Radiation Protection Dosimetry Advance Access published April 20, 2015 Radiation Protection Dosimetry (2015), pp. 1–6
doi:10.1093/rpd/ncv194
CLASSICAL APPROACHES TO MICRODOSIMETRY, WITH EXAMPLE OF USE IN RADIATION PROTECTION, MEDICINE AND MECHANISTIC UNDERSTANDING D. T. Goodhead* Medical Research Council, Harwell, Didcot OX11 0RD, UK *Corresponding author: [email protected]
INTRODUCTION The first international symposium on microdosimetry was held in Ispra, Italy, in 1967; the ensuing series has now led to the 16th symposium in Treviso, Italy, in October 2013. The topics covered by these symposia are generally in accord with the following(1): ‘A useful working definition of microdosimetry could be the study of the physical microscopic properties of ionizing radiations, their interactions, and their patterns of energy deposition, with particular emphasis on the inhomogeneities and stochastic nature of the interactions. This is in contrast to conventional dosimetry, which is based on average macroscopic quantities such as absorbed dose. In many situations absorbed dose is totally inadequate to describe radiation action in biological, or other, material because the mechanisms and effects are dominated by the inhomogeneous microscopic properties, especially at cellular and subcellular dimensions.’ The present article discusses classical approaches to microdosimetry within this broad definition, rather than the much narrower usage of the term that is sometimes used. Focus is on relevance to biological mechanisms and applications in radiation protection and medicine. It will be seen that the classical approaches continue to play a major role in modern applications. Slides to illustrate this article are available on the internet.(2) RADIATION INSULT VIA TRACKS The insult from ionising radiation to biological systems is always in the form of tracks of charged particles, which impose stochastic patterns of ionisations and excitations on the irradiated molecular and cellular structures. In photon exposures, a single ionising interaction releases an electron that typically, depending on its energy, causes tens to tens of thousands of
further ionisations and excitations to form its full erratic track (including its primary and secondary electrons). On average, the ionisations are sparsely scattered along the tracks; the electrons have relatively low stopping power or linear energy transfer (LET). Nevertheless, even within the tracks of these ‘lowLET’ radiations, there are many nanometre-scale regions of clustering of ionisations due to the higher stopping power of the abundant low-energy secondary electrons. From gamma ray exposures, of the order of a quarter of the absorbed dose is deposited by low-energy electrons(3). By contrast, tracks of high-LET natural alpha particles from radioactive decay have very dense ionisation along their straight paths and some slight lateral spread due to delta ray electrons of very short ranges (,0.1 mm). One gray of absorbed dose to tissue corresponds to about 1000 electron tracks in a typical mammalian cell nucleus from gamma rays but to only a few alpha particle tracks, with about the same total number of ionisations in both cases(3). Hence, gamma rays have a very much greater chance of causing ionisation(s) in a given target, but alpha particles cause much larger clusters of ionisations if they do hit the target. Intermediate are heavier charged particles of greater velocity, such as the 12C ions now being used for radiotherapy in several countries or the relativistic 26 Fe ions in galactic cosmic rays (GCR). In these cases, there is dense ionisation along the particle’s path as well as very close to it (from overlap of the lowest-energy delta rays) but also very wide lateral spread from higher-energy delta rays that can travel across many other cells. Track structure is important at all levels of biological organisation, from the dimensions of adjacent water molecules up through DNA, chromatin, chromosomes, the cell nucleus, neighbouring cells and local tissue. At all these levels, correlations of ionisation damage within a track can play a significant role
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Microdosimetry is the study and application of the microscopic features and stochastics of ionising radiations that cannot be described by the average macroscopic quantity absorbed dose. Microdosimetry is intimately related to radiation quality, but it also encompasses the inhomogeneities of interactions and energy depositions within a single radiation type. A variety of past and current approaches will be summarised and some examples given of implications to radiation protection and medicine, as well as to basic mechanistic studies of radiation effects.
D. T. GOODHEAD
in biological consequences. Of major importance are correlations (clustering) of ionisations on the nanometre scale of the DNA duplex and its immediate surroundings. PHYSICAL SPECIFICATION FOR EFFECTS
Already by the 1950s, attempts were made to illustrate the differences between low- and high-LET radiations, including some non-randomness and clustering of ionisations along one-dimensional tracks(4). Average two- and three-dimensional descriptions were developed during the next two decades, and, in the 1970s, with the advances in computer power and detailed data on particle interaction cross sections, came the major advance of Monte Carlo techniques for full interaction-by-interaction simulation of the tracks of individual particles(5). Figure 1 shows a two-dimensional projection of a short section of an alpha particle track, onto which are marked the five main microdosimetric approaches that were developed to describe radiation quality(1, 6). Each of these is discussed in turn in the following sections, and it is shown that most of them are still central to current descriptions of radiation quality as used in mechanistic studies in radiation biology and in practical radiation protection and radiotherapy.
Track entities Particularly for interest in radiation chemistry, an early description of radiation quality was based on subdivision of electron tracks (from photons or the delta rays of heavier charged particles) into three
Figure 1. Two-dimensional projection of a short section of an alpha particle track(1), with indications of the classical microdosimetric quantities used to describe its radiation quality. Each of the five quantities is discussed in the text.
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Physical specification of irradiation that leads to a given biological or health effect needs to include: (1) the quantity of radiation (usually as absorbed dose or as fluence), (2) variations in dose on the scales of interest (such as isodose contours in radiotherapy or smaller-scale variations in the case of internal radionuclides especially at low doses), (3) the time course of delivery (as dose rate, fluence rate, dose fractionation, etc.) and (4) specification of ‘quality’ of the radiation. For the latter, LET is commonly used, although it is inadequate as a full descriptor. These physical specifications are, of course, in addition to specification of the particular biological system and its environment. The field of microdosimetry centrally involves Item 4 mentioned earlier, as well as substantial aspects of Items 2 and 3, especially when low doses and/or microscopic aspects are of interest. The present article focuses on Item 4, i.e. specification of radiation quality. Other aspects, including work on short-ranged emissions from radionuclides, particularly Auger emitters, can be traced through the proceedings of the 16 symposia.
