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.     

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     

Microdosimetric analysis of various mammography spectra: lineal energy distributions and ionization cluster analysis

In view of recent recommendations on the frequency and the starting age of mammography screening in healthy women, it is desirable to quantify the enhanced relative biological effectiveness (RBE) of mammography X rays compared to hard X rays. While there is little doubt that the former are more potent in inducing biological damage than the latter, the magnitude of the effect is still hotly debated in the literature. We used Monte Carlo simulations and track structure analysis in micrometer and nanometer volumes to investigate differences in distributions of lineal energy and ionization clusters for a range of mammography X-ray qualities. Dose-averaged lineal energies, (yD), in breast tissue for various mammography qualities were found to result in quality factors about 40% higher than unity. Among the various mammography qualities studied, the popular molybdenum/molybdenum target/filter combination was found to have the highest (yD) in 1-microm spheres (about 5.0 keV/microm near the entrance surface of breast tissue). In 10-nm radius spheres, the mean ionization cluster order was found to be about 35% higher in mammography X rays compared to 300 keV electrons (roughly representing 60Co or 192Ir photon radiation). In even smaller spheres (2 nm radius), no significant differences were observed for the mean ionization cluster order between mammography X rays and 300 keV electrons. We conclude that the potential of mammography X rays to induce biological damage is probably not much higher than a factor of two compared to hard X rays.     

Differential and integral W-values for ionization in gaseous water under electron and proton irradiation: consistency of inelastic collision cross sections.

Differential and integral W-values for ionization in gaseous water for electron and proton irradiation have been analyzed from the theoretical point of view for consistency between ionization and total inelastic collision cross sections. For low-energy electrons, which are ubiquitous for all primary radiations, the experimental or compiled cross sections from different sources are sometimes not consistent with one another. A practical, self-consistent procedure is outlined in such cases. The high-energy asymptotic W-values for differential and integral ionization are calculated to be 33.7 and 34.7 eV, respectively, for electron irradiation and 34.6 and 32.5 eV, respectively, for proton irradiation. The computed variations of the W-values with energy are generally in good agreement with experiment. Integral primary W-values due only to the interactions between the incident particle and the water vapor are calculated to be 43.5 and 45.0 eV for electrons and protons, respectively, in the high-energy asymptotic limit.     

DNA complex lesions induced by protons and ⋅-particles: track structure characteristics determining linear energy transfer and particle type dependence

The yield of DNA double-strand breaks (dsb) and DNA complex lesions induced by protons and α-particles of various energies was simulated using a Monte Carlo track structure code (MOCA15) and a simple model of the DNA molecule. DNA breaks of different complexity were analysed. The linear energy transfer (LET) and particle-type dependence of lesions of higher complexity seems to confirm the importance of clustered damage in DNA as a relevant step leading to biological endpoints such as cell inactivation. The detailed structure of proton and α-particle tracks was analysed to identify the main characteristics possibly responsible for such a dependence. The role of the primary ion and of its secondary electrons in inducing dsb and complex lesions is described, showing that the relative contribution of secondary electron tracks alone in inducing clustered lesions is almost negligible at high LET, but tends to dominate below ≈10 keV/μm. This is consistent with the observed similar effectiveness of low-LET fast particle radiation and sparsely ionizing radiation such as x-rays. The dependence on LET and particle type is mainly due to energy deposition events of the primary ion together with short range electrons surrounding the ion track; the yield of complex lesions due to secondary electron tracks alone is substantially LET independent. The radial distributions of the energy contributing to the induction of complex lesions were analyzed and compared with the radial distributions of energy deposition of the full tracks. The results suggest that the stochastic behaviour (i.e. cluster properties) of the energy deposition pattern within a radius of a few nanometers around the ion track plays a relevant role in determining the biological radiation effectiveness. Received: 20 December 1996 / Accepted in revised form: 5 March 1997     

