Applications of Nanodosimetry in Particle Therapy Planning and Beyond

Abstract

This topical review summarizes underlying concepts of nanodosimetry. It describes the development and current status of nanodosimetric detector technology. It also gives an overview of Monte Carlo track structure simulations that can provide nanodosimetric parameters for treatment planning of proton and ion therapy. Classical and modern radiobiological assays that can be used to demonstrate the relationship between the frequency and complexity of DNA lesion clusters and nanodosimetric parameters are reviewed. At the end of the review, existing approaches of treatment planning based on RBE models or dose-averaged linear energy transfer are contrasted with an RBE-independent approach based on nandosimetric parameters. Beyond treatment planning, nanodosimetry is also expected to have applications and give new insights into radiation protection dosimetry.

1. Introduction

The underlying concepts of dose and relative biological effectiveness (RBE) originated in the 1950s when the DNA double helix, a macromolecule of about 2nm diameter, had been discovered. Now we know that cells exposed to ionizing radiation will repair most of the resulting DNA damage from x-ray radiation and can also suffer from complex DNA damage that is more prevalent with charged particles used for radiation therapy and is difficult to repair by the enzymatic repair system common to all eukaryotic cells. It has been hypothesized that this complex DNA damage caused by ionization clusters in short DNA segments, is responsible for cell death, cell dysfunction, or cancer initiating DNA mutation. This knowledge is currently not directly taken into account in the fields of radiation treatment planning and radiation protection. In fact, the advancement in computational methods and mathematical modeling, and high throughput cell biology assays such as super-resolution imaging and genome sequencing achieved over the last decade set the stage for a new foundation of the radiation treatment planning principles.

The prevailing approach to planning x-ray radiation therapy assumes that a homogeneous distribution of physical dose deposited in a biologically homogeneous tumor volume results in a uniform biological effect, which is quantified (i) biologically as a probability of cell death and (ii) clinically as the tumor control probability (TCP) that need to assure tumor eradication. The uniform distribution of ionization events guarantees the uniform biological effect. This concept is reasonable for photons but for radiation modalities using 4-He and 12-C ions it requires modification. These particles and their secondaries often ionize more densely along the particle track than the secondaries of photons (mostly electrons). This creates a mixed and geometrically non-uniform ionization pattern on the nanometer scale. Ions, especially in the Bragg peak region, are, therefore, expected to be radiobiologically more effective and clinically advantageous compared to photons (Kamada et al 2015, Tommasino & Durante 2015, Durante et al 2017, Durante 2018). Calculating absorbed dose by averaging the number of ionizations per unit volume is clearly inadequate for the heavy ions but also for Bragg-peak-protons. Current treatment planning algorithms calculate the physical dose delivered by charged particles and also account for different biological effectiveness using one of several existing RBE models to achieve a uniform biological effect, see, e.g., (Karger & Peschke 2018, Fossati et al 2018, McNamara et al 2019, Mein et al 2020) and references therein for a review of all currently used models, and (Scholz et al 1997, Kanai et al 1999, Inaniwa et al 2015) for center specific models used in carbon ion therapy. However, despite mounting evidence of the importance of the nanoscopic patterns of ionizations, the RBE models increasingly being incorporated in the state-of-the-art treatment planning systems for particle therapy do not directly account for nanoscopic patterns because they are based on linear energy transfer (LET) or microdosimetric (not nanodosimetric) quantities.

In this review, we take a step back, re-think the basic concepts of dose and RBE, and then take two steps forward towards a new concept based on nanodosimetry and how it could be applied in radiation treatment planning and radiation protection. With the tools of modern physics, biology, and computation operating at the nanometer scale, this seems possible. In the following sections, we describe how the advancements in experimental nanodosimetry, Monte Carlo track structure simulation, as well as super-resolution confocal microscopy, and next generation sequencing methods can contribute to a fundamentally new approach to treatment planning in charged particle therapy. Such an approach, when scientifically validated, may improve the outcome of cancer patients and potentially may have much wider implications for the metrology of ionizing radiation and its effects on human health, in general.

2. Principles and concepts

The original metrological system of radiology (radiation therapy and diagnostic radiology), introduced in the 1950s, assumed that the same average amount of ionizations per unit mass, i.e., the same absorbed dose to water or air, and its distribution in space and time results in the same effect in a biological system. Soon it became clear, however, that this concept was fundamentally flawed. The same average number of ionizations distributed in the same manner in space and time can result in very different biological effects when radiation modalities of different quality are applied. Therefore, averaging concepts such as RBE and LET were developed in the 1950s and continue to be used today.

In the following years, it was recognized that energy deposition by ionizing radiation consists of a large number of discrete events randomly overlapping the DNA molecules. This led to the introduction of stochastic quantities in radiation physics, radiation chemistry, and radiation biology. Experimental and theoretical studies of stochastic energy distributions in microscopic volumes (microdosimetry) started in the 1960s and nanoscopic volumes (nanodosimetry) in the 1970s. The underlying concepts of microdosimetry were developed and matured before those of nanodosimetry. For a review of the experimental and theoretical concepts of microdosimetry see, e.g., the book by Rossi and Zaider (Rossi & Zaider 1996). The first comprehensive review of nanodosimetry and its principles and applications appeared in (Schulte et al 2011).

2.1. Energy imparted and specific energy

The energy deposit in a single radiation interaction (energy deposition event) is represented by the stochastic quantity, ϵ_i. Considering a defined volume, the energy imparted to that volume is defined as $ϵ={\sum }_i{ϵ}_i$, where the sum is carried out over all energy deposition events. The quotient of the energy imparted and the mass of the considered volume is defined as specific energy, z = ϵ/m. Note that ϵ_i, ϵ, and z are stochastic microdosimetric quantities.

2.2. Absorbed dose, LET, and RBE

According to the ICRU (ICRU 2011), the absorbed dose D is defined as the differential quotient of the mean energy imparted to mass, $D=d\overline{ϵ}/dm$ and is expressed in [J/kg]. The special unit of the absorbed dose is [Gy]. Absorbed dose can also be defined as the first moment of the probability distribution of specific energy z. The quantity absorbed dose is usually sufficient when prescribing and reporting radiation therapy with external beam delivered to macroscopic volumes, whereas for small volumes such as biological cells, the values of specific energy can differ greatly from absorbed dose.

The importance of stochastic variations of microscopic energy deposits for biological radiation effects on cells was unknown in the 1950s when absorbed dose and linear energy transfer (LET) were defined. However, it was already known that radiations of different LET results in different effects in the same biological system for the same amount of absorbed dose. The non-stochastic quantity LET of charged particles interacting with a material is defined as the differential quotient L_∆ = dE_∆/dl, where dE_∆ is the mean energy lost by the charged particle through the electronic collisions when traversing a distance dl, minus the sum of the kinetic energies of all the electrons released by charged particles with kinetic energies above ∆ (ICRU 2011). During the 1960s, two types of LET distribution were discussed, one associated with the fraction of track lengths t(L) and the other with the fraction of absorbed dose d(L) delivered by tracks between L and L + dL (ICRU 1970).

The initial remedy for taking into account different biological effectiveness of different radiation qualities in radiation therapy and protection was the introduction of the RBE concept. The RBE is defined as the ratio of the absorbed dose delivered by the reference radiation and the dose delivered by the radiation of different quality of interest, each resulting in the same biological effect in a given system under otherwise identical conditions (IAEA & ICRU 2008).

In the early 1960s, the ICRP and ICRU appointed a committee to study the concept and the use of RBE (ICRU 1963). The relationship between LET and RBE was recognized and two average LET values were proposed: the track-averaged LET, defined as ${\int }_0^{\infty }t\left(L\right)dL$, and the dose-averaged LET, defined as ${\int }_0^{\infty }d\left(L\right)dL$. The dose-averaged LET has found applications in biologically weighted proton treatment planning, see Sec. 5.

2.3. Concepts linking nanodosimetry to radiation chemistry and radiobiology

Over the last 30 years, it has become increasingly obvious that the biological effects of radiation are strongly related to the clustering of energy deposition events (mostly ionizations) at the level of nanometric volumes, most importantly, short segments of DNA. This led to the development of track structure concepts, micro and nanodosimetry, and track structure simulation methods. The overall goal is to link the size of stochastic energy deposition events to radiation chemistry and biologically relevant DNA damage. For an excellent overview of the relationship between radiation track structure and micro and nanodosimetric quantities as well as their importance for radiobiology see the review by Hill (Hill 2018).

Studying the stochastic interaction of radiation with matter requires the consideration of charged particle tracks. Early attempts to classify the non-uniform deposition of energy by ionizing radiation were undertaken by radiation chemists (Henglein 1991) and resulted in the distinction of direct and indirect effects. Ionization-induced radicals, after nanometer-scale diffusion, lead to DNA damage (indirect effect). On the other hand, direct ionization of the DNA molecule will create DNA radicals that can be converted to stable DNA lesions (direct effect). Thus, as a consequence of ionization and radical clustering over nanometer dimensions, one can expect the creation of DNA damage of different degrees of complexity (see Sec.4). Monte Carlo track structure simulations, see Sec. 3.2, later provided a more detailed description of charged particle interactions in materials of biological importance (usually liquid water). This description includes the geometric distribution of the interaction points and the nature of interaction (ionizations, excitations, nuclear interactions, and production of secondary particles) (Dingfelder 2012).

Experimental nanodosimetry (see Sec. 3.1) provides a technique to probe individual charged particle tracks with a nanometer-equivalent sensitive volume that typically has a cylindrical shape and simulates short DNA segments spanning the length of 1–2 helical turns or 10–20 base pairs (3.4–7.8nm). Sensitive volumes in experimental nanodosimetry typically range from 1–20nm in diameter and 1–100nm in length (see Sec. 3.1). A unit-density equivalent nanodosimetric volume is created using low pressure gas, e.g., propane or nitrogen at a few mbar of pressure. The goal of nanodosimetry is to register the number of individual ionizations, called the ionization cluster size (ν) in a nanodosimetric target volume per energy deposition event. The most relevant stochastic nanodosimetric quantities are summarized in Def. Box 1 (Palmans et al 2015). The ionization cluster size and its distribution (ICSD) can be absolute or conditional on a certain cluster size, e.g., ν ≥1 or ν ≥2. From the ICSD, we can derive the first moment (M₁ or ${\text{M}}_1^{C_2}$) and the complementary cumulative probabilities $\left({\text{F}}_k^{C_2}\right)$ of observing a cluster of a certain size k or larger (Conte et al 2018, Palmans et al 2015, Rabus et al 2020).

Def. Box 1, Nanodosimetric Quantities.

Ionization cluster size (ν):

The number of ionizations produced in a specified target volume of nanometer size by a single primary particle track and its secondaries.

Ionization cluster size distribution (ICSD):

Probability distribution of ionization cluster sizes ν, P_ν(Q,V), which depends on the radiation quality, Q, (particle type and velocity) and the shape, size, and material of the target volume, V. For a fixed volume, the dependence on V can be dropped. A conditional ICSD gives the conditional probability of a certain cluster size given that at least a given number of ionizations (typically 2) has occurred in the target volume. In this case, one adds a superscript, e.g., ${\text{P}}_{\nu }^{C_2}$

Mean cluster size (M₁ or ${\mathbf{M}}_1^{C_2}$):

First statistical moment of the ICSD or the conditional ICSD.

Complementary cumulative probabilities (F_k, ${\text{F}}_k^{C_2}$):

The probability of k or more ionizations in the target volume, calculated from the ICSD or the conditional ICSD.

After the initial physical stage, which is well described by track structure simulations, the next stage is the physico-chemical stage. During this stage, ionized and excited molecules relax, free electrons thermalize, molecular dissociation occurs, and diffusing free-radicals form. The subsequent heterogeneous chemical stage lasting for about 1ms is dominated by generation, diffusion, and the reaction of free radicals with themselves (recombination), small scavenging molecules, or macromolecules such as DNA. It is important to note that clusters of radicals formed by ionization clusters, mostly consisting of ^·OH, ${\text{e}}_{\text{aq}}^{-}$, and ${}^{\cdot }\text{H}$ only have a lifetime of the order of nanoseconds in the high scavenging environment of living cells (LaVerne & Pimblott 1993). During these short times, the free radicals can diffuse only a few nanometers before they react. The recombination of primary radicals may lead to secondary radicals that can also damage DNA. The non-uniform nature of charged particle tracks translates into distinct radiochemical track entities, including spurs (100eV or less), blobs (0.1–0.5keV), short tracks (0.5keV-5keV), and branch tracks (>5keV), where the numbers in parenthesis indicate the energy deposited in each track entity (Henglein 1991).

