Università degli Studi di Catania Dottorato di Ricerca in Fisica - XXII ciclo

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Università degli Studi di Catania

Dottorato di Ricerca in Fisica - XXII ciclo

FRANCESCO ROMANO

Monte Carlo simulations of carbon ions fragmentation in hadrontherapy

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HESIS

Tutor:

Chiar.mo Prof. Salvatore Lo Nigro Supervisor:

Dr. Giacomo Cuttone PhD coordinator:

Chiar.mo Prof. Francesco Riggi

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Introduction

Radiotherapy, also called radiation therapy, is the treatment of cancer and other diseases with ionizing radiation. Ionizing radiation deposits energy that in- jures or destroys cells in the area being treated, the "target tissue”, by damaging their genetic material and making it impossible for these cells to continue to grow. The major goal of Radiotherapy is to maximise the dose in the tumour volume and to spare the surrounding normal tissues as far as possible. In other words a compromise between the local control of the tumour and the possible emergence of complications has to be found in order to have an enhanced probability of success in the cure.

Hadrontherapy is a radiotherapy technique which uses “hadrons”, i.e. colli- mated beams of compound particles made of quarks, for the sterilization of tumour cells. With this collective word, several forms of radiation therapy are usually indicated, such as neutrons, protons, pions, antiprotons, light ions and heavy ions.

Heavy ion therapy is a novel technique of high precision external radiotherapy which, in particular, yields a better perspective for tumour cure of radio- resistant tumour and it has given indisputably a boost to the use of radiation in the fight against cancer.

Indeed, cancer represents today one of the most serious diseases which affect a continuously growing number of people in the world. In the developed country about 30% of people suffer from cancer and every year about 20000 oncological patients are treated with high-energy photons. Unfortunately, for the 18% of all cancer patients the local control of the primary tumour without metastases fails.

Hence, in this case, innovative and more advanced techniques, such as ion ther-

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apy, may increase the probability of cure.

The driving force in more than one hundred-year history of conventional radiotherapy was the search of higher precision and greater biological effectiveness of the applied dose. The former could be reached by increasing the energy of the photons yielding a shallow decay of the dose in depth. The higher effectiveness was tested by the additional application of hyperbaric oxygen and drugs as radiation sensitizers. Finally it was the higher physical precision that contributed to the elevated tumour control rate in conventional radiotherapy with x- rays. Nowadays, sophisticated treatments like IMRT (Intensity Modulated Ra- diation Therapy) try to optimize the dose distribution and confine it within the tumour.

In the contest of improving radiotherapy by better targeting and, on the other hand, achieving a larger effectiveness, the transition to hadron beams like neutrons, protons and heavier opens a new age in the radiation therapy field. First trials were done with neutrons, which showed how a greater tumour-control rate could be achieved, especially for radio-resistant tumours. However, because of their poor depth-dose distribution, the damage was too large also for normal tissues outside of the target volume, leading to sever side effects.

The clinical use of protons and carbon ions was firstly proposed at the Berk- ley Cyclotron by Wilson, who measured depth dose profiles with a significant increase in dose at the end of the particle range, giving rise to the so called Bragg peak. First patients were treated with protons in 1954 and some years later first trials with heavier ions started. The motivation of this transition relies on the fact that heavier ions combine the more favourable dose distribution of the protons to the benefits coming by an enhanced Relative Biological Effective- ness (RBE).

After several years of study and experimentation, around the 90’s the scientific community involved in hadrontherapy studies was concordant in indicating the carbon ions as the optimal choice. Till now about 3500 patients have been treated with carbon ions worldwide. Energies of about 400 AMeV are necessary to reach deep-seated tumours.

The rationale of this choice has to be searched at macroscopic as well as at

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Introduction

3 microscopic level. The advantages of carbon ions, indeed, can be summarized as follows:

- Carbon ions deposit most of their energy towards the end of the range, i.e. in the Bragg peak, where they can produce sever damage to the cells while sparing the transverse healthy tissues as well as tissues deeper located.

- They penetrate the patient with minor lateral scattering and longitudinal straggling, which are about 3 times lower than protons’ ones. Moreover, carbon beams can be formed as narrow focused and scanning pencil beams of variable penetration depth, so that any part of a tumour can be accurately covered.

- Carbon ion beams undergo nuclear interactions along their path inside the tissue, so that positron emitting isotopes are yielded, allowing the use of in- novative techniques such as the on-line PET (Positron Emission Tomogra- phy). The location where the dose is deposited can be determined with a high level of precision, therefore critical structures can be preserved.

- Beams of carbon ions show a favourable depth profile of the RBE. Indeed, in the entrance channel they mostly produce repairable damages, meanwhile in the last part of their path (where the target tumour is present) they cause more serious effects, showing enhanced RBE values in that region. Hence, for radio-resistant tumours they are more effective.

These points clearly indicate the benefits coming from the use of carbon ions respect to the conventional Radiotherapy with photons. Moreover, the last point probably represents the main advantage of carbon ions also respect to protons.

To completely take advantage from the use of carbon ions in radiation therapy, a powerful tool, able to handle all the physical and biological parameters involved in this radiation technique, has to be used. This task is fulfilled by the Treatment Planning System (TPS). The TPS is a complex computer tool which permits the computation of the biological effective dose to be delivered to the patients, translating the prescribed dose in a set of information necessary to the radiation treatment design. Some commercial products are already implemented in some ion therapy centres, but substantial improvements could be achieved.

For this aim, INFN (Istituto Nazionale di Fisica Nucleare) has recently approved

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the “TPS project”, in which the Laboratori Nazionali del Sud (LNS) of Catania are involved.

In the last years INFN has showed a great scientific interest on hadrontherapy. Moreover at LNS a long experience in this field has already been matured.

Since 2002, indeed, the facility CATANA (Centro di Adroterapia e Applicazioni Nucleari Avanzate) is in operation at LNS for the treatment of eye melanoma.

Proton beams are accelerated by a Superconducting Cylocron (CS) and extracted at 62 MeV. With this energy, the depth of 3 cm in eye-tissue can be reached and thickness of some cm can be covered exploiting the passive scattering beam line realized at the CATANA facility. Up to now, about 200 patients have been treated and a local control of the tumour has been obtained in the 96% of cases.