A Monte Carlo code for the simulation of heavy-ion tracks in water

TILDA, a new Monte Carlo track structure code for ions in gaseous water that is valid for both high-LET (approximately 10(4) keV/microm) and low-LET ions, is presented. It is specially designed for a comparison of the patterns of energy deposited by a large range of ions. Low-LET ions are described in a perturbative frame, whereas heavy ions with a very high stopping power are treated using the Lindhard local density approximation and the Russek and Meli statistical method. Ionization cross sections singly differential with energy compare well with the experiment. As an illustration of the non-perturbative interaction of high-LET ions, a comparison between the ion tracks of light and heavy ions with the same specific energy is presented (1.4 MeV/nucleon helium and uranium ions). The mean energy for ejected electrons was found to be approximately four times larger for uranium than for helium, leading to a much larger track radius in the first case. For electrons, except for the excitation cross sections that are deduced from experimental fits, cross sections are derived analytically. For any orientation of the target molecule, the code calculates multiple differential cross sections as a function of the ejection and scattering angles and of the energy transfer. The corresponding singly differential and total ionization cross sections are in good agreement with experimental data. The angular distribution of secondary electrons is shown to depend strongly on the orientation of the water molecule.     

Comparison and assessment of electron cross sections for Monte Carlo track structure codes.

The purpose of this study was to make an intercomparison and assessment of cross sections for electrons in water used in electron track structure codes. This study is intended to shed light on the extent to which the differences between the input data and physical and chemical assumptions influence the outcome in biophysical modeling of radiation effects. Ionization cross sections and spectra of secondary electrons were calculated by various theories. The analyses were carried out for water vapor cross sections, as these are more abundant and readily available. All suitable published experimental total ionization cross sections were fitted by an appropriate function and used for generation of electron tracks. Three sets of compiled data were used for comparison of total excitation cross sections and mean excitation energy. The tracks generated by a Monte Carlo track code, using various combinations of cross sections, were compared in terms of radial distributions of interactions and point kernels. The spectrum of secondary electrons emitted by the ionization process was found to be the factor that has the most influence on these quantities. A different set of cross sections for excitation and elastic scattering did not affect the electron track structure as much as did ionization cross sections. It is concluded that all codes, using different cross sections and in different phase, currently used for biophysical modeling exhibit close similarities for energy deposition in larger size targets while appreciable differences are observed in B-DNA-size targets. We recommend fitted functions to all available suitable experimental data for the total ionization and elastic cross sections. We conclude that most codes produce tracks in reasonable agreement with the macroscopic quantities such as total stopping power and total yield of strand breaks. However, we predict differences in frequencies of clustering in tracks from the different models.     

A new calculation on spectrum of direct DNA damage induced by low-energy electrons

In this work, direct DNA damage induced by low-energy electrons (<5 keV) is simulated using Monte Carlo methods, and the resulting yield of various strand breaks and base damages in cellular environment is presented. The simulation is based on a new inelastic cross section for the production of electron track structure in liquid water, and on ionization cross sections of DNA bases to generate base radical. Especially, a systematic approach of simulating detailed base damage is suggested. This approach includes improvement of a volume model of DNA, generation of the DNA base sequence, conversion of ionization events in liquid water at hit site to the ionization interaction of electrons with DNA bases and development of an algorithm to convert a base radical to a damage. The results obtained in terms of strand breaks are compared with those of experiments and other theoretical calculations, and good agreement was obtained. The yield of detailed base damages and clustered DNA damages caused by the combination of various strand breaks and base damages is presented, and the corresponding distribution characteristics are analyzed. The influence of the relative content of base pairs A-T and G-C in a DNA segment on the yield of both strand breaks and base damages is also explored. The present work provides fundamental information on DNA damage and represents the first effort toward the goal of obtaining the spectrum of clustered DNA damage including detailed base damages, for the mechanistic interpretation and prediction of radiation effects.     

Electron spectra and the RBE of X rays

For an assessment of the possible difference in effectiveness between mammography X rays and conventional X rays, the energy and LET spectra of the released electrons are examined. At photon energies below 20 keV and above 100 keV, the energy of the electrons increases with increasing photon energy, which implies that higher-energy photons produce less densely ionizing radiation and are therefore somewhat less effective per unit dose. However, in the intermediate energy range from 20 keV to 100 keV-the range that is relevant to medical diagnostics-the change from the photoelectric effect to the Compton effect causes a transient decrease of electron energies. The ionization density is therefore similar for 200 kVp X rays and 30 kVp mammography X rays, and the distributions of dose in LET suggest an RBE of 30 kVp mammography X rays compared to 200 kVp X rays of up to 1.3. This is in line with an earlier assessment by Brenner and Amols in terms of microdosimetric data, but it is strongly at variance with a recent claim that X rays for mammography are about four times more effective at small doses than conventional X rays and that they cause a correspondingly greater risk for breast cancer. Since LET need not be the only relevant factor, general response functions are examined here that specify-at low dose-the effect per electron of initial energy E and account, for example, for a particular role of the electron range. It is shown that, with any response per electron track that is a nondecreasing function of its starting energy, the low-dose RBE of the mammography X rays relative to the 200 kVp X rays must be substantially less than 2. The Auger electron that accompanies most photoelectrons, but only a minority of the Compton electrons, may increase the effectiveness of the mammography X rays somewhat, but it cannot explain the reported high values of the RBE.     

