Nuclear physics and particle therapy

Abstract The use of charged particles and nuclei in cancer therapy is one of the most successful cases of application of nuclear physics to medicine. The physical advantages in terms of precision and selectivity, combined with the biological properties of densely ionizing radiation, make charged particle approach a clinically preferred choice in a number of cases. Hadron therapy is in continuous development and nuclear physicists can give important contributions to this discipline. In this work, some of the relevant aspects in nuclear physics will be reviewed. Graphical Abstract


Introduction
Charged Particle Therapy (CPT in the following), or hadron therapy, is a form of cancer radiotherapy based on charged nuclear particles (protons and light ions) for treatment of early and advanced tumors. In 1946, Robert Wilson proposed the therapeutic use of protons for treating cancer [1]. This is considered as the start of hadron therapy with charged particles. Proton therapy has now become an advanced clinical modality, and CPT with heavier ions (generally 12 C) is now starting to spread. The clinical interest in hadron therapy resides in the fact that it delivers precision treatment of tumors, exploiting the characteristic shape of the Bragg curve of charged hadrons, i.e. dose deposition as a function of depth of traversed matter, exhibiting a sharp peak (the Bragg peak) at the end of the particle range. As compared to the standard X-ray radiotherapy, CONTACT G. Battistoni giuseppe.battistoni@mi.infn.it accurate and efficient irradiation of the tumor can be obtained reducing the dose to the surrounding healthy tissue, thus achieving less complication probability. Especially for heavy ions, an increased Relative Biological Effectiveness (RBE) in killing cancer cells can also be obtained, making this approach very interesting for the case of radio-resistant tumors. After a rather long period in which hadron treatments were exclusively delivered in research laboratories, the first hospitalbased treatment center to be established was that of Loma Linda (USA) in 1990. Today proton therapy has grown into an advanced, cutting-edge clinical modality. According to a recent statistics of 2014 [2], more than 137,000 patients worldwide have been now treated with charged hadrons (about 10% with carbon ions). At the same date, 48 CPT facilities were in operation, and this number is increasing: at the beginning of 2015, more than 30 particle therapy centers, with a total of about 80 treatment rooms, were under construction worldwide. Of course, these numbers represent a tiny fraction of standard radiotherapy, which at present is used for about 1.5 millions of patients per year (about 50% of all cancer cases), in several thousands of radiotherapy departments in the world. Hadron therapy represents a paradigmatic case of an interdisciplinary topic in between research and actual clinical practice. It is a discipline in evolution to which physicians, biologists, and physicists contribute to its development. In this review, we wish to summarize some of the aspects in which nuclear physics is still playing a fundamental role to help CPT to reach in practice the high level of precision which would be in principle attainable. Several R&D projects are in progress with two main goals: to reduce the costs of infrastructures and treatments and reduce existing uncertainties, such as those connected to radiobiology, the knowledge of particle range inside the patient, and its monitoring during the treatment.
In order to reach these goals, nuclear physicists contribute to different items: (i) Optimization of treatment planning; (ii) Implementation of radiobiological models in calculation models and estimate of their effects; (iii) Development of new detectors and imaging techniques to achieve specific and optimized monitoring; (iv) Development of detectors for beam monitoring, dosimetry, and of devices for dose delivery systems; (v) Improvement of the knowledge of relevant nuclear processes, like fragmentation, and their modeling; (vi) Development of new therapeutic beams using alternative ion species, like 4 He and 16 O.
If we extend the category of nuclear physics also to accelerator technology [3], we can also consider the research and development of new acceleration techniques, in view of more compact and less expensive systems, and the development of new optimized components, like for instance high-performance ion sources [4]. The Nuclear Physics European Collaboration Committee has dedicated its 2014 report to the contribution of nuclear physics to medicine [5] where a comprehensive review of the key issues in CPT can be found. A discussion of the evolution of CPT technology, mostly in the context of proton therapy, is presented in Ref. [6]. Here we limit ourselves to a few selected issues. In Section 2, we summarize the basic principles of CPT, while Section 3 will be focused on the relevant nuclear physics for CPT. Section 4 aims to point out some aspects of physics in Monte Carlo (MC) models. The topic of particle range uncertainties and the development of a specific imaging approach will be presented in Section 5, while Section 6 will be dedicated to real-time monitoring techniques based on the exploiting of nuclear interactions.

