Physics of ion beam cancer therapy: a multiscale approach

Condensed Matter Systems Exposed to Radiation: Multiscale Theory, Simulations, and Experiment

This roadmap reviews the new, highly interdisciplinary research field studying the behavior of condensed matter systems exposed to radiation. The Review highlights several recent advances in the field and provides a roadmap for the development of the field over the next decade. Condensed matter systems exposed to radiation can be inorganic, organic, or biological, finite or infinite, composed of different molecular species or materials, exist in different phases, and operate under different thermodynamic conditions. Many of the key phenomena related to the behavior of irradiated systems are very similar and can be understood based on the same fundamental theoretical principles and computational approaches. The multiscale nature of such phenomena requires the quantitative description of the radiation-induced effects occurring at different spatial and temporal scales, ranging from the atomic to the macroscopic, and the interlinks between such descriptions. The multiscale nature of the effects and the similarity of their manifestation in systems of different origins necessarily bring together different disciplines, such as physics, chemistry, biology, materials science, nanoscience, and biomedical research, demonstrating the numerous interlinks and commonalities between them. This research field is highly relevant to many novel and emerging technologies and medical applications.

Ion-Type Dependence of DNA Electronic Excitation in Water under Proton, α-Particle, and Carbon Ion Irradiation: A First-Principles Simulation Study

Understanding how the electronic excitation of DNA changes in response to different high-energy particles is central to advancing ion beam cancer therapy and other related approaches, such as boron neutron capture therapy. While protons have been the predominant ions of choice in ion beam cancer therapy, heavier ions, particularly carbon ions, have drawn significant attention over the past decade. Carbon ions are expected to transfer larger amounts of energy according to linear response theory. However, molecular-level details of the electronic excitation under heavier ion irradiation remain unknown. In this work, we use real-time time-dependent density functional theory simulations to examine the quantum-mechanical details of DNA electronic excitations in water under proton, α-particle, and carbon ion irradiation. Our results show that the energy transfer does indeed increase for the heavier ions, while the excitation remains highly conformal. However, the increase in the energy transfer rate, measured by electronic stopping power, does not match the prediction by the linear response model, even when accounting for the velocity dependence of the irradiating ion's charge. The simulations also reveal that while the number of holes generated on DNA increases for heavier ions, the increase is only partially responsible for the larger stopping power. Larger numbers of highly energetic holes formed from the heavier ions also contribute significantly to the increased electronic stopping power.

H2O˙+ and OH+ reactivity versus furan: experimental low energy absolute cross sections for modeling radiation damage

Radiotherapy is one of the most widespread and efficient strategies to fight malignant tumors. Despite its broad application, the mechanisms of radiation-DNA interaction are still under investigation. Theoretical models to predict the effects of a particular delivered dose are still in their infancy due to the difficulty of simulating a real cell environment, as well as the inclusion of a large variety of secondary processes. This work reports the first experimental study of the ion-molecule reactions of the H2O˙+ and OH+ ions, produced by photoionization with synchrotron radiation, with a furan (c-C4H4O) molecule, a template for deoxyribose sugar in DNA. The present experiments, performed as a function of the collision energy of the ions and the tunable photoionization energy, provide key parameters for the theoretical modelling of the effect of radiation dose, like the absolute cross sections for producing protonated furan (furanH+) and a radical cation (furan˙+), the most abundant products, which can amount up to 200 Å2 at very low collision energies (<1.0 eV). The experimental results show that furanH+ is more fragile, indicating how the protonation of the sugar component of the DNA may favor its dissociation with possible major radiosensitizing effects. Moreover, the ring opening of furanH+ isomers and the potential energy surface of the most important fragmentation channels have been explored by molecular dynamics simulations and quantum chemistry calculations. The results show that, in the most stable isomer of furanH+, the ring opening occurs via a low energy pathway with carbon-oxygen bond cleavage, followed by the loss of neutral carbon monoxide and the formation of the allyl cation CH2CHCH2+, which instead is not observed in the fragmentation of furan˙+. At higher energies the ring opening through the carbon-carbon bond is accompanied by the loss of formaldehyde, producing HCCCH2+, the most intense fragment ion detected in the experiments. This work highlights the importance of the secondary processes, like the ion-molecule reactions at low energies in the radiation damage due to their very large cross sections, and it aims to provide benchmark data for the development of suitable models to approach this low collision energy range.

Effects of semicore electrons on stopping power in helium-irradiated aluminum nanosheets

The stopping power of energetic He ions traversing an Al film is studied by combining the time-dependent density-functional theory method with molecular dynamics simulations. We investigated the dependence of the semicore electron excitation of the Al film on the projectile's trajectory and its charge state. Our results show that for the off-channeling trajectories the semicore electrons contribute significantly to the stopping power of the Al film as the He⁺ ion velocity exceeds 1.0 a.u, and in contrast, it is negligible for the channeling trajectories. Most importantly, we found two unexpected effects of semicore electrons on the stopping power in helium-irradiated aluminum nanosheets, i.e., (1) the semicore electrons can contribute to the energy loss for both high and low energy projectiles under the off-channeling trajectory; (2) as the projectile velocity increases from 0.4 a.u. to 2.0 a.u. although semicore electron excitation (including transition in the target, ionization away from the target and transfer to the projectile ion) of the target atom is gradually inhibited, the influence of semicore electrons on valence electron excitation is gradually enhanced. Our finding allows us to gain new insights into the stopping of ions in metals.