Calculation on spectrum of direct DNA damage induced by low-energy electrons including dissociative electron attachment

In this work, direct DNA damage induced by low-energy electrons (sub-keV) is simulated using a Monte Carlo method. The characteristics of the present simulation are to consider the new mechanism of DNA damage due to dissociative electron attachment (DEA) and to allow determining damage to specific bases (i.e., adenine, thymine, guanine, or cytosine). The electron track structure in liquid water is generated, based on the dielectric response model for describing electron inelastic scattering and on a free-parameter theoretical model and the NIST database for calculating electron elastic scattering. Ionization cross sections of DNA bases are used to generate base radicals, and available DEA cross sections of DNA components are applied for determining DNA-strand breaks and base damage induced by sub-ionization electrons. The electron elastic scattering from DNA components is simulated using cross sections from different theoretical calculations. The resulting yields of various strand breaks and base damage in cellular environment are given. Especially, the contributions of sub-ionization electrons to various strand breaks and base damage are quantitatively presented, and the correlation between complex clustered DNA damage and the corresponding damaged bases is explored. This work shows that the contribution of sub-ionization electrons to strand breaks is substantial, up to about 40–70%, and this contribution is mainly focused on single-strand break. In addition, the base damage induced by sub-ionization electrons contributes to about 20–40% of the total base damage, and there is an evident correlation between single-strand break and damaged base pair A–T.     

Ionization and charge-transfer: basic data for track structure calculations

It is widely accepted that an understanding of the detailed structure of charged particle tracks is essential for interpreting the mechanistic consequences of energy deposition by high linear energy transfer (LET) radiation. The spatial relationship of events along the path of a charged particle, including excitation, ionization, and charge-transfer, govern subsequent chemical, biochemical, and biological reactions that can lead to adverse biologic effects. The determination of spatial patterns of ionization and excitation relies on a broad range of cross-section data relating the interactions of charged particles to the molecular constituents of the absorbing medium. It is important that these data be absolute in magnitude, comprehensive in scope, and reliable if accurate assessment of track structure parameters is to be achieved. Great strides have been made in the development of this database, understanding the underlying theory, and developing analytic models, particularly for interactions involving electrons and protons with atoms and molecules. The database is less comprehensive for interactions involving heavier charged particles, especially those that carry bound electrons, and for interactions in condensed phase media. Although there has been considerable progress in understanding the physical mechanisms for interactions involving fast heavy ions and atomic targets during the past few years, we still lack sufficient understanding to confidently predict cross-sections for these ions with biologically relevant material. In addition, little is known of the interaction cross-sections for heavy charged particles as they near the end of their track, i.e., for low velocity ions where collision theory is less well developed and where the particle's net charge fluctuates owing to electron capture and loss processes. This presentation focuses on the current status of ionization and charge-transfer data. Compilations, reviews, Internet sources, theoretical models, and recent data applicable to track structure calculations are discussed.     

The role of atomic inner shell relaxations for photon-induced DNA damage

The influence of relaxations of atoms making up the DNA and atoms attached to it on radiation-induced cellular DNA damage by photons was studied by very detailed Monte Carlo track structure calculations, as an unusually high importance of inner shell ionizations for biological action was suspected from reports in the literature. For our calculations cross sections for photons and electrons for inner shell orbitals were newly derived and integrated into the biophysical track structure simulation programme PARTRAC. Both the local energy deposition in a small sphere around the interacting relaxed atom, and the number of relaxations per Gy and Gbp were calculated for several target geometries and many monoenergetic photon irradiations. Elements with the highest order number yielded the largest local energy deposition after interaction. The atomic relaxation after ionization of the L1 shell was found to be more biologically efficient than that of the K shell for high Z atoms. Generally, the number of inner shell relaxations produced by photon irradiation was small in comparison to the total number of double strand breaks generated by such radiation. Furthermore, the energy dependence of the total number of photon-induced and electron-induced relaxations at the DNA atoms does not agree with observed RBE values for different biological endpoints. This suggests that the influence of inner shell relaxations of DNA atoms on radiation-induced DNA damage is in general rather small.     