The basic principles of CPT
Charged particles lose energy primarily by inelastic collisions with the atomic electrons, resulting in ionization and atomic excitation. The amount of energy lost due to Coulomb interactions with the material nuclei is instead very small. For charged particles other than electrons, the mean ionization energy loss (or electronic stopping power (SP)) can be described by the Bethe-Bloch equation [7]: the growing energy loss with decreasing particle velocity causes the characteristic Bragg peak. The range if a particle can be defined as the path depth in the medium at which half of the particles undergoing electromagnetic interactions have stopped. In practice, a dose measurement is used, where the range is defined as the distal 80% point of the Bragg peak [8].
The Bragg peak is not perfectly sharp. First of all, the ionization energy loss of a charged particle traversing a medium is a stochastic process, so that the actual range of each single particle deviates from the expected mean value (range straggling). In second place, a beam is never perfectly mono-energetic. Depending on the machine, the spread can be up to about 1% of the nominal energy [9].
An example of actual longitudinal dose deposition in water is given in Figure 1, where we show a comparison of experimental data and simulation for different proton beam energies [10] as measured at the CNAO facility in Italy [11].
In the clinical practice, one of the main aims is to have a full irradiation coverage of the tumor volume. Longitudinally this is achieved by superimposing different beams with slightly different energies and weights, as depicted in Figure 2, generating a Spread Out Bragg Peak (SOBP) that deposits the wanted dose in the treatment volume.
However the absorbed dose is not enough to determine the biological effect of different radiation qualities, as the most striking difference between photons, protons, and nuclear projectiles concerns their microscopic spatial energy dis-  tribution. Medical physicists make use of the concept of Linear Energy Transfer (LET), which is analogous to the SP, and it is defined as the energy deposited per unit length in the target medium a decelerating particle, measured in keV/µm. In some cases, it can be useful to exclude interactions that carry energy far away from the original track, imposing an upper threshold for the energy of secondary ionization electrons. This is usually referred as Restricted LET. If the threshold tends to infinity, the quantity is called Unrestricted LET and it equals the electronic SP. From a practical point of view, the LET focuses on the energy locally given to the medium, rather than on the energy loss by the incident particle being an effective instrument for studying the biological effects of radiation. In their path through matter, ions emit electrons, or δ-rays, by means of Coulomb interactions with the target. Those electrons are scattered and subsequently transported in the medium by elastic and inelastic collisions, possibly generating further excitations and ionizations. High-LET particles, such as ionized nuclei, give rise to an energy deposition in matter with a higher spatial density with respect to protons (and photons). Most of the induced secondary electrons deposit the dose in the center of the primary ions tracks, whose typical diameter is on the order of nanometers. This leads to a larger probability of closely correlated DNA damages like single or double-strand breaks, resulting in an increased cell killing capability.
A common way to analyze the different effects between photons and charged hadrons is by means of the concept of RBE which is defined as the ratio between the absorbed dose of a reference radiation (D ref typically X-rays) and that of the test radiation (D test , in our case charged hadrons) required to produce the same biological effect: Typically, RBE is determined considering the dose needed to reduce the survival probability of irradiated cell to 10%. Survival probability is usually parameterized according to the so-called Linear Quadratic model: where S is the survival fraction, D is the absorbed dose, and α and β parameters to be determined experimentally or by means of a radiobiological model. The α/β ratio is linked to the radiosensitivity of cells. The smaller this ratio, the larger the DNA repair capability will be. In spite of its simple definition, RBE is a very complicated radiobiological concept, which depends on several factors and variables. For a given cell type, RBE varies with LET, dose, dose rate, fractionation, biological endpoint, oxygen concentration, etc. In proton therapy, the LET of protons exhibits a limited variation as a function of penetration depth (from about 1 keV/µm in the entrance channel to 2-6 keV/µm in the SOBP [12]). The corresponding variation of RBE is limited, and mainly concentrated in the final part of the SOPB. Therefore, in proton therapy a single RBE factor of 1.1 throughout the entire radiation field is considered an acceptable approximation. The situation in heavyion therapy is much more complex because of larger variations of LET along the ion path: values exceeding 100 keV/µm are reached in the SOBP region. Figure 3 shows a collection of measured RBE values as a function of LET, for different ions, in cells with different sensitivities. RBE increases with LET up to an iondependent maximum value, and then decreases for higher LET values. Since RBE changes along tissue penetration, due to the change in energy and LET of the particles, the optimization of SOBP in ion therapy can be obtained as shown in the example of Figure 4. For this purpose, a radiobiological model has to be . RBE at 10% survival as a function of LET for different monoenergetic particle beams grouped in different sensitivity ranges (α/β). Note: Reproduced from Ref. [14] with permission.
included in the treatment planning system. An example of discussion of related uncertainties in carbon ion therapy is given in Ref. [13].