On the Thermal Behavior during Spatial Anisotropic Femtoseconds Laser-DNA Interaction: The Crucial Role of Hermite Polynomials

A novel analytical formalism based on the quantum heat transport equation is proposed for the interaction of fs-laser pulses with deoxyribonucleic acid (DNA) strands. The formalism has the intensity of the laser beam and the interaction time between the laser and the DNA as input parameters. To this end, the thermal distribution generated in the irradiated DNA strands was introduced by splitting the laser beam into transverse Hermite-Gauss modes. To achieve this goal, a new powerful mathematical model was developed and applied. Fluctuations in laser intensity were taken into account by modeling them as superpositions of Hermite-Gauss laser modes. These analyses were carried out for a laser pulse duration of 100 fs, where a tiny heat-affected zone is expected, with positive predicted effects on the stability and repeatability of this technology. The main conclusion is that the laser beam spatial distribution intensity plays an essential role in the generation of the shape and magnitude of the thermal field at the junction of the irradiated DNA strands. The model may prove useful in modeling laser beam processing under significant intensity fluctuations. There are at least two main areas of application for the present model of heat transfer from laser to DNA: (i) the study of DNA elongation without destroying the target information (for a sample temperature variation lower than 10 K; in the case of H[1,y]); and (ii) cancer treatment (especially of skin tissue), where we should obtain a temperature variation higher than 10 K (but lower than 30 K; in the case of H[2,y], H[4,y]), in order to eradicate the diseased cells.

Complexes of hydrogen peroxide molecules with DNA nucleic bases

The analysis of complexes formation of hydrogen peroxide molecule with DNA nucleic bases is carried out using methods of quantum chemistry. Optimized geometries of complexes are determined and the interaction energies that lead to complex formation are calculated. Comparison with the same calculations for water molecule is made. It is shown that complexes with hydrogen peroxide molecule are energetically more stable than the same complexes with water molecule. Such energetic advantage is achieved particularly due to geometrical properties of hydrogen peroxide molecule, especially presence of dihedral angle. Position of hydrogen peroxide molecule in close vicinity to DNA could lead to blocking of its recognition by proteins or direct damage via hydroxyl radical formation. These results can have significant impact in understanding of mechanisms of cancer therapy.Communicated by Ramaswamy H. Sarma.

Photoelectron-photoion(s) coincidence studies of molecules of biological interest

Photoelectron-photoion(s) coincidence, PEPICO, experiments with synchrotron radiation have become one of the most powerful tools to investigate dissociative photoionization thanks to their selectivity. In this paper their application to the study of molecular species of biological interest in the gas phase is reviewed. Some applications of PEPICO to the study of potential radiosensitizers, amino acids and small peptides and opportunities offered by the advent of novel methods for the production of beams of these molecules are discussed.

Multicomponent Quantum Mechanics/Molecular Mechanics Study of Hydrated Positronium

We propose a model for solvated positronium (Ps) atoms in water, based on the sequential quantum mechanics/molecular mechanics (s-QM/MM) protocol. We developed a Lennard-Jones force field to account for Ps-water interactions in the MM step. The repulsive term was obtained from a previously reported model for the solvated electron, while the dispersion constant was derived from the Slater-Kirkwood formula. The force field was employed in classical Monte Carlo (MC) simulations to generate Ps-solvent configurations in the NpT ensemble, while the quantum properties were computed with the any-particle molecular orbital method in the subsequent QM step. Our approach is general, as it can be applied to other liquids and materials. One basically needs to describe the solvated electron in the environment of interest to obtain the Ps solvation model. The thermodynamical properties computed from the MC simulations point out similarities between the solvation of Ps and noble gas atoms, hydrophobic solutes that form clathrate structures. We performed convergence tests for the QM step, with particular attention to the choice of basis set and expansion centers for the positronic and electronic subsystems. Our largest model was composed of the Ps atom and 22 water molecules in the QM region, corresponding to the first solvation shell, surrounded by 128 molecules described as point charges. The mean electronic and positronic vertical detachment energies were (4.73 ± 0.04) eV and (5.33 ± 0.04) eV, respectively. The latter estimates were computed with Koopmans' theorem corrected by second-order self-energies, for a set of statistically uncorrelated MC configurations. While the Hartree-Fock wave functions do not properly account for the annihilation rates, they were useful for numerical tests, pointing out that annihilation is more sensitive to the choice of basis sets and expansion centers than the detachment energies. We further explored a model with reduced solute cavity size by changing the Ps-solvent force field. Although the pick-off annihilation lifetimes were affected by the cavity size, essentially the same conclusions were drawn from both models.

