Partial Separability of the Schrödinger Equation Combined with a Jastrow Factor.

Describing the Coulomb interactions between electrons in atomic or molecular systems is an important step to help us obtain accurate results for the different observables in the system. One convenient approach is to separate the dynamic electronic correlation, i.e., Coulomb electron-electron repulsion, from the motion of the electrons in the nucleus electric field. The wave function is written as the product of two terms, one accounting for the electron-electron interactions, which is symmetric under identical particle exchange, and the other is antisymmetric and represents the dynamics and exchange of electrons within the nuclear electric field. In this work, we present a novel computational scheme based on this idea that leads to an expression of the energy as the sum of two terms. To illustrate the method, we look into few-body Coulombic systems, H2, H3+, and Li(1s2,2s), and discuss the possible extension to larger systems. A simple correlation factor, based on the Jastrow exponential term, is employed to represent the dynamics of the electron pairs, leading to simple analytical forms and accurate results. We also present and illustrate a different approach with the Li atom based on the partial separability applied to a portion of the atom.

Dual aspect of radioenhancers and free radical scavengers.

Combining an external beam of ionizing particles with agents to augment the dose effects of cell damages for therapeutic purpose is an important goal of radiotherapy. This last decade intensive works have focused on metal compounds or metal nanoparticles as radiosensitizers to increase the oxidative damages under irradiation. In principle the nanoparticles can be coated with a functionalized shell, to achieve a specific targeting of the tissues, making such approach attractive. The functionalized coating is made of polymers. These molecules are able to scavenge the free radicals, thus, the coating can decrease the overall efficacy of the radiation. The purpose of the present model is to analyse the role of free hydroxyl radicals in the dual behaviour of the added agent. Consideration of the efficiency of the added agents versus the Linear Energy Transfer - LET - of the ionizing particles is made. It is shown that an efficient agent combined with a low-LET particle beams might become less efficient when high-LET particles like heavy-ions are used. These general considerations should be useful to optimize the design of the nanoparticles to be combined with the different kind of ionizing particles.

Combination of agents modifying effects in hadrontherapy: modelization of the role of HO° free radicals.

Purpose: A study is presented of the irradiation of cancerous cervical cell line HeLa loaded with a platinum salt, betamethasone and deoxyglucose. The presence of the platinum increases the free-radical concentration and augments the cell death rate, whereas betamethasone or deoxyglucose induces radiosensitization by the alteration of metabolic pathways. Two by two combinations of these chemicals are made to investigate the possible benefit when two radiosensitizers are present. A model is proposed to understand the results of the presence of two modifying agents on the dose effects.Materials and methods: The cells were incubated for 6 h in the presence of the following molecules: dichloro terpyridine platinum, concentration C = 350 µM, betamethasone and deoxyglucose with concentrations of C = 0.2 µM and C = 6 mM, respectively. The cells were subsequently irradiated by carbon C6+ ion 290 MeV/amu up to a dose of 2.5 Gy, under atmospheric conditions.Results: The presence of the platinum salt or bethamethasone augments the cell death rate. The combination of betamethasone with the platinum salt also increases the cell death rate, but less than for the platinum salt alone. The explanation is that any radiosensitizer also behaves as a scavenger of free radicals. This dual behavior should be considered in any optimization of the design of radiosensitizers when different ionizing particles are used.

Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere.

A model of confinement of the covalent bond by a finite potential beyond the Born-Oppenheimer approximation is presented. A two-electron molecule is located at the center of a penetrable spherical cavity. The Schrödinger equation has been solved by using the diffusion Monte Carlo method. Total energies, internuclear distances, and vibrational frequencies of the confined molecular system have been obtained. Even for confining potentials of a few electronvolts, a noticeable increase in the bond energy and the nuclear vibrational frequency is observed, and the internuclear distance is lowered. The gap between the zero point energy of different molecular isotopes increases with confinement. The confinement of the electron pair might play a role in chemical reactivity, providing an alternative explanation for the tunnel effect, when large values of primary kinetic isotopic effect are observed. The Swain-Schaad relation is still verified when confinement changes the zero point energy. A semiquantitative illustration is proposed using the data relative to an hydrogen transfer involving a C-H cleavage catalyzed by the bovine serum amine oxidase. Changes on the confining conditions, corresponding to a confinement/deconfinement process, result in a significant decrease in the activation energy of the chemical transformation. It is proposed that confinement/deconfinement of the electron-pair bonding by external electrostatic forces inside the active pocket of an enzyme could be one of the basic mechanisms of the enzyme catalysis.

