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
]. 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 . Then under suitable illumination they absorb a large amount of light (). Almost all the absorbed light is converted to heat via a series of nonradiative processes [2
]. Therefore the cancer cells containing gold nanoparticles receive sufficient heat to induce their necrosis [3
] with minimal damage to their surrounding (localized heat delivery).
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
]. In these windows, the gold nanoparticles absorb the light millions of times more than the organic molecules [1
]. 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
] 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
]. 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
]. Hollow nanospheres and nanoshells can guarantee such tunable behavior at different wavelengths ranging from VIS to NIR, by adjusting their size parameters [7
]. Nevertheless, hollow nanospheres are synthesized with great precision and controlled dimensions [7
] whereas, forming a uniform shell on the silica core remains challenging [2
Some advantages of nanorods are reported in Ref. [2
]. For instance, using nanorods illuminated by pulsed laser source, the destruction of a single cell can be achieved (selectivity improvement), the nanorods being reshaped into nanospheres (in situ) [8
]. This degradation of the nanorod prevents further death of cell [8
] (as nanospheres have very limited absorption in NIR). Moreover, in most comparative studies, the nanorods were shown to be more efficient than the nanoshells and therefore require lower laser intensity for photothermal therapy [2
]. However these studies [10
] covered some samples of nanoshells, which had not been optimized (the absorption efficiency Qabs
is restricted to 18 whereas it could achieve 30 using Ag nanoshells). In these comparisons, the incoming light is assumed to be linearly polarized along the nanorod longitudinal axis, whereas in therapeutic applications the nanorods are randomly oriented. This random orientation prevents to achieve the maximum absorption efficiency. To enhance the treatment efficiency, a circular polarization is used to activate as many nanorods as possible [12
]. Therefore both the circular polarization and the linear polarization are considered in this study. We propose to find the size parameters that enable the maximum absorption efficiency for each type of nanoparticle, and to compare them (only few previous studies were devoted to the numerical optimization of nanoshells [13
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
], 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
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.