SPECIFICATIONS OF RADIATION QUALITY
CLASSICAL APPROACHES TO MICRODOSIMETRY
compartments (Figure 1d), depending on the electron initial energy, namely ‘spurs’ (which were regarded as the main product of low-LET radiations), ‘blobs’ and ‘short tracks’(7). These concepts have been widely used in radiation chemistry, but there has been relatively little application in radiation biology and essentially none in radiation protection or medicine, so they will not be discussed further here. Linear energy transfer (LET)
Amorphous track radial dose The amorphous track description of charged particles provides an average radial dose distribution around the track(10) (Figure 1c). This has the advantage of providing information on the lateral spread of the tracks, but it totally ignores the stochastics of the tracks along their paths or laterally. Being an average dose to the entire concentric elementary shell at a distance r from the path of the charged particle, the radial dose at r does not provide the actual dose at a point, or in a macromolecular target at distance r. Instead, an actual target at this position, unless very close to the particle path, is likely to receive no dose
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LET is the average rate of energy loss of a charged particle per unit path length (Figure 1a), specified either as the total energy loss or restricted to losses below a specified cut-off energy(8). LET provides no information on stochastic fluctuations in energy loss, or on the lateral spread of the track due to delta rays. The numerical value of LET is equal to the electronic stopping power and depends on Z 2/v 2, where Z is the charge of the particle and v is its velocity. Hence, particles of different charge but the same LET can have grossly different track structures due to their different velocities. The track-average (i.e. frequency-average) LET is directly applicable to situations for which the effect of interest is directly proportional to LET; the dose-average (i.e. LET-weighted average) LET is directly applicable when the effect of interest is directly proportional to the square of the LET(1). Few practical situations match either of these precisely. For photon or electron irradiations, LET provides a particularly poor specification of quality because of the tortuous and branching nature of electron tracks; a wide range of LET values are obtained, depending on the chosen energy cut-off value and which mean is specified. For many biological effects of interest, typical dose responses are curvilinear (‘shouldered’) for low-LET radiations, while for high-LET radiations they are usually steeper and more linear. The relative biological effectiveness (RBE) of a given test radiation for a given type and level of the effect is defined as the ratio of dose of the reference radiation to the dose of the test radiation that produces this level of effect. Hence, the RBE is often dependent not only on the test and reference radiations but also on the level of effect, dose rate and particular biological system. Nevertheless, when RBE is plotted against LET, it is commonly found that for a wide variety of effects in mammalian cells, the RBE increases to a maximum in the LET region of 100– 200 keV mm21 and then falls off for higher LET values. Radiations of interest with LET in or near the region of maximum effectiveness include alpha particles from radioactive decay, accelerated 12 C particles used for radiation therapy and 1 GeV nucleon21 56Fe particles in GCR. The details of the RBE –LET relationship depend on several variables, including the biological system, level of effect, dose rate and particle velocity at a given LET. Nevertheless,
the general features of the relationship indicate that for many cellular effects, concentration of ionisations within fewer, but more dense, tracks leads to increase in biological effectiveness per unit absorbed dose, up to a limit, and then a decrease due to excessive reduction in the number of tracks. That is, more-damaging ‘hits’ of some target material more than outweigh the reducing probability of hitting the targets, until, at very high LET, the number of tracks becomes too small. This general inference alone does not specify the size scale of importance for the concentration, but early analyses of tracks even on the basis of simple quantities such as LET have historically provided useful hypotheses and insights into the distances of most relevance. For example, when experimental cell killing and mutation data were analysed on the basis of LET with some incorporation of stochastic clusters of ionisations, it was suggested that the biologically critical features of the radiations were clusters of ionisations within about 3 nm for low-LET radiations and about 10 nm for high-LET radiations(6). The parameter LET has had very many applications, including as an approximate quality parameter for simple ordering of data from different radiations. LET (L) is a basic requirement for conversion between particle fluence (F) and absorbed dose (D), as D ¼ kFL, where k is a proportionality constant (of numerical value 0.16 when F is specified in units of particles per micrometre squared, L in keV mm21 and D in Gy). In radiation protection, the quality factor (Q) has been specified by ICRP as a function of LET, and this remained the case for operational radiation protection quantities even after weighting factors (wR) were introduced for prospective radiation protection. In cancer therapy with high-LET radiations (neutrons or heavy charged particles), increased LET has been regarded as a general indicator of increased RBE and decreased dependence on oxygenation of the tumour (decreased oxygen enhancement ratio). For planning treatment at the Heavy Ion Medical Accelerator (HIMAC) facility in Japan, the RBE model for ‘biological dose’ has been based on linear-quadratic dose –responses with parameters empirically dependent on LET(9).