Moreover nuclear interactions of the projectile nucleus give origin to the production of lighter fragments, which in general have a RBE factor different from that of primaries. Those lighter fragments will have a longer range, thus producing an ionization tail beyond the Bragg peak position (see Figure 5). These aspects introduce the topic of nuclear interactions examined in more detail in the next section.

Nuclear physics: what really matters
Several nuclear processes are relevant in hadron therapy. Inelastic interactions are responsible for beam attenuation along the penetration depth, while elastic scattering, especially in the case of proton therapy, contributes to the transverse profile of dose distribution. In ion therapy, fragmentation of both projectile and target is probably one of the most relevant processes to be studied in detail, since it affects the attenuation of the primary beam and biological effects. In fact, as mentioned in the previous Section, when compared to the radiation field of the primary ions, secondary fragments lead to an altered spatial dose distribution due to differing ranges and angular distributions of the fragments and to a modification of the LET spectra which results in a difference of RBE for the same delivered dose.  Comparison of experimental data and simulation for ionization energy loss in water for a 12 C projectile (338 MeV/u) as measured at CNAO [11]. Note:The simulation has been performed with the FLUKA code [18,19].
As far as the case of ion therapy is concerned, the most frequently occurring nuclear reactions are peripheral collisions where the beam particles may lose one or several nucleons. This process is often described by the abrasion-ablation model [20]: nucleons in the overlapping zone of the interacting projectile and target nuclei are abraded and form the hot reaction zone (fireball), whereas the outer nucleons (spectators) are only slightly affected by the collision. In the second step (ablation), the remaining projectile and target fragments as well as the fireball de-excite by evaporating nucleons and light clusters. Those emitted from the projectile fragments appear forward peaked in the laboratory frame due to the high velocity of the projectile. The projectile-like fragments continue traveling with nearly the same velocity and direction, and contribute to the dose deposition until they are completely slowed down or undergo further nuclear reactions. Neutrons and clusters from target-like fragments are emitted almost isotropically and with much lower velocities. The particles ablated from the fireball cover in energy the range between the projectile and target emission. Nuclear fragmentation reactions lead to an attenuation of the primary beam flux and the build-up of lower-Z fragments with increasing penetration depth since the range of particles (at the same velocity) scales with A/Z 2 . As already mentioned in Section 2, these fragments are responsible for the tail beyond the Bragg peak (as shown in Figure 5). Beam models adopted in treatment planning programs for heavy-ion therapy must take into account these effects and their validation against experimental data is mandatory. The composition of particle field and LET distributions has to be known at each point of the treatment volume.
Not only are charged fragments important, but the neutron contribution should be considered as well. Dose contribution from secondary neutrons can be treated by considering their indirect interaction using the KERMA factors (kinetic energy released per unit mass, defined as the initial kinetic energy of all secondary charged particles liberated by neutrons per unit mass at the point of interest [21]). Alternatively, fluence-to-dose conversion factors can be used, usually derived from MC calculations.
In order to study such secondary fragments, many experiments have been performed with thick targets made of water-or tissue-equivalent materials. The most recent measurements of this kind were performed for carbon ion collisions with water [22][23][24][25][26]. These tests showed that fragmentation products are peaked in the forward region and mostly contained within few degrees of the beam axis, apart from protons that represent the largest sample and show tails at large emission angles and energies (see Figure 6). Devoted experiments aimed to measure nuclear cross-sections at energies relevant for CPT have also been designed [27,28].
Nuclear reactions experienced by the primary and its possible fragments are also responsible for radioactive isotope production. These isotopes may be used for monitoring purposes and this topic will be discussed in Section 6 for the case of β + decaying radionuclides. Last, but not least, nuclear evaporation deexcitation has to be considered, mostly from the production of the lowest energy nucleons in the target. Prompt photon production from gamma decay following de-excitation is a particularly interesting case which can be exploited for realtime monitoring. Of great interest, for the same reason, is the production of secondary fast charged particles.
Accurate modeling of all the mentioned processes is one of the most important contributions of nuclear physicists to CPT. The precise prediction of nuclear particle interactions and resulting residual nuclei distributions are needed both for treatment planning and those imaging techniques which aim at in vivo dose monitoring. Recently, there has been progress in the development of MC models, but there are still uncertainties that have not been resolved. The level of agreement between different models in the predictions of nuclear reaction models and experimental data is encouraging but there is still ample room for improvement. However, the amount of available experimental data and their limited precision (especially in the case of nucleus-nucleus interaction in the interesting range of energies and masses) is not enough to provide a complete benchmarking.