The overlap of radical clusters with the DNA molecule combined with direct ionization of the DNA results in chemical modification of nucleotides, often forming DNA lesion clusters. Abstraction of hydrogen atoms from the sugar-phosphate backbone of DNA either by direct ionization or via interaction with radiation-induced ^·OH radicals generates sugar radicals, that, when centered on certain sugar atoms, lead to strand damage, including breakage and base losses. DNA base damage is caused by ${\text{e}}_{\text{aq}}^{-}$ radical attack or direct ionization. For a review of the radiation chemistry phase of DNA damage, see, for example, (von Sonntag 2006).

To a first approximation, the size of the DNA lesion clusters is proportional to the size of ionization and subsequent radical clusters formed in nanometer size DNA volumes, including the adjacent water layer. Another essential point is that ionization clusters are single-particle events produced linearly with primary particle fluence, and so are the DNA lesions they create. If the ionization cluster contains two or more ionizations, the resulting DNA lesion clusters are typically comprised of two or more strand breaks on the opposing strands leading to double strand breaks (DSB) of different complexity (see Sec. 4).

Different approaches can be used to convert nanodosimetric ICSD to distribution of DNA lesion cluster sizes or classes of DNA lesions of different complexity such as simple and complex DSB (see Sec. 4.1.1). One approach is to define the probability of creating a single strand break or a single base lesion per single ionization in the cluster based on experimental data (Garty et al 2010), and then use binomial or trinomial statistics to describe the distribution of certain DNA lesion clusters. However, this approach does not consider the fact that this probability would depend on the radical recombination probability and, thus, the cluster size itself, creating some uncertainty at the high-end of DNA lesion cluster sizes. Another approach is to use detailed Monte Carlo track structure codes that include the transport and reaction constants of each radiation induced radical that can lead to DNA lesions, see Sec. 3.2 and references therein. This approach also has inherent uncertainties due to the multiple reaction channels, some of which have uncertain reaction kinetics. Lastly, an additional element of uncertainty is due to the fact that the probability of DNA lesion creation will depend on chromatin structure and oxygen concentration.

Fig. 1 summarizes how the nanodosimetric ICSD, which is a physical characteristic of ionizing radiation measurable in gas and computationally derived in water, can be linked to the complexity of DSB. DSB can be microscopically visualized in cell nuclei using, for example, fluorescently labeled phosphorylated histone H2AX (γ-H2AX). The distribution of these radiation-induced foci is uniform in the case of low-LET photons (Fig. 1A) and non-uniform in the case of high-LET ion tracks (Fig. 1B). However, this method cannot tell us anything about the complexity of DSB except that foci formed by complex DSB may be resolved with much slower kinetics. The complexity of DNA damage may be inferred from advanced ionizing radiation-induced foci assays and next generation labeling and sequencing assays as discussed in Sec. 4.2. On the other hand, the frequency of large ionization clusters can be measured and calculated to be utilized for treatment planning of particle therapy (Sec. 5). Thus, it is important to understand and predict the relationship of ICSD to a frequency distribution of simple and complex DSB.

Figure 1.

Schematic illustration of the relationship between observable radiation damage (panels A and B) and nanodosimetric quantities (panels E through G). Photons produce uniformly distributed DNA lesions in cell nuclei, here marked by fluorescently labeled phosphorylated γ-H2AX foci (panel A). High LET ion tracks produce γ-H2AX foci non-uniformly distributed along particle tracks (panel B). Panels C and D show single ionizations on the scale of about 50nm for each radiation quality. The small red circles correspond to DNA segments, i.e., sensitive nanometric volumes of 2–3 nm diameter and 10–20 nm length (panel E) for registration of single ionizations (green dots). This allows quantification of ionization cluster size distributions shown in panels F and G. The conversion of an ionization cluster to a DNA lesion cluster consisting of strand breaks (red x) and base damages (blue x) via free water radicals (blue dots) and direct DNA ionizations (green dots) is shown in Panel E.

A nanodosimetric ionization cluster consisting of five ionizations, for example, may translate into a complex DNA lesion cluster of four DNA lesions (two strand breaks and two base damages), as shown in Fig. 1 panel E. Ionization clusters of different sizes can be measured in the gas phase and simulated in gas and condensed (liquid water) phases by Monte Carlo track structure codes (Sec. 3). A representative ICSD is shown in Fig. 1 panel F and Fig. 1 panel G for photons and high-LET charged particles, respectively. This demonstrates that large ionization clusters and large DNA lesion clusters can be assumed to be more common for high-LET radiation.

The frequency of ionization clusters of a size equal to or greater than a threshold value should have particular relevance for the biological effectiveness of radiation. For the purpose of planning charged particle therapy based on ICSD, it is important to define ‘small’ and ‘large’ ionization clusters. For example, in Fig. 1 panel F and Fig. 1 panel G, the green bars correspond to ionization clusters with ≥4 ionizations per event, which one may call large clusters. Large ionization clusters are more likely to lead to irreparable, complex DNA lesion clusters. On the other hand, single ionization events, ν=1, can be considered biologically irrelevant as they typically lead to single DNA lesions. The remaining clusters of size ν=2 and ν=3, i.e., small clusters, would mostly result in repairable DNA lesions clusters (Sec. 4.1). Note that the definition of small and large ionization clusters is preliminary and is awaiting further study before this definition can be used in particle therapy treatment planning (see Sec. 5).

3. Experimental nanodosimetry and track structure simulations

Experimental nanodosimetry and track structure simulation had their origin in the 1970s when it was recognized that ionization clusters at the nanoscale could be important for the biological effects of charged particle radiation. Both scientific fields developed in parallel, at first, without much interaction. Experimental nanodosimeters were conceptually proposed in the mid-1970s, and the first practical implementations were designed and built during the 1990s. Monte Carlo track structure simulation codes were also developed first in the 1970s as ionization and excitation cross-sections of water vapor became available. Since then, many more sophisticated Monte Carlo track structure codes have been developed, supported by improved cross-sections of liquid water and the ever-increasing computational speed. In this section, we will review the development and status of experimental and computational methods in nanodosimetry.

3.1. Experimental nanodosimetry

Experimental nanodosimetry was originally identified as the study of ionization cluster size distributions in a low pressure gas, typically comprised of propane or nitrogen. Fig. 2 schematically shows the principle of experimental nanodosimetry. Ionizations produced inside a low pressure gas in the range of 1–3mbar are sampled by an equivalent nanometer-size sensitive volume. Due to the low pressure, the distance between ionizations scales to millimeter dimensions, making the sensitive volume equivalent to DNA segments in the cell nucleus. An extracting electric field focuses and accelerates the ions or electrons produced in single ionizations inside the sensitive volume towards an ion or electron counter. The primary charged particle, which either intersects or passes the sensitive volume, can be tracked in its position and triggers the data acquisitions system, thereby relating the number of ionizations (ionization cluster size) to a single primary particle traversal. Collecting many primary particle events, one can acquire ionization cluster size distributions (ICSD). Primary particle fields can consist of monoenergetic particles or mixed fields of different particle energies and types. In addition, one can acquire ICSD for randomly traversing primary particles or primary particles tracked at a certain distance (impact parameter) from the sensitive volume axis (track nanodosimetry).

Figure 2.

A schematic illustration of the conceptual nanodosimeter design. The scheme closely matches the design of the ion-counting nanodosimeter, but the concept is also applicable to the other gas-based nanodosimeters.

The development of experimental nanodosimetry started in the mid-1970s (Pszona 1976). Over the last 30 years, several gas-based experimental nanodosimeters have been built and are maintained mostly in European labs (Bantsar et al 2018).

The Jet Counter (JC) was the first ion-counting nanodosimeter and was developed by a research group at the National Center of Nuclear Research (NCBJ, Warsaw/Świerk, Poland) (Pszona & Gajewski 1994). The nanometer-size sensitive volume, less than 20nm equivalent in diameter, is accomplished with an expanding nitrogen gas jet produced by a piezoelectric valve with a repetition rate of 1–8Hz and a pulse length of 600 µs. A single charged particle (electron, ion) crossing the sensitive volume at its center forms a cluster of ionizations that is registered with an efficiency of ∼80%. Experimental results have been published for alpha particles (²⁴¹Am) (Pszona et al 2000), low energy electrons (Bantsar et al 2009), ¹²⁵I Auger electrons (Pszona et al 2012), and carbon ions (Bantsar et al 2014, Bantsar et al 2015). Of note, the Polish research group also compared their experimental results with those obtained by Monte Carlo simulations (Pszona et al 2006, Bantsar et al 2006, Pszona et al 2012).

The ion-counting (IC) nanodosimeter was developed by detector physicists at the Weizmann Institute of Science (Israel) in collaboration with Loma Linda University (LLU) and the University of California San Diego (CA, USA) (Garty et al 2002). It is currently maintained at the Physikalisch-Technische Bundesanstalt (PTB, Braunschweig, Germany). The low pressure gas volume inside the IC nanodosimeter contains a wall-less sensitive volume of less than 5nm equivalent in diameter and a length between 2nm and 200nm that can be selected by adjusting the ion drift time window. The low pressure gas volume (propane) is stabilized at ∼1 Torr by a Baratron pressure gauge and pressure control system to an accuracy of better than 0.01 Torr. The positive ions created by primary charged particles in the low pressure gas volume drift due to an electric field towards the bottom of the chamber. Those ions created in the sensitive volume that are extracted through a 1mm diameter aperture into a vacuum region where they are focused, accelerated, and transported to an ion counter. The extraction efficiency varies spatially across the sensitive volume but is generally higher than 80% in a cylindrical volume of about 2nm diameter (Schulte et al 2006). Ions extracted through the aperture are detected with near 100% efficiency. Note that ionization cluster size registration is triggered by the primary particle which hits a downstream particle detector. The ICSD recorded by the IC nanodosimeter were initially published for alpha particles at 4.25MeV, protons at 22, 11, 7 MeV, and carbon ions at 25, 49, 63MeV (Garty et al 2002). Later, the collaboration published additional measurements for alpha particles at 4.8MeV, protons at 250, 17, 5, and 1.5MeV, and electrons from a Sr-90/Y-90 source using the IC nanodosimeter equipped with a trigger/tracking detector (Bashkirov et al 2006, Bashkirov et al 2009). At PTB, systematic measurements with the IC nanodosimeter were performed initially for monoenergetic protons and 4-He ions with energies of 0.1 to 20MeV in propane and nitrogen gas (Hilgers 2010, Hilgers et al 2015) and later extended to 12-C ions with energies between 45 and 150MeV and 4-He ions with energies between 2 and 20MeV, as well as 4-He ions produced by a 241-Am source (Hilgers et al 2017). Lastly, the PTB investigators unfolded the contribution to ICSD from secondary ions produced during ion extraction (Hilgers et al 2019) and proposed a method to reduce this unwanted background effect, which is noticeable only for large cluster sizes (Hilgers & Rabus 2019). A new version of the IC nanodosimeter has been developed at LLU in collaboration with CERN and PTB (Casiraghi et al 2014, Casiraghi et al 2015, Vasi et al 2016). The device consists of a much smaller low pressure gas-filled chamber (propane, 1–10mbar) from which primary-particle-generated ions drift and are extracted into a multiple-hole detector where they create ion impact ionization. This allows ‘imaging’ of an entire track segment with nanometer resolution.