The work and the results discussed in this PhD thesis have been carried out at LNS within the research group acting in the hadrontherapy field and developed in the contest of the TPS project. In particular, the issues related to the production of secondary particles by inelastic interaction of the carbon ions with the matter have been faced. Indeed, a part of the highlighted advantages, the main drawback coming from the use of carbon ions relies on the nuclear fragmentation of carbon ion beams, with the consequent production of charged fragments.

The reaction products are mostly produced by projectile fragmentation, so that they are characterized by an emission velocity close to that of the primary parti- cles. Final result is the formation of a typical “tail” of dose just behind the Bragg peak, which is due to the contribution of fragments created along the path of primaries. The higher is the energy of the incident ion, the lower is the peak, because of a great number of inelastic interactions, and the greater is the amount of extra-dose in the tail.

Fragmentation reaction may occur already at the stage of acceleration of the beam, especially when passive scattering systems are used as beam delivery systems. Anyhow, the contribution of fragments production coming from the interaction of the beam along the beam transport line can be drastically reduced by means of relatively simple technical expedients. What is instead unavoidable is the nuclear fragmentation inside the patient itself, which is somewhat intrinsic.

This aspect has to be taken into account by the TPS calculations, especially

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Introduction

5 when critical structures are close to the distal part of the Bragg peak, where an undesired amount of dose could override the advantages above discussed. How- ever, consequences arising from carbon ion fragmentation have to be undertaken not only beyond the Bragg peak, but also in the whole radiation field, because nuclear reactions occur since the first depths in the patient-tissue. This fact means that, as the primary carbons traverse the matter a continuously growing number of secondary particles is produced “travelling” together with the primary ions and giving its contribute in terms of dose. In other words, a mixed radiation field is created along the depth, composed mostly by the primary but also by a not negligible number of nucleons and light ions. What complicates the description is the fact that each isotope is characterized by a different RBE. Biological effect, indeed, depends on various quantities, such as the atomic number and the local ionization density of the specific particle considered. The latter is quantita- tively described by the Linear Energy Transfer (LET). All these aspects get more importance in the case of using more than one irradiation field, creating even more complexity in mixed radiation fields.

A reliable TPS must take into account all these parameters in order to accurately compute the biological dose to be delivered. It is evident that a pure analytical algorithm could not be able to reproduce a so complex picture. At this aim Monte Carlo methods probably represent the most powerful tool for ac- counting all these different aspects and it should be used as a base of development or at least as a tool of verification for TPS systems design. Monte Carlo methods, indeed, permit the dose computation in a more realistic way than analytical approach and, moreover, can give feedbacks also in particular configura- tions where experimental verification is difficult or not possible. The aspects just mentioned are wide discussed in the first chapter.

In the present work, the Monte Carlo code Geant4 has been used. Geant4 is a simulation toolkit used for particle tracking, able to simulate the interaction of particles with the matter and the production of secondary particles in a wide range of energy. Already used worldwide in the medical domain, in this work it has been exploited to study the fragmentation of carbon ion beams at energy range of interest in hadrontherapy. A general description of its main features to-

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gether with the physical models of interest, are discussed in the second chapter.

The accuracy of a Monte Carlo simulations is related to the reliability of the physical processes implemented, in particular the nuclear ones. Hence, for a realistic estimation of fragmentation products, nucleus-nucleus models inside the code have to be validated versus experimental data. In this work the Geant4 Bi- nary Light Ion cascade model has been used. Not many recent and accurate data are available in literature for carbon ion interactions on thin targets at the energy range of interest in hadrontherapy (60-400 AMeV), especially for nuclear fragments production. The situation is slightly different for neutron yields experiment, for which more accurate data can be found. Hence, a preliminary valida- tion of the nucleus-nucleus Binary Light Ion cascade model has been carried out by comparing neutron double differential cross sections obtained with Geant4 at different angles with experimental data found in literature. In particular data on

12C ion beams at 135 AMeV impinging on C, Al, Cu and Pb targets have been selected for the benchmark. Results and discussion are shown in the third chapter.

Even if some data on fragments production are available at very low energy (up to about 20 AMeV), there is a lack of data for charged fragments production at more intermediate energies. To contribute on covering this “gap”, an extensive campaign of measurements has been carrying out at LNS. We have already performed a first experiment with ¹²C ion beams accelerated at 62 AMeV impinging on a thin Au target. The apparatus used for the reaction products detec- tion was a Hodoscope of two-fold and three-fold telescope detectors, displaced in order to detect most of light projectile fragments which are mainly forward produced. The experimental apparatus has been simulated using the toolkit Ge- ant4. Used methods together with comparisons of angular distributions of charged isotopes and double differential cross sections are shown in the forth chapter. A detailed work has been developed in order to find the best solution in the simulation approach, trying to obtain the final results with acceptable computation time, preserving the level of accuracy. A first realistic simulation approach has been followed by a simpler and more performing one, used for final production of outputs.

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Introduction

7 After this preliminary validation work, which by the way has to be con- stantly updated in future with new benchmarks and verifications, a characteriza- tion of the mixed radiation field due to carbon ions at 62 AMeV has been undertaken in the fifth chapter. Here, a comparison of the total depth dose distribution of a 62 AMeV carbon ion beams transported in air and interacting with a thick water phantom has been also discussed. The experiment has been carried out at LNS, acquiring the depth dose with a ionization chamber positioned at different distances from the phantom window, thanks to an automated system. A brief description of the experiment is done and a comparison with the simulation is shown. Results have been obtained using the Hadrontherapy application, which is an advanced example included in the public release of the Geant4 toolkit. It has been previously developed by our group for the simulation of the CATANA proton beam line, and here customized on purpose in order to reproduce the experimental beam line used for the carbon ion Bragg peak acquisition. Instead, in the second part of the chapter an estimation of the dose and fluence contribution due to the charged fragments produced by thick PMMA targets have been car- ried out, with the aim of characterizing the mixed radiation field produced fur- ther to the primary particles fragmentation. As already pointed out, a detailed description of the radiation quality, i.e. isotopes, fluences, kinetic energy spectra and LET, have to be known for a better correlation with the biological damage on tissue. A Monte Carlo calculation has been developed to take into account all these parameters, computing the depth distribution of avaraged LET weighted on the isotopes fluence, including the contribution of all the secondary particles produced along the carbon ions path. The implemented method could allow a better interpretation of biological responses obtained with human melanoma cells irradiations, whose results are still under analysis. The method, developed inside the Hadrontherapy application, is briefly discussed and predicted results are shown.

Finally, the conclusions are reported, where a summary of the main obtained results is presented with future developments and perspectives.