The relevance of existing discrepancies in numerical models (see e.g. Refs. [29,30]) should be discussed in the context of clinical applications. The detailed quantitative evaluation of biological dose distributions would require the simulation of a carbon ion treatment field including radiobiological modeling. Still, a simplified calculation for a single Bragg curve can give an estimate of the degree of the impact on the biological dose. The authors of Ref. [29] estimate by MC that, in the case of carbon ions, at maximum about 40% of the dose in the region between the entrance channel and the Bragg peak is delivered by fragments (about 15% of this dose is delivered by secondary protons). The existing uncertainties in the prediction of the relative abundances of these fragments could translate into a difference of 4-5% in both physical and biological dose.

MC codes and nuclear interaction models
MC techniques in the field of medical physics are rapidly increasing their relevance. This is specifically the case for hadron therapy. MC simulations are an essential tool for the design and commissioning of clinical facilities, allowing a detailed description of the beam line and the delivery system. They are also widely used for treatment room design, shielding, and radiation protection. MC calculations are a valuable tool for the commissioning of treatment planning systems (TPS). Furthermore, MC codes can represent a unique instrument for validation, and possibly improvement, of analytical TPS. In situations where the experimental validation is unavailable and/or analytical methods are inadequate, MC simulation allows patient-specific dose calculation. Aspects where MC techniques can be more effective compared to traditional, analytical methods may be summarized as follows: • MC methods are able to consider the detailed structure of patient anatomy and heterogeneity by inheriting information from CT images; • MC methods take into account more realistically the composition of the human body [31][32][33] in terms of elemental composition, with a possible advantage over the water-equivalent approach typically used in analytical TPS's; • MC methods naturally include mixed field description and threedimensional spread of the particle fluence taking into account a realistic transverse structure arising from large angle scattering and from nuclear interactions, reliably describing the transport and the interaction of the primary beam and of the secondaries [29,34]; • MC simulations, by taking into full account the complexity of the mixed radiation field and tissue stoichiometry, provide detailed predictions of particles originated in the nuclear interaction within human body. It is useful to develop in-beam monitoring systems for the irradiation treatment [33,[35][36][37].
There are different topics that need to be considered in MC calculations, but we limit ourselves to the crucial aspect of the modeling of nuclear processes. In most MC codes, the common approach to model nuclear interactions is to start with sampling the probability that a nuclear event happens. Depending on the incident particle and energy, these can be calculated on an event-by-event basis by means of nuclear cross sections from nuclear database parameterized physics models.
Examples of large nuclear database are the Evaluated Nuclear Data File [38], the Japanese Evaluated Nuclear Data Libraries [39], and the Exchange Format (EXFOR) database [40].
Subsequently, a nuclear interaction is sampled with appropriate models or from nuclear bases.
A proton interacting with a nucleus initiates a series of nucleon-nucleon collisions which lead to secondary emission (protons, neutrons, light fragments) and to equilibration of the remnant nucleus. This collision process can be described as a sequence of three stages [41]: (Generalized) Intra-nuclear cascade (INC), pre-equilibrium, and de-excitation. For the first two steps, the time of the process corresponds to the time-scale of strong interactions (10 −22 − 10 −23 s) while for the last step the timescale is 10 −18 − 10 −16 s.
(Generalized) INC [20,42] is commonly used in most modern MC codes to describe nuclear interactions of nucleons with energies above 50 MeV to hundreds of GeV.
The INC refers to the cascade inside the nucleus, different from the internuclear transport of a particle from one nucleus to another.
The basic idea is that the incident particle interacts with quasi-free nucleons in the target nucleus through a series of two-body interactions. The target nucleus is modeled as a Fermi gas of cold, free, nucleons. Nucleons inside this intranuclear medium are accounted for by a nuclear density distribution, a nuclear potential, and the Pauli exclusion principle. Not only protons and neutrons can be emitted, but also light nuclear fragments of high energy, through the coalescence mechanism, in which emitted nucleons, which are close in phase space, are grouped. The pre-equilibrium stage is reached when all particles are tracked down below a given energy threshold usually a few tens of MeV, but the nucleus is not yet in thermal equilibrium. It is commonly modeled in MC codes according to the exciton model [43,44], a semi-classical model introduced to explain high-energy emitted particles in nuclear reactions. Protons, neutrons, and light fragments (through coalescence) are emitted and the residual nucleus is left in an equilibrium state, with a certain excitation energy shared among the remaining nucleons.
The de-excitation of the remaining nucleons can be described in different ways: nuclear evaporation according to the Weisskopf-Ewing approach [45] (light fragments with kinetic energies of few MeV can be emitted from the excited nucleus as evaporating from a hot system), fission of the excited nucleus into two fragments (for high Z nuclei only), Fermi-break-up [46] (relevant for radiotherapy because applies to light nuclei where the excitation energy of the excited nucleus may be larger than the binding energy of some fragmentation channels), and gamma emission (the final excitation energy is given off through the emission of γ rays).
