A track structure model for simulation of strand breaks in plasmid DNA after heavy ion irradiation

We present a track structure model based on the local dose deposited around heavy ion tracks to explain the cross sections for single-strand and double-strand break induction in plasmid DNA in different aqueous buffers. The model is based only on measurable quantities, namely the effect distribution for inducing strand breaks after x-ray irradiation as a function of dose, and the radial dose distribution of the heavy ion track. The effect of indirect DNA damage mediated by free radicals produced in the water surrounding the DNA is accounted for by allowing the radial dose distribution to be smeared in space by an effective target size corresponding to the squared sum of the geometrical extension of the plasmid molecule and the mean free drift path of the radicals in the buffer solution. Our calculations reproduce well the measured cross sections for single-strand and double-strand break induction in SV40 plasmid DNA in various buffer solutions both as a function of the LET and of the specific energy of the heavy ion.     

Investigation into the foundations of the track-event theory of cell survival and the radiation action model based on nanodosimetry

This work aims at elaborating the basic assumptions behind the “track-event theory” (TET) and its derivate “radiation action model based on nanodosimetry” (RAMN) by clearly distinguishing between effects of tracks at the cellular level and the induction of lesions in subcellular targets. It is demonstrated that the model assumptions of Poisson distribution and statistical independence of the frequency of single and clustered DNA lesions are dispensable for multi-event distributions because they follow from the Poisson distribution of the number of tracks affecting the considered target volume. It is also shown that making these assumptions for the single-event distributions of the number of lethal and sublethal lesions within a cell would lead to an essentially exponential dose dependence of survival for practically relevant values of the absorbed dose. Furthermore, it is elucidated that the model equation used for consideration of repair within the TET is based on the assumption that DNA lesions induced by different tracks are repaired independently. Consequently, the model equation is presumably inconsistent with the model assumptions and requires an additional model parameter. Furthermore, the methodology for deriving model parameters from nanodosimetric properties of particle track structure is critically assessed. Based on data from proton track simulations it is shown that the assumption of statistically independent targets leads to the prediction of negligible frequency of clustered DNA damage. An approach is outlined how track structure could be considered in determining the model parameters, and the implications for TET and RAMN are discussed.

     

Cluster effects within the local effect model

The local effect model predicts the relative biological effectiveness (RBE) for different ions and cell lines starting from the corresponding experimental photon data and an amorphous track structure model. Here we present an extension of the model that takes cluster effects of single-strand breaks (SSBs) at the nanometer scale into account. In line with the main idea of the local effect model, we take the yields of SSBs and double-strand breaks (DSBs) from experimental photon data and use a Monte Carlo method to distribute them onto the DNA. We score clusters of SSBs where individual SSBs are separated by less than 25 bp as additional DSBs. Assuming that the number of DSBs is a measure of cell lethality, we derive a modified cell survival curve for photons that takes these cluster effects into account. In combination with an improved radial dose distribution, we find that the extended local effect model including cluster effects reproduces most experimental data better than the original local effect model and thus enhances the accuracy of the local effect model.     

Radiation-induced bystander effects and the DNA paradigm: an "out of field" perspective

Over the past 20 years there has been increasing evidence that cells and the progeny of cells surviving a very low dose of ionizing radiation [micro-mGy] can exhibit a wide range of non-monotonic effects such as adaptive responses, low dose hypersensitivity and other delayed effects. These effects are inconsistent with the expected dose-response, when based on extrapolation of high dose data and cast doubt on the reliability of extrapolating from high dose data to predict low dose effects. Recently the cause of many of these effects has been tentatively ascribed to so-called "bystander effects". These are effects that occur in cells not directly hit by an ionizing track but which are influenced by signals from irradiated cells and are thus highly relevant in situations where the dose is very low. Not all bystander effects may be deleterious although most endpoints measured involve cell damage or death. In this commentary, we consider how these effects impact the historical central dogma of radiobiology and radiation protection, which is that DNA double strand breaks are the primary radiation-induced lesion which can be quantifiably related to received dose and which determine the probability that a cancer will result from a radiation exposure. We explore the low dose issues and the evidence and conclude that in the very low dose region, the primary determinant of radiation exposure outcome is the genetic and epigenetic background of the individual and not solely the dose. What this does is to dissociate dose from effect as a quantitative relationship, but it does not necessarily mean that the effect is ultimately unrelated to DNA damage. The fundamental thesis we present is that at low doses fundamentally different mechanisms underlie radiation action and that at these doses, effect is not quantitatively related to dose.     