The response of E. coli Bs-1 to tritium-beta particles under aerated and anoxic conditions.

E. coli Bs-1 cells were exposed to acute doses of tritium-beta particles by suspension in tritiated water for known lengths of time. The resulting survival rate was compared with that obtained for external irradiation with 7 MeV electrons. The o.e.r. measured for tritium-beta s was not significantly different from the value of 2.15 measured for 7 MeV electrons. The r.b.e. of the tritium beta s relative to 7 MeV electrons was 1.21 in both air and nitrogen. These results were compared with existing data for low voltage electron irradiations and with track segment studies of the effect of varying LET on the radiosensitivity of E. coli Bs-1.     

Reparable and irreparable damage in yeast cells induced by sparsely ionizing radiation.

It is shown that in diploid yeast there are significant differences in the extent of irreparable damage after irradiation with X-rays, 60Co-gamma-rays and 30 MeV electrons. At extremely low dose rates, 60Co-gamma-rays were found to produce almost no irreparable damage at least up to 1200 Gy. X-rays, however, at the same low dose rate caused irreparable damage in the same dose range yielding a surviving fraction of 0.25 at 1200 Gy. For irradiations at high dose rate followed by liquid holding recovery the relative biological effectiveness of X-rays amounted to at least 4 for absorbed doses of up to 1000 Gy. With 30 MeV electrons at high dose rates an accumulation of sublethal and potentially lethal damage resulting in irreparable damage occurred above 1000 Gy. It is suggested that irreparable damage in yeast is due to a cooperative effect of neighbouring track ends.     

Microdosimetric structure of heavy ion tracks in tissue

Summary Energy dissipation in tracks of high energy heavy ions in tissue shows a lateral spread of several to many microns depending on the energy of the primary particle. Complete dosimetric characterization, therefore, requires in addition to the Linear Energy Transfer (LET) information on the radial energy distribution. The theory of track structure distinguishes two regions: core and penumbra. The core is a narrow central zone with a radius in tissue far below 1 micron where energy deposition occurs mainly in processes of excitation and electron plasma oscillation. According to the Equipartition Principle, half of the total energy dissipation accrues in this manner. The penumbra is a peripheral zone enveloping the core where energy deposition occurs mainly in ionization events by energetic secondary electrons released by the primary particle in the center of the core traveling at rather high speed thus spreading laterally. The extension of the penumbra depends in a complex manner on the maximum transferable energy to electrons which in turn depends on the speed of the primary particle. Local energy density in the penumbra decreases with the square of increasing radius. It therefore amounts only to a very small fraction of the core density already a few microns away from the center. In general terms, track structure can be described as exhibiting a core of enormous energy density with lateral dimensions remaining entirely on the submicroscopic level surrounded by a penumbra where energy density drops precipitously to very small levels. The relationships are illustrated with micrographs of different sections of a heavy particle track in nuclear emulsion and their counterpart graphical plots.     

Comparative microdosimetry of photoelectrons and Compton electrons: an analysis in terms of generalized proximity functions

A current discussion on mammography screening is focused on claims of high relative biological effectiveness (RBE) of mammography X rays compared to conventional 200 kV X rays. An earlier assessment in terms of the electron spectra of these radiations has led to the conclusion that the RBE is bound to be less than 2, regardless of specific model assumptions and the microdosimetric properties of electrons. The present study extends this result in terms of the microdosimetric proximity function, t(x), for electrons, which is essentially the spatial auto-correlation function of energy within particle tracks. If pairs of DNA lesions, e.g. chromosome breaks or deletions, bring about the observed damage, the value t(x) determines for a specified radiation the relative frequency of pairs of lesions a distance x apart. The effectiveness of the radiation is thus proportional to an average of the values of t(x) over the distances, x, for which lesions can combine. The analysis suggests that 15 keV electrons can have a low-dose relative biological effectiveness (RBE(M)) of 1.6 relative to 40 keV electrons if the interaction distances do not exceed about 1 micro m. An extension of the concept, the reduced proximity function, t(delta)(x), permits the inclusion of models with an energy threshold, such as delta = 100 eV, 500 eV or 2 keV, for the formation of each of the DNA lesions. This makes it possible to assess the potential impact of the Auger electrons which accompany most photoelectrons, but only a minority of the Compton electrons. It is found that the Auger electrons could make photoelectrons substantially more effective than Compton electrons at energies below 10 keV but not at energies above 15 keV. The conclusions obtained for the RBE of 15 keV electrons relative to 40 keV electrons will be roughly representative of the RBE of mammography X rays relative to conventional 200 kV X rays.     