The fundamental difference between nucleus-nucleus reactions and nucleonnucleus reactions is that the incoming nucleons are not free for the former.
During the fast stage (10 −22 − 10 −23 s), the projectile and target nuclei overlap, resulting in a kind of reaction zone. An excited quasi-projectile with most of the initial velocity is formed together with a quasi-target fragment at rest and several excited light fragments. During the slow stage (10 −18 − 10 −16 s), the remaining projectile, target, and light fragments de-excite by evaporating light nuclei or fragments.
Different models have been developed to describe the fast stage. As in nucleon-nucleus scattering, INC model handles high-energy nuclei with energies above about 100 MeV/u. The energy is lost through a series of two-body reactions and scattering off quasi-free nucleons.
Many codes make use of the Quantum Molecular Dynamics model, which handles nuclei with energies from 50 to about 400 MeV/u. Each nucleon is described by a Gaussian wave packet, and all nucleons in the projectile and target nuclei are participants in the collision process. By minimizing the Hamiltonian that describes nucleon-nucleon interactions in the overlapping projectile and target nuclei, it predicts the formation of secondaries. Such a model can also be implemented in a relativistic approach [47].
For energies below 100 MeV/u, there are multiple different attempts. As an example, we can quote that in the FLUKA code [18,19] a model based on Boltzmann-Master-Equation [48] is adopted to simulate the pre-equilibrium stage below 100 MeV/u down to the evaporation/fission/break-up stage. It describes how a statistical state far from equilibrium evolves to an equilibrium state, through a sequence of two-body interactions and emission of unbound particles (neutrons/protons) and clusters (heavy/light nuclei).

Imaging for hadron therapy: proton Computed Tomography
The spatial precision of the dose delivered to the volume to be treated is one of the major specific advantages of CPT. However (see Ref. [5]), the precise knowledge of the range of particles of a given energy in the patient remains one of the major uncertainties. In order to achieve the desired precision goals, the SP map of the patient should be reconstructed before the treatment to set up a detailed plan. At present, the SP maps are extracted from three-dimensional images obtained by X-ray Computed Tomography (CT); here the photon attenuation coefficients are translated into SP using conversion tables. This intermediate step introduces an intrinsic uncertainty resulting into an error in the proton range calculation that can be of several millimeters [49]. To mitigate this effect, the SP map could be directly determined using a proton beam with kinetic energy larger than the one used for treatment and with reduced intensity. Such an imaging system should be able to determine the three-dimensional SP map with a position resolution less than 1 mm and a density resolution of the order of 1%. A dedicated imaging can in principle be performed by means of proton beams of sufficiently high energy, thus achieving a proton Computed Tomography (pCT). This approach requires a specific detection system and an improved reconstruction algorithm with respect to the standard tomography with X-rays. In fact, due to the Multiple Coulomb Scattering (MCS) experienced by charged particles while crossing matter, the typical Filtered Back Projection (FBP) algorithms, back-tracing the measured data on straight parallel lines perpendicular to the projection direction, are not suited for pCT image reconstruction (see Figure 7). Typical objects under study could be as thick as 20 cm water equivalent: in this case a 200 MeV kinetic energy proton undergoes a r.m.s. MCS angle of the order of 40 mrad, which corresponds to an r.m.s. projected displacement of about 3.2 mm, considering a 8 cm minimum distance between the target and the detecting plane. Modified FBP has to be implemented in order to include a description of the proton path in the reconstruction so to increase spatial resolution.
An example of the research and development work for a prototype of pCT is described in Refs. [50,51]. The scanner is based on a tracker and a calorimeter to measure single protons trajectories and their residual energy. The tracker is composed of four planes of silicon microstrip detectors to measure proton entry and exit positions and angles. Residual energy is measured by a calorimeter composed of YAG:Ce scintillating crystals. A first prototype of this pCT scanner, with an active area of about 55 cm 2 , has been constructed and characterized with 60 MeV protons at the INFN Laboratori Nazionali del Sud (Catania, Italy). A first test to reconstruct the tomographic image of a 2 cm radius, 4 cm high PMMA cylinder has been performed. The phantom, mounted on a rotating platform, has been installed in the middle of the tracker (Figure 8) of the pCT prototype. A total of 36 data-sets, each of them containing on average 9.5 × 10 5 events, have been acquired. The phantom has been rotated by 10 • each run. The 36 profiles have been used as input to a 'FBP' tomographic reconstruction algorithm. Figure 8 displays two tomographic sections of the phantom: a section with 4 and 6 mm diameter holes in the top panel, while in the bottom panel a section of the homogeneous region is shown. The reconstruction algorithm has to be verified in a more clinical-like setting (i.e. higher proton energy and larger object thickness).

