measurement of their spectra to check the theoretical results (Fig. 5).

Effect of polarization on optimal setting of nanorod

The results reported in Tab. 1 show that the maximum absorption efficiency depends on the polarization. However the size parameters seem to hardly depend on this parameter (almost the same optimal size parameters for spheroid, capped cylinder and cylinder). In fact, the circular polarization should be able to excite almost all plasmon oscillation modes including the longitudinal one. The longitudinal mode (which appears when using parallel polarization) presents the most important absorption efficiency, therefore its contribution to Qabs when using circular polarization should be the most important. Then, the most absorbing structure, illuminated with a linear polarization, is likely to do as well when illuminated with circular polarization. The efficiency of linear polarization, is nearly twice that of circular polarization. This comes from the equal distribution of the energy of the incoming electric field, on the two perpendicular directions, for the circular polarization. This confirms the relevance of the heuristic reasoning made above.

Hollow nanosphere v.s. nanorod and influence of the Full Width at Half Maximum (FWHM) of the illumination

In each therapeutic case, the comparison between the optimized hollow nanosphere (linear polarization) and nanorod (circular polarization) can be based on the three following criteria: the absorption efficiency Qabs, the narrowness of the absorption band and gold volume. The results reported in Tab. 1, show that the optimized hollow nanosphere is more absorbent than the optimized nanorod in the VIS therapy case (633 nm and skin dermis as surrounding tissue). Both nanoparticles have almost similar behavior in the NIR therapy case (for the different possible shapes of nanorods). Thus, nanorods are not the most efficient nanoparticles for PTT. Regarding the absorption band, its narrowness enables a better match with the laser illumination and prevent the patient sensitivity to the parasite light. Figure 6 shows that the optimized nanorod has also a narrow absorption band, comparable to that of the hollow nanosphere, in the NIR. However its absorption band presents a second resonance in the VIS. Finally, the hollow nanospheres are small enough for their injection in tissue but are larger than nanorods (Tab. 1). The gold volume of the optimized hollow nanosphere, that may be crucial for the manufacturing cost, is 17×103 nm3 which is less than the optimized spheroid volume (similar results are obtained in the second therapeutic case: the gold part is approximatively 14×103 nm3 v.s. 24×103 for spheroid, 16×103 nm3 for capped cylinder and 13 ×103 nm3 for cylinder).

Fig. 6 Comparison of the absorption band of optimized capped cylinder and hollow nanosphere (Tab. 1), DDA is used to get the spectra of capped cylinder and Mie theory is used to get spectra of hollow nanosphere.

Hollow nanosphere and nanorod have similar efficiencies in therapeutic case 2. Therefore the influence of the FWHM of the illumination deserves to be studied to depict its impact on their efficiency. For this, the wavelength is varied within the quarter of the bandwidth i.e. 800+/−25 nm for both the hollow nanosphere and the capped cylinder in therapeutic case 2, as illustration. Their maximal absorption efficiencies are shown in Fig. 7.

Fig. 7 Maximal absorption efficiencies of hollow nanosphere and nanorod for wavelengths within the quarter of the bandwidth of the illumination i.e. 800±25 nm.

The maximal absorption efficiency of nanorods increases of less than 10% as the wavelength increases, showing that a higher wavelength ensures higher efficiency of optimized nanorods. However the hollow nanosphere presents only slight fluctuations of the maximal absorption efficiency. Given the values of absorption efficiency over the range of wavelengths, all of the optimized nanoparticles can be considered active (Fig. 7).

Within this range of wavelengths, slight variations are observed on optimal size parameters of both nanoparticles. The gold shell thickness e of the optimized hollow nanosphere remains equal to 2.5 nm (Tab. 1) over the whole range of wavelengths, and the inner radius r1 is between 18.5 to 22 nm. Despite the capped cylinder is more sensitive to the wavelength, its optimal diameter D remains equal to 19 nm over the range of wavelengths and only its length L increases from 41 nm to 48 nm. Consequently, the critical parameters are e for the hollow nanosphere, and D for the capped cylinder. The improvement of the fabrication process should be focused on a better control of these parameters; otherwise, the efficiency of nanoparticles could drop. These first results confirm those obtained in Ref. [13

13. T. Grosges, D. Barchiesi, T. Toury, and G. Gréhan, “Design of nanostructures for imaging and biomedical applications by plasmonic optimization,” Opt. Lett. 33, 2812–2814 (2008). [CrossRef] [PubMed]

], but deserve to be expanded through a study of design tolerance.