Molecular Dynamics Simulations of Shockwave Affected STMV Virus to Measure the Frequencies of the Oscillatory Response

Acoustic shockwaves are of interest as a possible means of the selective inactivation of viruses. It has been proposed that such inactivation may be enhanced by driving the virus particles at frequencies matching the characteristic frequency corresponding to acoustic modes of the viral structures, setting up a resonant response. Characteristic frequencies of viruses have been previously studied through opto-mechanical techniques. In contrast to optical excitation, shockwaves may be able to probe acoustic modes without the limitation of optical selection rules. This work explores molecular dynamics simulations of shockwaves interacting with a single STMV virus structure, in full atomistic detail, in order to measure the frequency of the response of the overall structure. Shockwaves of varying energy were set up in a water box containing the STMV structure by assigning water molecules at the edge of the box with an elevated velocity inward—in the direction of the virus. It was found that the structure compressed and stretched in a periodic oscillation of frequency 65 ± 6.5 GHz. This measured frequency did not show strong dependency on the energy of the shockwave perturbing the structure, suggesting the frequency is a characteristic of the structure. The measured frequency is also consistent with values predicted from elastic theory. Additionally, it was found that subjecting the virus to repeated shockwaves led to further deformation of the structure and the magnitude of the overall deformation could be altered by varying the time delay between repeated shockwave pulses.

Lethal DNA damage caused by ion-induced shock waves in cells

The elucidation of fundamental mechanisms underlying ion-induced radiation damage of biological systems is crucial for advancing radiotherapy with ion beams and for radiation protection in space. The study of ion-induced biodamage using the phenomenon-based multiscale approach (MSA) to the physics of radiation damage with ions has led to the prediction of nanoscale shock waves created by ions in a biological medium at the high linear energy transfer (LET). The high-LET regime corresponds to the keV and higher-energy losses by ions per nanometer, which is typical for ions heavier than carbon at the Bragg peak region in biological media. This paper reveals that the thermomechanical stress of the DNA molecule caused by the ion-induced shock wave becomes the dominant mechanism of complex DNA damage at the high-LET ion irradiation. Damage of the DNA molecule in water caused by a projectile-ion-induced shock wave is studied by means of reactive molecular dynamics simulations. Five projectile ions (carbon, oxygen, silicon, argon, and iron) at the Bragg peak energies are considered. For the chosen segment of the DNA molecule and the collision geometry, the number of DNA strand breaks is evaluated for each projectile ion as a function of the bond dissociation energy and the distance from the ion's path to the DNA strands. Simulations reveal that argon and especially iron ions induce the breakage of multiple bonds in a DNA double convolution containing 20 DNA base pairs. The DNA damage produced in segments of such size leads to complex irreparable lesions in a cell. This makes the shock-wave-induced thermomechanical stress the dominant mechanism of complex DNA damage at the high-LET ion irradiation. A detailed theory for evaluating the DNA damage caused by ions at high-LET is formulated and integrated into the MSA formalism. The theoretical analysis reveals that a single ion hitting a cell nucleus at high-LET is sufficient to produce highly complex, lethal damages to a cell by the shock-wave-induced thermomechanical stress. Accounting for the shock-wave-induced thermomechanical mechanism of DNA damage provides an explanation for the "overkill" effect observed experimentally in the dependence of cell survival probabilities on the radiation dose delivered with iron ions. This important observation provides strong experimental evidence of the ion-induced shock-wave effect and the related mechanism of radiation damage in cells.

Molecular dynamics study of the competitive binding of hydrogen peroxide and water molecules with DNA phosphate groups

The interaction of hydrogen peroxide molecules with the DNA double helix is of great interest for understanding the mechanisms of anticancer therapy utilising heavy ion beams. In the present work, a molecular dynamics study of competitive binding of hydrogen peroxide and water molecules with phosphate groups of the DNA double helix backbone was carried out. The system of DNA double helix in a water solution with hydrogen peroxide molecules and Na[Formula: see text] counterions was simulated. The results show that the hydrogen peroxide molecules bind to oxygen atoms of the phosphate groups of the double helix backbone replacing water molecules of its hydration shell. The complexes of hydrogen peroxide molecules with the phosphate groups are stabilized by one or two hydrogen bonds and by Na[Formula: see text] counterions, forming ion-mediated contacts between phosphate groups and hydrogen peroxide molecules. The complex characterized by one H-bond between the hydrogen peroxide molecule and phosphate group is dominant, the other complexes are rare. The hydrogen peroxide molecule bound to the phosphate group of the double helix backbone can inhibit the formation of hydrogen bonds indispensable for the DNA biological functioning.

A Mathematical Radiobiological Model (MRM) to Predict Complex DNA Damage and Cell Survival for Ionizing Particle Radiations of Varying Quality

Predicting radiobiological effects is important in different areas of basic or clinical applications using ionizing radiation (IR); for example, towards optimizing radiation protection or radiation therapy protocols. In this case, we utilized as a basis the ‘MultiScale Approach (MSA)’ model and developed an integrated mathematical radiobiological model (MRM) with several modifications and improvements. Based on this new adaptation of the MSA model, we have predicted cell-specific levels of initial complex DNA damage and cell survival for irradiation with ¹¹Β, ¹²C, ¹⁴Ν, ¹⁶Ο, ²⁰Νe, ⁴⁰Αr, ²⁸Si and ⁵⁶Fe ions by using only three input parameters (particle’s LET and two cell-specific parameters: the cross sectional area of each cell nucleus and its genome size). The model-predicted survival curves are in good agreement with the experimental ones. The particle Relative Biological Effectiveness (RBE) and Oxygen Enhancement Ratio (OER) are also calculated in a very satisfactory way. The proposed integrated MRM model (within current limitations) can be a useful tool for the assessment of radiation biological damage for ions used in hadron-beam radiation therapy or radiation protection purposes.