Real time monitoring
Beyond the question of SP determination, the need for a real-time monitoring, i.e. during the treatments, of actual particle range in the patient is another important goal addressed in present research activity. The uncertainty on the position of the dose release in CPT treatments can be due to different factors, such as quality and calibration of the CT images or possible morphologic changes occurring between CT and each of the several irradiation sessions, operated in different days, that compose a treatment in CPT. Finally also patient mis-positioning and organ motion during the treatment itself can be sources of uncertainty. All these effects can add up to give an overall uncertainty of the order of few millimeters [52]. A real-time monitoring procedure can therefore add valuable information that can be used for the quality assurance of a CPT treatment. The techniques proposed for in vivo range monitoring aim to exploit the secondary particle production coming from the hadronic interactions of the therapeutic beams with matter. In Refs. [53][54][55], a discussion of range verification methods and of the related physics can be found. Three are the nuclear processes that can yield a radiation suited for this purpose: production of β + emitters nuclei, gamma de-excitation of nuclei, and charged particle production in inelastic interactions. In order to make use of these processes, the comparison of measured and precalculated distributions of secondary particles is needed (see the discussion in Section 3 about MC models). The practical implementation of a real-time system for range monitoring in clinical practice is still object of discussion. This is a bit outside the realm of nuclear physics. However, among the different issues, two are the major points to be considered in the development work: the achievable spatial precision and the timescale at which the information has to be made available, considering that a single irradiation fraction may last few minutes.

Measurement of β + activity
Nuclear β + decays produce positrons that can be traced by exploiting their annihilation with electrons yielding almost back-to-back 511 keV photon pairs. Since organic tissue is mostly constituted of carbon, hydrogen, and oxygen, the most likely β + emitting isotopes that can be formed are 10 C, 11 C, 15 O, and 13 N. Figure 9 shows, for different ions, the amount of β + activation as a function of penetration depth in water along the beam direction, as compared to the calculated depth-dose distribution, so to point out the correlation between the distal part of both quantities [56].
The measurement of induced activity by means of Positron Emission Tomography (PET) has been studied for several years. Original discussion and first investigations are reported in Ref. [57][58][59]. At present, after the experimentation at GSI, there is not yet a standard clinical implementation of PET monitoring in real time. Off-room measurement of activity immediately after the irradiation is being performed at Heidelberg and results of a clinical study have been reported in Ref. [60]. An example of recent research and development activity to design a device to be actually used in clinical operation, during the treatment, is reported in Ref. [61]. The proposed system consists of two planar detector heads [62] each having an area of 10 × 10 cm 2 based on the use of segmented scintillating LYSO crystal matrix. The equipment has been tested at CNAO. In order to avoid hampering due to the high background of prompt photons and neutrons during the irradiation, the PET acquisition is allowed during the pauses between two synchrotron spills or immediately after the irradiation. Measured activity was compared with predictions from the FLUKA MC generator [18,19] and examples of results are reported in Figure 10. For PMMA phantoms, the difference between the MC prediction and the data, considering the distance between the 50% rise and 50% fall-off position of the activity distribution is less than 1 mm [63]. The Figure 9. Longitudinal profile of β + activation induced in water by different ion beams as compared to the dose distribution [56]. system is proved to be able to detect the change of beam range produced by inhomogeneities in the phantom. A new optimized system, based on fast pixellated LYSO scinillators coupled to SiPMs is at present in the development [64] to be tested at CNAO. The readout electronics, designed to cope with the count rate expected from synchrotron beams during the spill phase, provides the energy and timestamp of each detected event for a time-resolved analysis of the acquired signals.

Prompt photon detection
Nuclear interactions of the beam in the patient can also excite target nuclei along the particle path. When nuclei are being used, also the projectile and its fragments get excited as a result from their interactions with the target. The final stage of de-excitation proceeds through the emission of characteristic gamma rays, as qualitatively sketched in Figure 11. De-excitation photons have an energy range extending up to about 10 MeV and are emitted in a very short (< 1 ns) decay time interval, so that they can be defined as prompt photons.
Two are the aspects that are being studied: the characteristics of the emitted radiation (photon rates and energy spectra for different ion types, directions and energies) and the development of appropriate detectors.