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1. Radiotherapy with carbon ion beams

Cancer can broadly be defined as the uncontrolled growth and proliferation of groups of cells. In 1985, 750000 deaths were attributed to cancer, in the countries of European Community, which means one out of five cancer patients dies from this disease [1]. In developed countries about 30% of people suffer from cancer, 58% of them at the stage of a localised primary tumour. Unfortunately an increasing trend of the cases is still observed and nowadays about 1 million deaths per year are due to this disease [2]. The growing number of patients suf- fering from cancer requests for adequate treatments, which may depend on tumour type, stage and diagnosis. In Europe about 45% of all the patients is

“cured”, which means that these patients have a symptom-free survival period exceeding five years. Today, there are various possible methods to heal cancer:

surgical removal of the tumour tissue, radiotherapy, chemotherapy and immuno- therapy. Surgery and radiotherapy alone are successful in 22% and 12% of cases respectively and, when combined, they account for another 6% of cases. How- ever, for the 18% of all cancer patients the local control of the primary tumour without metastases fails; in these cases, patients could be cured successfully if improved local treatment techniques were available. One of these is the radiotherapy with proton and ion beams, more recently developed, which today is very attractive as regards the maintenance of high quality of life [3].

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1.1 From the conventional Radiotherapy to the Ion Beam Therapy

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1.1 From the conventional

Radiotherapy to the Ion Beam Therapy

There has rarely been another finding of a physical phenomenon with a similar impact to medicine as Wilhelm Conrad Roentgen’s discovery of the X-rays in 1895. A carefully reasoned description of his work together with the famous radiograph of his wife’s hand was published in a short time: “Eine neue Art von Strahlen” (i.e.: “On a new kind of rays”). While the implication for medical di- agnostic had already immediately been foreseen by Roentgen himself, the idea of a benefit from their use in benign and malignant conditions came later. The first successful treatment, which also gave a scientific proof of the therapeutic effectiveness of X-rays was carried out in 1896 by Prof. Leopold Freund in Vi- enna, who irradiated and removed a hairy mole on the forearm of a patient [4].

But though some negative effects on the skin were soon observed, it took until 1904, when Edison’s assistant Clarence Dally died following injuries to his hands and arms [5], that physicians and physicists took the possibly fatal power of the X-rays into account. Up this time and also for some years later radiation therapy remained a more or less empirical science where the major progress originated from clinical application. In the historical development of radiotherapy two general tendencies are visible: the clinical results are improved on one hand by a greater conformity of the applied radiation to the target volume and on the other hand by an increased biological effectiveness of the radiation [6].

Regarding the first one, improvements in radiation therapy are sensibly influenced by the technological progress, which implies the born of different tech- niques. The earliest radiation sources were provided by gas-filled x-ray tubes. It was W. D. Coolidge who, in 1913, did the groundwork for the present-day x-ray techniques by developing a vacuum tube with a hot tungsten cathode. The earli- est tubes of this type, manufactured for general use, operated at a peak voltage of 140 kV with a 5 mA current. Unfortunately, x-rays generated by these tubes were fairly soft and, from the medical point of view, the depth-dose curves were

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particularly disadvantageous since the maximum dose would be delivered at the skin surface and then would rapidly fall off with the depth in the tissue (Figure 1.1).

Figure 1.1. Depth dose profiles of X-rays, Co-gamma and Roentgen-Bremmstrahlung. It is clearly visible the different dose contribute to the skin.

For this reason, during the early experience with vacuum x-ray tubes, first attempts were also made at searching for sources of a more penetrating radiation with attention focused on gamma emitting radionuclides. We are around in the 1950’s, which represents the era of cobalt sources for radiotherapy, containing several kilo curies of ⁶⁰Co. The energy of the emitted gamma made it possible to obtain far better depth-dose curves, showing a maximum at about 5 mm below the skin surface and markedly decreasing the dose to the superficial tissues, as visible in . However, the most important developments in radiotherapy arise from the megavoltage therapy. A high voltage accelerator was developed in 1932 by R. Van de Graaff and five years later the first hospital-based accelerator of this type, a 1 MeV air-insulated machine, was installed in Boston. Dramatic increase in the photon radiation energy was made possible by the development of the betatron, by D. W. Kerst, who in 1943 suggested its use as a radiation therapy tool. Anyway, the rilevant weight together with the low beam intensity

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11 and the small treatment field area, have contributed to the discontinuation of its production thirty years later. In the mean time, the advances made during the World War II made it possible to use microwave generators for electron accel- eration, leading to the born of the first radiofrequency linear accelerators, which were soon to take up a dominant place on the world market of medical accelerators [3].

By that time to today several technological improvements have led up to the development of innovative techniques, with the aim of overcoming limitations of an exponentially decreasing depth dose distribution and achieving an acceptable level of conformation. Nowadays, the most recent Intensity Modulated Radio- therapy (IMRT) uses multiple beams (6-10 entrance ports) pointing towards the geometrical centre of the target in order to conform the dose to the target and spare as more as possible the surrounded healthy tissues. The beams may be non-coplanar and their intensity is varied across the irradiation field by means of variable collimators (“multi-leaf” collimators), that are computer controlled.

Nowadays in the developed countries, every years about 20000 patients out of 10 million inhabitants, are treated with high-energy photons and about 8000 electron linear accelerators (linacs) are used worldwide for cancer treatment [7].

In other techniques, radioactive sources of low range emitters are implanted directly into the tumour to achieve a target-conform exposure. Intra-operative irradiation also tries to spare healthy tissue while maximizing the tumour dose at the same time.

As already mentioned, the second tendency which drives the historical development of radiotherapy is the searching of an increased biological effectiveness of the radiation. This interest led to the study of the effects of hypoxic sensitizers to decrease the radio-tolerance of some radioresistant tumours [8]. This method, however, fell short of expectations. Anyway, the greater interest to se- lectively increase the biological effectiveness opened also investigations on different kind of radiations, attempting to replace the electromagnetic radiation. In- deed, in order to overcome both the physical and the biological limitations of the conventional radiotherapy the use of neutrons, protons and heavier charged particles was proposed, which led to the born of the “Hadrontherapy”.

