Dimitris Emfietzoglou

A Complete Dielectric Response Model for Liquid Water: A Solution of the Bethe Ridge Problem

Abstract Emfietzoglou, D., Cucinotta, F. A. and Nikjoo, H. A Complete Dielectric Response Model for Liquid Water: A Solution of the Bethe Ridge Problem. Radiat. Res. 164, 202–211 (2005). We present a complete yet computationally simple model for the dielectric response function of liquid water over the energy-momentum plane, which, in contrast to earlier models, is consistent with the recent inelastic X-ray scattering spectroscopy data at both zero and finite momentum transfer values. The model follows Ritchies extended-Drude algorithm and is particularly effective at the region of the Bethe ridge, substantially improving previous models. The present development allows for a more accurate simulation of the inelastic scattering and energy deposition process of low-energy electrons in liquid water and other biomaterials. As an example, we calculate the stopping power of liquid water for electrons over the 0.1–10 keV range where direct experimental measurements are still impractical and the Bethe stopping formula is inaccurate. The new stopping power values are up to 30–40% lower than previous calculations. Within the range of validity of the first Born approximation, the new values are accurate to within the experimental uncertainties (a few percent). At the low end, the introduction of Born corrections raises the uncertainty to perhaps ∼10%. Thus the present model helps extend the ICRU electron stopping power database for liquid water down to about two orders of magnitude with a comparable level of uncertainty.

The Effect of Model Approximations on Single-Collision Distributions of Low-Energy Electrons in Liquid Water

Abstract Emfietzoglou, D. and Nikjoo, H. The Effect of Model Approximations on Single-Collision Distributions of Low-Energy Electrons in Liquid Water. Radiat. Res. 163, 98–111 (2005). The development of cross sections for the inelastic interaction of low-energy electrons with condensed tissue-like media is best accomplished within the framework of the dielectric theory. In this work we investigate the degree to which various model approximations, used in the above methodology, influence electron single-collision distributions. These distributions are of major importance to Monte Carlo track structure codes, namely, the energy-loss spectrum, the inelastic inverse mean free path, and the ionization efficiency. In particular, we make quantitative assessment of the influence of (1) the optical data set, (2) the dispersion algorithm, and (3) the perturbation and exchange Born corrections. It is shown that, although the shape and position of the energy-loss spectrum remains almost fixed, its peak height may vary by up to a factor of 1.5. Discrepancies in the calculated inelastic inverse mean free path are largely within 20–30% above 100 eV; they increase drastically, though, at lower energies. Exchange and perturbation Born corrections increase gradually below 1 keV leading to a ∼30 to 40% reduction of the inverse mean free path at 100 eV. The perturbation effect contributes more than the exchange effect to this reduction. Similar to the dispersion situation, the effect of Born corrections at lower energies is also unclear since the models examined disagree strongly below 100 eV. In comparison, the vapor data are higher than the liquid calculations by 20 to 50% as the energy decreases from 1 to 0.1 keV, respectively. The excitation contribution is the main cause of this difference, since the ionization efficiency in the liquid levels off at ∼90%, whereas the plateau value for the vapor is ∼70%. It is concluded that electron inelastic distributions for liquid water, although in some respects distinctively different from the vapor phase, have associated uncertainties that are comparable in magnitude to the phase differences. The situation below 100 eV is uncertain.

Accurate Electron Inelastic Cross Sections and Stopping Powers for Liquid Water over the 0.1-10 keV Range Based on an Improved Dielectric Description of the Bethe Surface

Abstract Emfietzoglou, D. and Nikjoo, H. Accurate Electron Inelastic Cross Sections and Stopping Powers for Liquid Water over the 0.1–10 keV Range Based on an Improved Dielectric Description of the Bethe Surface. Radiat. Res. 167, 110–120 (2007). Electron inelastic cross sections and stopping powers for liquid water over the 0.1–10 keV range are presented based on a recently developed dielectric response model for liquid water (D. Emfietzoglou, F. Cucinotta and H. Nikjoo, Radiat. Res. 164, 202–211, 2005) that is consistent with the experimental data over the whole energy-momentum plane. Both exchange and second-order Born corrections are included in a material-specific way using the dielectric functions of liquid water. The numerical results are fitted by simple analytic functions to facilitate their further use. Compared to previous studies, differential cross sections are shifted toward smaller energy losses resulting in smaller inelastic and stopping cross sections with differences reaching, on average, the ∼20% and ∼50% level, respectively. Contrary to higher energies, it is shown that the dispersion model for the momentum dependence of the dielectric functions (Bethe ridge) is as important as the optical model used. Within the accuracy of the experimental data (a few percent) upon which our dielectric model is based, the calculations are “exact” to first order, while the uncertainty of the results beyond first order is estimated at the 5–10% level. The present work overcomes the limitations of Bethes theory at low energies by a self-consistent account of inner-shell effects and may serve to extend the ICRU electron stopping power database for liquid water down to 100 eV with a level of uncertainty similar to that for the higher-energy values.