A review of results on the yields of photons emitted during irradiation with proton and Carbon beams can be found in Ref. [65]. The initial studies were focused on proton beams [66,67] and they showed a correlation between the distal falloff of the Bragg Peak and the emission profile of prompt gammas. Figure 12 shows the longitudinal emission profile of photons (E > 2 MeV), as resulting from a MC simulation of the irradiation of a PMMA target with a 12 C beam at 180 MeV/u, compared to the longitudinal dose profile.   [18,19].
At phantom entrance, the average number of detected prompt γ 's was found to be of the order of 10 −4 per incident carbon ion and 10 −5 per incident proton.
The energy spectrum of the outgoing radiation was both simulated and measured [68,69]. The photon spectrum presents a continuum component and several de-excitation lines. Such lines have different intensities depending on the traversed tissue, thus allowing for the determination of its composition, in particular the oxygen concentration [70]. As an example, Figure 13 shows the Figure 13. Energy spectrum of photons emitted by a PMMA target irradiated by 12 C projectiles at 220 MeV/u as obtained from a Monte Carlo simulation using the FLUKA code [18,19].
simulated spectrum of photons emitted by a PMMA target irradiated with a 12 C beam of 220 MeV/u.
The most abundant lines originate from excited fragments of Oxygen and Carbon. In particular, 11 C and 12 C (the last one often resulting from the fragmentation of 16 O) contribute to the structure close to 4.4 MeV. In the laboratory frame, emission lines are broadened by the process of fragment recoil. Furthermore, depending on the angle of observation with respect to the beam direction, photons emitted by projectile fragments may have a Lorentz boost. Below 1 MeV, the photon energy spectrum may be dominated by other processes, mostly the annihilation of positrons originating from nuclear β + decay and from e + e − pair production by photons.
As far as carbon beams are concerned, prompt photon emitters are distributed in the region before the Bragg Peak with no significant enhancement [71][72][73]. The energy spectra are dominated by the carbon line (4.44 MeV) due to its presence both in the beam and in the target [74,75].
As far as the photon rate is concerned, one of the most accurate measurements [74] reports an observed rate in the case of a carbon ion beam with E = 80 MeV/u of (3.04 ± 0.20) × 10 −6 gammas per impinging carbon ion with energy E γ > 2 MeV at 90 • with respect to the beam incoming direction. Correcting for efficiency and acceptance, the production rate was estimated to be dN γ /dN C /d (E γ > 2 MeV, 90 • ) = (2.32 ± 0.15) × 10 −3 sr −1 .
The potentiality of the prompt gamma monitoring technique is mostly related to the possibility of correlating the falloff of the dose distribution with the distribution of photon emission point. The accuracy on this correlation significantly depends on the detector choice. Standards detectors used for Single Photon Emission Computed Tomography are not suitable, due to the higher energy of de-excitation photons with respect to the typical ranges of gammas used in nuclear medicine (e.g. the 140 keV photon from 99m Tc). Therefore, new devices must be designed for the detection of prompt photon flux with the bulk of the energy spectrum in the 1 − 8 MeV range. The main background to this signature is represented by the other products of the nuclear interactions between the beam and the patient, mostly neutrons and delayed photons induced by the neutrons interaction with the environment. The background depends on the surrounding materials, on the irradiation field features, and on the patient morphology itself.
The first studies [66,67] made use of a gamma camera with a collimator to determine the direction of the incoming photon and a borated shielding against neutrons.
There have been several attempts to optimize the detector geometry, in particular using slit cameras [76] and knife-edge-shaped collimators [77]. An accuracy of the order of 1 mm on a single proton pencil beam is reported [76] coupling a knife-edge slit camera with LYSO crystal scintillators read-out by SiPM. A first clinical test has recently been performed in Dresden [78].

Detection of charged particles
The detection of charged particles can be a promising alternative approach, mostly in the case of CPT performed with ions heavier than protons. Recent studies have been focused on the possibility of exploiting secondary particle production (and in particular the high penetrating proton component) for monitoring purposes, since it can be used to estimate the position of the distal edge of the dose profile. Beyond the experimental studies of carbon ion in water [22][23][24][25] mentioned in Section 3, measurements performed at small angle [79,80] suggested that, using solid state tracking devices at 30 • with respect to the beam direction, the distal edge of the beam could be estimated with an accuracy of 1.3 mm. In addition, variations in the beam width could be measured with a precision of 0.9 mm. In principle, due to obvious geometrical considerations, production at large angle is the most interesting case. The quality of the reconstruction of the trajectory of the single charged particle compensates for the reduced statistics expected at large angle. Experimental data about charged particle emission under irradiation by a therapeutic ion beam can be taken by Ref. [81], in which a 20 × 5 × 5 cm 3 PMMA target was irradiated with a 220 MeV/u 12 C beam at the GSI Laboratories. Charged particles were identified with tracks reconstructed in a Drift Chamber and a LYSO crystal detector providing Time-Of-Flight and scintillation light output information, so to allow particle identification. Measurements were performed at 90 • and at 60 • with respect to the beam direction.