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“Hadrontherapy” is a collective word covering all forms of radiation thera- pies which use beams of particles made up of quarks: neutrons, protons, pions, antiprotons, light ions and heavy ions¹. As in the case of conventional radiotherapy, the use of hadrons for medical applications is sensibly influenced by the technological progress and it is strictly related to the historical development of the accelerators. Hadrontherapy started in 1930 with the invention of the cyclotron by Ernest Lawrence. In 1935 he asked his brother John, who was a medical doctor in Yale, to join him in Berkley and use the new powerful accelerator for medical purposes [10]. The two main applications were the production of radio- isotopes and, later, the therapeutic use of fast neutron beams. At the end of 1938, the first patients were treated with neutrons but the technique was primitive and the doses given to healthy tissues too high. Indeed, even if a better tumour control was achieved thanks to the increased biological effectiveness of neutrons respect to photons [11], the poor depth dose profile unfortunately compensated this advantage with severe late effects in normal tissues. For this reason, some years later, in 1948, after the effects evaluated on 226 patients, R. Stone con- cluded that neutron therapy had not to be continued [12]. Presently, therapy with low-energy neutrons has mostly phased out but high-energy neutrons and boron neutron capture are still subjects of clinical interest [13].

The beginning of hadrontherapy with charged particles is due to Robert Wil- son, who was one of Lawrence’s students. In 1945 he designed a new 160 MeV cyclotron and, one year later, one year later proposed the use of proton beams in radiation oncology [14]. In fact he had measured depth dose profiles at the Berk- ley cyclotron with a significant increase in dose at the end of particle range, the so called “Bragg peak”, which had been observed fifty years before in the tracks of alpha particles by W. Bragg² [16].

1 The term “Hadrontherapy” was widely accepted and increasingly used since the 1^st In- ternational Symposium on Hadrontherapy held in 1993 in Como and organized by U.

Amaldi, who first proposed this word in 1992 [9].

2 Already in 1904 W. Bragg described the peak absorption in the air of alpha particles, which he depicts as “[...] a more efficient ionizer towards the extreme end of its course”

[17].

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13 Figure 1.2. One of the original plots of the Bragg curve, from papers of W. Bragg [17].

Due to Bragg peak, the dose can be concentrated on the tumour target sparing healthy tissues better than what can be done with X-rays. It is interesting to remark that in his paper Wilson mainly discusses protons but he also mentions alpha particles and carbon ions. Two years later, researchers at the Lawrence Berkley Laboratory (LBL) conducted extensive studies on protons and confirmed the predictions made by Wilson. In 1954, the first patient was treated at Berkley with protons, followed by helium treatment in 1957 and neon ions in 1975 [15]. In the first trials at Berkeley, beam application methods used in the treatments were adapted from conventional photon therapy, in which the photon beam is passively shaped by collimators and absorbers. Thus, the energy modu- lation of charged particle beams was first performed with modified collimator and absorber techniques [19]. This was due to the fact that, at these early times, computer power was too poor for a control system necessary for more modern active beam techniques (see 1.4.1). Although these first methods did not take advantage of the possibilities of charged particles to a maximum, dose distributions could be reached which were superior than those of photon therapy of that time. Especially the increase towards the end of the particle range produced doses that are higher in the target than in the entrance channel (see 1.2.1). In ad-

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dition, the fast fall off of dose beyond the Bragg maximum allowed field geome- tries never possible with electromagnetic radiation.

These treatments were performed by mean of particle accelerators that had originally been built for nuclear Physics experiments and were then adapted to tumour therapy. This was the case in Berkeley as well as at Harvard proton cyclotron, which made the largest impact on the development of protontherapy and where, up to now, the highest number of patients have been successfully treated.

Some years later, other nuclear physics laboratory in USSR and Japan set up proton beams for therapy and in 1984 the Paul Scherrer Institute (Switzerland) did the same. The clinical proton beam currently used in the facility CATANA for eye melanoma treatments at Laboratori Nazionali del Sud (LNS, Catania, It- aly) is also an example of beams produced by a superconducting cyclotron (SC) for nuclear Physics experiments and adapted for the therapy.

Even if many times it was felt and said that the hadrontherapy field could not develop without dedicated facilities, this step took almost twenty years. Indeed, the first hospital-based centre was built at the Loma Linda University Center (California), which signed an agreement with Fermilab and treated the first patient in 1990. Afterwards, a smooth conversion from a physics laboratory to a hospital facility took place in Japan, where from 1983 to 2000 about 700 patients were treated at the Proton Medical Research Center (PMRC). Finally, USA proton therapy was further expanded during the 1990s. Over 50000 patients have worldwide been treated with proton beams by now and other facilities are under construction or in planning stages. [15].

As already mentioned ions heavier than protons, such as helium and argon, first came in use at Berkley in 1957 and 1975 respectively, where about 2800 patients received treatments to the pituitary gland with helium beams. Because of their increased biological effects, the interest toward this kind of beams grew up, so that about twenty years later argon beams were tried at the Bevalac facility (LBL). The main reason for an elevated biological effect is the increase in ionization density in the individual tracks of the heavy particles, where cellular damage becomes clustered and therefore more difficult to repair [20]. This pro- priety was found useful for treatment of radio-resistant tumours, but problems

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1.2 Rationale of ion beam therapy

15 arose owing to non-tolerable side effects in the normal tissues. Indeed first trials with silicon and neon ions did not give good results and, towards the end of the program, it was found that the charge of these ions was too large: undesired effects were produced in the traversed and downstream healthy tissues [21].

Bevalac stopped operation in 1993.

After several studies and experimental results, only at the beginning of the

‘90s carbon ions were chosen as the optimal ion option. In fact in the entrance their effects are similar to X rays and protons ones, while just at the end of their path in the matter, ionization density is definitely larger and more serious damage are there produced to the cellular systems (see 1.2.2). Thus light ions produce a radiation field qualitatively different from ones due either to photons or protons and succeed in controlling radio-resistant tumours, which respond poorly to conventional radiotherapy. The carbon choice was made in Japan by Y. Hirao, who proposed and built HIMAC (Heavy Ion Medical Accelerator in Chiba) in the Chiba Prefecture [22]. In 1994 the facility treated the first patient with a carbon ion beam of energy up to 400 AMeV, corresponding to a maximum range of 27 cm in water. In the same years the “pilot” project is launched by G. Kraft at GSI (Darmstadt, Germany). Since 1994 other three hospital-based

“dual facilities” (for carbon ions and protons) have either started treating patients or entered the construction phase.