D. T. GOODHEAD
‘Proportional counter’ microdosimetry A particularly strong theme in microdosimetry during the 1970s was based on low-pressure proportional counter measurements and radiation quality quantities defined for them (Figure 1b). It is still quite common to hear the term ‘microdosimetry’ confined to this sub-field. The development of low-pressure proportional counters, especially ‘Rossi’ counters(16), enabled simulation of micron-sized spheres in tissue by
means of spherical counters of a few centimetres diameter filled with tissue-equivalent gas at pressures that equated the energy loss of a charged particle crossing the counter gas to that crossing the tissue sphere. The counter detected the ionisations from individual particle events, and thereby providing amplified electrical pulses that were approximately proportional to the energy depositions within the counter. Hence, the quantities lineal energy and specific energy were defined as the energy deposited in the sphere divided by the mean chord length of the sphere or by the mass of the sphere, respectively(8). The units are the same as for LET and absorbed dose, respectively, but these newer quantities provided frequency distributions of the individual stochastic events occurring in microscopic volumes. The frequency distributions measured in mixed radiation fields often enable the contributions from different types of charged particles to be resolved. The distributions are commonly reduced to frequency-mean or dose-mean quantities in similar ways to LET, as mentioned earlier(1). Usefully, the event frequency per unit dose (i.e. the probability of hitting the target volume per unit dose) is given by the reciprocal of the frequency-mean lineal energy. Practical limitations of proportional counters limit their use to simulated volumes of dimensions about .0.3 mm. Various ‘nanodosimetric’ techniques have been attempted to provide measurements of lineal energy and specific energy in much smaller simulated volumes. For well-defined radiation fields, these quantities can now also be calculated from track structure simulation. An early application of the dose-mean specific energy was in the ‘theory of dual radiation action’ (tdra), which was first put forward as a fundamental mechanistic model of radiobiological effects to explain and predict the effectiveness of radiations of different qualities(17). Subsequent experimental tests of basic assumptions of the model showed that they are not valid and later developments(18) of the model lost its link to lineal energy and specific energy, as outlined by Goodhead(4). Nevertheless, the model may remain usable as a phenomenological model for limited purposes. The more recent microdosimetric kinetic model (MKM) of cell death combines together aspects of several models (including the original tdra) into a practical mathematical formalism that includes lineal and specific energy(19). For radiation protection, a task group proposed specifying Q as a function of dose-mean specific energy(20), instead of LET, but the proposal was never adopted by ICRP. In practical instrumentation, measurement of energy deposition from single events in microscopic volumes (with proportional counters or related devices) continues to have wide application in radiation monitoring on earth and in space, for example, to estimate the LET spectrum and hence Q(L) of a radiation field and hence the dose-equivalent rate.
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at all or otherwise a significant dose due to a delta ray electron passing through it. The maximum width of the tracks is determined by the longest delta rays, which in turn are dependent on the velocity of the charged particle. Therefore, two particles of different charge but the same velocity (i.e. same energy per nucleon) will have the same width and relative radial dose distribution, but the energy density within them depends on the ratio Z 2/v 2, as for LET. For most heavy charged particles, the radial dose falls off approximately as 1/r 2(10, 11). This quite rapid fall-off is often misinterpreted to infer that little of the energy in the track is transported far from the primary particle. However, the energy deposition falls off much more slowly (approximately as r 21); so, for therapy particles and GCR, a large proportion of the energy (or dose) is deposited far from the primary particle and outside of the traversed cell(12). For example, in the case of 1 GeV nucleon21 Fe particle traversing a typical cell nucleus, more than 50 % of the dose is deposited beyond the nucleus and some as far away as many millimetres, by delta rays that have traversed many additional cells. An early development and application of the radial dose description of the quality of charged particle radiation were in the amorphous track structure model of Katz(13). This phenomenological model of radiobiological responses to heavy charged particles was based on a methodology of folding together the particle radial dose profile and the dose response from gamma ray exposure. It was remarkably successful in fitting diverse cell survival data with a small number of parameters. In this model, particle RBE is characterised by Z 2/b 2 rather than LET, where b is the particle velocity relative to the speed of light. Aspects of the parameterisation of the model have recently been carried over to the current NASA cancer risk model for radiation protection in space(14). NASA specifies the quality factor in terms of Z 2/b 2 and uses the Katz parameterisation to evaluate the quality factor. The amorphous track radial dose distribution forms the basis also of the local effects model (LEM)(15) used for 12C particle radiotherapy in Germany. This phenomenological model has some conceptual similarities to the Katz model, notably in folding together particle radial dose profiles and photon dose response, but the methodology is substantially different.
CLASSICAL APPROACHES TO MICRODOSIMETRY
In radiotherapy, a mathematical approach based on the MKM, including use of the quantities lineal energy and specific energy, has been used to estimate the RBE-weighted ‘biological dose’ for planning of carbon-ion treatment at the HIMAC facility(21). Track structure simulation
CONCLUSION Microdosimetry is an extensive and powerful field of study. This article has discussed it only in the context of biological effects of radiation, but there are clear analogies also in other fields, such as micro-electronics. The classical approaches to microdosimetry, mostly initiated during the 1960s–1980s, continue to play a major role in current developments and applications in the field. Due to the interlinked nature of the various