The Startrack (acronym for Structure of hadronic track) counter (SC) is a gas-based nanodosimeter that was originally developed and is maintained by the INFN Laboratori Nazionali di Legnaro (LNL, Italy) (De Nardo, Alkaa, Khamphan, Conte, Colautti, Ségur & Tornielli 2002, Denardo et al 2007, Conte et al 2010). It is a single-electron counting rather than a single-ion counting nanodosimeter. Similar to the IC nanodosimeter, the SC nanodosimeter contains a wall-less sensitive volume, typically ∼20nm equivalent in diameter, embedded in a low pressure (2–3mbar) propane ionization volume. Electrons produced by primary charged particle tracks that cross or pass the sensitive volume are collected in a drift chamber that allows the separation of electrons in time so that they can be counted individually by a multi-step avalanche chamber (MSAC). Track nanodosimetry is enabled by combining two collimators positioned upstream of the particle source and in front of a silicon trigger detector. The efficiency of single-electron counting with the SC is limited by three factors: the extraction efficiency from the sensitive volume, the efficiency of electron transfer through the drift chamber, and the electron detection efficiency of the MSAC. The overall efficiency was measured to be about 30% at a gas pressure of 3mbar. Despite of this relatively low efficiency of electron counting the investigators showed that one could derive the true ICSD using a binomial relationship (De Nardo, Colautti, Conte, Baek, Grosswendt & Tornielli 2002). Measurements of ICSD were initially performed at gas pressures of 3.5 and 3mbar and distances between 0 and 70nm from the sensitive volume axis for alpha particles (5.4MeV) and 12-C ions (72, 96MeV) (De Nardo, Colautti, Conte, Baek, Grosswendt & Tornielli 2002). In a more recent measurement campaign, ICSD were measured at a gas pressure of 2mbar for protons (20MeV), deuterons (16MeV), 6-Li ions (48MeV), 7-Li ions (26.7MeV) and 12-C ions (96MeV) (Conte et al 2012) and 12-C ions (240MeV) (Conte et al 2014, Grosswendt et al 2014). In their most recent measurement campaign (Selva et al 2020), the investigators measured ICSD at 2.0 and 1.7mbar propane gas pressure for protons (25MeV), 7-Li ions (16.4MeV), 12-C ions (72MeV), and alpha particles (5.8 MeV). In another set of measurements during this campaign, ICSD of 7-Li ions (16.4MeV) were measured as a function of propane gas pressure from 3.0mbar down to 1.5mbar in steps of 0.1mbar.

3.2. Monte Carlo track structure simulations

Monte Carlo track structure simulation codes enable the simulation of individual charged particle tracks on an event-by-event basis. Events include ionizations, excitations, and nuclear interactions of the particle. For applications in biology and medicine, double differential cross-sections are needed for the materials present in cells and tissues, foremost for liquid water. Because these cross-sections are experimentally difficult to obtain, the development of these codes had a slow start and is not complete to the present day. It is important to distinguish between general purpose condensed history and track structure Monte Carlo simulation codes. General purpose codes such as EGS, FLUKA, Geant4, MCNP, PHITS, and PENELOPE were mostly developed for high energy physics applications and using the condensed history technique, generally from the keV to GeV/TeV energy range. These codes do not provide a detailed description of all interactions and the physical models required for simulations at the nanometer scale. Track structure simulation codes, on the other hand, provide event-by-event simulations with energies down to eV or sub-eV threshold and are, therefore, the most appropriate approach for simulations of nanodosimetry. In the following paragraph, we give a brief review of the development of track structure simulation codes that, as we believe, are relevant for the use of nanodosimetry in charged particle treatment planning applications.

The first track structure simulation code was developed for electrons in water vapor by radiation physicists at the Gesellschaft fur Strahlenforschung (GSF, Germany) (Paretzke 1974). This code was further refined and later led to the water vapor MOCA code series developed by Paretzke and Wilson (Wilson & Paretzke 1981). During the late 1990s, their common work became the basis for the liquid water track structure simulation code PARTRAC (Friedland et al 2011, Friedland et al 2017), which features a detailed geometrical chromatin-DNA model (Friedland et al 1998). For a review of other biophysical track structure simulation codes see, for instance, (Nikjoo et al 2006, Dingfelder 2012).

The PARTRAC track structure simulation code, as well as other codes with biophysical applications, had a limited user base and were not developed specifically for treatment planning of particle therapy. In 2001, the Geant4-DNA project was initiated by Petteri Nieminen at the European Space Agency (ESA) as an extension of the general purpose Geant4 toolkit (Agostinelli et al 2003, Allison et al 2006, Allison et al 2016) to allow track structure Monte Carlo simulations. The Geant4-DNA project has been carried out and maintained by the Geant4-DNA Collaboration and was specifically developed to model and predict biological radiation damage to the DNA (Chauvie et al 2006, Incerti et al 2010, Bernal et al 2015, Incerti et al 2016, Incerti et al 2018). The Geant4-DNA extension is fully included in the open-source Geant4 toolkit.

In 2012, a group of medical physics researchers and software developers in the United States used the general purpose Geant4 toolkit to create a software simulation package for medical applications (TOPAS), making the attractive features of Geant4 readily available to the community of research and clinical physicists (Perl et al 2012). An extension, TOPAS-nBio, was developed more recently to model radiation physics, chemistry, and biology at the DNA level (Schuemann et al 2019). TOPAS-nBio is a Geant4-DNA extension and includes interactions of particles at very low energy down to vibrational energies on an event-by-event basis.

The Geant4-DNA and TOPAS-nBio projects for modeling biological damage induced by ionizing radiation at the DNA level are likely to continue in the foreseeable future. For a comprehensive review of current activities see (Incerti et al 2016). These activities include development of models for physics, physico-chemistry, and chemistry processes, e.g., (Shin et al 2019, Peukert et al 2019), geometries of biological targets, e.g., (Tang et al 2019, McNamara et al 2018), and multi-scale applications in medicine, including radiation therapy, e.g., (Schuemann et al 2018, Sakata et al 2020). A full list of references to the Geant4-DNA and TOPAS-nBio projects can be found on their respective websites (Geant4-DNA-Collaboration 2020, TOPAS-nBio-Collaboration 2020).

In 2021 the general purpose Monte Carlo code PHITS (particle and heavy ion transport code) was upgraded to include the track structure simulation code KURBUC (Kyushu University and Radiobiology Unit Code) (Nikjoo et al 2006). In the combined PHITS-KURBUC mode it is now possible to calculate microdosimetric and nanodosimetric quantities for mixed radiation fields, e.g., those in the spread out Bragg peak of protons and carbon ions (Matsuya et al 2021).

3.3. Relationship between experimental and simulated nanodosimetric quantities

A track structure simulation code, specifically focusing on the calculation of nanodosimetric quantities in low pressure gas (nitrogen and propane) and liquid water was developed at the PTB and later called PTra (Grosswendt 2002, Grosswendt & Pszona 2002, Grosswendt et al 2004). This code, which transports secondary electrons down to an energy threshold value of 10eV, has been used to compare experimental and simulated ICSD produced by the Jet-Counter (Grosswendt et al 2002, Bantsar et al 2004), the Ion-Counter (Garty et al 2002, Wroe et al 2006), and the Startrack-Counter (De Nardo, Colautti, Conte, Baek, Grosswendt & Tornielli 2002, Conte et al 2011, Conte et al 2012, Grosswendt et al 2014, Conte et al 2020). In general, good agreement between the ICSD in low pressure gas and liquid water has been found. One should also mention that Geant4-DNA has been used successfully for analyzing and reproducing nandosimetric experimental data; see, e.g., (Burigo et al 2016).

An important aspect of ICSD derived from either experimental, gas-based nanodosimetry or track structure simulations is the degree of similarity for the same radiation quality. Because the PTra code allows ICSD calculation in nitrogen, propane, and liquid water, Grosswendt was able to study this important aspect (Grosswendt 2004, Grosswendt et al 2004). In general, radiation interaction in gaseous systems, particularly when excitations are considered, is quite different from radiation interaction in liquid water. However, when focusing on ionization cluster formation, the difference may be less dependent on the target molecules. Based on the results of the Startrack-Counter experiments (De Nardo, Alkaa, Khamphan, Conte, Colautti, Ségur & Tornielli 2002), Grosswendt derived a scaling method using the ratio of mean-free ionization path length in both media that allowed direct scaling of sensitive volume sizes in both gas and liquid water. The comparison of measured and simulated ICSD for 4-He ions of 4.6 and 5.4 MeV in sensitive volumes of nitrogen and propane scaled to the equivalent size of those of liquid water showed that cluster size formation in gas corresponded to that in liquid water, and the ICSD were quite similar (Grosswendt et al 2004).

Future extensions of track structure simulation codes should include implementation of cross-sections of gases commonly used in experimental nanodosimeters (nitrogen and propane), in particular for low energy electrons. This would allow a direct comparison between experimental and simulated nanodosimetric quantities in radiation treatment planning. The introduction of gas cross-sections for nitrogen and propane, is, for example, a planned feature for Geant4 in 2021 (Geant4 Collaboration 2021).

4. Quantification and characterization of DNA damage

Ionizing radiation deposits energy (mostly) in individual ionizations associated with particle tracks. These subsequently produce many secondary non-ionizing products, including electrons with energies below the ionization threshold and diffusion-limited reactive chemical species (free radicals). Both can form different types of nucleotide modifications (DNA lesions) that can be correlated with the ionization cluster that created them. Many of the intermediate products and details of the initial physical, physico-chemical, and chemical processes, which occur on the femto- to picosecond time scales, are still unknown, and describing the status of related research is beyond the scope of this review. From a practical point of view, the important point is that the local ionization cluster size on the nanometer scale is the starting condition for all subsequent processes that lead to the observed DNA damage. The complexity of the damage determines the repair pathways chosen by cells and, in turn, will dictate the final biological outcomes that are important for radiation therapy. In this section, we first review the spectrum of DNA damages and the repair pathways associated with them. Then we give an overview of classical, more recent, and evolving techniques to quantify and characterize different forms of radiation-induced DNA damage and its complexity.

4.1. The complexity and repair of DNA damage

4.1.1. DNA damage complexity

It is widely recognized that, on the nanometer scale, individual DNA damages affecting a single nucleotide or a nucleotide pair linked by a base pair (bp) can occur within 1–2 helical turns and form a lesion cluster. Individual DNA lesion clusters are comprised of adjacent DNA lesions that are not more than 10bp apart. The lesion cluster most responsible for cell death and mutation due to irradiation is the double strand break (DSB) (Toulany 2019). A simple DSB is comprised of two individual strand breaks occurring within a distance of 10 bp and complementary DNA overhangs of variable length (0–10 bp). It has also been recognized that DSB are entities with different levels of complexity, i.e., strand breaks can be associated with additional DNA lesions within 1–2 helical turns. For example, a DSB associated with additional DNA lesions is then defined as complex DSB. Besides DSB, simple or complex non-DSB lesion clusters exist, lacking the two or more strand breaks on opposing strands that create a DSB.

The existence of DNA damage with multiple lesions in close proximity was originally predicted based on radiation chemistry considerations (Ward 1985, Brenner & Ward 1992, Ward 1994). By now, the existence of DNA lesion clusters, which have also been called locally multiply damaged sites (LMDS), has been supported by many track structure simulation studies that included the chemical phase and induction of DNA lesions (Goodhead 1994, Nikjoo et al 1997, Nikjoo et al 1999, Watanabe et al 2015, Nikjoo et al 2016, Friedland et al 2017, Chatzipapas et al 2020).

Several classification schemes of DNA damage based on Monte Carlo track structure simulations have been suggested. A classification of radiation induced DNA damage that combines several elements of the commonly used DNA breakage classification schemes by Nikjoo et al. (Nikjoo et al 1997, Nikjoo et al 2001) and Friedland et al. (Friedland et al 2017) is shown in Def. Box 2. Nikjoo and colleagues defined two classification schemes: the first according to the complexity of a lesion cluster, and the second according to the origin of the breaks resulting from direct or indirect effects (Nikjoo et al 1997, Nikjoo et al 2001). While base damages were simulated, they were not taken into account in these classifications. Besides simple DSB, they distinguished two categories of complex DSB (DSB⁺, DSB⁺⁺) according to the number of additional strand breaks not further away from other strand breaks in the lesion cluster than 10 bp. In their simulations, the authors found that DNA lesion clusters rarely extended beyond 20 bp. Friedland and colleagues devised a similar, though not identical classification scheme for the complexity of DNA breakage simulated with PARTRAC (Friedland et al 2017). In addition to simple DSB, defined in the same way as by Nikjoo et al., they introduced a notion of DSB clusters, defined as two or more DSB within a segment of 25 bp. They also defined DSB multiplicity as the mean number of DSB in DSB clusters, an LET dependent quantity. One should note that different scoring schemes may result in different DNA damage yields (Pater et al 2014). A new Standard DNA Damage (SDD) data format for describing the geometric relationship between DNA strand breaks and base damages simulated with Monte Carlo track structure simulation codes has been proposed by Schuemann and collaborators (Schuemann et al 2018). This standard can be helpful to relate nanometer-scale energy deposition and ionizations to DNA damage complexity.

Def. Box 2, Radiation-induced DNA damage.

DNA lesion:

stable chemical modification(s) of a single or a pair of nucleotides resulting from a single ionization event, including strand break, base damage (base oxidation, abasic site), or DNA-protein cross-link; these events occur before enzymatic repair.