1.2 Rationale of ion beam therapy

The main aim of radiotherapy is the loco-regional control of the tumour and, in some situations, of surrounding diffusion paths. In order to reach this scope, a sufficiently high dose must be delivered to the tumour, which may be considered as the target, in physical terms. It could be said that the target tumour is success- fully treated only if the applied dose is arbitrarily high enough but in practice it is more complicated. This can be easily understood starting from the definition of dose and looking at the so-called dose-effect curve.

By definition, the absorbed dose (D), or simply dose, is the ratio between the energy ED imparted by the irradiation to a small volume of material (tissue) and

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the mass of this volume of material. The ratio D = E_D/m is measured in gray (Gy). In conventional radiotherapy doses of the order of 60-70 Gy are deposited in the tumour tissues in amounts of about 2 Gy per session over about 30 days.

In the hypothesis of a fairly accurate identification of the target, it is possible to evaluate the probability of obtaining the local control of the tumour through the analysis of the dose-effect curves. They represent for tumour tissues the possibil- ity of obtaining the desired effect as a function of the dose delivered, and for healthy tissues the probability of producing serious or irreversible damage, al- ways as a function of the dose absorbed by the same tissue. In Figure 1.3 the thick line represents, as function of dose absorbed, a hypothetical dose-effect curve for a generic tumour tissue.

Figure 1.3. Dose-effect curves for neoplastic (A) and normal (B) tissues; compromise between local control of the tumour and damage to the surrounding healthy tissues is de- scribed by the ratio D2/D1.

The dashed line represents a dose-effect curve for the healthy tissue involved in the irradiation. As shown, to the absorbed dose necessary to achieve the probability close to 100% of obtaining local control of the tumour corresponds also a very high probability of producing serious complications in the healthy tissue, when this receives the same dose [2]. So, in the daily practice, the compromise between the local control of the tumour and the possible emergence of complica-

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17 tions has to be found and it represents the key to have more chance of success in cancer treatment. The possibility to find such a compromise can be expressed quantitatively by the therapeutic ratio. It is defined as the ratio D₂/D₁ between the dose corresponding to a 50% probability of producing complications D2 and the dose corresponding to a 50% probability of obtaining the local control of the tumour D₁. On the basis of these considerations, it is clear that the probability of curing the tumour without unwanted side effect increases in line with the ballis- tic selectivity or conformity of the irradiation delivered [3]. As it will be discuss more in detail in section 1.2.1, the probability of curing tumours can be increased by using charged hadrons beams because the adsorbed dose is more confined in the tumour tissue than electrons and photons one; this allows an enhanced ballistic precision. Moreover hadrons show increased biological effects respect to electromagnetic radiation and also respect to protons (see section 1.2.2). This last feature makes them more successful also in the treatment of radio-resistant tumours. Thus, considering these two different aspects, the therapeutic advantages of ion beams when compared to electron, photon and also pro- ton beams can be found at a macroscopic scale (high level conformation) as well as at the microscopic scale (possibility of varying the radiobiological properties).

The latter deals with microscopic distribution of the deposited energy, which changes when different ion beams are considered. For this reason it is often said hadrons as densely ionizing radiation, in contrast to the sparsely ionizing radia- tion such as X-rays, γ-rays and electrons.

1.2.1 Physical basis of ion beam therapy

The most prominent feature of charged particle beams for their use in radia- tion therapy is the inversed dose profile, i.e. the increase of energy deposition with penetration depth, which represents the most evident difference respect to electromagnetic radiation. As already mentioned, the increase of ionization density with range was first described for α particles in a publication by Bragg in 1903 [23], and was later confirmed for protons and heavier ions by Wilson[14].

In the interaction of photons with the matter the energy loss is mainly due to three processes: photoelectric effect, Compton scattering and electron-positron

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pair production. The relative probability of one of these interactions is a function of the incident photon energy and the atomic number Z of the absorbing mate- rial. On the other hand, the energy of the ions is mostly transferred to the target electrons that are emitted as δ-electrons (see section A.1). More than three quar- ter of the dissipated energy is used for the ionization process and only 10 to 20

% for the target excitation [24]. The interaction strength is directly correlated with the interaction time. At high energies the energy transfer to the target is small but grows when the particles are slowed down. The different physical processes which characterize respectively electromagnetic radiation and charged particles directly affect the different depth dose profiles. In Figure 1.4 (on the left) the depth dose profiles of proton and ion beams is compared to those of protons, neutrons and electromagnetic radiation.

Figure 1.4. On the left: comparison of depth dose profiles of photon, neutron, proton and carbon ion beams; the “inverse” dose profile of protons and ions is clearly visible in contrast to the less favourable profiles of electromagnetic radiation and neutrons. On the rigth: Construction of an extended Bragg-peak by superimposition of single Bragg-peaks of different energy.

For low-energy X-rays the stochastic absorption by photoelectric and Comp- ton processes yields an exponential decay of absorbed dose with penetration. For greater photon energies the produced Compton electrons are strongly forwardly scattered and transport some of the transferred energy from the surface to greater depth, yielding an increase in dose in the first few centimetres. For high energy

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19 electron Bremsstrahlung, which is mostly used in conventional therapy, this maximum is shifted a few centimetres from the surface of the patient’s body sparing the very radio-sensitive skin. In contrast, the energy deposition of charged particles like protons or heavier ions shows a completely different trend.

When ions enter an absorbing medium, they are slowed down by losing their kinetic energy. The specific ionization increases with decreasing particle velocity, giving rise to a sharp maximum in ionization near the end of the range. Thus the depth-dose distribution is characterized by a relatively low dose in the entrance region (plateau) near the skin and a sharply elevated dose at the end of the range, which in this case is finite and energy dependent (peak). The ballistic pre- cision of charged particles respect to electromagnetic radiation is evident. In- deed, in the surrounding healthy tissues before or just behind the Bragg peak the dose released is minimized as more as possible respect to the target volume and a better compromise is achieved.

However, a monoenergetic beam with a narrow Bragg peak makes possible to irradiate a very small, localized region within the body with an entrance dose lower than that in the peak region [26]. In practical use in therapy, the tumour volume to be treated is normally much larger than the width of the Bragg peak and the lateral spot of the particle beam. In order to fill the target volume with the necessary amount of stopping power particles the peak has to be “spread out”

in the longitudinal direction. This is achieved by superimposing several Bragg peaks of different depths obtained by appropriate selection of distribution of ion energies. The resulting dose depth distribution, known as spread-out Bragg peak (SOBP) shows an “extended” Bragg peak area which has to accurately overlap the target volume (Figure 1.4, right). The use of ion beams allows tumor conform treatments of enhanced quality respect to those obtained by conventional radiotherapy [25]. In fact, even if the peak-plateau ratio decreases for SOBP respect to a pristine Bragg peak, the final result is still satisfying if we look at depth dose profile for photon beams.