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.     

Role of secondary electrons and metastable atoms in the electron-beam activation of argon-silane mixtures

The energy and spatial degradation of the primary beam electrons and the production of high-energy secondary electrons in ionizing collisions are analyzed by solving the Boltzmann integral equation for the electron distribution function. The effect of the primary and secondary electrons on the direct ionization of an Ar-SiH₄ mixture, the production of metastable argon atoms, and the dissociation of monosilane molecules is investigated over a wide range of the beam electron energies, argon pressures, and monosilane concentrations. The influence of metastable Ar* atoms on the dissociation of SiH₄ is studied by using the balance equation for metastable argon atoms and the equation for the ambipolar diffusion of ions and low-energy secondary (plasma) electrons in the beam plasma. It is shown that the main contribution to the activation of an Ar-SiH₄ mixture in an electron-beam plasma is provided by secondary electrons with energies higher than the excitation threshold for argon and the dissociation threshold for monosilane, whereas the contribution from metastable argon atoms, though potentially being comparable with that from secondary electrons, is less than in gas-discharge plasmas.     

Ultraviolet photoionization of the photosensitizers khellin and visnagin in aqueous solution and in micelles: one-photon ionization is a minor process.

One-photon ionization, leading to formation of hydrated electrons and radical cations, has been proposed as a possible mechanism of action of some sensitizers in photobiology. In this contribution, we have investigated this proposal for the compounds khellin and visnagin, used in photomedical applications. Nanosecond transient absorption spectroscopy covering a wide range of laser pulse energies was employed to measure the formation of radical cations and hydrated electrons in aqueous solution and in cationic (CTAB) as well as anionic (SDS) micellar solutions. A model allowing for simultaneous one- and two-photon processes and fully accounting for the nonlinearity of the pulse energy dependence was used to simulate the data. The results did not support the hypothesis of a significant role of one-photon ionization, the upper limits of the quantum yields of radical cation formation being phi < 0.01 for visnagin and phi < 0.004 for khellin.     

FLUKA capabilities for microdosimetric analysis

Delta-ray transport is important in microdosimetric studies, and how Monte Carlo models handle delta electrons using condensed histories is important for accurate simulation. The purpose of this study was to determine how well FLUKA can simulate energy deposition spectra in a tissue-equivalent proportional counter (TEPC) and produce a reliable estimate of delta-ray events produced when a TEPC is exposed to high-energy heavy ions (HZE) like those in the galactic cosmic-ray (GCR) environment. A 1.27-cm spherical TEPC with a low-pressure gas simulating a 1-μm site, typical of the one flown on the ISS, was constructed in FLUKA, and its response was compared to experimental data for an (56)Fe-ion beam at 360 MeV/nucleon. Several narrow beams at different impact parameters were used to explain the response of the same detector exposed to a uniform field of radiation. Additionally, the effect that wall thickness had on the response of the TEPC and the range of delta rays in the tissue-equivalent (TE) wall material was investigated, and FLUKA produced the expected wall effect for primary particles passing outside the sensitive volume. A final comparison to experimental data was made for the simulated TEPCs exposed to various broad beams in the energy range of 200-1000 MeV/nucleon. FLUKA overestimated energy deposition in the gas volume in all cases. The FLUKA results differed from the experimental data by an average of 25.2% for y(F) and 12.4% for y(D). It is suggested that this difference can be reduced by adjusting the FLUKA default ionization potential and density correction factors. Accurate transport codes are desirable because of the high cost of beam time for experimental evaluation of energy deposition spectra produced by HZE ions and the flexibility that calculations offer in the TEPC engineering and design process.