Design tolerance for the size parameters

The probability laws governing the uncertainties are neither identified nor quantified experimentally, hence a study of the propagation of uncertainty may be hazardous. On the other hand, the tolerance analysis helps to deduce the critical parameters, on which effort to control the fabrication should be made. This approach consists of considering an acceptable threshold of the efficiency, and deducing the corresponding tolerance for the size parameters [34

34. T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2(6), 1584–1596 (2011). [CrossRef] [PubMed]

]. Above this threshold, the nanoparticles are considered as active for the therapy. The activity of the nanoparticles depends on both the incoming illumination properties and those of the tissue. Nevertheless, the arbitrary choice of the threshold enables to quantify the relative tolerances for each geometrical parameter.

Table 2. Design tolerance for the size parameters (min-max values) for a threshold 90% of maximal absorption efficiency (obtained from the optimum setting of the size parameters) in both therapeutic cases.

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Fig. 8 Size parameters (shell thickness e and inner radius r1) of hollow nanosphere ensuring 90% of maximal absorption efficiency of hollow nanosphere in therapeutic case 1 (nanoparticles injected in skin dermis and illuminated by a 633 nm laser) and case 2 (nanoparticles injected in subcutaneous fat and illuminated by a 800 nm laser).

Regarding the different shapes of nanorods, results show a tolerance for length of about ±15 nm and a tolerance for width of about ±5 nm (Tab. 2). For the both size parameters, the relative tolerance falls between 21% and 26%. The proposed samples of nanorods (with tolerances) can be synthesized successfully as the fabrication precisions are less than 5 nm [38

38. T. Qiu, W. Zhang, and P. K. Chu, “Recent progress in fabrication of anisotropic nanostructures for surface-enhanced raman spectroscopy,” Recent Patents Nanotechnol. 3, 10–20 (2009). [CrossRef]

, 39

39. F. Ratto, P. Matteini, F. Rossi, and R. Pini, “Size and shape control in the overgrowth of gold nanorods,” J. Nanoparticle Res. 12, 2029–2036 (2010). [CrossRef]

]. Nevertheless, to increase the ratio of active nanoparticles, and therefore to decrease their concentration while maintaining constant the therapeutic efficiency, the uncertainties on their geometrical parameters should be decreased. The relative tolerance for the aspect ratio (AR) is much more restrictive (≤ 5.3%). Therefore, the nanorods can have different lengths (what is usually obtained after synthesis) but should have a given aspect ratio, for a given therapy case.

4. Conclusions

For further applications (other laser wavelengths, tissue of different optical indexes, or both), the same numerical tools can be used to find the optimal parametric setting. It could be interesting to produce the optimized samples suggested in this study mainly to identify which shape better describes the real nanorods. Experiments could also help to recover the true optical index of gold nanoparticles, depending on the process of fabrication.

Acknowledgments

Authors thank the Région Champagne-Ardennes, the Conseil Régional de l’Aube and the Nanoantenna European Project (FP7 Health-F5-2009-241818) for financial supports.

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C. R. Patra, R. Bhattacharya, D. Mukhopadhyay, and P. Mukherjee, “Fabrication of gold nanoparticles for targeted therapy in pancreatic cancer,” Adv. Drug Delivery Rev. 62, 346–361 (2010). [CrossRef]

31.

D. Pissuwan, S. M. Valenzuel, and M. B. Cortie, “Prospects for gold nanorod particles in diagnostic and therapeutic applications,” Biotechnol. Genetic Eng. Rev. 25, 93–112 (2008). [CrossRef]

32.