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Monte Carlo techniques(22) provide the means to simulate very large numbers of tracks, providing detailed stochastic descriptions of the radiation (Figure 1e). But what should be done with this very large array of computer data? The data can, of course, be reduced to the well-established microdosimetric quantities summarised earlier—LET, track entities, radial dose profiles, lineal energy, specific energy, etc.—not only for comparison with experimental data, but also for extension into regions where experimental measurements are not practical. New microdosimetric quantities could be defined and calculated, without constraints of experimental limitations. In particular, quantities on the nanometre scale are accessible, with potential relationships to DNA and DNA structures or other molecules and organelles of potential interest in radiation effects. Track simulations have very wide application in modelling of radiation processes and effects, not only to provide quantitative descriptions of known phenomena and available data, but also to provide new insights and generate new hypotheses on the mechanisms underlying radiation effects. Clustered damage in DNA provides a historic example of personal interest to the author. In early studies, from geometric sampling of radiation tracks, it soon became apparent that there are only limited regions of target volume and energy deposition (or numbers of ionisations) that can correlate reasonably with the RBEs of different radiations for effects of interest, such as cell killing or mutation induction. Such comparisons led to hypotheses of critical properties of radiation, namely correlation of cellular effects with energy depositions of more than about 100 eV within 3–4 nm for low-LET effects and more than about 340 eV (15 ionisations) within about 5–10 nm for typical high-LET effects(4); it was clear from the analyses that a single property could not account for both high- and low-LET radiations. Much more recently, coming from a very different perspective, analyses of photon, neutron and carbon-ion radiotherapy beams have led to the suggestion that dose-mean specific energy in volumes of 10 nm spheres provides close correlation with clinical RBE(23). To probe further into underlying mechanisms, yields and types of DNA damage can be estimated from track structure simulations that include damage from direct interactions in the DNA and from water radicals produced in the immediate vicinity. Very low-energy secondary electrons are highly effective at producing clusters of ionisations within volumes of nanometre
dimensions. Hence, such electrons are effective at producing ‘clustered damage’(4, 24) in DNA. Simulations show that a wide variety of clustered DNA damage occurs, ranging from a simple double-strand break (DSB) to more complex DSB (with additional strand breaks and/or base damages within a few base pairs) and also non-DSB clustered damage (multiple base damages with or without an associated single break). Simulations from many thousands of tracks led to the conclusion that 20 % of DSBs from low-LET gamma rays and hard X rays are complex by having one or more additional associated strand break and 50 % are complex due to additional base damage and/or strand breakage. For high-LET alpha particles, these proportions rise to 70 and 90 %. High-LET radiations produce a modestly greater absolute number of DSB per unit dose, a greater proportion of which are complex, and also increased degrees of complexity within the damage spectrum. The more complex DSBs are less likely to be faithfully repaired and hence have greater biological ‘severity’(25). This expectation is supported by many experimental studies showing that the repair kinetics of DSB depend on radiation quality, with a greater proportion of slow-repairing DSB after higher-LET radiations(26), and that complex DSBs are more likely to be lethal or mutagenic(27). Hence, the well-known RBE– LET relationship is likely to be due in large part to the ionisation-clustering properties of the radiation tracks on the nanometre scale of DNA, the consequent clustered DNA damage and the limited repair capabilities of the cell. However, correlations of damage within single radiation tracks over larger dimensions, from chromatin up to multicellular regions of tissue, are also relevant in determining the overall radiobiological effectiveness. The previously mentioned example of analysis of DNA damage from track structure is just one of many possible uses of track structure simulations to probe the mechanisms of radiation action or provide descriptions of observed phenomena. In another wide-ranging example(28), modelling has been done over dimensions of many orders of magnitude from DNA up through chromosomes and chromosome territories to the entire cell nucleus, biochemical repair processes and extracellular signalling. In general, the scope for application of track structure simulations is immense for both descriptive and investigative studies.
D. T. GOODHEAD
concepts, quantities and objectives, it remains appropriate to retain the term ‘microdosimetry’ for the entire field, as represented by the topics of the 16 international symposia to date, rather than restricting it to any one narrow aspect. REFERENCES
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1. Goodhead, D. T. Relationship of microdosimetric techniques to applications in biological systems. In: The Dosimetry of Ionizing Radiation, Vol. 2. Kase, K. R., Bjarngard, B. E. and Attix Kase, F. H., Eds. Academic Press, pp. 1– 89 (1987). 2. Goodhead, D. T. ResearchGate. (2013) https://www. researchgate.net/profile/Dudley_Goodhead/publications/ ?pubType=inProceedings&ev=prf_pubs_inp. 3. Goodhead, D. T. Initial events in the cellular effects of ionizing radiations: clustered damage in DNA. Int. J. Radiat. Biol. 65, 7– 17 (1994). 4. Goodhead, D. T. Energy deposition stochastics and track structure: what about the target? Radiat. Prot. Dosim. 122, 3– 15 (2006). 5. Paretzke, H. G. Advances in energy deposition theory. In: Advances in Radiation Protection and Dosimetry in Medicine. Thomas, R. H. and Perez-Mendez, V., Eds. Plenum Press, pp. 51– 73 (1980). 6. Goodhead, D. T. The initial physical damage produced by ionizing radiations. Int. J. Radiat. Biol. 56, 623–634 (1989). 7. Mozumder, A. and Magee, J. L. Model tracks of ionizing radiations for radical reaction mechanisms. Radiat. Res. 28, 203 –214 (1966). 8. ICRU (International Commission on Radiation Units and Measurements). Fundamental Quantities and Units for Ionizing Radiation (Revised). ICRU Report 85a. JICRU, Vol 11(1). Oxford University Press, (2011). 9. Kanai, T., Furusawa, K., Itsukaishi, H., Eguchi-Kasai, K. and Ohara, H. Irradiation of mixed beam and design of spread-out Bragg peak for heavy-ion radiotherapy. Radiat. Res. 147, 78– 85 (1997). 10. Kiefer, J. and Straaten, H. A model of ion track structure based on classical collision dynamics. Phys. Med. Biol. 31, 1201–1209 (1986). 11. Cucinotta, F. A., Nikjoo, H. and Goodhead, D. T. Applications of amorphous track models in radiation biology. Radiat. Environm. Biophys. 38, 81–92 (1999). 12. Cucinotta, F. A., Nikjoo, H. and Goodhead, D. T. Model for radial dependence of frequency distributions of energy imparted in nanometer volumes from HZE particles. Radiat. Res. 153, 459 –468 (2000). 13. Katz, R., Ackerson, B., Homayoonfar, M. and Sharma, S. C. Inactivation of cells by heavy ion bombardment. Radiat. Res. 47, 402– 425 (1971).