The interesting behaviour of charged particles is due to their electromagnetic interactions with the matter. Within the range of therapeutically relevant energies of some hundred AMeV down to rest, the process of energy loss is domi-

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20

nated by inelastic collisions with atomic electron. The average energy loss per unit path length, the so called electronic stopping power, is well described by the Bethe-Block formula [27-29]:

( )

v f dx Z

dE ₂

=

− (1.1)

with Z and v respectively the charge and velocity of the projectile. Details on the dependencies of the formula and relative corrections are given in section A.1.1.

In the energy range of interest in hadrontherpy, dE/dx is mainly dominated by the term 1/v² ≈ 1/E. Moreover, at very low energies, when the projectile velocity is comparable to the velocity of the orbital electron in the materials, there is a high probability that the projectile picks up these electrons. Thus the charge changes and Z has been replaced by Z_eff (the effective projectile charge) which is well described by the Barkas formula [30]:

) 1

( ³

2

125 Z

eff Z e

Z = − ⁻ ^β (1.2)

with β = v/c. Considering these dependences, at not relativistic energies, the energy loss rate grows up as the kinetic energy of the projectile decreases along the penetration depth, in particular in the last few millimetres of the particle path where it shows a much steeper rise. That is the reason why the distribution of the ionizing density produced by the charged particle along the track is characterized by a rather constant plateau, followed by a sharp maximum towards the end, where gives rise at the Bragg peak. Anyway, at the end of the path the stopping power drops because of the rapid reduction of the effective charge Z_eff to very low energy values. The relation between electronic stopping power and particles energy is shown in Figure 1.5 for energy range and ions which are of interest in hadrontherapy. As expected, each particle exhibits a dE/dx curve which is dis- tinct from the other particle types.

Once the stopping power is known, it is possible to calculate the range R of a charged particle. It is the distance it travels before coming to rest. The reciprocal of the stopping power is the distance travelled per unit energy loss.

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21 Figure 1.5. Energy loss of different particles as function of the energy; as the atomic number increases the stopping power grows up.

Therefore the range R(E) of a charged particle having kinetic energy E is the integral of the reciprocal of the negative stopping power [34]:

∫

^⎜_⎝^⎛ ^⎟_⎠^⎞⁻

=

0 1

0

) (

E

dx dE E dE

R (1.3)

This equation provides a well defined value but in reality the energy loss processes are affected by statistical fluctuations which are responsible of a dis- persion of the path length (range straggling).

Moreover, fluctuations in energy loss and multiple scattering processes yield an almost Gaussian energy loss distribution f(∆E) given by [31][32]:

( )

⁽ ² ⁾

2

1 _σ

πσ

E E

e E

f

∆

−

∆

=

∆ (1.4)

where σ is the straggling parameter which expresses the half-width at the (1/e)-th height [33]. Hence, statistical fluctuations of energy loss cause a smearing of the range of the stopping particle beam and, consequently, a larger width of the Bragg peak experimentally measured. Range straggling effects for ion beams vary approximately inversely to the square-root of the atomic mass and increase

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22

as the penetration depth grows up. Indeed, at the same penetration depth heavier ions show narrower Bragg peaks and also a steeper distal fall-off, which has a positive effect on the final level of conformation of the radiation to the tumour.

A typical fragmentation tail is also well distinguished in case of heavy ions, but this aspect with its implication will be discussed ahead (Figure 1.6).

Figure 1.6. Depth dose distribution of photons, protons and carbon ions of 254 AMeV and 300 AMeV; comparison with 135 MeV protons (having the same range value) shows the difference in the Bragg peak width. Moreover, higher incident energies (i.e.

higher ranges) correspond to higher peak widths.

For greater particle energies and longer penetration the half width of the Bragg maximum becomes larger and the height smaller. Typical values for Car- bon ions are given in Table 1.1 [35].

Energy (MeV/u) 90 180 270 330

Range (mm) 21.3 82.8 144.3 200.5

FWHM (mm) 0.7 2.3 5.0 7.0

Table 1.1. Typical values for carbon ions Bragg curve.

Anyway, more significant for clinical applications are the consequences of

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23 multiple scattering processes in the lateral scattering of the beam, especially when the beam has to pass near critical structures which sometimes can be placed adjacent to the tumour volume. Multiple scattering of an incident ion stems from the small angle deflection due to collisions with nuclei of the traversed material. Numerous small angle deflections in an ion beam lead to lateral spreading of the incident ions away from the central trajectory resulting in larger divergence of the beam. Elastic Coulomb scattering dominates this process with a small strong-interaction scattering correction. The angular distribution of the scattered particles is roughly Gaussian for small deflection angles, and the mean beam deflection is approximately proportional to the penetration depth. The Coulomb scattering of the projectiles is described very precisely in the theory of Molière [36] [37]. Measurements of proton scattering confirmed this theory [38]

and a parameterization for small angle scattering having an angular distribution f(α) [39]:

( )

^α^σ^α

πσα

α ²

2

1 ⁻

= e

f (1.5)

with

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ +

=

rad rad

p L

d L

Z d pc MeV

log10

9 1 1 1

. 14

σ_α β (1.6)

where σα is the standard deviation, p the momentum, Lrad the radiation length and d the thickness of the material. At low energy, multiple coulomb scattering in- creases and, in general, the effects are more evident for lighter ions. In Figure 1.7 (left) the lateral scattering of a therapy beam is compared for 21 MeV photons, for protons and carbon ions of a range of 14.5 cm in water. The comparison clearly that for protons the lateral scattering exceeds the photon value for penetration depth larger than 7 cm. The lateral deflection of carbon beams is better than 1 mm up to a penetration depth of 20 cm. As expected, carbon ions exhibit a less pronounced lateral deflection, and they are well confined respect to proton beams. This fact represents another advantage of the clinical use of carbon ion

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24

beams and it also contributes to an enhanced ballistic precision.

Figure 1.7. On the left: comparison of the lateral scattering of photon, proton and carbon beams as function of the penetration depth [35]. On the right: comparison between lateral distribution of dose deposited by proton and carbon ion beams having approximately the same range; the comparison clearly shows the improved selectivity of carbon ion beams respect to protons [40].