A general approach to study molecular fragmentation and energy redistribution after an ionizing event

We propose to combine quantum chemical calculations, statistical mechanical methods, and photoionization and particle collision experiments to unravel the redistribution of internal energy of the furan cation and its dissociation pathways. This approach successfully reproduces the relative intensity of the different fragments as a function of the internal energy of the system in photoelectron-photoion coincidence experiments and the different mass spectra obtained when ions ranging from Ar+ to Xe25+ or electrons are used in collision experiments. It provides deep insights into the redistribution of the internal energy in the ionized molecule and its influence on the dissociation pathways and resulting charged fragments. The present pilot study demonstrates the efficiency of a statistical exchange of excitation energy among various degrees of freedom of the molecule and proves that the proposed approach is mature to be extended to more complex systems.

Relative Role of Physical Mechanisms on Complex Biodamage Induced by Carbon Irradiation

The effective use of swift ion beams in cancer treatment (known as hadrontherapy) as well as appropriate protection in manned space missions rely on the accurate understanding of the energy delivery to cells that damages their genetic information. The key ingredient characterizing the response of a medium to the perturbation induced by charged particles is its electronic excitation spectrum. By using linear-response time-dependent density functional theory, we obtained the energy and momentum transfer excitation spectrum (the energy-loss function, ELF) of liquid water (the main constituent of biological tissues), which was in excellent agreement with experimental data. The inelastic scattering cross sections obtained from this ELF, together with the elastic scattering cross sections derived by considering the condensed phase nature of the medium, were used to perform accurate Monte Carlo simulations of the energy deposited by swift carbon ions in liquid water and carried away by the generated secondary electrons, producing inelastic events such as ionization, excitation, and dissociative electron attachment (DEA). The latter are strongly correlated with cellular death, which is scored in sensitive volumes with the size of two DNA convolutions. The sizes of the clusters of damaging events for a wide range of carbon-ion energies, from those relevant to hadrontherapy up to those for cosmic radiation, predict with unprecedented statistical accuracy the nature and relative magnitude of the main inelastic processes contributing to radiation biodamage, confirming that ionization accounts for the vast majority of complex damage. DEA, typically regarded as a very relevant biodamage mechanism, surprisingly plays a minor role in carbon-ion induced clusters of harmful events.

Generalized stochastic microdosimetric model: The main formulation

The present work introduces a rigorous stochastic model, called the generalized stochastic microdosimetric model (GSM^{2}), to describe biological damage induced by ionizing radiation. Starting from the microdosimetric spectra of energy deposition in tissue, we derive a master equation describing the time evolution of the probability density function of lethal and potentially lethal DNA damage induced by a given radiation to a cell nucleus. The resulting probability distribution is not required to satisfy any a priori conditions. After the initial assumption of instantaneous irradiation, we generalized the master equation to consider damage induced by a continuous dose delivery. In addition, spatial features and damage movement inside the nucleus have been taken into account. In doing so, we provide a general mathematical setting to fully describe the spatiotemporal damage formation and evolution in a cell nucleus. Finally, we provide numerical solutions of the master equation exploiting Monte Carlo simulations to validate the accuracy of GSM^{2}. Development of GSM^{2} can lead to improved modeling of radiation damage to both tumor and normal tissues, and thereby impact treatment regimens for better tumor control and reduced normal tissue toxicities.

Electron nuclear dynamics with plane wave basis sets: complete theory and formalism

Electron nuclear dynamics (END) is an ab initio quantum dynamics method that adopts a time-dependent, variational, direct, and non-adiabatic approach. The simplest-level (SL) END (SLEND) version employs a classical mechanics description for nuclei and a Thouless single-determinantal wave function for electrons. A higher-level END version, END/Kohn-Sham density functional theory, improves the electron correlation description of SLEND. While both versions can simulate various types of chemical reactions, they have difficulties to simulate scattering/capture of electrons to/from the continuum due to their reliance on localized Slater-type basis functions. To properly describe those processes, we formulate END with plane waves (PWs, END/PW), basis functions able to represent both bound and unbound electrons. As extra benefits, PWs also afford fast algorithms to simulate periodic systems, parametric independence from nuclear positions and momenta, and elimination of basis set linear dependencies and orthogonalization procedures. We obtain the END/PW formalism by extending the Thouless wave function and associated electron density to periodic systems, expressing the energy terms as functionals of the latter entities, and deriving the energy gradients with respect to nuclear and electronic variables. END/ PW has a great potential to simulate electron processes in both periodic (crystal) and aperiodic (molecular) systems (the latter in a supercell approach). Following previous END studies, END/PW will be applied to electron scattering processes in proton cancer therapy reactions.