C. Ungureanu, R. G. Rayavarapu, S. Manohar, and T. V. Leeuwen, “Discrete dipole approximation simulations of gold nanorod optical properties: Choice of input parameters and comparison with experiment,” J. Appl. Phys. 105, 102032–102039 (2009). [CrossRef]

33.

D. Barchiesi, D. S. Kessentini, and T. Grosges, “Sensitivity analysis for designing active particles in photothermal cancer therapy,” in Advances in Safety, Reliability and Risk Management, C. Bérenguer and A. Grall, eds. (Taylor & Francis, London, 2011), pp. 2197–2204.

34.

T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express 2(6), 1584–1596 (2011). [CrossRef] [PubMed]

35.

V. V. Tuchin, Tissue optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE, Bellingham, Washington, 2007).

36.

J. Vera and Y. Bayazitoglu, “A note on laser penetration in nanoshell deposited tissue,” Int. J. Heat Mass Transfer 52, 3402–3406 (2009). [CrossRef]

37.

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

38.

T. Qiu, W. Zhang, and P. K. Chu, “Recent progress in fabrication of anisotropic nanostructures for surface-enhanced raman spectroscopy,” Recent Patents Nanotechnol. 3, 10–20 (2009). [CrossRef]

39.

F. Ratto, P. Matteini, F. Rossi, and R. Pini, “Size and shape control in the overgrowth of gold nanorods,” J. Nanoparticle Res. 12, 2029–2036 (2010). [CrossRef]

OCIS Codes
(170.0170) Medical optics and biotechnology : Medical optics and biotechnology
(170.1020) Medical optics and biotechnology : Ablation of tissue
(170.5180) Medical optics and biotechnology : Photodynamic therapy
(350.5340) Other areas of optics : Photothermal effects

ToC Category:
Nanotechnology and Plasmonics

History
Original Manuscript: November 29, 2011
Revised Manuscript: January 25, 2012
Manuscript Accepted: January 27, 2012
Published: February 22, 2012

Citation
Sameh Kessentini and Dominique Barchiesi, "Quantitative comparison of optimized nanorods, nanoshells and hollow nanospheres for photothermal therapy," Biomed. Opt. Express 3, 590-604 (2012)
http://www.opticsinfobase.org/boe/abstract.cfm?URI=boe-3-3-590


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  32. C. Ungureanu, R. G. Rayavarapu, S. Manohar, and T. V. Leeuwen, “Discrete dipole approximation simulations of gold nanorod optical properties: Choice of input parameters and comparison with experiment,” J. Appl. Phys.105, 102032–102039 (2009). [CrossRef]
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  34. T. Grosges, D. Barchiesi, S. Kessentini, G. Gréhan, and M. Lamy de la Chapelle, “Nanoshells for photothermal therapy: a Monte-Carlo based numerical study of their design tolerance,” Biomed. Opt. Express2(6), 1584–1596 (2011). [CrossRef] [PubMed]
  35. V. V. Tuchin, Tissue optics: Light Scattering Methods and Instruments for Medical Diagnosis (SPIE, Bellingham, Washington, 2007).
  36. J. Vera and Y. Bayazitoglu, “A note on laser penetration in nanoshell deposited tissue,” Int. J. Heat Mass Transfer52, 3402–3406 (2009). [CrossRef]
  37. J. Z. Zhang, “Biomedical application of shape-controlled plasmonic nanostructure: a case study of hollow gold nanospheres for photothermal ablation therapy of cancer,” J. Phys. Chem. Lett.1, 686–695 (2010). [CrossRef]
  38. T. Qiu, W. Zhang, and P. K. Chu, “Recent progress in fabrication of anisotropic nanostructures for surface-enhanced raman spectroscopy,” Recent Patents Nanotechnol.3, 10–20 (2009). [CrossRef]
  39. F. Ratto, P. Matteini, F. Rossi, and R. Pini, “Size and shape control in the overgrowth of gold nanorods,” J. Nanoparticle Res.12, 2029–2036 (2010). [CrossRef]

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