Tumor therapy and track structure

The elevated relative biological effectiveness (RBE) of heavy ions like carbon is the main reason for their use in radiotherapy and is due to the microscopic distribution of dose inside each particle track. High local doses produce lesions that are expected to have a diminished possibility of repair. Thus, RBE depends on track structure and on the biological repair capacity of the tissue that is affected by the irradiation. For tumor treatment planning with heavy ions, the beam quality and the tissue sensitivity have to be taken into account. Using the dependence of radial dose distribution on particle energy and atomic number on the physical side and x-ray dose response for the repair capacity on the biological side, the response to particle irradiation can be calculated in the local effect model (LEM) and used for treatment planning. This article traces the route from electron emission as the basis of track structure to the RBE calculation and the application in treatment planning. Received: 21 April 1999 / Accepted in revised form: 1 September 1999     

Radial dose distribution for 18.3 MeV/n alpha beams in tissue-equivalent gas

Experimental measurements of the radial restricted linear energy transfer (LETr) for alpha beams of 18.3 MeV/n in tissue-equivalent gas were presented. The radial dose distribution for the alpha beam was deduced from the restricted LET measurements. A differential W value for the alpha particle in the tissue-equivalent gas was also deduced. The result for the differential W value was 29.0 +/- 0.9 eV/ion pair. The radial dose varied according to an inverse-square function with distance from the track center for radii larger than 0.026 micron. The maximum extension of the track, the penumbra radius, as 2.73 +/- 1.67 microns, which was less than predicted by calculations (7-9 microns).     

Estimation of double-strand break quality based on track-structure calculations

The aim of this study was to investigate whether double-strand break (DSB) quality is related to the complexity of radiation-induced damage or to the spatial distribution of initial DSBs. The analysis was based on track structure calculations and DNA damage modelling. The results obtained indicate that the quality of DSBs is related to their initial spatial distribution rather than to their complexity.     

Review: total doses in fractionated radiotherapy--implications of new radiobiological data

The total dose in radiotherapy has been adjusted in the past for different fractionation schedules by the use of empirical formulae such as NSD, TDF and CRE. It is now appropriate to consider fractionation factors which include more biological insight in their formulation than was possible earlier. It has become clear, from both clinical and experimental animal data, that the total dose in multi-fraction irradiations depends more critically on size of dose-per-fraction for late than for early damage to normal tissues. This difference has been interpreted as due to different shapes of the underlying dose-response curves. The late reactions respond with more curvature in the dose-response curve, i.e. with more repair capability at very low doses per fraction, than the early tissue reactions. A linear-quadratic relationship for the dose-response curves has been found to fit experimental data well, with few exceptions. This paper reviews this interpretation and explores some of its implications for radiotherapy and for radiobiology applied to therapy. Of many repair factors that have been suggested, the ratio alpha/beta (of the linear to the quadratic coefficients) is one that should be independent of the level of damage assayed. Values of alpha/beta of about 10 Gy have been reported for a number of early tissue responses but a range of values from about 1 to 5 or 6 Gy for late responses. It is a current challenge to radiobiology to explain why this difference occurs. Once such values are known for different tissues--and the dangers of premature assumptions are emphasized--calculations are possible which might be useful in radiotherapy as an alternative to NSD, TDF, CRE etc. Some data are presented on the magnitude of differences from these previously used empirical formulae, with a discussion about how easily detected the discrepancies might be in clinical practice. Applications to hypofractionation, hyperfractionation and accelerated fractionation are illustrated.     