14. Cucinotta, F. A., Kim, M-H. Y. and Chappel, L. J. Space Radiation Cancer Risk Projections and Uncertainties – 2012. NASA/TP-2013–217375. National Aeronautics and Space Administration. 15. Elsa¨sser, T. and Scholz, M. Cluster effects within the local effects model. Radiat. Res. 167, 319– 329 (2007). 16. Rossi, H. H. and Rosenzweig, W. A device for the measurement of dose as a function of specific ionization. Radiology 64, 404 –411 (1955). 17. Kellerer, A. M. and Rossi, H. H. The theory of dual radiation action. Curr. Top. Radiat. Res. Q. 8, 85–158 (1972). 18. Kellerer, A. M. and Rossi, H. H. A generalized formulation of dual radiation action. Radiat. Res. 5, 471–488 (1978). 19. Hawkins, R. B. The relationship between the sensitivity of cells to high-energy photons and the RBE of particle radiation used in radiotherapy. Radiat. Res. 172, 761–776 (2009). 20. ICRU (International Commission on Radiation Protection and Measurements). The Quality Factor in Radiation Protection. ICRU Report 40. Bethesda, Maryland, USA (1986). 21. Sato, T. and Furusawa, Y. Cell survival fraction estimation based on the probability densities of domain and cell nucleus specific energies using improved microdosimetric kinetic models. Radiat. Res. 178, 341–356 (2012). 22. Dingfelder, M. Monte Carlo Track Structure Simulations. The Health Risks of Extraterrestrial Environments. (2014). http://three.usra.edu/articles/monte-carlo-Ding felder.pdf. ˚ . and 23. Lindborg, L., Hultquist, M., Carlsson Tedgren, A Nikjoo, H. Lineal energy and radiation quality in radiation therapy: model calculations and comparison with experiment. Phys. Med. Biol. 58, 3089– 3105 (2013). 24. Goodhead, D. T. Fifth Warren K. Sinclair keynote address: issues in quantifying the effects of low-level radiation. Health Phys. 97, 394–406 (2009). 25. Goodhead, D. T., Thacker, J. and Cox, R. Weiss Lecture. Effects of radiations of different qualities on cells: molecular mechanisms of damage and repair. Int. J. Radiat. Biol. 63, 543– 556 (1993). 26. Asaithamby, A., Hu, B., Delgado, O., Ding, L-H., Story, M. D., Minna, J. D., Shay, J. W. and Chen, D. J. Irreparable complex DNA double-strand breaks induce chromosome breakage in organotypical three-dimensional human lung epithelial cell culture. Nucleic Acid Res. 39, 5478–5488 (2011). 27. Dobbs, T., Palmer, P., Maniou, Z., Lomax, M. and O’Neill, P. Interplay of two major repair pathways in the processing of complex double-strand DNA breaks. DNA Repair 7, 1372– 1383 (2008). 28. Friedland, W. and Kundrat, P. Track structure based modelling of chromosome aberrations after photon and alphaparticle irradiation. Mutat. Res. 756, 213–223 (2013).
doi:10.1093/rpd/ncv194
CLASSICAL APPROACHES TO MICRODOSIMETRY, WITH EXAMPLE OF USE IN RADIATION PROTECTION, MEDICINE AND MECHANISTIC UNDERSTANDING D. T. Goodhead* Medical Research Council, Harwell, Didcot OX11 0RD, UK *Corresponding author: [email protected]
INTRODUCTION The first international symposium on microdosimetry was held in Ispra, Italy, in 1967; the ensuing series has now led to the 16th symposium in Treviso, Italy, in October 2013. The topics covered by these symposia are generally in accord with the following(1): ‘A useful working definition of microdosimetry could be the study of the physical microscopic properties of ionizing radiations, their interactions, and their patterns of energy deposition, with particular emphasis on the inhomogeneities and stochastic nature of the interactions. This is in contrast to conventional dosimetry, which is based on average macroscopic quantities such as absorbed dose. In many situations absorbed dose is totally inadequate to describe radiation action in biological, or other, material because the mechanisms and effects are dominated by the inhomogeneous microscopic properties, especially at cellular and subcellular dimensions.’ The present article discusses classical approaches to microdosimetry within this broad definition, rather than the much narrower usage of the term that is sometimes used. Focus is on relevance to biological mechanisms and applications in radiation protection and medicine. It will be seen that the classical approaches continue to play a major role in modern applications. Slides to illustrate this article are available on the internet.(2) RADIATION INSULT VIA TRACKS The insult from ionising radiation to biological systems is always in the form of tracks of charged particles, which impose stochastic patterns of ionisations and excitations on the irradiated molecular and cellular structures. In photon exposures, a single ionising interaction releases an electron that typically, depending on its energy, causes tens to tens of thousands of
further ionisations and excitations to form its full erratic track (including its primary and secondary electrons). On average, the ionisations are sparsely scattered along the tracks; the electrons have relatively low stopping power or linear energy transfer (LET). Nevertheless, even within the tracks of these ‘lowLET’ radiations, there are many nanometre-scale regions of clustering of ionisations due to the higher stopping power of the abundant low-energy secondary electrons. From gamma ray exposures, of the order of a quarter of the absorbed dose is deposited by low-energy electrons(3). By contrast, tracks of high-LET natural alpha particles from radioactive decay have very dense ionisation along their straight paths and some slight lateral spread due to delta ray electrons of very short ranges (,0.1 mm). One gray of absorbed dose to tissue corresponds to about 1000 electron tracks in a typical mammalian cell nucleus from gamma rays but to only a few alpha particle tracks, with about the same total number of ionisations in both cases(3). Hence, gamma rays have a very much greater chance of causing ionisation(s) in a given target, but alpha particles cause much larger clusters of ionisations if they do hit the target. Intermediate are heavier charged particles of greater velocity, such as the 12C ions now being used for radiotherapy in several countries or the relativistic 26 Fe ions in galactic cosmic rays (GCR). In these cases, there is dense ionisation along the particle’s path as well as very close to it (from overlap of the lowest-energy delta rays) but also very wide lateral spread from higher-energy delta rays that can travel across many other cells. Track structure is important at all levels of biological organisation, from the dimensions of adjacent water molecules up through DNA, chromatin, chromosomes, the cell nucleus, neighbouring cells and local tissue. At all these levels, correlations of ionisation damage within a track can play a significant role
# The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: [email protected]
Downloaded from http://rpd.oxfordjournals.org/ at University of Michigan Flint on April 25, 2015
Microdosimetry is the study and application of the microscopic features and stochastics of ionising radiations that cannot be described by the average macroscopic quantity absorbed dose. Microdosimetry is intimately related to radiation quality, but it also encompasses the inhomogeneities of interactions and energy depositions within a single radiation type. A variety of past and current approaches will be summarised and some examples given of implications to radiation protection and medicine, as well as to basic mechanistic studies of radiation effects.