Ring Formation and Hydration Effects in Electron Attachment to Misonidazole

We study the reactivity of misonidazole with low-energy electrons in a water environment combining experiment and theoretical modelling. The environment is modelled by sequential hydration of misonidazole clusters in vacuum. The well-defined experimental conditions enable computational modeling of the observed reactions. While the NO 2 - dissociative electron attachment channel is suppressed, as also observed previously for other molecules, the OH - channel remains open. Such behavior is enabled by the high hydration energy of OH - and ring formation in the neutral radical co-fragment. These observations help to understand the mechanism of bio-reductive drug action. Electron-induced formation of covalent bonds is then important not only for biological processes but may find applications also in technology.

A New Standard DNA Damage (SDD) Data Format

Our understanding of radiation-induced cellular damage has greatly improved over the past few decades. Despite this progress, there are still many obstacles to fully understand how radiation interacts with biologically relevant cellular components, such as DNA, to cause observable end points such as cell killing. Damage in DNA is identified as a major route of cell killing. One hurdle when modeling biological effects is the difficulty in directly comparing results generated by members of different research groups. Multiple Monte Carlo codes have been developed to simulate damage induction at the DNA scale, while at the same time various groups have developed models that describe DNA repair processes with varying levels of detail. These repair models are intrinsically linked to the damage model employed in their development, making it difficult to disentangle systematic effects in either part of the modeling chain. These modeling chains typically consist of track-structure Monte Carlo simulations of the physical interactions creating direct damages to DNA, followed by simulations of the production and initial reactions of chemical species causing so-called "indirect" damages. After the induction of DNA damage, DNA repair models combine the simulated damage patterns with biological models to determine the biological consequences of the damage. To date, the effect of the environment, such as molecular oxygen (normoxic vs. hypoxic), has been poorly considered. We propose a new standard DNA damage (SDD) data format to unify the interface between the simulation of damage induction in DNA and the biological modeling of DNA repair processes, and introduce the effect of the environment (molecular oxygen or other compounds) as a flexible parameter. Such a standard greatly facilitates inter-model comparisons, providing an ideal environment to tease out model assumptions and identify persistent, underlying mechanisms. Through inter-model comparisons, this unified standard has the potential to greatly advance our understanding of the underlying mechanisms of radiation-induced DNA damage and the resulting observable biological effects when radiation parameters and/or environmental conditions change.

Energy Spectra of Protons and Generated Secondary Electrons around the Bragg Peak in Materials of Interest in Proton Therapy

The number and energy of secondary electrons generated around the trajectories of swift protons interacting with biological materials are highly relevant in proton therapy, due to the prominent role of low-energy electrons in the production of biodamage. For a given material, electron energy distributions are determined by the proton energy; and it is imperative that the distribution of proton energy at depths around the Bragg peak region be described as accurately as possible. With this objective, we simulated the energy distributions of proton beams of clinically relevant energies (50-300 MeV) at depths around the Bragg peak in liquid water and the water-equivalent polymer poly(methyl methacrylate) (PMMA). By using a simple model, this simulation has been conveniently extended to account for nuclear fragmentation reactions, providing depth-dose curves in excellent agreement with available experimental data. Special care has been taken to describe the electronic excitation spectrum of the target, taking into account its condensed phase nature. A predictive formula has been obtained for the mean value and the width of the proton energy distribution at the Bragg peak depth, quantities which are found to grow linearly with the initial energy of the beam, in good agreement with available data. To accurately characterize (in number and energy) the electrons generated around the proton paths, the energy distributions of the latter at each depth have been convoluted with the energy-dependent ionization inverse mean free paths. This results in a number of low-energy electrons around the Bragg peak larger than when only the proton beam average energy at the given depths is considered. The convoluted ionization inverse mean free path closely resembles the Bragg curve shape. The average energy of the secondary electrons is nearly constant (∼55 eV for liquid water and ∼43 eV for PMMA) in the plateau of the Bragg curve, independent of the proton incident energy and suddenly decaying once the Bragg peak is reached. These findings highlight the importance of a precise calculation of the proton beam energy distribution as a function of the target depth to reliably characterize the secondary electrons generated around the Bragg peak region.

Electron Nuclear Dynamics Simulations of Proton Cancer Therapy Reactions: Water Radiolysis and Proton- and Electron-Induced DNA Damage in Computational Prototypes

Proton cancer therapy (PCT) utilizes high-energy proton projectiles to obliterate cancerous tumors with low damage to healthy tissues and without the side effects of X-ray therapy. The healing action of the protons results from their damage on cancerous cell DNA. Despite established clinical use, the chemical mechanisms of PCT reactions at the molecular level remain elusive. This situation prevents a rational design of PCT that can maximize its therapeutic power and minimize its side effects. The incomplete characterization of PCT reactions is partially due to the health risks associated with experimental/clinical techniques applied to human subjects. To overcome this situation, we are conducting time-dependent and non-adiabatic computer simulations of PCT reactions with the electron nuclear dynamics (END) method. Herein, we present a review of our previous and new END research on three fundamental types of PCT reactions: water radiolysis reactions, proton-induced DNA damage and electron-induced DNA damage. These studies are performed on the computational prototypes: proton + H₂O clusters, proton + DNA/RNA bases and + cytosine nucleotide, and electron + cytosine nucleotide + H₂O. These simulations provide chemical mechanisms and dynamical properties of the selected PCT reactions in comparison with available experimental and alternative computational results.