Binding and interstitial penetration of liposomes within avascular tumor spheroids.

The liposomal delivery of cancer therapeutics, including gene therapy vectors, is an area of intense study. Poor penetration of liposomes into interstitial tumor spaces remains a problem, however. In this work, the penetration of different liposomal formulations into prostate carcinoma spheroids was examined. Spheroid penetration was assessed by confocal microscopy of fluorescently labeled liposomes. The impact of liposomal surface charge, mean diameter, lipid bilayer fluidity and fusogenicity on spheroid penetration was examined. A variety of different liposome systems relevant to clinical or preclinical protocols have been studied, including classical zwitterionic (DMPC:chol) and sterically stabilized liposomes (DMPC:chol:DOPE‐PEG2000), both used clinically, and cationic liposomes (DMPC:DOPE:DC‐chol and DOTAP), forming the basis of the vast majority of nonviral gene transfer vectors tested in various cancer trials. Surface interactions between strongly cationic vesicles and the tumor cells led to an electrostatically derived binding‐site barrier effect, inhibiting further association of the delivery systems with the tumor spheroids (DMPC:DC‐chol). However, inclusion of the fusogenic lipid DOPE and use of a cationic lipid of lower surface charge density (DOTAP instead of DC‐chol) led to improvements in the observed intratumoral distribution characteristics. Sterically stabilized liposomes did not interact with the tumor spheroids, whereas small unilamellar classical liposomes exhibit extensive distribution deeper into the tumor volume. Engineering liposomal delivery systems with a relatively low charge molar ratio and enhanced fusogenicity, or electrostatically neutral liposomes with fluid bilayers, offered enhanced intratumoral penetration. This study shows that a delicate balance exists between the strong affinity of delivery systems for the tumor cells and the efficient penetration and distribution within the tumor mass, similar to previous work studying targeted delivery by ligand‐receptor interactions of monoclonal antibodies. Structure‐function relationships from the interaction of different liposome systems with 3‐dimensional tumor spheroids can lead to construction of delivery systems able to target efficiently and penetrate deeper within the tumor interstitium and act as a screening tool for a variety of therapeutics against cancer.

Monte Carlo simulation of the energy loss of low-energy electrons in liquid water

A Monte Carlo code that performs detailed (i.e. event-by-event) simulation of the transport and energy loss of low-energy electrons (approximately 50-10 000 eV) in water in the liquid phase is presented. The inelastic model for energy loss is based on a semi-empirical dielectric-response function for the valence-shells of the liquid whereas an exchange corrected semi-classical formula was used for K-shell ionization. Following a methodology widely used for the vapour phase, we succeeded in parametrizing the dielectric cross-sections of the liquid in accordance with the Bethe asymptote, thus providing a unified approach for both phases of water and greatly facilitating the computations. Born-corrections at lower energies have been implemented in terms of a second-order perturbation term with a simple Coulomb-field correction and the use of a Mott-type exchange modification. Angular deflections were determined by empirical schemes established from vapour data. Electron tracks generated by the code were used to calculate energy- and interaction-point-kernel distributions at low electron energies in liquid water. The effect of various model assumptions (e.g., dispersion, Born-corrections, phase) on both the single-collision and slowing-down distributions is examined.

Inelastic cross-sections for electron transport in liquid water: a comparison of dielectric models

Abstract Various methodologies for constructing inelastic cross-sections for low-energy ( δ -oscillator models of Ashley and Liljequist, and two forms of Ritchies extended-Drude model. They all have been used in Monte-Carlo (MC) codes for analog electron transport in the condensed phase. Results in the form of differential and total inelastic cross-sections are presented. Where possible, comparisons with results of other studies are made. It was found that, despite the application of general constraints (e.g. sum rules), the optical model has a notable influence on the single-collision energy loss spectrum. In addition, both the shape and peak position of the total and differential cross-section distributions depend strongly on the dispersion model adopted. The work is particularly relevant to the development of event-by-event MC transport codes for liquid water, as well as, to the calculations of stopping-powers below the range of applicability of Bethes formula.