D. T. GOODHEAD
in biological consequences. Of major importance are correlations (clustering) of ionisations on the nanometre scale of the DNA duplex and its immediate surroundings. PHYSICAL SPECIFICATION FOR EFFECTS
Already by the 1950s, attempts were made to illustrate the differences between low- and high-LET radiations, including some non-randomness and clustering of ionisations along one-dimensional tracks(4). Average two- and three-dimensional descriptions were developed during the next two decades, and, in the 1970s, with the advances in computer power and detailed data on particle interaction cross sections, came the major advance of Monte Carlo techniques for full interaction-by-interaction simulation of the tracks of individual particles(5). Figure 1 shows a two-dimensional projection of a short section of an alpha particle track, onto which are marked the five main microdosimetric approaches that were developed to describe radiation quality(1, 6). Each of these is discussed in turn in the following sections, and it is shown that most of them are still central to current descriptions of radiation quality as used in mechanistic studies in radiation biology and in practical radiation protection and radiotherapy.
Track entities Particularly for interest in radiation chemistry, an early description of radiation quality was based on subdivision of electron tracks (from photons or the delta rays of heavier charged particles) into three
Figure 1. Two-dimensional projection of a short section of an alpha particle track(1), with indications of the classical microdosimetric quantities used to describe its radiation quality. Each of the five quantities is discussed in the text.
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Physical specification of irradiation that leads to a given biological or health effect needs to include: (1) the quantity of radiation (usually as absorbed dose or as fluence), (2) variations in dose on the scales of interest (such as isodose contours in radiotherapy or smaller-scale variations in the case of internal radionuclides especially at low doses), (3) the time course of delivery (as dose rate, fluence rate, dose fractionation, etc.) and (4) specification of ‘quality’ of the radiation. For the latter, LET is commonly used, although it is inadequate as a full descriptor. These physical specifications are, of course, in addition to specification of the particular biological system and its environment. The field of microdosimetry centrally involves Item 4 mentioned earlier, as well as substantial aspects of Items 2 and 3, especially when low doses and/or microscopic aspects are of interest. The present article focuses on Item 4, i.e. specification of radiation quality. Other aspects, including work on short-ranged emissions from radionuclides, particularly Auger emitters, can be traced through the proceedings of the 16 symposia.
SPECIFICATIONS OF RADIATION QUALITY
CLASSICAL APPROACHES TO MICRODOSIMETRY
compartments (Figure 1d), depending on the electron initial energy, namely ‘spurs’ (which were regarded as the main product of low-LET radiations), ‘blobs’ and ‘short tracks’(7). These concepts have been widely used in radiation chemistry, but there has been relatively little application in radiation biology and essentially none in radiation protection or medicine, so they will not be discussed further here. Linear energy transfer (LET)
Amorphous track radial dose The amorphous track description of charged particles provides an average radial dose distribution around the track(10) (Figure 1c). This has the advantage of providing information on the lateral spread of the tracks, but it totally ignores the stochastics of the tracks along their paths or laterally. Being an average dose to the entire concentric elementary shell at a distance r from the path of the charged particle, the radial dose at r does not provide the actual dose at a point, or in a macromolecular target at distance r. Instead, an actual target at this position, unless very close to the particle path, is likely to receive no dose
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LET is the average rate of energy loss of a charged particle per unit path length (Figure 1a), specified either as the total energy loss or restricted to losses below a specified cut-off energy(8). LET provides no information on stochastic fluctuations in energy loss, or on the lateral spread of the track due to delta rays. The numerical value of LET is equal to the electronic stopping power and depends on Z 2/v 2, where Z is the charge of the particle and v is its velocity. Hence, particles of different charge but the same LET can have grossly different track structures due to their different velocities. The track-average (i.e. frequency-average) LET is directly applicable to situations for which the effect of interest is directly proportional to LET; the dose-average (i.e. LET-weighted average) LET is directly applicable when the effect of interest is directly proportional to the square of the LET(1). Few practical situations match either of these precisely. For photon or electron irradiations, LET provides a particularly poor specification of quality because of the tortuous and branching nature of electron tracks; a wide range of LET values are obtained, depending on the chosen energy cut-off value and which mean is specified. For many biological effects of interest, typical dose responses are curvilinear (‘shouldered’) for low-LET radiations, while for high-LET radiations they are usually steeper and more linear. The relative biological effectiveness (RBE) of a given test radiation for a given type and level of the effect is defined as the ratio of dose of the reference radiation to the dose of the test radiation that produces this level of effect. Hence, the RBE is often dependent not only on the test and reference radiations but also on the level of effect, dose rate and particular biological system. Nevertheless, when RBE is plotted against LET, it is commonly found that for a wide variety of effects in mammalian cells, the RBE increases to a maximum in the LET region of 100– 200 keV mm21 and then falls off for higher LET values. Radiations of interest with LET in or near the region of maximum effectiveness include alpha particles from radioactive decay, accelerated 12 C particles used for radiation therapy and 1 GeV nucleon21 56Fe particles in GCR. The details of the RBE –LET relationship depend on several variables, including the biological system, level of effect, dose rate and particle velocity at a given LET. Nevertheless,