Measurements and simulations of microscopic damage to DNA in water by 30 keV electrons: A general approach applicable to other radiation sources and biological targets

The determination of the microscopic dose-damage relationship for DNA in an aqueous environment is of a fundamental interest for dosimetry and applications in radiation therapy and protection. We combine geant4 particle-scattering simulations in water with calculations concerning the movement of biomolecules to obtain the energy deposit in the biologically relevant nanoscopic volume. We juxtaposition these results to the experimentally determined damage to obtain the dose-damage relationship at a molecular level. This approach is tested for an experimentally challenging system concerning the direct irradiation of plasmid DNA (pUC19) in water with electrons as primary particles. Here a microscopic target model for the plasmid DNA based on the relation of lineal energy and radiation quality is used to calculate the effective target volume. It was found that on average fewer than two ionizations within a 7.5-nm radius around the sugar-phosphate backbone are sufficient to cause a single strand break, with a corresponding median lethal energy deposit being E_{1/2}=6±4 eV. The presented method is applicable for ionizing radiation (e.g., γ rays, x rays, and electrons) and a variety of targets, such as DNA, proteins, or cells.

Exploring water radiolysis in proton cancer therapy: Time-dependent, non-adiabatic simulations of H+ + (H2O)1-6

To elucidate microscopic details of proton cancer therapy (PCT), we apply the simplest-level electron nuclear dynamics (SLEND) method to H⁺ + (H₂O)_1-6 at E_Lab = 100 keV. These systems are computationally tractable prototypes to simulate water radiolysis reactions—i.e. the PCT processes that generate the DNA-damaging species against cancerous cells. To capture incipient bulk-water effects, ten (H₂O)_1-6 isomers are considered, ranging from quasi-planar/multiplanar (H₂O)_1-6 to “smallest-drop” prism and cage (H₂O)₆ structures. SLEND is a time-dependent, variational, non-adiabatic and direct method that adopts a nuclear classical-mechanics description and an electronic single-determinantal wavefunction in the Thouless representation. Short-time SLEND/6-31G* (n = 1–6) and /6-31G** (n = 1–5) simulations render cluster-to-projectile 1-electron-transfer (1-ET) total integral cross sections (ICSs) and 1-ET probabilities. In absolute quantitative terms, SLEND/6-31G* 1-ET ICS compares satisfactorily with alternative experimental and theoretical results only available for n = 1 and exhibits almost the same accuracy of the best alternative theoretical result. SLEND/6-31G** overestimates 1-ET ICS for n = 1, but a comparable overestimation is also observed with another theoretical method. An investigation on H⁺ + H indicates that electron direct ionization (DI) becomes significant with the large virtual-space quasi-continuum in large basis sets; thus, SLEND/6-31G** 1-ET ICS is overestimated by DI contributions. The solution to this problem is discussed. In relative quantitative terms, both SLEND/6-31* and /6-31G** 1-ET ICSs precisely fit into physically justified scaling formulae as a function of the cluster size; this indicates SLEND’s suitability for predicting properties of water clusters with varying size. Long-time SLEND/6-31G* (n = 1–4) simulations predict the formation of the DNA-damaging radicals H, OH, O and H₃O. While “smallest-drop” isomers are included, no early manifestations of bulk water PCT properties are observed and simulations with larger water clusters will be needed to capture those effects. This study is the largest SLEND investigation on water radiolysis to date.

Water radiolysis by low-energy carbon projectiles from first-principles molecular dynamics

Water radiolysis by low-energy carbon projectiles is studied by first-principles molecular dynamics. Carbon projectiles of kinetic energies between 175 eV and 2.8 keV are shot across liquid water. Apart from translational, rotational and vibrational excitation, they produce water dissociation. The most abundant products are H and OH fragments. We find that the maximum spatial production of radiolysis products, not only occurs at low velocities, but also well below the maximum of energy deposition, reaching one H every 5 Å at the lowest speed studied (1 Bohr/fs), dissociative collisions being more significant at low velocity while the amount of energy required to dissociate water is constant and much smaller than the projectile's energy. A substantial fraction of the energy transferred to fragments, especially for high velocity projectiles, is in the form of kinetic energy, such fragments becoming secondary projectiles themselves. High velocity projectiles give rise to well-defined binary collisions, which should be amenable to binary approximations. This is not the case for lower velocities, where multiple collision events are observed. H secondary projectiles tend to move as radicals at high velocity, as cations when slower. We observe the generation of new species such as hydrogen peroxide and formic acid. The former occurs when an O radical created in the collision process attacks a water molecule at the O site. The latter when the C projectile is completely stopped and reacts with two water molecules.

Determination of Energy-Transfer Distributions in Ionizing Ion-Molecule Collisions

The ionization and fragmentation of the nucleoside thymidine in the gas phase has been investigated by combining ion collision with state-selected photoionization experiments and quantum chemistry calculations. The comparison between the mass spectra measured in both types of experiments allows us to accurately determine the distribution of the energy deposited in the ionized molecule as a result of the collision. The relation of two experimental techniques and theory shows a strong correlation between the excited states of the ionized molecule with the computed dissociation pathways, as well as with charge localization or delocalization.