DNA lesion cluster:

two or more DNA lesions within 1–2 helical turns.

simple DNA lesion cluster:

cluster with exactly two DNA lesions.

simple DSB:

DNA lesion cluster with exactly two strand breaks on opposing strands but without any other lesions.

complex DNA lesion cluster:

cluster with more than two separate DNA lesions.

complex DSB:

DNA lesion cluster with two strand breaks on opposing strands that are associated with additional DNA lesions.

non-DSB lesion cluster:

a simple or complex lesion cluster lacking two or more stand breaks on opposing strands.

Indirect evidence of DNA lesion clusters comes from the observation that non-DSB lesion clusters can be converted to a DSB during base-excision repair, e.g., in case of a single strand break in combination with one or more base damages on opposing strands (Gulston et al 2004). With the recognition of the biological importance of both strand breaks and based damages for the formation of complex DNA lesion clusters we have redefined the different degrees of DNA damage complexity in Def. Box 2. This revised definition, which goes beyond the original classifications, may form a basis for comparing the frequency of local ionization clusters with the resulting local DNA damage clusters.

In Sec. 2.3, we pointed out a connection between ionization cluster size distributions (ICSD) and the frequency of complex DNA damage. To correlate ICSD with damage complexity, we may distinguish between simple and complex DNA lesion clusters in general and simple and complex DSB in particular (see Def. Box 2). The correlation between ICSD and the frequency of DNA lesion clusters is expected to be strong if single ionizations cause individual DNA lesions, which is a reasonable assumption. Small ionization clusters should correlate with simple DNA lesion clusters and large ionization clusters with complex DNA lesion clusters. The exact definition of ‘small’ and ‘large’ ionization clusters and their correlation with simple and complex DNA lesion clusters awaits further experimental and track structure simulation studies.

4.1.2. DNA damage repair

Efficient pathways for DNA damage recognition, signaling, and repair, collectively called the DNA damage response (DDR), have evolved to respond to DNA damage resulting from cellular metabolic processes or external agents such as radiation; for a general review, see (Zhou & Elledge 2000). Inability to respond adequately to DNA insults can lead to various disorders and predisposition to cancer (Hakem 2008, Maynard et al 2015). The mutagenicity and lethality of DSB have been attributed to problems with the repair of complex DSB (O’Driscoll & Jeggo 2006). After the initial recognition, signaling, and signal amplification, the cell commits to one of several possible pathways, including DNA repair or various forms of cell cycle arrest or cell death.

There are two principal mechanisms of DSB repair, called non-homologous end-joining (NHEJ) (Mahaney et al 2009, Chang et al 2017) and homologous recombination (HR) (Wright et al 2018). While some details are still missing, in the following, we present an emerging view, supported by the scientific literature, that describes how the pathway choice, speed, and fidelity of DSB repair depends on DSB complexity and cell cycle phase (Fig. 3).

Figure 3.

Emerging view of the interaction between DSB complexity and cell-cycle dependent repair; simple and complex DSB are defined in the Def. Box 2. The helical nature of the DNA duplex has been omitted for clarity. The four DSB repair pathways, labeled (I)-(IV), their cell-cycle availability and the key repair proteins are shown. The major signaling and damage amplification proteins (ATM, ATR, and H2AX) common to all four pathways are not shown in this scheme. Left: simple DSB are processed by resection independent canonical non-homologous end-joining (c-NHEJ). Polynucleotide kinase/phosphatase (PNKP) enzymatically restores chemically modified 5’-phosphate and 3’-hydroxyl termini. The DSB ends are then religated in a Ku70/Ku80-DNA PKcs-complex dependent process. This pathway is available throughout the entire cell cycle and rejoins simple DSB representing more than 80% of DSB generated by low-LET radiation, fast and mostly error-free. Right: Complex DSB are repaired with much slower kinetics by resection dependent c-NHEJ, an (uncommon) alternative NHEJ pathway (alt-NHEJ), or homologous recombination (HR). Both slow NHEJ pathways are used outside the G2 phase, c-NHEJ during G1, and alt-NHEJ during other phases. In G2, complex DSB are directed towards the HR pathway, if it is available.

Radiation-induced simple DSB, similar to enzymatically created DSB with perfectly complementary strands (Lieber 2010), are repaired by the fast canonical NHEJ (c-NHEJ) pathway (Löbrich & Jeggo 2017). This pathway re-ligates complementary DSB ends within minutes and repairs more than 80% of low-LET-induced DSB in a time frame of 2–4 hours. Since radiation-induced DSB ends are often chemically modified, this repair mechanism involves enzymatic restoration of 5’-phosphate and 3’-hydroxyl termini using polynucleotide kinase/phosphatase (PNKP) before ligation (Weinfeld et al 2011). The fast c-NHEJ pathway is available throughout the entire cell cycle. It does not have an intrinsic sequence-restoring function. Different from HR, base information lost at the DSB ends, in particular, at DSB with blunt ends or short overhangs, may not be completely restored, leading to short deletions (Daley & Wilson 2005). However, repair of most simple DSB will be error-free, and those DSB that are not accurately repaired will only have small deletions. In contrast, larger deletions and rearrangements are typically observed after NHEJ of complex DSB (see below).

Complex DSB, which are more commonly induced by high-LET radiation, are repaired either by HR, only available during late S and G2, or by the slow, resection dependent c-NHEJ pathway (Ensminger & Löbrich 2020, Shibata et al 2011). For complex DSB, the c-NHEJ pathway requires generation of single-stranded DNA at the DSB site in a process called resection, which involves the creation of a hairpin intermediate. This is followed by the removal of the hairpin intermediate by the ATM-dependent nuclease Artemis to facilitate ligation by the XRCC4-Ligase IV complex (Riballo et al 2004, Löbrich & Jeggo 2017). Another form of slow end-joining, alternative NHEJ (alt-NHEJ), refers to a less-efficient, uncommon mechanism of complex DSB repair in case c-NHEJ is not available. It involves a different set of NHEJ proteins, including poly-ATP ribose polymerase 1 (PARP 1) (Löbrich & Jeggo 2017, Chiruvella et al 2013), and appears to be available in all cell cycle phases. The c-NHEJ pathway appears to be confined to the G1 phase, whereas the alt-NHEJ pathway is also available during other cell cycle phases. Only the HR mechanism is error-free, whereas the slow c-NHEJ and alt-NHEJ mechanisms frequently lead to deletions and chromosomal translocations. The slow nature of these repair processes can explain why unrepaired DSB are more commonly seen after high-LET radiation (Asaithamby et al 2008, Asaithamby et al 2011). The increased mutagenicity of high-LET radiation may originate from the repair of complex DSB outside G2 by the error-prone NHEJ pathways (Falk et al 2010).

In addition to the cell cycle phase, chromatin structure has a large influence on DNA damage response, in particular, DNA damage repair, e.g., (Cann & Dellaire 2011). The recent literature supports the view that heterochromatin and euchromatin differ with respect to DNA damage induction and the preferred DNA repair pathway (Goodarzi et al 2008, Goodarzi et al 2010, Goodarzi & Jeggo 2012, Falk et al 2010, Lorat et al 2016). The heterochromatin architecture protects the DNA from free-radical attack, typical for low-LET radiation, but not from clusters of direct ionization that will lead to complex DNA damage (Falk et al 2010). Thus heterochromatin preferentially harbors complex DSB. The repair of DNA damage in heterochromatin requires initial decondensation of heterochromatin that is followed by slow c-NHEJ (in G1) or HR (in S/G2) (Geuting et al 2013).

4.2. DNA damage and repair assays

The application of nanodosimetry and track structure simulations to particle therapy planning requires many steps of validation. One important aspect is to use DNA damage assays to validated theories related to the conversion of ionization clusters to stable forms of DNA damage and connecting damage complexity to its repairability. Over the last 30 years, many assays for detecting and quantifying DNA damage with plasmids or minichromosomes, quantification of SSB and DSB in cells, and the visualization of ionizing radiation-induced foci under the microscope have been developed. In more recent times, end labeling and next generation sequencing methods have been added to the repertoire of DNA damage and repair assays. This review of assays will focus on those that play a role in validating nanodosimetry and track structure simulations.

4.2.1. Plasmid and minichromosomal DNA assays.

Plasmids and minichromosomes are separate DNA molecules that can replicate independently within a cell. Plasmids commonly occur in bacteria as relatively small, supercoiled, double-stranded DNA molecules not associated with histones. They range in size from a few hundred base pairs (bp) to about 10kbp. Minichromosomes, such as the simian DNA virus SV40, have a typical size of several Mbp. Different from plasmids, minichromosomes have a chromatin-like structure where DNA is associated with histone-containing nucleosomes. Plasmids and minichromosomes can easily be isolated and purified in their natural supercoiled conformation and dissolved in water, providing the basis for in vitro strand break assays.

During irradiation, plasmids and minichromosomes are transformed from their original supercoiled form to a relaxed form by at least one SSB and linear form by at least one DSB. Irradiation of these DNA molecules in aqueous solutions followed by agarose gel electrophoresis has been used widely to measure the yields of SSB and DSB in units of Mbp⁻¹ Gy⁻¹. The relaxed and linear forms separate from the intact supercoiled form during agarose gel electrophoresis and can be quantified by fluorescent staining. In early work, the mathematical model by Cowan et al. (Cowan et al 1987), or simplified equations approximating the original equations of this model, were used to quantify the yield of SSB and DSB from the measured amount of relaxed and linear forms of DNA. More recently, another model was introduced by McMahon and Currell (McMahon & Currell 2011), which was shown to reproduce experimental plasmid data more robustly than the Cowan model (Vyšín et al 2015).

Much has been learned from plasmid, minichromosome, and other in vitro DNA studies about the production of ^·OH radicals and their reaction with DNA under dry conditions and aqueous solutions using a range of scavenging conditions. In studies with bacterial plasmids and eukariotic minichromosemes (SV40), the scavenging concentrations have been systematically varied, ranging from pure aqueous solutions (no added radical scavengers) to solutions with full scavenging capacity of the cellular environment (10⁹ s⁻¹) (Milligan et al 1993, Jones et al 1993). In pure aqueous solutions, the SSB yield is much larger than the DSB yield (ratio of about 100:1). It is determined by single ^·OH radicals diffusing, on average, long distances (hundreds of nanometers) before randomly reacting with a DNA molecule. With increasing ^·OH scavenging concentrations up to the level of cellular scavenging capacity, the yield of SSB decreases more than that of DSB, leading to a decreased SSB/DSB ratio (about 30:1 for low-LET and lower for high-LET radiation) (Jones et al 1993, Krisch et al 1991). Under cellular scavenging conditions, or when DNA is highly compacted, ^·OH radicals diffuse a few nanometers before they react. In this case, only local ionizations, ionization clusters, and the radicals they induce are responsible for SSB and DSB induction (Ward 1988, Goodhead 1994).

More recently, there has been an increasing interest in using ultra-thin plasmid DNA films in different states of hydration, from dry to fully hydrated DNA, to study the various contributions of direct and indirect radiation effects on SSB and DSB yields (Purkayastha et al 2005, Sharma et al 2008, Vyšín et al 2015, Souici et al 2017). The results from these studies have shown that the radiation physics and chemistry at the interface of DNA and water is complex and not well understood, pointing to the need for additional studies.

In summary, a comparison of experimental SSB and DSB yields derived from extracellular DNA experiments is an important tool to inform and improve radiation chemistry models, which can be either stand-alone (Udovicić et al 1991, Bluett & Green 2006, Al-Samra & Green 2017) or a component of Monte Carlo track structure simulations (Champion et al 2015, Friedland et al 2017, Ramos-Méndez et al 2018) (also see Sec. 3.2).

4.2.2. Single-cell gel electrophoresis (comet) assay.

The comet assay is a DNA damage quantification technique that combines single-cell gel electrophoresis under neutral or alkaline conditions and fluorescent microscopy. The original technique, which used neutral pH conditions, was introduced by (Ostling & Johanson 1984) as a method to measure SSB caused by the relaxation of DNA supercoils. A modified version using alkaline pH conditions was developed and published by (Singh et al 1988), allowing the distinction between SSB and DSB. Another modification, which was then named the comet assay, was introduced by Olive (1990) to measure DNA damage induced by ionizing radiation (Olive et al 1990). This was further optimized to quantify the DNA damage due to DSB (Olive et al 1991). Over the years, further refinements occurred to allow detection of DNA cross-links, base damages, and apoptotic cells; for a review, see (Olive & Banáth 2006). For a detailed description and discussion of the comet assay protocol, see (Lu et al 2017).