the general features of the relationship indicate that for many cellular effects, concentration of ionisations within fewer, but more dense, tracks leads to increase in biological effectiveness per unit absorbed dose, up to a limit, and then a decrease due to excessive reduction in the number of tracks. That is, more-damaging ‘hits’ of some target material more than outweigh the reducing probability of hitting the targets, until, at very high LET, the number of tracks becomes too small. This general inference alone does not specify the size scale of importance for the concentration, but early analyses of tracks even on the basis of simple quantities such as LET have historically provided useful hypotheses and insights into the distances of most relevance. For example, when experimental cell killing and mutation data were analysed on the basis of LET with some incorporation of stochastic clusters of ionisations, it was suggested that the biologically critical features of the radiations were clusters of ionisations within about 3 nm for low-LET radiations and about 10 nm for high-LET radiations(6). The parameter LET has had very many applications, including as an approximate quality parameter for simple ordering of data from different radiations. LET (L) is a basic requirement for conversion between particle fluence (F) and absorbed dose (D), as D ¼ kFL, where k is a proportionality constant (of numerical value 0.16 when F is specified in units of particles per micrometre squared, L in keV mm21 and D in Gy). In radiation protection, the quality factor (Q) has been specified by ICRP as a function of LET, and this remained the case for operational radiation protection quantities even after weighting factors (wR) were introduced for prospective radiation protection. In cancer therapy with high-LET radiations (neutrons or heavy charged particles), increased LET has been regarded as a general indicator of increased RBE and decreased dependence on oxygenation of the tumour (decreased oxygen enhancement ratio). For planning treatment at the Heavy Ion Medical Accelerator (HIMAC) facility in Japan, the RBE model for ‘biological dose’ has been based on linear-quadratic dose –responses with parameters empirically dependent on LET(9).
D. T. GOODHEAD
‘Proportional counter’ microdosimetry A particularly strong theme in microdosimetry during the 1970s was based on low-pressure proportional counter measurements and radiation quality quantities defined for them (Figure 1b). It is still quite common to hear the term ‘microdosimetry’ confined to this sub-field. The development of low-pressure proportional counters, especially ‘Rossi’ counters(16), enabled simulation of micron-sized spheres in tissue by
means of spherical counters of a few centimetres diameter filled with tissue-equivalent gas at pressures that equated the energy loss of a charged particle crossing the counter gas to that crossing the tissue sphere. The counter detected the ionisations from individual particle events, and thereby providing amplified electrical pulses that were approximately proportional to the energy depositions within the counter. Hence, the quantities lineal energy and specific energy were defined as the energy deposited in the sphere divided by the mean chord length of the sphere or by the mass of the sphere, respectively(8). The units are the same as for LET and absorbed dose, respectively, but these newer quantities provided frequency distributions of the individual stochastic events occurring in microscopic volumes. The frequency distributions measured in mixed radiation fields often enable the contributions from different types of charged particles to be resolved. The distributions are commonly reduced to frequency-mean or dose-mean quantities in similar ways to LET, as mentioned earlier(1). Usefully, the event frequency per unit dose (i.e. the probability of hitting the target volume per unit dose) is given by the reciprocal of the frequency-mean lineal energy. Practical limitations of proportional counters limit their use to simulated volumes of dimensions about .0.3 mm. Various ‘nanodosimetric’ techniques have been attempted to provide measurements of lineal energy and specific energy in much smaller simulated volumes. For well-defined radiation fields, these quantities can now also be calculated from track structure simulation. An early application of the dose-mean specific energy was in the ‘theory of dual radiation action’ (tdra), which was first put forward as a fundamental mechanistic model of radiobiological effects to explain and predict the effectiveness of radiations of different qualities(17). Subsequent experimental tests of basic assumptions of the model showed that they are not valid and later developments(18) of the model lost its link to lineal energy and specific energy, as outlined by Goodhead(4). Nevertheless, the model may remain usable as a phenomenological model for limited purposes. The more recent microdosimetric kinetic model (MKM) of cell death combines together aspects of several models (including the original tdra) into a practical mathematical formalism that includes lineal and specific energy(19). For radiation protection, a task group proposed specifying Q as a function of dose-mean specific energy(20), instead of LET, but the proposal was never adopted by ICRP. In practical instrumentation, measurement of energy deposition from single events in microscopic volumes (with proportional counters or related devices) continues to have wide application in radiation monitoring on earth and in space, for example, to estimate the LET spectrum and hence Q(L) of a radiation field and hence the dose-equivalent rate.