A dielectric response study of the electronic stopping power of liquid water for energetic protons and a new I-value for water

The electronic stopping power of liquid water for protons over the 50 keV to 10 MeV energy range is studied using an improved dielectric response model which is in good agreement with the best available experimental data. The mean excitation energy (I) of stopping power theory is calculated to be 77.8 eV. Shell corrections are accounted for in a self-consistent manner through analytic dispersion relations for the momentum dependence of the dielectric function. It is shown that widely used dispersion schemes based on the random-phase approximation (RPA) can result in sizeable errors due to the neglect of damping and local field effects that lead to a momentum broadening and shifting of the energy-loss function. Low-energy Born corrections for the Barkas, Bloch and charge-state effects practically cancel out down to 100 keV proton energies. Differences with ICRU Report 49 stopping power values and earlier calculations are found to be at the approximately 20% level in the region of the stopping maximum. The present work overcomes the limitations of the Bethe formula below 1 MeV and improves the accuracy of previous calculations through a more consistent account of the dielectric response properties of liquid water.

Heavy charged particles in radiation biology and biophysics

Ionizing radiations induce a variety of molecular and cellular types of damage in mammalian cells as a result of energy deposition by the radiation track. In general, tracks are divided into two classes of sparsely ionizing ones such as electron tracks and densely ionizing tracks such as heavy ions. The paper discusses various aspects and differences between the two types of radiations and their efficacies in radiation therapy. Biophysical studies of radiation tracks have provided much of the insight in mechanistic understanding of the relationship between the initial physical events and observed biological responses. Therefore, development of Monte Carlo track-structure techniques and codes are paramount for the progress of the field. In this paper, we report for the first time the latest development for the simulation of proton tracks up to 200MeV similar to beam energies in proton radiotherapy and space radiation. Vital to the development of the models for ion tracks is the accurate simulation of electron tracks cross sections in liquid water. In this paper, we report the development of electron track cross sections in liquid water using a new dielectric model of low-energy electrons accurate to nearly 10% down to 100eV.

Inelastic collision characteristics of electrons in liquid water

Calculations of inelastic mean-free-paths and collision stopping-powers for low energy electrons (<10 keV) in liquid water are presented and compared with the existing values in the literature. A semi-empirical inelastic model was developed which makes use of (a) the dielectric formalism for the valence shells responsible for condensed-phase effects, and (b) the binary-encounter-approximation for the K-shell. The energy and momentum dependence dielectric-response function of liquid water was constructed based on a modified Drude model, optical data, and appropriate dispersion algorithms. Binding effects for the K-shell were based on the initial (unperturbed) molecular state. Calculations were performed under the first Born approximation with the inclusion of empirical correction functions at very low energies (<300 eV).

The Auger effect in physical and biological research

Purpose: The paper reports on progress in physics of radiationless transitions and new Auger spectra of 125I and 124I. We report progress in Monte Carlo track structure simulation of low energy electrons comprising majority electrons released in decay most Auger emitters. Materials and methods: The input data for electron capture (EC) and internal conversion(IC) were obtained from various physics data libraries. Monte Carlo technique was used for the simulation of Auger electron spectra. Similarly, electron tracks were generated using Monte Carlo track structure methods. Results: Data are presented for the EC, IC and binding energy (BE) of radionuclides 124I and 125I. For each of the radionuclides 125I and 124I some examples of electron spectra of individual decays are given. Because most Auger electrons are low energy and short range, data and a short discussion are presented on recent Monte Carlo track structure development in condensed media and their accuracy. Conclusions: Accuracy of electron spectra calculated in the decay of electron shower by Auger emitting radionuclides depends on availability of accurate physics data. There are many gaps in these libraries and there is a need for detailed comparison between analytical method and Monte Carlo calculations to refine the method of calculations. On simulation of electron tracks, although improved models for sub-keV electron interaction cross sections for liquid water are now available, more experimental data are needed for benchmarking. In addition, it is desirable to make data and programs for calculations of Auger spectra available online for use by students and researchers.