Effets non ciblés (bystander, abscopal) de la radiothérapie externe : potentielles implications pour le clinicien ?

Abstract

This study investigates the diffusion process of calcium cations confined in the interlayer space of 5 mm disks of vermiculite swelling clay minerals during the Na-for-Ca exchange process. Diffusion experiments were performed at four NaCl salinities (3 × 10−3, 5 × 10−2, 0.1 and 1 M) of the exchanger solution. A macroscopic analysis of the diffusion process based on the aqueous calcium concentrations released in the solution and on Ca-profiles obtained in the solid was performed using a pore diffusion model that has been classically used in the literature. The results obtained at the macroscopic scale showed that the apparent diffusion coefficients describing both aqueous and profiles data for Ca depend on the diffusion time and salinity of the aqueous reservoir. Such variations suggested that interlayer diffusion was driven by (1) the gradient of the sorbed species in the interlayer, which depends on the diffusion time due to the ion exchange equilibrium; and (2) the discontinuity, due to Donnan equilibrium, existing at the limit between the “internal disk border” and the “external disk border” in contact with the aqueous reservoir. Then, a set of molecular and Brownian dynamics simulations was used to (1) assess such interpretations and (2) quantitatively predict aqueous and profile data obtained at the macroscopic scale. For an aqueous reservoir with high salinity (1 M NaCl), a good agreement was obtained between the macroscopic data and the predictions obtained from Brownian dynamics simulations, confirming the role played by the gradient of the interlayer species that is suggested at the macroscopic scale and which is at the basis of the “surface diffusion models” published in literature. In addition, for aqueous reservoirs with lower salinity (5 × 10−2 M), the results obtained by Brownian dynamics simulations and normalized to the exchange rate measured at infinite time showed that the diffusion properties of the species in the aqueous reservoir cannot be neglected to correctly interpret macroscopic data. This behavior confirms the role played by the ionic flux that exists at the “disk border”, which can limit the global diffusion process in a low salinity reservoir, even if it is well stirred. Moreover, by assuming a tortuosity equal to 1 for monocrystals, the self-diffusion coefficient issued from molecular dynamics simulations is in good agreement with the apparent diffusion coefficient describing macroscopic data when the gradient of sorbed concentrations within the solid is null; this latter condition is obtained in our case at infinite time (20 days) when the initial Ca-saturated disks are fully exchanged with Na cations. Finally, the use of monocrystals allows us to have only interlayer porosity and then to obtain a self-diffusion coefficient for Ca from Molecular Dynamic simulations, which is in good agreement with Ca-surface mobility, which was defined by some authors to predict the “surface diffusion process” at the macroscopic scale.