Microdosimetry of rat alveolar type II cells irradiated with alpha particles from 239PuO2

The alveolar type II cell is one of the critical cells for radiation damage in the lungs after inhalation of radioactive aerosols. With the aid of a Quantimet-970 image analyzer and a VAX-11/780 computer, we calculated the radiation dose to rat alveolar type II cells from alpha particles emitted by 239PuO2. A series of dosimetric parameters for type II cells, including track length distribution, linear energy transfer (LET), values of the specific energy for a single hit of a spherical target (z1), cellular dose, hit number, and their spatial distributions were calculated. By comparing the volume density of type II cells and lung tissue with energy deposited in alveolar type II cells, we found that the energy deposited per unit volume of type II cells was larger than that of lung tissue excluding type II cells. The z1 for spherical targets and the LET across type II cells were less than those in lung tissue excluding type II cells. The age of the rat and damage to lung by inhalation may significantly influence some of the parameters. The neoplastic transformation probability for type II cells is also discussed. The results suggest that the type II cell is an important target cell in the rat lung for exposure to inhaled 239PuO2.     

Genomic instability, bystander effects and radiation risks: implications for development of protection strategies for man and the environment

The last few years has seen what people are now referring to as a "shifting Paradigm" in our way of thinking about radiation effects on biological systems. The concept of the central role of DNA damage due to double strand breaks induced by a radiation "hit" has been itself hit by many studies showing persistent effects in the distant progeny of radiation exposed cells. This phenomenon is known as radiation induced genomic instability. More recently evidence has been accumulating that not even the parent cell need be exposed to radiation (the bystander effect). The new paradigm suggests that cellular stress responses or damage signalling through a range of signal transduction pathways are involved and that cell-cell contact or secretion of damage signalling molecules can induce responses in undamaged and unirradiated cells. Are these new effects relevant to risk assessment, or does it matter HOW radiation affects cells if we have good epidemiological evidence of which to base our risk estimates? The aim of this paper is to introduce the new concepts and to consider reasons why they might alter our methods of risk estimation. The paper also considers the impact of the new concepts on environmental protection and discusses the need for research in the field of comparative radiobiology if we are to develop policies which can adequately protect biodiversity.     

On robustness and model flexibility in survival analysis: transformed hazard models and average effects

Yin and Ibrahim (2005a, Biometrics 61, 208-216) use a Box-Cox transformed hazard model to acknowledge uncertainty about how a linear predictor acts upon the hazard function of a failure-time response. Particularly, additive and proportional hazards models arise for particular values of the transformation parameter. As is often the case, however, this added model flexibility is obtained at the cost of lessened parameter interpretability. Particularly, the interpretation of the coefficients in the linear predictor is intertwined with the value of the transformation parameter. Moreover, some data sets contain very little information about this parameter. To shed light on the situation, we consider average effects based on averaging (over the joint distribution of the explanatory variables and the failure-time response) the partial derivatives of the hazard, or the log-hazard, with respect to the explanatory variables. First, we consider fitting models which do assume a particular form of covariate effects, for example, proportional hazards or additive hazards. In some such circumstances, average effects are seen to be inferential targets which are robust to the effect form being misspecified. Second, we consider average effects as targets of inference when using the transformed hazard model. We show that in addition to being more interpretable inferential targets, average effects can sometimes be estimated more efficiently than the corresponding regression coefficients.     

DNA Damage Responses following Exposure to Modulated Radiation Fields

During the delivery of advanced radiotherapy treatment techniques modulated beams are utilised to increase dose conformity across the target volume. Recent investigations have highlighted differential cellular responses to modulated radiation fields particularly in areas outside the primary treatment field that cannot be accounted for by scattered dose alone. In the present study, we determined the DNA damage response within the normal human fibroblast AG0-1522B and the prostate cancer cell line DU-145 utilising the DNA damage assay. Cells plated in slide flasks were exposed to 1 Gy uniform or modulated radiation fields. Modulated fields were delivered by shielding 25%, 50% or 75% of the flask during irradiation. The average number of 53BP1 or γH2AX foci was measured in 2 mm intervals across the slide area. Following 30 minutes after modulated radiation field exposure an increase in the average number of foci out-of-field was observed when compared to non-irradiated controls. In-field, a non-uniform response was observed with a significant decrease in the average number of foci compared to uniformly irradiated cells. Following 24 hrs after exposure there is evidence for two populations of responding cells to bystander signals in-and out-of-field. There was no significant difference in DNA damage response between 25%, 50% or 75% modulated fields. The response was dependent on cellular secreted intercellular signalling as physical inhibition of intercellular communication abrogated the observed response. Elevated residual DNA damage observed within out-of-field regions decreased following addition of an inducible nitric oxide synthase inhibitor (Aminoguanidine). These data show, for the first time, differential DNA damage responses in-and out-of-field following modulated radiation field delivery. This study provides further evidence for a role of intercellular communication in mediating cellular radiobiological response to modulated radiation fields and may inform the refinement of existing radiobiological models for the optimization of advanced radiotherapy treatment plans.     