Gadolinium-based nanoparticles to improve the hadrontherapy performances.

Nanomedicine is proposed as a novel strategy to improve the performance of radiotherapy. High-Z nanoparticles are known to enhance the effects of ionizing radiation. Recently, multimodal nanoparticles such as gadolinium-based nanoagents were proposed to amplify the effects of x-rays and g-rays and to improve MRI diagnosis. For tumors sited in sensitive tissues, childhood cases and radioresistant cancers, hadrontherapy is considered superior to x-rays and g-rays. Hadrontherapy, based on fast ion radiation, has the advantage of avoiding damage to the tissues behind the tumor; however, the damage caused in front of the tumor is its major limitation. Here, we demonstrate that multimodal gadolinium-based nanoparticles amplify cell death with fast ions used as radiation. Molecular scale experiments give insights into the mechanisms underlying the amplification of radiation effects. This proof-of-concept opens up novel perspectives for multimodal nanomedicine in hadrontherapy, ultimately reducing negative radiation effects in healthy tissues in front of the tumor. FROM THE CLINICAL EDITOR: Gadolinium-chelating polysiloxane nanoparticles were previously reported to amplify the anti-tumor effects of x-rays and g-rays and to serve as MRI contrast agents. Fast ion radiation-based hadrontherapy avoids damage to the tissues behind the tumor, with a major limitation of tissue damage in front of the tumor. This study demonstrates a potential role for the above nanoagents in optimizing hadrontherapy with preventive effects in healthy tissue and amplified cell death in the tumor.

Comment on 'Therapeutic application of metallic nanoparticles combined with particle-induced x-ray emission effect'.

A recent paper (Kim et al 2010 Nanotechnology 21 425102) presented results on the combination of irradiation by atomic ions of cells loaded by particles made of heavy atoms. They propose that the projectile induced x-rays emission (PIXE) mechanism has an important contribution to the enhancement of the cell death rate. Experiments made in our group to study the effects of such a combination have shown that the Auger effect induced in the high-Z atoms and the following induction of surrounding water radiolysis has an important contribution to the enhancement of the cell death rate. In the light of our studies we propose an alternative interpretation of the results presented in the paper by Kim et al.

Variational Monte Carlo Method with Dirichlet Boundary Conditions: Application to the Study of Confined Systems by Impenetrable Surfaces with Different Symmetries.

Variational Monte Carlo method is a powerful tool to determine approximate wave functions of atoms, molecules, and solids up to relatively large systems. In the present work, we extend the variational Monte Carlo approach to study confined systems. Important properties of the atoms, such as the spatial distribution of the electronic charge, the energy levels, or the filling of electronic shells, are modified under confinement. An expression of the energy very similar to the estimator used for free systems is derived. This opens the possibility to study confined systems with little changes in the solution of the corresponding free systems. This is illustrated by the study of helium atom in its ground state (1)S and the first (3)S excited state confined by spherical, cylindrical, and plane impenetrable surfaces. The average interelectronic distances are also calculated. They decrease in general when the confinement is stronger; however, it is seen that they present a minimum for excited states under confinement by open surfaces (cylindrical, planes) around the radii values corresponding to ionization. The ground (2)S and the first (2)P and (2)D excited states of the lithium atom are calculated under spherical constraints for different confinement radii. A crossing between the (2)S and (2)P states is observed around rc = 3 atomic units, illustrating the modification of the atomic energy level under confinement. Finally the carbon atom is studied in the spherical symmetry by using both variational and diffusion Monte Carlo methods. It is shown that the hybridized state sp(3) becomes lower in energy than the ground state (3)P due to a modification and a mixing of the atomic orbitals s, p under strong confinement. This result suggests a model, at least of pedagogical interest, to interpret the basic properties of carbon atom in chemistry.

Comparison of DNA breaks at entrance channel and Bragg peak induced by fast C6+ ions--influence of the addition of platinum atoms on DNA.