Water versus DNA: new insights into proton track-structure modelling in radiobiology and radiotherapy

Water is a common surrogate of DNA for modelling the charged particle-induced ionizing processes in living tissue exposed to radiations. The present study aims at scrutinizing the validity of this approximation and then revealing new insights into proton-induced energy transfers by a comparative analysis between water and realistic biological medium. In this context, a self-consistent quantum mechanical modelling of the ionization and electron capture processes is reported within the continuum distorted wave-eikonal initial state framework for both isolated water molecules and DNA components impacted by proton beams. Their respective probability of occurrence-expressed in terms of total cross sections-as well as their energetic signature (potential and kinetic) are assessed in order to clearly emphasize the differences existing between realistic building blocks of living matter and the controverted water-medium surrogate. Consequences in radiobiology and radiotherapy will be discussed in particular in view of treatment planning refinement aiming at better radiotherapy strategies.

Thermomechanical effects caused by heavy ions propagating in tissue

The thermomechanical effects caused by ions propagating in tissue are discussed. Large energy densities in small regions surrounding ion paths cause shock waves propagating in tissue. The strength of the shock waves depends on the linear energy transfer. Molecular dynamics simulations help in determining the necessary strength of shock waves in order for the stresses caused by them to directly produce DNA strand breaks. At much smaller values of linear energy transfer, the shock waves may be instrumental in propagating reactive species formed close to the ion's path to large distances, successfully competing with diffusion.

Novel experimental setup for time-of-flight mass spectrometry ion detection in collisions of anionic species with neutral gas-phase molecular targets

We report a novel experimental setup for studying collision induced products resulting from the interaction of anionic beams with a neutral gas-phase molecular target. The precursor projectile was admitted into vacuum through a commercial pulsed valve, with the anionic beam produced in a hollow cathode discharge-induced plasma, and guided to the interaction region by a set of deflecting plates where it was made to interact with the target beam. Depending on the collision energy regime, negative and positive species can be formed in the collision region and ions were time-of-flight (TOF) mass-analysed. Here, we present data on O₂ precursor projectile, where we show clear evidence of O^- and O₂^- formation from the hollow cathode source as well as preliminary results on the interaction of these anions with nitromethane, CH₃NO₂. The negative ions formed in such collisions were analysed using time-of-flight mass spectrometry. The five most dominant product anions were assigned to H^-, O^-, NO^-, CNO^- and CH₃NO₂^-.

Revealing the mechanism of the low-energy electron yield enhancement from sensitizing nanoparticles

We provide a physical explanation for the enhancement of the low-energy electron production by sensitizing nanoparticles due to irradiation by fast ions. It is demonstrated that a significant increase in the number of emitted electrons arises from the collective electron excitations in the nanoparticle. We predict a new mechanism of the yield enhancement due to the plasmon excitations and quantitatively estimate its contribution to the electron production. Revealing the nanoscale mechanism of the electron yield enhancement, we provide an efficient tool for evaluating the yield of the emitted electron from various sensitizers. It is shown that the number of low-energy electrons generated by the gold and platinum nanoparticles of a given size exceeds that produced by the equivalent volume of water and by other metallic (e.g., gadolinium) nanoparticles by an order of magnitude. This observation emphasizes the sensitization effect of the noble-metal nanoparticles and endorses their application in novel technologies of cancer therapy with ionizing radiation.

Angular and energy distributions of electrons produced in arbitrary biomaterials by proton impact

We present a simple method for obtaining reliable angular and energy distributions of electrons ejected from arbitrary condensed biomaterials by proton impact. Relying on a suitable description of the electronic excitation spectrum and a physically motivated relation between the ion and electron scattering angles, it yields cross sections in rather good agreement with experimental data in a broad range of ejection angles and energies, by only using as input the target composition and density. The versatility and simplicity of the method, which can be also extended to other charged particles, make it especially suited for obtaining ionization data for any complex biomaterial present in realistic cellular environments.

Future development of biologically relevant dosimetry

Proton and ion beams are radiotherapy modalities of increasing importance and interest. Because of the different biological dose response of these radiations as compared with high-energy photon beams, the current approach of treatment prescription is based on the product of the absorbed dose to water and a biological weighting factor, but this is found to be insufficient for providing a generic method to quantify the biological outcome of radiation. It is therefore suggested to define new dosimetric quantities that allow a transparent separation of the physical processes from the biological ones. Given the complexity of the initiation and occurrence of biological processes on various time and length scales, and given that neither microdosimetry nor nanodosimetry on their own can fully describe the biological effects as a function of the distribution of energy deposition or ionization, a multiscale approach is needed to lay the foundation for the aforementioned new physical quantities relating track structure to relative biological effectiveness in proton and ion beam therapy. This article reviews the state-of-the-art microdosimetry, nanodosimetry, track structure simulations, quantification of reactive species, reference radiobiological data, cross-section data and multiscale models of biological response in the context of realizing the new quantities. It also introduces the European metrology project, Biologically Weighted Quantities in Radiotherapy, which aims to investigate the feasibility of establishing a multiscale model as the basis of the new quantities. A tentative generic expression of how the weighting of physical quantities at different length scales could be carried out is presented.