When subjected to the electric field, undamaged nuclei preserve their round shape, whereas nuclei with damaged DNA create a fluorescent signal resembling a comet tail. The length and intensity of the tail are related to the quantity and quality of DNA damage, i.e., SSB and DSB. The comet assay is a universal, inexpensive, fast, and accurate approach to quantify DNA damage in single-cells. However, the information obtained is limited because of its need for relatively high radiation doses and its inability to quantify the number of DSB per cell nucleus. On the other hand, the comet assay still has several useful applications in radiobiology (Olive 2009), including measuring the fraction of radiobiologically hypoxic cells, non-targeted effects on bystander cells, and the effects of protons and ions on DNA fragmentation patterns. However, the comet assay is not suitable for distinguishing the DSB produced by different forms of high-LET radiation due to the lack of sensitivity for the small DNA fragments that are associated with DNA lesion clusters.

4.2.3. Pulsed-field gel electrophoresis (PFGE) assay.

The second broadly used method for DSB quantification is pulsed-field gel electrophoresis (PFGE). Different from continuous field electrophoresis, a PFGE uses electric fields that periodically change direction and magnitude relative to the gel resulting in a net forward migration. PFGE thus allows the resolution of large DNA fragments in the range between 1 Mbp and 10 Mbp. The technique was originally proposed by Schwartz and Cantor in 1984 (Schwartz & Cantor 1984) and was first used to measure the yield of DSB from low-LET radiation in yeast by Contopoulo in 1987 (Contopoulou et al 1987) and in mammalian cells by Stamato and Denko in 1990 (Stamato & Denko 1990). In the early 2000s, Sutherland and co-investigators at Brookhaven National Laboratory, with access to heavy ions, developed a PFGE-based assay to quantify non-DSB lesion clusters (Sutherland et al 2003).

In PFGE-based assays, DNA damage is measured as a fraction of DNA released from an agarose plug that contains the isolated cells. When genetic material from a cell population is subjected to PFGE, intact chromosomes are not released from the gel plug, while DNA fragments are visible as smeared bands. Estimation of DNA damage by PFGE based on smear intensity is possible to doses as low as 0.5Gy, but is not very precise in case of very low or very high numbers of DSB (Gradzka & Iwanenko 2005). For a detailed description of a typical PFGE protocol and analysis, see, e.g., (Sharma-Kuinkel et al 2016). The usage of DNA size markers allows measuring the length distribution of broken DNA fragments. This fragmentation analysis is crucial for the determination of DSB frequencies with high-LET radiation (Prise 1998). Protocols have been developed separating the DNA into up to four different gels, thereby increasing the sensitivity for smaller DNA fragments to the order of 10kbp (Löbrich et al 1996, Newman et al 1997).

In the early days of PFGE assays, the fragmented DNA was typically obtained from radioactive labeling techniques. The fraction of DNA released from the plug was called the fraction of activity released (FAR). It is important to note that the number of DSB is non-linearly related to the FAR, depending on the randomness of the DSB distribution. There is clear evidence for non-random DNA breakage with high-LET radiation where DSB occur in a correlated manner along particle tracks (Löbrich et al 1996, Newman et al 1997).

Most of the PFGE DSB studies have focused on kbp-Mbp size fragments (Löbrich et al 1996, Newman et al 1997, Rydberg 2001), which are caused by regionally multiply damaged sites (RMDS) (Rydberg 1996, Pinto et al 2004). RMDS should not be confused with locally multiply damaged sites (LMDS) that are synonymous with complex DNA lesion clusters (see Def. Box 2). While PFGE improves the sensitivity of the comet assay for smaller-fragment detection, in particular the RMDS-generated fragments produced by high-LET radiation, it still cannot detect individual DSB and their location within the genome. Therefore, new methods, including imaging of fluorescent DSB markers, and DSB end-labeling combined with next generation sequencing, had to be developed. These newer methods are described in the next two subsections.

4.2.4. DNA damage foci assays.

Individual DSB (or other DNA lesion clusters) can be stained immunohistochemically or tagged with fluorescent proteins enabling their imaging as discrete foci under the microscope. This possibility led to introducing a new class of DNA damage quantification and repair assays in the late 1990s and early 2000s. For the study of radiation-induced DSB, these foci are usually called ionizing radiation-induced foci (IRIF). The histone subunit H2AX was the first DSB-signaling protein introduced as an immunolabeled fluorescent DSB marker (Rogakou et al 1998). In initial work, it was shown that individual DSB lead to phosphorylation of H2AX at serine Ser139 (γ-H2AX) that can be recognized by a specific antibody. The modification of H2AX to γ-H2AX extends over a relatively large chromosomal region ranging from 0.5 to 1.7 Mbp flanking the DSB (Iacovoni et al 2010, Rogakou et al 1999). The accurate quantification of radiation-induced DSB with microscopic foci assays requires strict adherence to established protocols. For a detailed review of the use, methods of analysis, and results of IRIF assays see, e.g., (Olive 2004, Nakamura et al 2006, Rothkamm et al 2015) and references therein.

γ-H2AX foci form rapidly after radiation exposure of cells. The half-maximum number of foci is reached after 1–3 minutes, and the maximum number of foci after 10–30 minutes following irradiation (Rogakou et al 1999). After the maximum, the number of foci declines over a period of hours, which can be described by a bi-exponential model (Plante et al 2019). There is evidence showing that each γ-H2AX focus corresponds to an individual DSB (Sedelnikova et al 2002). The number of countable foci is, therefore, closely correlated with the number of DSB, and the rate of foci clearance is correlated with DSB repair (Löbrich et al 2010). Since DSB are created by single particle tracks, a linear dose response relationship is expected and has been found up to a dose level of a few Gy; for higher doses γ-H2AX start coalescing and the dose response relationship becomes non-linear (MacPhail et al 2003, Olive 2004).

The γ-H2AX assay was the first and has been the most widely used assay to detect and quantify DSB after exposure to different forms of radiation. The additional proteins that are recruited to the DSB site during repair co-localize with γ-H2AX (Takahashi et al 2008, Coster & Goldberg 2010, Scully & Xie 2013, Panier & Boulton 2014). Antibodies for these phosphorylated proteins are therefore effective for the detecting, localizing, and quantifying DSB. In addition, the proteins that are specific for certain repair pathways or pathway decisions are of interest for identifying different types of DSB, including simple and complex DSB. Among these are 53BP1 and BRCA1 that are involved in the decision making between resection independent and resection dependent c-NHEJ (Daley & Sung 2014, Löbrich & Jeggo 2017). Further, MRE11 that is involved in the choice between resection dependent c-NHEJ and HR during the G2 phase (Shibata et al 2014), and the RPA, RAD51, MDC1, BRCA2 proteins that, among others, are involved in the HR pathway of complex DSB repair (Löbrich & Jeggo 2017), see Fig. 3.

The analysis of the spatiotemporal dynamics of DSB induction and repair in live cells was another major advancement, which was pioneered at the GSI Helmholtz Centre for Heavy Ion Research for the study of foci induced by high-LET ions and first published in 2005 (Jakob et al 2005, Jakob et al 2009, Jakob et al 2011, Tobias et al 2013). Time-lapse fluorescence microscopy images of live cells that have been transfected with a plasmid encoding a green fluorescent protein fused with a specific repair protein show the course of DSB recognition and repair in a LET-dependent manner. The study of DSB induction and repair with different proteins in live cells has now become a standard method to monitor the DDR in many laboratories (Beckta et al 2012, Mosconi et al 2011, Drexler et al 2015, Sollazzo et al 2018, Roobol et al 2020). This method, especially when combined with high- or low-LET microbeams, should prove very useful for the correlation of nanodosimetric parameters with DSB repair. It may allow to differentiate between the repair of simple and complex DSB based on repair kinetics and recruitment of specific proteins to these DNA lesion clusters.

Another recent exciting breakthrough in the study of IRIF has been the application of super-resolution light microscopy (SRLM) to obtain novel information about the spatial organization of DSB on the molecular level and the temporal progress of DSB repair. Several super-resolution microscopy techniques evolved in the 2000s, see, e.g., the review by Hell (Hell 2007). With these techniques, the resolution of confocal microscopy, which is limited to about 200nm by the diffraction barrier, was improved to approximately 10nm (Bennett et al 2009). With this resolution, it has become possible to resolve the nanostructure of γ-H2AX and other repair foci (Depes et al 2018, Bobkova et al 2018, Scherthan et al 2019).

SRLM is complementary to techniques using transmission electron microscopy (TEM) to detect DNA repair proteins within cell nuclei with nanometer resolution. It is worth mentioning here the work by Rübe and Lorat using gold-labeled repair protein complexes to study DSB repair in euchromatic versus heterochromatic regions (Rübe et al 2011, Lorat et al 2012, Lorat et al 2015, Lorat et al 2016, Timm et al 2018). TEM is well established for super-resolution imaging, but it is not likely to become a mainstream assay in the study of IRIF because of the complexity of sample preparation. The importance of super-resolution TEM and SRLM assays is that they may help us eventually to answer the important question whether the problem of DNA repair with complex DSB is due to their quality or the high density of occurrence over the distances of less than 200nm.

4.2.5. End labeling and NGS assays.

Rapid advances in next generation sequencing (NGS) technologies since the completion of the human genome project in 2003 have opened the possibility for genome-wide detection of individual DSB.

One of the early methods, called ChIP-seq, combines chromatin immunoprecipitation (ChIP) with DNA sequencing to identify the binding sites of DSB-associated proteins such as γ-H2AX. It was the first method that enabled the genome-wide mapping of DSB in yeast (Szilard et al 2010) and mammalian cells (Iacovoni et al 2010, Seo et al 2012). Alternatively, ChIP-seq can also be performed with an antibody directed against DNA repair proteins such as the HR-associated proteins Rad52 (Zhou et al 2013) and NBS1 protein (Khair et al 2015). The ChIP-seq method is indirect and, therefore, has several disadvantages. It depends on many factors, including repair pathway choice, the time after DSB induction, and the quality of the antibody. As other types of DNA damages may also result in phosphorylation of the H2AX protein, this method does not allow for specific detection of DSB. Moreover, its spatial resolution is generally low (several hundred base pairs).

More recently, several direct DSB labeling methods based on NGS were developed that can be divided into three groups: (i) terminal deoxynucleotidyl transferase- (TdT-) based methods, (ii) translocation-dependent methods, and (iii) methods relying on adapter ligation. Here, we only briefly review the first two and give some more insight into the third group of methods. The idea behind the TdT-based methods is to label DSB with biotinylated nucleotides that are added to 3’OH DNA ends by TdT. This method has several disadvantages, including poor spatial resolution (a few hundred bp) and sensitivity to both SSB and DSB. The second group, translocation-dependent methods, detect DSB that translocate to ”bait DSB”. The translocation takes place in living cells and is mediated by slow c-NHEJ repair (Löbrich & Jeggo 2017). A unique advantage of this method is the ability to detect all translocated DSB occurring over an extended period of time. The group of translocation-dependent methods could be of interest to specifically detect the misrepair of complex DSB.

The development of methods relying on adapter ligation started with the technique called BLESS (direct in situ breaks labeling, enrichment on streptavidin, and next generation sequencing) pioneered by Crossetto and colleagues in 2013 (Crosetto et al 2013). For the first time, this strategy enabled direct, high throughput, and specific detection of DSB with single-nucleotide resolution. BLESS has been applied in many studies of DSB generation and repair, including generation of the first map of human genomic regions sensitive to replication stress conditions induced by the DNA polymerase inhibitor aphidicolin (Crosetto et al 2013) and a study of the dynamics of the repair of DSB in relation to their mobility (Aymard et al 2017).

BLESS data is compromised by high noise (Hu et al 2016), which led to the development of two improved techniques based on BLESS, namely DSBCapture (Lensing et al 2016), and END-seq (Canela et al 2016). Both methods utilize modified adapters, reducing the number of polymerize chain reaction (PCR) cycles used in the procedure, therefore, lowering PCR bias and eliminating the problem with unbalanced libraries caused by the usage of barcoded adapters in BLESS. Additionally, END-seq employs encapsulation of cells in agarose plugs to further protect DNA from mechanical damage, which greatly improves the signal to noise ratio and thus the sensitivity of this technique.