When energetic carbon ion beam (GeV range) goes through the matter, inelastic processes such as electronic ionization, molecular and nuclear fragmentation occur. For carbontherapy (hadrontherapy) purpose, it is of interest to compare the number of DNA breaks -single SSB or double DSB- for a given dose at the entrance channel and at the Bragg peak to look for a possible differential effect in the number of DNA breaks induced at these two locations. Samples of free plasmids DNA and complexes of plasmids DNA added with molecules containing platinum have been placed at different locations of an experimental setup simulating penetration depths of the ion beam in water and irradiated by carbon ions 290 MeV/amu. The DNA breaks have been quantified by subsequent electrophoresis on agarose gels. To disentangle the respective role of the direct and indirect effect, a free radical scavenger of hydroxyl radicals HO degree-dimethylsulfoxide DMSO- has been added in some of the experiments. In the range of Linear Energy Transfer-LET 13 - 110 keV/microm-, the number of the DSB was found to be constant versus the LET for a given dose. Contrary, the number of the SSB decreases at the Bragg peak compared to the entrance channel. In the presence of platinum, the number of single and double breaks was considerably enhanced, and follows a similar behaviour than in the free-DNA experiments. Quantitative results on DNA damages do not show significant enhancement due to the nuclear or to the molecular fragmentation in the present experiments.

Platinum nanoparticles: a promising material for future cancer therapy?

Recently, the use of gold nanoparticles as potential tumor selective radiosensitizers has been proposed as a breakthrough in radiotherapy. Experiments in living cells and in vivo have demonstrated the efficiency of the metal nanoparticles when combined with low energy x-ray radiations (below conventional 1 MeV Linac radiation). Further studies on DNA have been performed in order to better understand the fundamental processes of sensitization and to further improve the method. In this work, we propose a new strategy based on the combination of platinum nanoparticles with irradiation by fast ions effectively used in hadron therapy. It is observed in particular that nanoparticles enhance strongly lethal damage in DNA, with an efficiency factor close to 2 for double strand breaks. In order to disentangle the effect of the nano-design architecture, a comparison with the effects of dispersed metal atoms at the same concentration has been performed. It is thus shown that the sensitization in nanoparticles is enhanced due to auto-amplified electronic cascades inside the nanoparticles, which reinforces the energy deposition in the close vicinity of the metal. Finally, the combination of fast ion radiation (hadron therapy) with platinum nanoparticles should strongly improve cancer therapy protocols.

Clinical significance of atomic inner shell ionization (ISI) and Auger cascade for radiosensitization using IUdR, BUdR, platinum salts, or gadolinium porphyrin compounds.

PURPOSE: Halogenated pyrimidines (iododeoxyuridine [IUdR] and bromodeoxyuridine [BUdR]), platinum salts, and gadolinium porphyrins are heavy atom compounds used as radiosensitizers. For IUdR, it has been hypothesized that iodine inner shell ionizations (ISI) and Auger cascades could be one of the primary radiosensitization mechanisms. The purpose of this paper is to estimate the number of ISI produced per tumor cell and per 2 Gy irradiation in clinically relevant modelings. MATERIALS AND METHODS: ISI were evaluated using a two-step method. Photon-induced ISI were calculated using the MCNP-4C Monte Carlo code, heavy atom concentrations from clinical data published in the literature, and at various depths in a water phantom irradiated with 6-MV, (60)Co, (137)Cs, or (192)Ir sources. Electron knock-on induced ISI on K, L, and M atomic shells were evaluated with an hybrid method, using simulated electron spectra and cross-sections derived from the Møller formalism. Using a biological dose equivalence of 0.05 Gy per cell ISI, relative biological effectiveness (RBE) values were calculated for each situation. RESULTS: For platinum and gadolinium, ISI occurs in far less than 0.1% of the cell, whichever is the configuration. For IUdR and BUdR, ISI occurs in between 45% to 483% of the cell. Due to spectrum degradation, about 3 times more photoelectric ISI are generated at greater than shallower depths, and 10 times more for (192)Ir compared with (60)Co or 6-MV X-rays. Photoelectric ISI are about 3 times more frequent for iodine than bromine, but electron knock-on ISI are more frequent on bromine, and at the end about the same number of ISI are generated for both elements. RBEs were found to be between 1.01 and 1.12 for clinically relevant irradiation settings. CONCLUSIONS: The mechanisms of radiosensitization for platinum and gadolinium are clearly not related to an Auger cascade. For halogenated pyrimidines, however, clinically relevant numbers of ISI are generated within each cell. For IUdR, ISI appears to be strongly tied to the photon spectra. Halogenated pyrimidines should be evaluated again clinically, but using lower energy photons like a (192)Ir implant.