Processing of clustered DNA damage generates additional double-strand breaks in mammalian cells post-irradiation

Clustered DNA damage sites, in which two or more lesions are formed within a few helical turns of the DNA after passage of a single radiation track, are signatures of DNA modifications induced by ionizing radiation in mammalian cells. Mutant hamster cells (xrs-5), deficient in non-homologous end joining (NHEJ), were irradiated at 37 degrees C to determine whether any additional double-strand breaks (DSBs) are formed during processing of gamma-radiation-induced DNA clustered damage sites. A class of non-DSB clustered DNA damage, corresponding to approximately 30% of the initial yield of DSBs, is converted into DSBs reflecting an artefact of preparation of genomic DNA for pulsed field gel electrophoresis. These clusters are removed within 4 min in both NHEJ-deficient and wild-type CHO cells. In xrs-5 cells, a proportion of non-DSB clustered DNA damage, representing approximately 10% of the total yield of non-DSB clustered DNA damage sites, are also converted into DSBs within approximately 30 min post-gamma but not post-alpha irradiation through cellular processing at 37 degrees C. That the majority of radiation-induced non-DSB clustered DNA damage sites are resistant to conversion into DSBs may be biologically significant at environmental levels of radiation exposure, as a non-DSB clustered damage site rather than a DSB, which only constitutes a minor proportion, is more likely to be induced in irradiated cells.     

Correlated hit probability and cell transformation in an effect-specific track length model applied to in vitro alpha irradiation

In estimating the risk from low doses of alpha particles such as those emitted by radon progeny, it is important to consider the correlation between cellular inactivation and transformation that can exist at the cellular level. A phenomenological model of radiation- induced cellular inactivation and transformation at this level is presented here which incorporates aspects of a state vector model of radiation carcinogenesis and of correlated hit probabilities for inactivation and transformation. The general form of the model assumes that both inactivation and initial initiation damage are produced through the interaction of sublesions induced by radiation passing through cell nuclei, with the production of sublesions governed by hit probabilities and a characteristic probability-per-unit track length. The inactivation and initiation events are partially correlated through the use of hit probabilities. In addition, promotional events are incorporated for the case of cellular transformation based on a previously published state vector model. The model provides good fits to available data on the relationship between inactivation, transformation and LET for doses of alpha above 0.1 Gy in the range of LETs commonly produced by radon and progeny; by ”good fits” we mean here the ability to yield the correct shapes of dose-response data using parameter values that vary smoothly with LET and using inactivation parameters that are applied consistently between inactivation and transformation assays. The resulting model correctly predicts recent findings indicating an increased transformation frequency per surviving cell when a population receives a distribution of hits compared to irradiation where all cells receive the same number of hits. Received: 1 June 2001 / Accepted: 7 September 2001     

The probabilities of one- and multi-track events for modeling radiation-induced cell kill

