Experimental Evaluation of 65Zn Decorporation Kinetics Following Rapid and Delayed Zn-DTPA Interventions in Rats. Biphasic Compartmental and Square-Root Law Mathematical Modeling

The decorporation kinetics of internal radionuclide contamination is a long-term treatment raising modeling, planning, and managing problems, especially in the case of late intervention when the radiotoxic penetrated the deep compartments. The decorporation effectiveness of the highly radiotoxic 65ZnCl2 by Zn-DTPA (dosed at 3.32 mg and 5 mg/0.25 mL/100 g body weight) was investigated in Wistar male rats over a ten-day period under various treatments (i.e., as a single dose before contamination; as a single dose before and 24 h after contamination; and as daily administrations for five consecutive days starting on day 12 after contamination). The radioactivity was measured using the whole-body counting method. Mono- and bi-compartmental decorporation kinetics models proved applicable in the case of a rapid intervention. It was found that a diffusion model of the radionuclide from tissues to blood better describes the decorporation kinetics after more than ten days post treatment, and the process has been mathematically modeled as a diffusion from an infinite reservoir to a semi-finite medium. The mathematical solution led to a square-root law for describing the 65Zn decorporation. This law predicts a slower release than exponential or multiexponential equations, and could better explain the very long persistence of radionuclides in the living body. Splitting data and modeling in two steps allows a better understanding, description and prediction of the evolution of contamination, a separate approach to the treatment schemes of acute and chronic contamination.

A Fractional Single-Phase-Lag Model of Heat Conduction for Describing Propagation of the Maximum Temperature in a Finite Medium

In this paper, an investigation of the maximum temperature propagation in a finite medium is presented. The heat conduction in the medium was modelled by using a single-phase-lag equation with fractional Caputo derivatives. The formulation and solution of the problem concern the heat conduction in a slab, a hollow cylinder, and a hollow sphere, which are subjected to a heat source represented by the Robotnov function and a harmonically varying ambient temperature. The problem with time-dependent Robin and homogenous Neumann boundary conditions has been solved by using an eigenfunction expansion method and the Laplace transform technique. The solution of the heat conduction problem was used for determination of the maximum temperature trajectories. The trajectories and propagation speeds of the temperature maxima in the medium depend on the order of fractional derivatives occurring in the heat conduction model. These dependencies for the heat conduction in the hollow cylinder have been numerically investigated.

Wetting Front Analysis of the Richards’ Equation with Impervious Boundary

It is analyzed the wetting front of the Richards’ equation (RE) for horizontal infiltration problem with impervious layer in a finite medium, and obtained an approximate analytical solution by the series expansion technique. The present approximation is suitable for arbitrary diffusivity in RE and applied to simulate the changes of saturation after the front pass through the impervious point. Two examples about power law diffusivity are analyzed to confirm the accuracy of present solution.

Anisotropic Elastic Field of 3D Prismatic Dislocation Loops in Bounded and Voided Single Crystal Films

Dislocations in a finite medium bring about image stresses. These image stresses play important roles in the dislocation behavior in finite sized systems such as thin films. Since the ratio of surface to volume is higher for thin films than for bulk materials, dislocation behaviors in thin films are greatly different from those in a corresponding infinite medium, which make it necessary to take into account the effects of free surfaces on the evolution of dislocations in thin films. In the investigations[4, 5], image stresses in an elastic cylinder and thin films are calculated by employing a Fourier transform (FFT) approach and isotropically elastic fields due to dislocations are adopted in their formulation. However, most crystals are anisotropic, and the anisotropic ratio changes with environment physical parameters, such as the temperature, moisture, electron field, magnetic field. A theorem based on anisotropic Stroh’s formula for calculating the image stress of infinite straight dislocations in anisotropic bicrystals has been developed by Barnett and Lothe[6]. Wu et al.[3] recently also make use of the FFT technique to investigate the general dislocation image stresses of cubic thin films, thus extending the formalism by Weinberger et al.[4,5] from isotropic to anisotropic thin films. It is clear that for the assumed in-plane elastic fields to be periodically defined within an unbounded region is an essential and indispensable prerequisite for the above FFT-based approach to be effectively implemented, thus ruling out the possibility of its being employed to analyse image stresses in bounded and/or voided thin cubic films. Our motivation here is then to make an further extension by first calculating the anisotropic elastic fields of dislocation loops in an unbounded thin film with cavities and then invoking FEM and the principle of superposition to seek the image stress solution.