A third improved version of BLESS, called i-BLESS, was developed shortly after END-seq (Biernacka et al 2018). The i-BLESS method was designed specifically for smaller cells, such as yeast, and, similarly to END-seq, involves encapsulation of cells but employs agarose beads much smaller than agarose plugs, therefore, reducing the time and cost of the procedure. Moreover, i-BLESS proved to be the most sensitive detection method for DSB to date, allowing detecting a DSB present at a given position in 1 per 100,000 cells. This technique has been applied, for example, for the characterization of DSB induced by the radiomimetic drug Zeocin in regions prone to form very stable DNA secondary structures (Zhu et al 2019).

In another modification of the original BLESS method called BLISS (breaks labeling in situ and sequencing) (Yan et al 2017), the adapters were thoroughly redesigned to enable amplification of labeled DNA fragments by T7-RNA-polymerase-mediated in vitro transcription. Linear amplification by bacteriophage T7 RNA polymerase introduces less bias than PCR, which is crucial for DSB labeling in low-input samples. Therefore, BLISS can be used not only for cell cultures but also for primary cells and tissue samples. Moreover, BLISS adapters contain unique molecular identifiers, enabling distinguishing DSB at DNA fragment sites from PCR duplicates arising during library preparation. In turn, this allows for a more accurate quantitative assessment of the true DSB yield.

Zhu and colleagues (Zhu et al 2019) proposed an alternative approach for quantification of DSB called qDSB-seq that relies on the introduction of so-called ”spike-in” DSB in cells. Spike-in DSB are induced by restriction enzymes, and their cutting efficiency is determined based on qPCR or gDNA sequencing, allowing to establish the ratio between the number of reads at a given genomic locus and the underlying DSB frequency. This ratio is then used to calculate the absolute DSB frequencies in cells treated, for example, with radiation.

New perspectives in single-cell genomics and transcriptomics have emerged recently with the development of several microfluidic platforms that address the need for genome-wide detection and quantification of DSB on the single-cell level. For example, the C1 platform (Fluidigm Corporation, USA) uses an integrated microfluidic chip to capture, image, and perform cell lysis and DNA or RNA processing for up to 800 single-cells (Wang et al 2019). A similar system, iCess8 (Takara Bio USA, Inc.), employs a nanogrid microchip with over 5000 nanowells, to which cells are distributed by a robotic nanodispenser (Goldstein et al 2017). Also, several droplet-based platforms have been recently developed, including the 10x Genomic Chromium (Klein et al 2015, Zheng et al 2017), and Drop-seq (Macosko et al 2015). In these systems, single cells are captured inside droplets that act as individual reaction vesicles. Many protocols are already available for these new platforms, and investigators are encouraged to use them in new applications, including single-cell DSB sequencing.

4.3. Validation of nanodosimetry and track structure simulations

New nanodosimetric concepts for treatment planning applications require careful biological validation. In this section, we have highlighted the importance of DSB and the local complexity of DSB lesion clusters over a distance of 1–2 helical turns and the resulting DNA damage response and repairability of DSB. We have given an overview of classical and modern DNA damage assays using in vitro cell-free and cellular systems to measure and study this response. These studies can and should be extended to in vivo assays in the future. The association of biological endpoints, e.g., cell survival, with nanodosimetric quantities, such as complementary cumulative probabilities F_k derived from ICSD, has only recently been investigated. Most existing radiobiological data for different radiation qualities have been studied as a function of LET. However, since the first moment M₁ of ICSD is proportional to LET, a correlation between radiobiological data as a function of LET, on the one hand, and ICSD parameters as a function of M₁, on the other hand, is meaningful.

Conte and colleagues, within the Italian MITRA (MIcrodosimetry and TRAck structure) project and the EU project BioQuart (Biologically Weighted Quantities in Radiotherapy), performed experiments, in which ICSD produced by protons and carbon ion beams of different energies were measured with the LNL SC and the PTB IC nanodosimeters described in Sec. 3.1 (Conte et al 2017, Conte et al 2018). They studied the dependence of various cumulative frequencies F_k as a function of M₁ and compared it with inactivation cross-sections of cell survival of different cell lines. The investigators found that the F₃ parameter dependence on M₁ mirrored the inactivation cross-section, σ_α, of human salivary gland (HSG) and Chinese hamster ovary (CHO) cells at low doses as a function of LET, with a steady increase with increasing values of M₁/LET followed by a saturation at high LET values (see Fig. 4). In future work, studies like those by Conte et al. should be extended to nanodosimetric parameters derived from Monte Carlo simulations and also include other in vivo and in vitro endpoints.

Figure 4.

Comparison of the dependence of the inactivation cross-sections σ_α for HSG and CHO cells (colored symbols) on LET (upper axis) and the dependence of the scaled nanodosimetric F₃ parameter (solid lines) on M₁ (lower axis). To better separate the data, the HSG values were multiplied by a factor 10. The references given in the insert are from the original publication (Conte et al 2017).

Another important aspect of validating nanodosimetric measurements and simulations involves the comparison with the model predictions of detailed track structure simulations that are based on energy imparted as the criterion for strand break inductions (Nikjoo et al 1997, Friedland et al 2017, Zhu et al 2020). Nikjoo et al., for example, established a data base of frequencies of strand breaks of different type and complexity for electrons, soft X-rays and ions, based on Monte Carlo track structure simulations (Nikjoo et al 1997, Nikjoo et al 1999, Nikjoo et al 2002, Nikjoo et al 2008). Friedland et al. published DNA damage data after proton irradiation simulated with the PARTRAC track structure code (Friedland et al 2003). Garty et al. used the data by Friedland et al. (Friedland et al 2003) to compare the LET dependence of DSB yields predicted by nanodosimetric simulations in combination with their own model (Garty et al 2010). These efforts are expected to grow as more simulated and experimental nanodosimetric data become available.

5. Particle treatment planning and beyond

Simulation of nanodosimetric parameters offers an opportunity for improving biologically optimized charged particle treatment planning. Currently, treatment planning for proton and carbon ion therapy utilizes constant RBE (for protons) and RBE models (for carbon ions) to calculate the biologically weighted dose assumed to be isoeffective relative to photons. RBE models have also been proposed for proton therapy, but these are not yet clinically implemented. The use of RBE models is not without problems, and there is a need for a new treatment planning strategy. In this section, we summarize the state-of-the-art biologically weighted treatment planning and discuss the potential use of a nanodosimetry-based treatment planning strategy without invoking the RBE concept. The implementation of this new concept requires innovative computing and optimization strategies. Nanodosimetry may also have applications beyond particle therapy planning in radiation protection.

5.1. Current approaches to biologically weighted particle therapy

During the early 1990s, proton and carbon ion therapy moved from the physics laboratory into a dedicated clinical environment with the first hospital-based proton center at Loma Linda University Medical Center opening in 1990 and the HIMAC (Heavy Ion Medial Accelerator) of the National Institute of Radiological Sciences (NIRS) in Chiba, Japan opening in 1994. In Europe, the medical heavy ion treatment program developed at GSI was transferred to the Heavy Ion Treatment Center (HIT) at the Heidelberg University hospital during the 2000s, starting operation in 2009. During this transition phase, the question how the biological weighting of absorbed dose in treatment planning should be performed had to be addressed. The general approach has been to use average microscopic physical quantities, including LET_d (dose-averaged LET), radial dose, or lineal energy, as input to empirical or mechanistic RBE models (Stewart et al 2018, McNamara et al 2019). Physical quantities can also be used directly for treatment plan optimization without invoking RBE models (McMahon et al 2018, Unkelbach & Paganetti 2018).

5.1.1. RBE models - carbon ions

In current carbon ion therapy planning, the dose delivered with ion beams is calculated so that it equals the isoeffective photon dose D_photon=RBE×D_ion for the same fractionation scheme. The main justification for using RBE in carbon ion therapy is to generate a sufficiently high and uniform biologically effective dose in the tumor volume. The challenge of particle therapy treatment planning is to find the RBE values that apply to a specific dose-fractionation schedule, patient, and the mixed radiation field produced in the patient. There is a close relationship between LET_d and RBE, which invites the use of LET_d for developing RBE models. With modern MC-based dose calculations, it is possible to provide a voxelized LET_d map and calculate the carbon ion RBE for each voxel. However, it has been noted that x-rays, protons, and ions with the same LET_d can exhibit different RBE (Goodhead et al 1992, Friedrich et al 2013, Guan et al 2015). For example, for carbon ion therapy, when ion fragmentation leads to a complicated mix of primary and lighter ions with different RBE for the same LET_d, the usefulness of LET_d based planning breaks down (Grün et al 2019).

The clinical RBE models for carbon ion therapy were implemented in a center-specific manner. The Japanese mixed beam model, which was based on cell survival of HSG tumor cells in combination with clinical experience with fast neutrons, was the first RBE model implemented and used at the HIMAC facility (Kanai et al 1999, Kanai et al 2006, Matsufuji et al 2007). After active beam scanning was introduced at the HIMAC facility in 2010, a modified version of the microdosimetric kinetic model (MKM), originally developed during the early 1990s by Hawkins (Hawkins 1994, Hawkins 1998), became the standard RBE model for carbon ion treatment planning in Japan. The MKM was validated again with HSG cells for actively scanned carbon ion beams (Inaniwa et al 2010). The next generation of the MKM that is now used for carbon ion treatment planning in Japan is a further development of the MKM. It is called stochastic microdosimetric kinetic (SMK) model (Inaniwa & Kanematsu 2018).

The local effect model (LEM), also called the amorphous track structure model, was developed by Scholz and Kraft for the GSI pilot program of carbon ion therapy (Scholz 1996, Scholz et al 1997) and later adopted by the Heidelberg Ion Therapy (HIT) center in Germany. The LEM is based on the premise that equal microscopic absorbed doses in a cell nucleus will lead to equal biological effects. Knowing the x-ray specific parameters of the linear-quadratic (LQ) model of a given cell line, it is assumed that an equivalent biological effect can be calculated by changing the ion fluence. The initial version of the model (LEM I) was extensively tested with CHO cells and various ion beams at GSI and then further refined up to the LEM IV for different biological endpoints (Elsässer et al 2010). However, only the LEM I has been in clinical use at the HIT facility in Heidelberg; it is also being used at the CNAO facility in Italy.

In a comparative review, Stewart et al. (Stewart et al 2018) evaluated three mechanistically inspired models for ion (1-H, 4-He, 12-C) RBE: the LEM IV, the MKM, and the repair-misrepair-fixation (RMF) model. All three models are based on the premise that biological processing of potentially lethal damage eventually leads to loss of cell survival. The models are used to estimate LQ model parameters as a function of microscopic radial dose (LEM), the lineal energy (MKM), or the square of the effective charge divided by the velocity, (Z_eff/β)² (RMF). Importantly, the authors reported that the models were remarkably different in the prediction of RBE of DSB induction, the dependence of LQ parameter β on particle LET, and RBE of cell survival for LET >150keV/µm.

A comparison of the two clinical RBE models (LEM I and MKM) showed that the resulting physical dose prescriptions could be up to 15% different (Fossati et al 2012, Molinelli et al 2016, Mein et al 2020). These clinically important differences and the fact that RBE depends on many physical and biological parameters, highlights the problem of using RBE models for treatment planning of carbon ions. This creates a barrier for meaningful multi-institutional clinical trials with carbon ions (Fossati et al 2018). In addition, there are plans to extend ion therapy to 4-He and 16-O ions, which further complicates the issue of biologically weighted treatment planning.

5.1.2. RBE models - protons

For proton therapy, the ICRU Report 78 recommends to prescribe and report the RBE-weighted absorbed dose, with a patient- and depth-independent value of 1.1 as a clinically practical approximation (ICRU 2007). A constant RBE of 1.1 has also been adopted by the joint IAEA and ICRU Report 461, which uses the term radiation quality weighted dose instead of RBE-weighted dose (IAEA & ICRU 2008). However, this constant RBE disregards the experimental evidence that the RBE varies with depth, biological endpoint, and biological system. Of note, the LET_d of the spread out Bragg peak (SOBP) is increasing steeply near the distal end of the SOBP (Calugaru et al 2011, Britten et al 2013, Wouters et al 2015). Experimentally measured RBE values across proton SOBP generally vary between 0.9 and 1.7 (Paganetti 2014). The depth dependence of RBE is more pronounced for lower initial proton energies (Wouters et al 2015) and smaller dose fractions (Marshall et al 2016).