Energy deposition of H and He ion beams in hydroxyapatite films: a study with implications for ion-beam cancer therapy

Ion-beam cancer therapy is a promising technique to treat deep-seated tumors; however, for an accurate treatment planning, the energy deposition by the ions must be well known both in soft and hard human tissues. Although the energy loss of ions in water and other organic and biological materials is fairly well known, scarce information is available for the hard tissues (i.e., bone), for which the current stopping power information relies on the application of simple additivity rules to atomic data. Especially, more knowledge is needed for the main constituent of human bone, calcium hydroxyapatite (HAp), which constitutes 58% of its mass composition. In this work the energy loss of H and He ion beams in HAp films has been obtained experimentally. The experiments have been performed using the Rutherford backscattering technique in an energy range of 450-2000 keV for H and 400-5000 keV for He ions. These measurements are used as a benchmark for theoretical calculations (stopping power and mean excitation energy) based on the dielectric formalism together with the MELF-GOS (Mermin energy loss function-generalized oscillator strength) method to describe the electronic excitation spectrum of HAp. The stopping power calculations are in good agreement with the experiments. Even though these experimental data are obtained for low projectile energies compared with the ones used in hadron therapy, they validate the mean excitation energy obtained theoretically, which is the fundamental quantity to accurately assess energy deposition and depth-dose curves of ion beams at clinically relevant high energies. The effect of the mean excitation energy choice on the depth-dose profile is discussed on the basis of detailed simulations. Finally, implications of the present work on the energy loss of charged particles in human cortical bone are remarked.

Inelastic cross sections for low-energy electrons in liquid water: exchange and correlation effects

Low-energy electrons play a prominent role in radiation therapy and biology as they are the largest contributor to the absorbed dose. However, no tractable theory exists to describe the interaction of low-energy electrons with condensed media. This article presents a new approach to include exchange and correlation (XC) effects in inelastic electron scattering at low energies (below ∼10 keV) in the context of the dielectric theory. Specifically, an optical-data model of the dielectric response function of liquid water is developed that goes beyond the random phase approximation (RPA) by accounting for XC effects using the concept of the many-body local-field correction (LFC). It is shown that the experimental energy-loss-function of liquid water can be reproduced by including into the RPA dispersion relations XC effects (up to second order) calculated in the time-dependent local-density approximation with the addition of phonon-induced broadening in N. D. Mermin's relaxation-time approximation. Additional XC effects related to the incident and/or struck electrons are included by means of the vertex correction calculated by a modified Hubbard formula for the exchange-only LFC. Within the first Born approximation, the present XC corrections cause a significantly larger reduction (∼10-50%) to the inelastic cross section compared to the commonly used Mott and Ochkur approximations, while also yielding much better agreement with the recent experimental data for amorphous ice. The current work offers a manageable, yet rigorous, approach for including non-Born effects in the calculation of inelastic cross sections for low-energy electrons in liquid water, which due to its generality, can be easily extended to other condensed media.

Biodamage via shock waves initiated by irradiation with ions

Radiation damage following the ionising radiation of tissue has different scenarios and mechanisms depending on the projectiles or radiation modality. We investigate the radiation damage effects due to shock waves produced by ions. We analyse the strength of the shock wave capable of directly producing DNA strand breaks and, depending on the ion's linear energy transfer, estimate the radius from the ion's path, within which DNA damage by the shock wave mechanism is dominant. At much smaller values of linear energy transfer, the shock waves turn out to be instrumental in propagating reactive species formed close to the ion's path to large distances, successfully competing with diffusion.

Semiempirical model for the ion impact ionization of complex biological media

We present a semiempirical model for calculating the electron emission from any organic compound after ion impact. With only the input of the density and composition of the target we are able to evaluate its ionization cross sections using plausible approximations. Results for protons impacting in the most representative biological targets (such as water or DNA components) show a very good comparison with experimental data. Because of its simplicity and great predictive effectiveness, the method can be immediately extended to any combination of biological target and charged particle of interest in ion beam cancer therapy.

Multiscale physics of ion-induced radiation damage

This is a review of a multiscale approach to the physics of ion-beam cancer therapy, an approach suggested in order to understand the interplay of a large number of phenomena involved in the radiation damage scenario occurring on a range of temporal, spatial, and energy scales. We describe different effects that take place on different scales and play major roles in the scenario of interaction of ions with tissue. The understanding of these effects allows an assessment of relative biological effectiveness that relates the physical quantities, such as dose, to the biological values, such as the probability of cell survival.

Analytical model of chemical phase and formation of DSB in chromosomes by ionizing radiation

Mathematical analytical model of the processes running in individual radical clusters during the chemical phase (under the presence of radiomodifiers) proposed by us earlier has been further developed and improved. It has been applied to the data presented by Blok and Loman characterizing the oxygen effect in SSB and DSB formation (in water solution and at low-LET radiation) also in the region of very small oxygen concentrations, which cannot be studied with the help of experiments done with living cells. In this new analysis the values of all reaction rates and diffusion parameters known from literature have been made use of. The great increase of SSB and DSB at zero oxygen concentration may follow from the fact that at small oxygen concentrations the oxygen absorbs other radicals while at higher concentrations the formation of oxygen radicals prevails. It explains the double oxygen effect found already earlier by Ewing. The model may be easily extended to include also the effects of other radiomodifiers present in medium during irradiation.