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at all or otherwise a significant dose due to a delta ray electron passing through it. The maximum width of the tracks is determined by the longest delta rays, which in turn are dependent on the velocity of the charged particle. Therefore, two particles of different charge but the same velocity (i.e. same energy per nucleon) will have the same width and relative radial dose distribution, but the energy density within them depends on the ratio Z 2/v 2, as for LET. For most heavy charged particles, the radial dose falls off approximately as 1/r 2(10, 11). This quite rapid fall-off is often misinterpreted to infer that little of the energy in the track is transported far from the primary particle. However, the energy deposition falls off much more slowly (approximately as r 21); so, for therapy particles and GCR, a large proportion of the energy (or dose) is deposited far from the primary particle and outside of the traversed cell(12). For example, in the case of 1 GeV nucleon21 Fe particle traversing a typical cell nucleus, more than 50 % of the dose is deposited beyond the nucleus and some as far away as many millimetres, by delta rays that have traversed many additional cells. An early development and application of the radial dose description of the quality of charged particle radiation were in the amorphous track structure model of Katz(13). This phenomenological model of radiobiological responses to heavy charged particles was based on a methodology of folding together the particle radial dose profile and the dose response from gamma ray exposure. It was remarkably successful in fitting diverse cell survival data with a small number of parameters. In this model, particle RBE is characterised by Z 2/b 2 rather than LET, where b is the particle velocity relative to the speed of light. Aspects of the parameterisation of the model have recently been carried over to the current NASA cancer risk model for radiation protection in space(14). NASA specifies the quality factor in terms of Z 2/b 2 and uses the Katz parameterisation to evaluate the quality factor. The amorphous track radial dose distribution forms the basis also of the local effects model (LEM)(15) used for 12C particle radiotherapy in Germany. This phenomenological model has some conceptual similarities to the Katz model, notably in folding together particle radial dose profiles and photon dose response, but the methodology is substantially different.
CLASSICAL APPROACHES TO MICRODOSIMETRY
In radiotherapy, a mathematical approach based on the MKM, including use of the quantities lineal energy and specific energy, has been used to estimate the RBE-weighted ‘biological dose’ for planning of carbon-ion treatment at the HIMAC facility(21). Track structure simulation
CONCLUSION Microdosimetry is an extensive and powerful field of study. This article has discussed it only in the context of biological effects of radiation, but there are clear analogies also in other fields, such as micro-electronics. The classical approaches to microdosimetry, mostly initiated during the 1960s–1980s, continue to play a major role in current developments and applications in the field. Due to the interlinked nature of the various
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Monte Carlo techniques(22) provide the means to simulate very large numbers of tracks, providing detailed stochastic descriptions of the radiation (Figure 1e). But what should be done with this very large array of computer data? The data can, of course, be reduced to the well-established microdosimetric quantities summarised earlier—LET, track entities, radial dose profiles, lineal energy, specific energy, etc.—not only for comparison with experimental data, but also for extension into regions where experimental measurements are not practical. New microdosimetric quantities could be defined and calculated, without constraints of experimental limitations. In particular, quantities on the nanometre scale are accessible, with potential relationships to DNA and DNA structures or other molecules and organelles of potential interest in radiation effects. Track simulations have very wide application in modelling of radiation processes and effects, not only to provide quantitative descriptions of known phenomena and available data, but also to provide new insights and generate new hypotheses on the mechanisms underlying radiation effects. Clustered damage in DNA provides a historic example of personal interest to the author. In early studies, from geometric sampling of radiation tracks, it soon became apparent that there are only limited regions of target volume and energy deposition (or numbers of ionisations) that can correlate reasonably with the RBEs of different radiations for effects of interest, such as cell killing or mutation induction. Such comparisons led to hypotheses of critical properties of radiation, namely correlation of cellular effects with energy depositions of more than about 100 eV within 3–4 nm for low-LET effects and more than about 340 eV (15 ionisations) within about 5–10 nm for typical high-LET effects(4); it was clear from the analyses that a single property could not account for both high- and low-LET radiations. Much more recently, coming from a very different perspective, analyses of photon, neutron and carbon-ion radiotherapy beams have led to the suggestion that dose-mean specific energy in volumes of 10 nm spheres provides close correlation with clinical RBE(23). To probe further into underlying mechanisms, yields and types of DNA damage can be estimated from track structure simulations that include damage from direct interactions in the DNA and from water radicals produced in the immediate vicinity. Very low-energy secondary electrons are highly effective at producing clusters of ionisations within volumes of nanometre
dimensions. Hence, such electrons are effective at producing ‘clustered damage’(4, 24) in DNA. Simulations show that a wide variety of clustered DNA damage occurs, ranging from a simple double-strand break (DSB) to more complex DSB (with additional strand breaks and/or base damages within a few base pairs) and also non-DSB clustered damage (multiple base damages with or without an associated single break). Simulations from many thousands of tracks led to the conclusion that 20 % of DSBs from low-LET gamma rays and hard X rays are complex by having one or more additional associated strand break and 50 % are complex due to additional base damage and/or strand breakage. For high-LET alpha particles, these proportions rise to 70 and 90 %. High-LET radiations produce a modestly greater absolute number of DSB per unit dose, a greater proportion of which are complex, and also increased degrees of complexity within the damage spectrum. The more complex DSBs are less likely to be faithfully repaired and hence have greater biological ‘severity’(25). This expectation is supported by many experimental studies showing that the repair kinetics of DSB depend on radiation quality, with a greater proportion of slow-repairing DSB after higher-LET radiations(26), and that complex DSBs are more likely to be lethal or mutagenic(27). Hence, the well-known RBE– LET relationship is likely to be due in large part to the ionisation-clustering properties of the radiation tracks on the nanometre scale of DNA, the consequent clustered DNA damage and the limited repair capabilities of the cell. However, correlations of damage within single radiation tracks over larger dimensions, from chromatin up to multicellular regions of tissue, are also relevant in determining the overall radiobiological effectiveness. The previously mentioned example of analysis of DNA damage from track structure is just one of many possible uses of track structure simulations to probe the mechanisms of radiation action or provide descriptions of observed phenomena. In another wide-ranging example(28), modelling has been done over dimensions of many orders of magnitude from DNA up through chromosomes and chromosome territories to the entire cell nucleus, biochemical repair processes and extracellular signalling. In general, the scope for application of track structure simulations is immense for both descriptive and investigative studies.
D. T. GOODHEAD
concepts, quantities and objectives, it remains appropriate to retain the term ‘microdosimetry’ for the entire field, as represented by the topics of the 16 international symposia to date, rather than restricting it to any one narrow aspect. REFERENCES
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