Several RBE models for biologically weighted proton treatment planning have been proposed but none is currently in clinical use. The main justification for using a proton RBE model is the RBE spike near the end of the proton beam range, which is usually placed in normal tissue due to proton range uncertainties. There is, therefore, hesitance among radiation oncologists to aim proton beams at critical organs at risk (OAR).

Two types of proton RBE models have been developed over the last two decades, phenomenological models fitting LQ parameters to existing experimental data and mechanistically inspired models predicting the proton RBE based on microscopic physical quantities. The reader should refer to the recent review by McNamara for a comprehensive overview of these models (McNamara et al 2019).

5.1.3. LET_d-based approaches

Particle therapy treatment planning aims at delivering a uniform biologically effective dose to the target, sparing surrounding OAR to the maximum possible degree. This poses a mathematical optimization problem that can be solved in various ways (Chen et al 2012, Wedenberg et al 2018). Compared to photon therapy, additional planning uncertainties, including the uncertainty in biologically effective dose, have to be folded into the treatment planning process. The effect of these uncertainties can be particularly severe when range uncertainties and steep gradients in LET_d occur near OAR (Wedenberg et al 2018). Efforts to reduce the effect of these uncertainties have led to various forms of robust optimization (ICRU 2007, Pflugfelder et al 2008, Unkelbach et al 2009, Casiraghi et al 2014, Fredriksson & Bokrantz 2014, Li et al 2015). A thorough discussion of these optimization approaches is beyond the scope of this paper, and the reader is referred to these publications for additional details.

While the early attempts of robust optimization focused on geometric uncertainties such as setup and range errors, more recent work has focused on the inclusion of LET_d into the robust optimization approach. Generally, the margin between the clinical target volume (CTV) and the gross tumor volume (GTV) and containing OAR, should be exposed to radiation of lower LET_d. The higher LET_d regions should be limited to the tumor itself (GTV). An approximately linear relationship between LET_d and proton RBE has been used as a justification for averaging LET_d of overlapping proton beams in robust optimization approaches for proton therapy (Grassberger et al 2011, Giantsoudi et al 2013, Unkelbach et al 2016, Unkelbach & Paganetti 2018).

Initial work with Monte Carlo simulations, pioneered by the MGH group, demonstrated that IMPT planning allows the modification of LET_d distributions without changing the physical dose distribution (Grassberger et al 2011, Giantsoudi et al 2013). For example, Pareto-optimal IMPT plans for five head and neck cancer patients varied in LET_d up to 30% in the target and up to a factor of two in OAR (Giantsoudi et al 2013). Based on these results, Unkelbach et al. devised an IMPT optimization method avoiding high-LET_d values in OAR without affecting the physical dose distribution, thus making LET_d×dose an optimization parameter (Unkelbach et al 2016, Unkelbach & Paganetti 2018). More recently, it has been recognized that the metric dose×(1 + κLET_d) is better than LET_d×dose when predicting biologically effective dose as a function of LET_d. For example, McMahon and colleagues found that for κ =0.055, they were able to predict high in vitro RBE in experimental studies and the high RBE regions in clinical IMPT plans better than the LET_d×dose metric (McMahon et al 2018).

Additional work on LET_d-based proton treatment planning has focused on developing logistic regression models to predict radiation necrosis in patients treated with high-dose proton therapy of head and neck and brain tumors (Eulitz et al 2019, Bahn et al 2020, Niemierko et al 2021). Two of these studies (Eulitz et al 2019, Bahn et al 2020) did find a correlation between the voxel locations with high dose and high values of the product of dose and LET_d and the location of brain necrosis in multivariate logistic regression models. The third study (Niemierko et al 2021) did not find a correlation with the development of brain necrosis with neither LET_d nor the product of dose and LET_d. They suggested that inter-patient variations are dominant over the LET_d and dose variation.

There are limitations of the use of LET_d in particle treatment planning with protons and ions. Based on our own experience in multi-field treatment planning of proton beams and correlating RBE-weighted dose with late effects (Garbacz et al 2021), and also noted by others (Wedenberg et al 2018), converting LET_d to an RBE value leads to lower LET_d of individual fields compared to combined fields. Therefore, the RBE resulting from the multi-field optimization tends to be lower than the RBE of individual fields. Furthermore, as noted above, when using ions heavier than protons, LET_d is not a suitable quantity for treatment planning (Grün et al 2019). These limitations have raised the interest in nanodosimetric quantities as the basis for biologically weighted treatment planning. In the following sections, we outline the present status of recent approaches in this direction.

5.2. Novel approaches based on nanodosimetry

During in the 1970s, it was recognized that the microscopic energy deposition pattern of mixed radiation fields used, for example, in radiation therapy with charged particles, is an important determinant of radiation quality. This led to microdosimetric cell survival models based on the isoeffective LQ formalism, as reviewed by (Bellinzona et al 2021). More recently, other formalisms that go beyond the LQ formalism have been proposed (Besserer & Schneider 2015a, Besserer & Schneider 2015b).

With the development of experimental nanodosimetry and Monte Carlo track structure simulations (Sec. 3), a correlation of nanodosimetric parameters with cell survival data has been reported (Nettelbeck & Rabus 2011, Conte et al 2017, Conte et al 2018). This has opened possibilities to use nanodosimetry and track structure simulations as a future approach for particle therapy treatment planning and optimization (Selva et al 2018, Burigo et al 2019, Braunroth et al 2020, Rabus et al 2020, Vasi et al 2020, Ngcezu & Rabus 2021). In the following we describe in more detail recent work in this field distinguishing nanodosimetric RBE and non-RBE approaches.

5.2.1. Nanodosimetric RBE models

Models of DNA damage based on the number of ionizations or energy imparted in nanometer-sized volumes allow the distinction of simple and complex DNA damage (see Sec. 4.1 and references cited there). In contrast, classical microdosimetric RBE models, taking as input various stochastic or average quantities in micrometer-sized volumes, are rooted in the assumption of microscopic sublesions (DSB) without considering their complexity and repairability (Bellinzona et al 2021). In the following, we review the development of nanodosimetric RBE models.

RBE modeling approaches incorporating nanodosimetric parameters started in the late 1990s in parallel with the development of experimental nanodosimetry. Schulte et al. proposed the two-compartment model, which classified biologically significant DNA damage into the compartment of repairable damage caused by energy depositions of 40–150eV or 2–5 ionizations and irreparable damage caused by energy depositions >150eV or 2–10 ionizations in a cylindrical nanodosimetric site of 2nm diameter and 16nm length (Schulte 1997, Schulte et al 2001). It was further assumed that the dose dependence of repairable damage was linear-quadratic and that dose dependence of irreparable damage was linear. The effectiveness of larger ionization clusters >10 was hypothesized to diminish due to charge and radical recombination in regions of high local ionization density (Becker et al 1996, Schulte et al 2001). Using MC-simulated energy deposition spectra in the cylindrical volumes converted to ICSD, the two-compartment model reproduced the main features of LET- and dose dependence of V79 cell survival after irradiation with protons and helium ions in two different cell cycle phases (Schulte et al 2001). As experimental ICSD became available, a more sophisticated model was developed to predict yields of simple and complex DSB in plasmids (Leloup et al 2005, Garty et al 2010) as well as calculate quality factors of high-LET ions, defined as the ratio of simple and complex DSB yields (Schulte et al 2008).

A microdosimetry-inspired RBE model reducing the micron spherical sensitive volume of conventional microdosimetry to a spherical volume of a few nanometers was proposed by Lindborg and Grindborg (Lindborg & Grindborg 1997). The authors suggested that the ratio of dose mean lineal energy $\left({\overline{y}}_D\right)$ for different radiation qualities, derived from experimentally measured microdosimetric spectra, can be used to estimate the ratio of alpha values of the LQ model for two radiation qualities. Knowing the low-LET alpha value of a given cell line, one can derive a dose-dependent RBE value. Of note, the uncertainty of the ${\overline{y}}_D$ values for a 60-Co beam went up to ±30% for the smallest nanodosimetric volumes they investigated (6nm and 9nm). This created a relevant uncertainty also in the clinical RBE value. In two follow-up papers, Hultqvist et al. and Lindborg et al. presented model calculations of ${\overline{y}}_D$ for the SOBP of a 12-C ion beam (290MeV/u) and 60-Co as a reference radiation (Hultqvist et al 2010, Lindborg et al 2013). They found that for a sensitive volume of about 10nm the α-ratio increased linearly with the ${\overline{y}}_D$-ratio for the SOBP for carbon ions and other investigated beam qualities for comparison (290MeV proton beam and a therapeutic neutron beam). Predicted and published RBE values closely matched for the 10nm volume but not for the 100nm volume.

In another publication, Lindborg et al. noted that ${\overline{y}}_D$ measurements in the nanometer range are technically difficult. As one alternative, they proposed model calculations using a combination of condensed history MC and detailed track structure simulations to determine ${\overline{y}}_D$ values (Lindborg et al 2015). The proposed method weighted the relative dose fractions of the primary and secondary charged particles with their respective energy-dependent dose mean lineal energies using a library of ${\overline{y}}_D$ values from MC track structure calculations for a wide range of charged particles and energies.

More recently, Dai and colleagues provided a systematic nanodosimetric simulation study to address the issue that different particles with the same dose-averaged LET value could have different dose mean lineal energy values (Dai et al 2020). They calculated LET profiles of ion beams with a range of about 13cm, and obtained lineal energy spectra and ${\overline{y}}_D$ in a 4nm spherical site for various clinical ion beams. The lineal energy spectra and ${\overline{y}}_D$ values were compared for ion beams with the same LET values. They demonstrated that the lighter ion beams with a smaller number of nucleon yielded greater ${\overline{y}}_D$ values than heavier ion beams for the same LET. They concluded that the relationship between RBE and LET is ion-type dependent and that ionization cluster sizes on the nanometer scale are relevant for this dependence.

Dai and co-authors also proposed a method to calculate nanodosimetric quantities, including mean cluster size (M₁ and ${\text{M}}_1^C$) and complementary cumulative probability (F₂ and ${\text{F}}_3^{C_2}$) sing both track structure and condensed history Monte Carlo simulations (Dai et al 2019). These quantities were calculated at different positions for clinically relevant carbon ion pencil beams of 260MeV/u. A novel modeling approach was suggested to determine cell survival RBE based on these nanodosimetric parameters. The authors found that the RBE values for HSG cancer cells were 1.07 in the plateau and 3.13 in the Bragg peak of the monoenergetic carbon ion beam. In addition, they observed a good agreement between the calculated and experimentally measured RBE values for this HSG cell line.

Henthorn et al. presented the results of Geant4-DNA track structure simulations to score simple and complex DNA damages on the nanometer scale using the scheme suggested in (Schuemann et al 2019). Three different DNA geometries in which energy deposition events occurred were simulated. Nanodosimetric quantities were scored using three different methods, one of them including the number of ionization events. The scoring of DNA damage included simple and complex DSB as presented in Def. Box 2. They showed that frequencies of simple and complex DSB were related to the spatial clustering of energy deposition events on the nanometer scale. They concluded that rather than combining dose and LET as predictive factors, DNA damage types could be more predictive and beneficial for nanodosimetry-based treatment planning.

A nanodosimetric RBE model based on a track-event theory proposed previously by Besserer and Schneider (Besserer & Schneider 2015a, Besserer & Schneider 2015b) was recently presented in (Schneider et al 2019). The track-event theory distinguishes between one-track events (OTE) and two-track events (TTE), where an event consists of two or more ionizations in a sphere of 2nm diameter, creating a sublesion (DSB). This track event theory had previously been shown to be superior to the LQ formalism for predicting cell survival in the high-dose range. The RBE model of Schneider et al. can be considered as a further development of the dual-radiation action theory (Kellerer & Rossi 1974). A lethal or potentially lethal event is defined as at least two DSB occurring in a lethal interaction volume of nanometer size (a model parameter). Further, it is assumed that sublesions (DSB) are created by two or more ionizations in a nanometric spherical volume of about 5–10bp diameter. The complexity of the DSB was not taken into account in this model. The model by Schneider et al. depends on the complementary cumulative probability F₂, linking RBE to a measurable or simulated stochastic nanodosimetric parameter. In a follow-up publication, the authors showed that their RBE predictions for ultra-soft x-rays agreed well with experimental data over a wide energy range (0.28keV-1MeV). They concluded that the dependence of the cell survival on the soft x-ray energy is directly determined by the F₂ parameter of the radiation.