Effects on lateral broadening are much more evident looking at the so called apparent penumbra, which is the sharpness of the lateral dose fall-off [40].

Heavier ion beams exhibit sharper lateral dose fall-offs at the field boundary than lighter ions: in Figure 1.7 the penumbras of proton and carbon beams are compared. The penumbra width increases essentially linearly with the penetration depth of the beam. For low-Z ions, such as protons, sharpest dose fall-offs are obtained when the final collimator is at the surface of the patient. For higher- Z ion beams, such as carbon ion beams, active scanning techniques without col- limations will produce narrow penumbras.

So far, physical effects related to electromagnetic interaction has been discussed. When a heavy ion beam passes through beam line elements and finally traverses the tissues, nuclear reactions take place as well, which cause a small but not negligible amount of nuclear fragments. The result is a reduced number of primary particles reaching the tumour which are replaced by a certain number of secondary particles. An interesting potential for quality control arises from nuclear fragmentation, which by far compensate for the disadvantages, discussed

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25 ahead. Concerning the advantages, the stripping of one or two neutrons from the projectile ¹²C yields the positron emitting isotopes ¹¹C and ¹⁰C with half-lifes of 20 min and 19 sec, respectively. The stopping point of these isotopes can be monitored by measuring the coincident emission of the two annihilation gamma quanta following the β⁺ decay. In general, most of the lighter fragments have the same velocity as the primary ions at the collision [42]. The range of these fragments is given by the formula:

2 2

fr pr

fr pr pr

fr M Z

M R Z

R = (1.7)

with R being the range, Z the atomic number, Mfr and Mpr the masses of the fragments and the projectiles, respectively [25]. Hence, the range of carbon isotopes is only slightly shorter than that of the primary particle:

) 12 ( ) 11

(¹¹ ¹²

2 R C R C

Z

R∝ A → = (1.8)

Thus, from the measured distribution of the annihilation quanta, the range of the stopping particles can be controlled and compared to the calculated range in the treatment planning, providing an in-situ beam monitoring using Positron Emission Tomography (PET). In fact, it is further expected that the spatial distri- bution of β⁺-activity induced by heavy-ion beams is strongly correlated with the corresponding dose distribution. Even if carbon beams mostly produce ¹¹C and

10C nuclei via projectile fragmentation, also ¹⁵O nuclei are produced from the target [41].

In Figure 1.8 depth-dose distributions of β⁺-emitters and primary particles in case of proton and carbon ion beams are shown. In contrast to the proton irradiation, the maximum of β⁺-activity produced by carbon ions is clearly visible. In this second case, the β⁺-activity shows a prominent maximum, shortly before the peak, formed by ¹¹C and ¹⁰C fragments of the ¹²C projectiles. Hence, all the ¹²C isotopes are stopped before the Bragg peak and the sharp fall-off in the β⁺- activity distribution clearly indicates the position of the Bragg peak [43].

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26

Figure 1.8. Calculated depth distributions of deposited energy (dash-dotted curves) and β⁺activity (histograms) for (a) 110 MeV protons and (b) 212.12 AMeV ¹²C nuclei in the PMMA phantom. The distributions of ¹¹C, ¹⁰C and ¹⁵O nuclei are shown by the long- dashed, dashed and dotted histograms, respectively, and their sum is shown by the solid- line histogram. The distribution of actual e⁺-annihilation points is shown by the solid- line histogram [43]. All the distributions have been calculated with the Monte Carlo code Geant4.

PET monitoring is of great interest in the hadrontherapy field because provides a direct measurement of the beam distribution inside the patient and it represents as well another great advantage coming from the exploitation of carbon ions in radiotherapy. The calculation of projectile range is, in fact, a critical point in treatment planning because human body is composed of a large variety of materials with different densities (bones, muscles, fat, air-filled cavities, etc).

Unfortunately, from another point of view beam fragmentation represents also the main disadvantage of using carbon ion beams for tumour treatments. Ion beams suffer nuclear reactions by interacting with the elements present along the

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27 beam line as well as inside the tissue itself, as already discussed. The first contribution can be opportunely reduced, and it is strictly dependent on the beam delivery system used; active systems are in this sense advisable (see 1.4.1). The second one is an intrinsic contribution and therefore not eliminable, but it is important to know in details the effects on the delivered dose. According to the equation (1.7) the lighter fragments have a longer range than the primary particles and, thus, are responsible for the undesired dose behind the Bragg peak, usually called tail. In Figure 1.9, the normalized depth-dose distributions in case of SOBP are showed for proton, carbon and neon ion beams having the same range and the tails are clearly visible for ions.

Figure 1.9. Comparison of spread out Bragg peak (SOBP) for proton, carbon and neon beams with the same range in water. Tails due to fragmentation are evident for ion beams and more dramatic for neon ion beams [19].

The increasing of the dose just boyind the paek strongly depends on the mass of the ion: in this specific case, it is of the order 15% of the dose in the SOBP for ions like carbon and oxygen, while it can reach 30% in the case of neon ions.

This is one of the reasons why, at least from the physical point of view, it is not justified to use ions heavier than oxygen for a really conformal therapy. More-

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28

over, also biological reasons can be address for the exclusion of very heavy ions, as discussed in the next section. Considering also the surface dose in percentage in the plateau region, carbon ions represent a good compromise.

However, the effects of fragmentation have to be carefully taken into account in treatment planning also because of the different biological effects characterizing the secondary particles produced, which give rise to a mixed radiation field. The study of fragmentation of carbon ion beam and the calculation of the fragments contribution in terms of dose and ionization density is a key point in hadrontherapy and it represents one of the aims of this work (see chapters 4 and 5). Indeed, for a volume irradiated by a parallel beam of ions, the absorbed dose D can be expressed as function of the ion fluence Φ and the stopping power (- dE/dx) by:

⎟⎠

⎜ ⎞

⎝⎛−

= Φ

dx dE D x

ρ )

( (1.9)

where ρ is the density of the stopping material. Because of the fragmentation processes, the particle fluence decreases with the penetration distance according to the relation:

)

) (

0 ( )

(x =Φ e⁻^µ^x

Φ (1.10)

where Φ(0) is the entrance fluence and µ is the linear attenuation coefficient, proportional to the total microscopic reaction cross-section σ for the ion-tissue interaction [34]. In principle, the dose distribution from each beam could be summed to obtain the total dose distribution. In practical radiotherapy it is not possible, because absorbed dose must be modified by a radiation weighting fac- tor that is energy dependent and changes according to the ion species considered.