In view of the clinical importance of hypofractionated radiotherapy, track models which are based on multi-hit events are currently reinvestigated. These models are often criticized, because it is believed that the probability of multi-track hits is negligible. In this work, the probabilities for one- and multi-track events are determined for different biological targets. The obtained probabilities can be used with nano-dosimetric cluster size distributions to obtain the parameters of track models. We quantitatively determined the probabilities for one- and multi-track events for 100, 500 and 1000 keV electrons, respectively. It is assumed that the single tracks are statistically independent and follow a Poisson distribution. Three different biological targets were investigated: (1) a DNA strand (2 nm scale); (2) two adjacent chromatin fibers (60 nm); and (3) fiber loops (300 nm). It was shown that the probabilities for one- and multi-track events are increasing with energy, size of the sensitive target structure, and dose. For a 2 × 2 × 2 nm³ target, one-track events are around 10,000 times more frequent than multi-track events. If the size of the sensitive structure is increased to 100–300 nm, the probabilities for one- and multi-track events are of the same order of magnitude. It was shown that target theories can play a role for describing radiation-induced cell death if the targets are of the size of two adjacent chromatin fibers or fiber loops. The obtained probabilities can be used together with the nano-dosimetric cluster size distributions to determine model parameters for target theories.     

New challenges in radiobiology research with microbeams

There is a continuing interest in the use of microbeam systems designed to deliver ionizing radiation (both photons and particles) with a resolution of a few micrometers or less in biological targets. With more than 30 facilities currently in operation, several new research topics can be explored. In the 9th International Microbeam Workshop held in Darmstadt, Germany, in July 2010, several new ideas and results have been presented, indicating that microbeams will be increasingly important in radiobiology. Subnuclear targeting of single cells for DNA repair studies and microirradiation of 3D or small animal models are among the most promising new research perspectives.     

LET,track structure and models

Summary Swift heavy ions when penetrating through matter strip off those electrons having a smaller orbital velocity than the ion velocity. The remaining electrons screen the nuclear charge yielding an effective charge. The effective charge of the ions interacts predominately with the target electrons causing excitation and ionizations of the target atoms. Using the Bethe Bloch formula for the energy loss combined with the Barkas formula for effective charge, the energy loss values as well as unrestricted and restricted linear transfer can be calculated within a few percent of accurancy. From the primary energy loss only a small fraction of 10% or less is transformed into excitation. The major part of the energy loss is used for the ionization of the target atoms and the emission of the corresponding electrons with a high kinetic energy. These electrons form the track around the trajectory of the primary ion in which two thirds of the primary energy is deposited by collisions of primary, secondary and later generations of electrons with the target molecules. In the electron diffusion process the energy is transported from the center of the track into the halo. The radial dose decreases with the square of the radial distance from the center. The diameter of the track is determined by the maximum range of the emitted electrons, i.e. by the maximum energy electrons. All ions having the same velocity i.e. the same specific energy produce electrons of the same energy and therefore tracks of the same diameters independent of the effective charge. But the dose inside the track increases with the square of the effective charge. Track structure models using this continuous dose distributions produce a better agreement with the experiment than models based on microdosimetry. The critical volume as used in microdosimetry is too large compared to the size of the DNA as critical structure inside the biological objects. Track structure models yield better results because the gross-structure of the track i.e. its lateral extension and the thin down toward the end of the track is included in these calculations. In a recent refinement the repair capacity of the cell has been included in a track structure model by using the complete shouldered x-ray survival curve as a template for the local damage produced by the particle tracks. This improved model yields presently the best agreement with the experiment.Invited paper given on the fourth workshop on Heavy Charged Particles in Biology and Medicine GSI, Darmstadt, FRG, September 23–25, 1991     

Radiation quality of tritium beta-rays: microdosimetric distributions for nanometer-size targets in a medium containing tritiated water

To elucidate the characteristics of the action of tritium beta-rays, the following parameters are derived: electron slowing down spectra of primary electrons (beta-rays) and delta-rays in a medium containing tritiated water; and frequency distributions for the microdosimetric quantity j (number of effective primary events per track per target), fj, for nanometer-size targets exposed to tritiated water. Features of the radiation quality of tritium beta-rays are discussed by comparing the present results with those for 60Co gamma-rays and 7 MeV electrons. It is concluded that, although tritium beta-rays, 60Co gamma-rays, and 7 MeV electrons are classified as the same low l.e.t. radiation, the radiation quality of tritium beta-rays is considerably different from those of 60Co gamma-rays and 7 MeV electrons, and has specific features such as a high average l.e.t., a small total electron fluence per unit absorbed dose, and a different microdosimetric distribution, fj, for nanometer-size targets.