5.2.2. Non-RBE nanodosimetric approach

As discussed in Sec. 5.1, significant differences exist in the RBE models currently applied at different carbon ion treatment centers. Nanodosimetry-based RBE models cannot overcome the underlying cause of these differences because every model relies on parameters, which are uncertain and will vary from patient to patient. One way to address this is to use RBE-independent approaches such as LET_d based treatment planning (Sec. 5.1.3). However, the LET_d based planning is not suitable for carbon ion therapy (Grün et al 2018). In the following, we describe the novel ionization detail (ID) approach. This term was first used by Ramos et al. in 2018 who referred to the parameters describing the geometric distribution of ionizations on the nanometer scale collectively as ionization detail (Ramos-Méndez et al 2018). The ID approach to proton and ion therapy treatment planning has been developed by a collaboration between investigators at the University of California San Francisco, Lawrence Berkeley National Laboratory, Loma Linda University, and the German Cancer Research Center (DKFZ) since 2015.

In the context of treatment planning, ID describes the spatial distribution of ionizations produced by a therapeutic particle beam at the nanometer level. Ionization of water and DNA is considered to be the primary source of reactive chemical species and DNA damage that can occur in the form of local DNA lesion clusters (see Sec. 4.1). Casiraghi and Schulte performed a preliminary study to test the feasibility of biologically weighted treatment planning using ICSD (Casiraghi & Schulte 2015). They created a simple water target volume consisting of five cubic voxels arranged in a linear column and simulated the irradiation of this volume with an opposing array of proton or carbon pencil beams using Geant4-DNA for detailed track structure simulations. The fluence of each pencil beam was adjusted to achieve a uniform distribution of the nanodosimetric parameters F₂ and F₃ in this volume. Using inverse planning techniques, they demonstrated that it is possible to create a uniform distribution of small and large ionization clusters and therefore, simple and complex DSB. They concluded that it might be possible to create a uniform biological effect in the target with this approach while not exceeding a threshold of large clusters in organs at risk.

In subsequent work, flagged uniform particle splitting, a standard variance reduction technique, was successfully implemented in TOPAS-nBio to allow for the preparation of a library of ICSD for primary and secondary protons and ions produced in a mixed proton and ion therapy radiation field (Ramos-Méndez et al 2017). Using this method, to improve computational efficiency, the investigators provided an extensive database of biologically important ID quantities (Ramos-Méndez et al 2018). The database includes ID data for eight different ions ranging from protons to oxygen with energies typically found in mixed particle radiation therapy fields. In the same publication, the authors demonstrated the clinical usefulness of this approach by presenting ID distributions for recalculated proton and carbon ion treatment plans in a digital head phantom (see Fig. 5).

Figure 5.

Color-wash display of the nanodosimetric parameter ${\text{F}}_3^{C_2}$, here averaged over the energy deposited by individual particle tracks for each voxel of the axial slice shown. The left image represents a proton treatment plan, and the right image a carbon ion treatment plan for the same clinical case of a skull base chordoma (Ramos-Méndez et al 2018), with permission. Beam directions are shown by arrows. Isodose lines are displayed at 95%, 85%, 60%, 30% and 15% of the prescribed dose (dashed lines). The tumor is contoured in black and the brainstem in red.

For clinical implementation, one needs to transition from clinically established RBE models to the new approach using ID-based quantities. Burigo et al. proposed a novel treatment planning strategy of optimizing a carbon ion treatment plan using both RBE-weighted dose with the LEM I model and the nanodosimetric ID, choosing the frequency of large clusters (more than 3 ionizations) as an RBE-independent measure of biological effectiveness (Burigo et al 2019). They demonstrated that with simultaneous optimization, the ID parameter could be optimized without negatively influencing the RBE-weighted dose distribution. The authors concluded that after validating against experimental and clinical data sets for protons and ions of therapeutic energies, this mixed optimization strategy could be applied to achieve higher tumor control and lower normal tissue complication probability. Eventually, it may be possible to implement an RBE-independent, ID-only approach in particle therapy treatment planning.

5.3. The future of nanodosimetry-based planning in particle therapy

In the following, we describe how, in the future, the new concept of ID-based treatment planning outlined above could be applied to proton and ion therapy. We outline the main steps that need to be taken to translate this new idea into practical use. The first step is to define in much more detail the ID formalism for applying it in particle treatment planning. Up to now, ICSD and derived ID parameters have been measured or calculated mostly for a single nanodosimetric volume and single particle tracks (single-event ICSD). For treatment planning, it will be necessary to have a formalism that converts single-event ICSD to ID parameters defined in a single treatment planning voxel.

Doses and fluences used in particle radiation therapy are considered low enough so that only single proton and ion tracks contribute to the ICSD of a nanodosimetric volume. Therefore, single-event ICSD can be combined linearly to calculate multi-event ICSD for a given voxel. Treatment planning voxels also should be small enough so that ID parameters derived from multi-event ICSD are representative of the entire voxel. From preliminary work presented in Sec. 5.2.2, voxel sizes of the order of 1mm³ are sufficient to fulfill this condition.

Complementary cumulative probabilities are currently considered the candidates for voxel-based ID parameters that best correlate with the radiobiological effect. However, the definition of ”large” and ”small” ionization clusters needs to be further refined to predict the generation of simple and complex DNA lesion clusters, respectively. For this step, we need to analyze existing or newly generated experimental data sets on cell inactivation and molecular biological endpoints characterizing the response of cells and tissues to high and low-LET radiation. It is foreseen that data sets from multiple ion types, including ions lighter and heavier than carbon, will be used to find the best ID parameters predicting biological effectiveness.

The single-event ICSD of primary and secondary charged particles typically encountered in therapeutic proton and ion beams can be pre-calculated, for example, with TOPAS-nBio, tabulated, and stored in a database (see Sec. 5.2.2). The voxel based ID parameters can then be calculated using this database with a condensed history Monte Carlo code. Note that one could calculate RBE values from these ID parameters, but we propose that inverse optimization of treatment plans can be entirely based on the frequency of large and small ionization clusters, thus making this approach RBE-independent.

Inverse planning using voxel-based ID parameters is straightforward. Existing optimization or feasibility seeking algorithms can be used to constrain ID parameters rather than RBE-weighted dose in target and OAR volumes. Treatment plans could be designed, for example, to create a uniform distribution of large and small ionization clusters throughout the target volume. Another option is to maximize the frequency of large ionization clusters in regions of tumor hypoxia (ID-painting). Furthermore, it is conceivable that a mixture of different ion beams can be applied to achieve this goal without exceeding thresholds of the number of large ionization clusters in voxels of OAR. Since voxel-defined ID parameters increase linearly with pencil beam fluence, existing algorithms, up to now used for RBE-weighted dose optimization, can be readily applied to ID-based optimization. Note that ID-based optimization does not optimize RBE-weighted dose but the absolute frequency of ionization clusters encapsulated in ID parameters. It is also possible to jointly optimize ID and RBE-weighted dose (Burigo et al 2019), as mentioned above (see Sec. 5.2.2). In the future, we foresee that RBE and ID parameters will be adjusted according to clinical results. The freely-choosable parameters for the ID approach, e.g., the boundary between small and large cluster sizes that best reproduce the production of complex DNA lesions may depend on tumor type and the presence of hypoxic cells. Further pre-clinical and clinical research is needed to develop the ID-based nanodosimetric approach to charged particle treatment planning.

5.4. Applications of nanodosimetry beyond particle therapy treatment planning

Beyond the application of nanodosimetry in proton and ion radiation therapy, a much wider field of application could be radiation protection. The harmful effects of low doses of ionizing radiation have been known for more than a century. National and international radiation protection commissions and agencies such as the National Commission for Radiation Protection (NCRP) in the US, and the International Commission on Radiological Protection (ICRP), with support from with International Commission on Radiation Units and Measurements (ICRU), have worked out a sophisticated system of instrumentation and recommendations to provide guidelines for radiation protection. On the other hand, absorbed dose and quality factors to modify absorbed dose have left us with much room for improvement. A ”radical reappraisal” of radiation protection dosimetry based on the recognition of the importance of ionization and DNA lesion clusters may be needed (Simmons & Watt 1999).

The authors of the current review concur with Simmons and Watt that for a significant radiobiological effect individual ionization events have to occur at a mean spacing of 2nm for the most efficient interaction of radiation with DNA and formation of DNA lesion clusters. Experimental and simulated nanodosimetry has taught us that closely spaced ionizations can be observed even with low-LET radiation but are much more common with high-LET charged particles. Ionization clusters are important for the generating simple and complex DNA lesion clusters, which are responsible for the induction of non-lethal but irreparable mutations or genomic rearrangements leading to malignant transformation.

Different from radiation therapy, the field of radiation protection is characterized by low fluences, doses, and dose rates. For fluences of <1 particle per cell, the concept of absorbed dose averaged over cells and entire organs loses its meaning. Furthermore, the interaction of simple DNA lesion clusters forming genomic rearrangements is much less likely at low fluences, leading to a linear relationship between particle fluence and risk. What appears to be most important in this case is the frequency of large ionization clusters leading to complex DNA lesions, and the failure of protective cellular mechanisms such as apoptosis and senescence could lead to cancer if these complex DNA lesion clusters are not repaired.

Nanodosimetry with gas-based detectors or track structure simulations provides an opportunity to measure and predict the formation of large ionization clusters in phantoms designed for radiation protection nanodosimetry. Thus, nanodosimetry may help establish a unified system of biologically weighted dosimetry for radiation treatment planning and radiation protection. This will require further development of detectors identifying the composition and energy of mixed radiation fields and establishing a mechanistic link between the size of ionization clusters and cancer risk. It is hoped that national and international radiation protection commissions and agencies will be open to reevaluate the current radiation protection system by including nanodosimetric instrumentation and quantities in the future.

6. Conclusions

In this topical review of nanodosimetry, we have summarized the underlying concepts, gave an overview of detector technology and detailed Monte Carlo track structure simulations, and reviewed radiobiological assays that will allow correlating the frequency of DNA lesion clusters with nanodosimetric quantities. Our review has been written for medical physicists, health physicists and researchers interested in new approaches in treatment planning for proton and ion therapy and new concepts of radiation protection dosimetry. In the following, we summarize the main conclusions of each section of this review.

In Sec. 2 we introduced the reader to current concepts of medical dosimetry, which are based on average quantities such as absorbed dose and linear energy transfer (LET). Absorbed dose is certainly a useful predictor of radiation effects in patients but has to be modified with an RBE factor to take different radiation qualities into account. Microdosimetry was the first field that considered the stochastic variation of energy deposition in small volumes, typically of micron size. The more recent development of nanodosimetry has focused on the number of ionization events occurring in even smaller volumes of nanometer size. This field is based on recognizing that the number of disruptive events in DNA may be more important than the energy deposited per unit mass or track length.

There is ample evidence that radiation effectiveness is related to the clustering of ionizations at the nanometer scale, more importantly near or in short segments of DNA of 1–2 helical turns. This has been a strong motivation to develop experimental nanodosimetry and detailed track structure simulation codes as reviewed in Sec. 3. Both developments have demonstrated that clustered ionization events occur at the nanometer level with high and low-LET radiation, although with different frequencies. Track structure simulations, including the physical, physico-chemical, and chemical stages, have shown that, in the chemical environment of the cell, ionization clusters are converted into clusters of water and DNA radicals that can interact locally to form DNA lesion clusters.

The concept of linking ionization clusters on the nanometer scale to the complexity and repair of DNA lesion clusters has to be carefully validated with various assays of DNA damage (see Sec. 4). Starting from classical DNA damage and repair assays, we have also reviewed the new super-resolution imaging of radiation induced foci and end-labeling/next generation sequencing assays that will increase the accuracy of characterizing and measuring the yield of simple and complex DNA lesion clusters. The next step in validating nanodosimetry will be the extension from cell-free and in vitro to in vivo assays. Linking the biological endpoints of these studies with nanodosimetric quantities will be an important topic of future work.

Current biologically weighted treatment planning for proton and carbon ion therapy relies on dose-averaged LET and RBE models, respectively. These two approaches may be replaced by a unified nanodosimetry-based and RBE-independent approach in the future (see Sec. 5). Initial steps in this direction have been taken and are supported by detailed track structure simulation codes and high performance computing. Once experimentally validated, this novel concept can be readily translated into clinical practice. Beyond proton and ion therapy treatment planning, nanodosimetry is also expected to have applications in radiation protection. This is possible because nanodosimetry is a fluence-based concept that specifies the frequency of DNA lesion clusters, which are likely the cause of cancer induction.