The composition of this very complex particle field has to be known for dose op- timization in heavy ion therapy, in order to take correctly into account the global biological effect in the tissue, due to secondary as well as primary particles.

Trying to summarize what as been discussed, these are the main advantages showed by carbon ion beams from the physical point of view [45]:

- Carbon ions deposit their maximum energy density in the Bragg peak at the

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29 end of their range, where they can produce severe damage to the cells while sparing both the transversely adjacent and deeper located healthy tissues.

- They penetrate the patient with minor lateral scattering and longitudinal straggling respect to photon irradiation as well as proton beams. Moreover, being charged, they can easily be formed as narrow focused and scanning single beams of variable penetration depth, so that any part of a tumour can be accurately irradiated with optimal precision.

- The location where the dose is deposited by carbon ions can be determined by means of on-line positron emission tomography (PET), which permits exploitation of the millimetre precision of a focused carbon beam, crucial in case of target close to or inside critical structures.

Figure 1.10. Comparison of the planned dose distributions of a carcinoma in the front part of the head. Upper left: IMRT palnning with high energy photons. Lower left: passive proton application. Upper right: active application of protons. Lower right: active application of carbon ions which yields the best dose distribution. (Figures from M Krengly, CNAO, Italy).

In conclusion, a comparison of treatment plans of the same clinical case for different modalities is showed in Figure 1.10. The isodose curves demonstrate as carbon ions yield the best distribution respect to IMRT and also respect to proton

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30

therapy, both for passive and active scanning systems.

1.2.2 Biological basis of ion beam therapy

As already widely discussed, ion therapy shows some interesting physical features respect to conventional radiotherapy and also to more recent proton therapy. However, what makes ion beams really attractive is their enhanced biological effect. In some sense, heavier ions combine more favourable dose distributions of the protons and benefits from the high local ionization and, in particular, carbon ions represent the best compromise between local control of the tumour and negative side effects.

Changes in the biological effectiveness are the result of complex interplay between physical parameters, such as ionization density and biological parameters. In order to understand the relation between these different aspects, it is important to discuss at least from a qualitative point of view the modality of energy deposition at a microscopic scale. The deposited dose in a volume is not the only variable to take into account, because it gives indication of the total energy released. For the biological response the track of the particle represents the key information. For an incident charged particle, the ionization occurs along the trajectory of the particle and most of the energy loss is transferred to the liberated electrons, which form a sort of “electron cloud” around the trajectory of the primary ion, i.e. the ion track. Finally, the action of these electrons determines the biological response together with the primary ionization. It is the higher electron-density, and consequently the ionization-density, that yields a greater biological effectiveness.

The formation of a particle track can be regarded more in detail as a two- steps process: first the emission of the electrons by the ion impact and second the transport of these electrons through the material around the particle track, causing secondary ionization and energy deposition. The calculation of track structure is not a trivial task and it has been subject of many publications in which different approaches have been examined. Some groups have developed semi-empirical or analytical models, starting by simplified assumptions [46][47], others have exploited Monte Carlo simulations where each basic interaction is

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31 treated individually [48-50]. Although the various models vastly differ in their basic assumptions and their input data, the obtained radial dose distributions are very similar.

The diameter of a track depends on the range of the electrons and, consequently, on the velocity of the ion. At higher energy the track is wide and the energy loss is low, therefore the ionization events are well separated. With decreasing energy, the track narrows and the energy loss becomes larger. Consequently, the produced damage has a higher local density resulting in a diminished repara- bility of the lesion and, therefore, an increased biological effect.

Figure 1.11. Left: schematic view of an undamaged part of DNA (A), two separate single strand breaks (B), a double strand break (C), and a “clustered lesion” (D); the (*) indicate a base damage. Right: the structure of a proton and a carbon track in nanometre resolution with a schematic representation of a DNA molecule; the higher density of secondary electrons, produced by carbon ions, creates a large amount of clustered DNA damage.

The main target of the radiation attack is the DNA (deoxyribonucleic acid) inside cells nuclei. DNA is a very complex system and its integrity is essential for cells survival. Therefore DNA is highly protected by an extremely elaborate repair system so that DNA violations like single strand breaks (SSB) or double strand breaks (DSB) are rapidly restored. But when DNA is exposed to very high local doses, where local refers to the scale of a few nanometres, the DNA lesions become concentrated or clustered and repair system fails to correct the damage, as seen in Figure 1.11 (left) [45].

In general, the energy released by the primary ions is distributed over the volume of the track with a steep gradient of local dose over many orders of

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32

magnitude, from milli-Grays at the maximum track radius- to mega-Grays in the center [44].

From the previous considerations is evident the difference between densely ionizing radiations, like carbon ions or more in general heavier particles, and sparsely ionizing radiations, like X-rays. The latter, in fact, produces damage in a stochastic manner, where the dose is distributed randomly throughout the cell, giving rise to more reparable lesions. For carbon ions, higher local ionization densities are reached also respect to those obtained with protons. Indeed, for the latter the energy loss is small and the individual ionization events are far from each other, giving rise to more easily reparable DNA damages (Figure 1.11, right).

From the quantitative point of view, the energy deposition along the track of the particles in the tissue is represented by the Linear Energy Transfer (LET), measured in keV/µm and defined as the ratio between the energy dE deposited by a charged particle in a track element and its length dx, considering only single collisions characterized by energy deposition within a specific value ∆:

∆

∆ ⎟

⎠

⎜ ⎞

⎝

=⎛ dx

L dE (1.11)

It is sometimes called also “restricted energy loss” or “restricted LET”. If no limitation in the amount of energy released in any single collision is considered, it is called “unrestricted energy loss” and it is indicated wit L_∞. Hence, the previous classification of radiations is strictly dependent on LET values: high LET radiations produce more microscopic damages and, thus, they are more biologi- cally effectiveness respect to low LET radiations. Thus, in a high LET track the damage is produced in high density and consequently as “clustered lesions” that are, to a large amount, irreparable. Moreover, by considering a specific kind of particle, LET is sensibly variable with the penetration depth.

Even if there is not a sharp limit between high and low LET values, for many cell systems the biological effectiveness starts being important if LET becomes greater than about 20 keV/µm. LET values of light ions are summarized in table 2 for the range corresponding to 200 MeV protons (262mm of water)

Università degli Studi di Catania Dottorato di Ricerca in Fisica - XXII ciclo