Quantifying tumor-selective radiation dose enhancements using gold nanoparticles: a monte carlo simulation study

Abstract

Gold nanoparticles can enhance the biological effective dose of radiation delivered to tumors, but few data exist to quantify this effect. The purpose of this project was to build a Monte Carlo simulation model to study the degree of dose enhancement achievable with gold nanoparticles. A Monte Carlo simulation model was first built using Geant4 code. An Ir-192 brachytherapy source in a water phantom was simulated and the calculation model was first validated against previously published data. We then introduced up to 10¹³ gold nanospheres per cm³ into the water phantom and examined their dose enhancement effect. We compared this enhancement against a gold-water mixture model that has been previously used to attempt to quantify nanoparticle dose enhancement. In our benchmark test, dose-rate constant, radial dose function, and two-dimensional anisotropy function calculated with our model were within 2% of those reported previously. Using our simulation model we found that the radiation dose was enhanced up to 60% with 10¹³ gold nanospheres per cm³ (9.6% by weight) in a water phantom selectively around the nanospheres. The comparison study indicated that our model more accurately calculated the dose enhancement effect and that previous methodologies overestimated the dose enhancement up to 16%. Monte Carlo calculations demonstrate that biologically-relevant radiation dose enhancement can be achieved with the use of gold nanospheres. Selective tumor labeling with gold nanospheres may be a strategy for clinically enhancing radiation effects.

Appendix

Radiation interaction coefficients for gold nanosphere solution σ _gold-nano and gold-water mixture σ _gold-water

If the total cross section of each target molecule is represented by σ, the cross section of each water molecule is σ _H2O and the cross section of each gold atom is σ _Au , then the total interaction probability of a photon with each phantom molecule is proportional to σ. However, σ differs between the gold-water mixture and the gold nanosphere solution. In the gold-water mixture model, if it has a gold concentration of 9.7% by weight,

$$ \begin{gathered} \sigma = \frac{{\frac{90.3}{18} \times N_A }}{{\left( {\frac{90.3}{18} + \frac{9.7}{197}} \right) \times N_A }} \times \sigma_{{H_2 O}} + \frac{{\frac{9.7}{197} \times N_A }}{{\left( {\frac{90.3}{18} + \frac{9.7}{197}} \right) \times N_A }} \times \sigma_{Au} \hfill \\ = 0.99 \times \sigma_{{H_2 O}} + 0.01 \times \sigma_{Au} \hfill \\ \end{gathered} $$

(1)

Where N _A  = 6.022 × 10²³ mol⁻¹ is the Avogadro constant.

In the gold nanosphere solution model, the cross section was calculated independently, that is

$$ \sigma = \sigma_{{H_2 O}} \;{\text{or}}\sigma_{Au} . $$

(2)

If we assume that the total number of water molecules is N₁ and the total number of gold atoms is N₂, then the total number of phantom molecules is N = (N₁ + N₂). In the gold-water mixture model, the total cross section was calculated as

$$ \sigma_{gold - water} = \left( {N_1 + N_2 } \right) \times \left( {0.99 \times \sigma_{{H_2 O}} + 0.01 \times \sigma_{Au} } \right). $$

(3)

In the gold nanoparticle solution model, the total cross section was calculated as

$$ \sigma_{gold - nano} = \left( {N_1 \cdot x\% } \right) \times \sigma_{{H_2 O}} + N_2 \cdot \left( {100 - x} \right)\% \times \sigma_{Au}, $$

(4)

Where x% and (100-x)% are the percentages of water molecules and gold atoms in the solution, which will depend on the distribution of gold nanoparticles in the solution. It is obvious that σ _gold-water is differs from σ _gold-nano , which accounts for the different dose enhancement estimations generated by the two models. The gold nanoparticle geometry model we created in our study simulated the gold nanoparticle solution more closely than gold-water mixture model used in the previous studies.