The production region of charged secondary particles has been studied extrapolating backwards the reconstructed tracks, demonstrating the possibility of correlating the spatial profile of emitted particles with the longitudinal dose profile. New preliminary results using 4 He and 16 O primary ions have been recently reported [82].
A fundamental point in the discussion about imaging with charged particles is the method to establish the correlation between the measurement of the longitudinal distribution of proton emission profile of the primary beam range, or Bragg Peak position. The relationship of the charged emission profile, and in particular of the profile falling edge, with the position of the Bragg peak is expected to provide a method to implement range monitoring. In Ref. [81], a function is proposed to fit the longitudinal distribution emission distribution of detected charged particles at large angle (Equation (3)). Figure 14 (top) shows the measured longitudinal emission distribution x PMMA for all the detected charged particles using the data sample collected at 90 • (solid line) for a 220 MeV/u 12 C primary beam, with a superimposed depth-dose profile as calculated with the FLUKA MC code [18,19] (hatched-area distribution). A clear correlation between the rising edge of the x PMMA distribution and the beam entrance position in the target can be observed. The bottom panel of Figure 14 shows how the distribution can be well described by the function of Equation (3) which turned out to be able to describe all the emission profiles measured for different isotopes and data samples taken with different geometrical conditions (beam entrances) and angle configurations (60 • and 90 • ). The bottom panel of Figure 14 also shows how two quantities, 40 and δ 40 have been defined in order to characterize the longitudinal particle profile. 40 represents the width of the f (x) distribution at 40% of its maximum with X left and X right being, respectively, the corresponding x values at the rising and falling edges. Instead, δ 40 is the distance between X left and the x-intercept of the tangent to f (x) at x = X right .
These two quantities can be correlated with the Bragg peak position by means of a calibration campaign to be performed with data taken with different ion species, ion energies, target thickness, and composition. Such measurements of secondary charged particles at large angles are also needed to benchmark MC codes in order to be able to provide reliable predictions in real-case treatments scenarios of online beam range monitoring.

Conclusions
The development of CPT is a task to which nuclear physicists can and must contribute in collaboration with physicians, biologists, and medical physicists. The contributions of nuclear physics to CPT can be of different nature and this review has covered only a very limited part of the relevant research items.
The main topics concern the study of the nuclear interactions of the hadron beams at therapeutic energies with the typical nuclei composing human tissues. This can be important to improve treatment planning. At the same time, the development of the nuclear interaction models is needed for the improvement in MC simulation codes. These tools are important to provide more accurate dose calculation algorithms and are also useful to verify and correct the prediction from analytical TPS. The coupling of MC codes to radiobiological models is a further research topic. A more reliable prediction of the production of different nuclear fragments is also important to increase the robustness of RBE evaluation.
CPT is mainly performed with proton beams. The interest on the use of heavier ions is now increasing. This can be not only convenient from the point of view of biological effectiveness, but also to achieve a sharper lateral spread, thanks to the reduced MCS. On the other hand, the impact of the nuclear fragmentation processes is of course more relevant for heavier ions.
A further important topic where nuclear physics is relevant is the development of new specific detection systems for imaging, dosimetry, and beam range monitoring. Actually, the reduction in range uncertainties is still one of the most important issues. No clinical standard for this purpose exists at this time and several research groups are working to develop the required techniques and devices. The goal is to have methods capable of providing monitoring in real time, during the treatment itself. The comparison of measurements with predictions, specifically calculated case by case, can help to get a prompt signal in case of a mismatch between the measured and planned beam range, thus allowing to stop the irradiation and considering its replanning. In order to achieve this possibility, both dedicated detection systems and fast data reconstruction techniques are necessary.
Last, but not least, one has to remind that the most serious limitation to the spread of CPT is still the higher costs with respect to photon radiotherapy, due to acceleration systems (expecially in the case of ion therapy), gantries, and dedicated buildings. In proton therapy, the economical impact of gantries might be of particular relevance. Ref. [83] analyzes the experience gained in more than 4300 clinical cases, introducing a discussion on the possibility of facilitating proton therapy by means of gantry-less facilities. The goal of achieving a more favorable balance between costs and benefits in particle therapy is now one of the priorities for the interested scientific community. To this aim, important contributions might come also from technological advances in accelerators and beam delivery systems.