Particle physics for biological interactions

This term is used to describe the variation in path length caused by differences in energy and velocity reduction through a medium or tissue, due largely to differences in interactions along the beam path due to variations in electron density/tissue composition and other stochastic events. It normally denotes a blurring-like effect on the beam towards its distal edge, but there is also some degree of lateral straggling for particles that are more easily scattered. Thus, the beam edge is not so sharp with protons, which are lighter than helium or carbon ions. For even heavier ions, such as carbon, there is a distinct fragmentation tail caused by nuclear interactions and emitted γ-rays, which results in a tail of dose beyond the end of the Bragg peaks. For lighter particles, such as protons, fragmented ions do not occur but, as with heavier particles, the tissue interactions can cause emission of γ-rays and some neutrons.

The coulombic forces due to the nuclear charge will cause charged particles to separate from each other gradually in proportion to their tissue depth, and also in inverse proportion to their mass and velocity. This will occur in a beam traversing a vacuum. This is often referred to as 'coulombic scattering', but in matter will also include much wider angle scattering due to repulsive charge interactions with atomic nuclei (as in the classical example of Rutherford scattering). So, protons (charge = 1, mass unit = 1) will separate less than electrons (charge = 1, mass ≈ 1/2000 of mass unit), Compared to protons, heavier ions (also containing neutrons so they have mass greater than their Z number) show lesser deviation despite their increased charge, even if fully 'stripped' of electrons before their acceleration, although some particles will gain electrons during their transit through matter.

There appears to be no formal term that describes the average or median inter-track separation distances, which may contribute to biological effect changes over and above the LET, as discussed below. It is easy to crudely estimate the mean inter-track separation distance (s) by the following basic approach (see figure 1.2).

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The overall area A is divided by the number of tracks to provide A/N, the average area surrounding each track; if this is assumed to be a small square area (represented by s²), then A/N = s². If, on average, the track occupies the centre of each square, then the average track separation will be s, which is √(A/N), and which can also be expressed as $\sqrt{\frac{1}{F}}$, where F is the fluence (defined above). This might be an important parameter to use in the analysis of cell-survival studies and treatment outcomes, as it could modify the effect of LET and dose. For example, even if the LET parameter is calculated to be the same at, say, the mid-Bragg peak for the same particle type but accelerated to two quite different energies resulting in Bragg peaks at two different depths (where the particle energies will then be the same), any reduction in bio-effectiveness could be due to greater separation of tracks in the case of the particles that were accelerated to the higher energy. Such a process would depend on increasing track separation due to coulombic scattering, and even more so on the deliberate use of scattering filters, causing ISL geometric dispersion of the beam at increasing depths.

This can be further expressed in a very simple way. Consider tracks of radius a, with volume πa² x when considered as a cylinder extending to depth x. The inter-track distance is s, so that the fractional volume occupied by a single track compared with its surrounding volume of s² x is

$$\begin{eqnarray*}&&\frac{\pi {a}^{2}x}{{s}^{2}x}=\frac{\pi {a}^{2}N}{A}=\pi {a}^{2}F\end{eqnarray*}$$

(since s² = 1/F = A/N).

For the same fluence, as the overall area (A) of a beam reduces, the closeness of tracks per unit area (and volume) increases. But if A increases, the fluence falls and the closeness of tracks decreases. For different ions the specific Katz track radius may be used.

Such an effect can actually be visualised using GEANT4 and FLUKA in-silico simulations, shown to the author by Dr David Colling (Imperial College) and Dr Francesca Fiorini (Oxford), respectively. Although LET may be similar for each track at each depth, their increased separation may be sufficient to diminish the bio-effect since more cell nuclear material or even whole cells may be un-irradiated. Some evidence for reduced bio-effectiveness with depth in the case of passively scattered beams is given below.

Synchrotrons and cyclotrons are the commonest accelerators used for charged particle medical beams. These terms can confuse since modern cyclotrons are in fact synchro-cyclotrons, but the more basic nomenclature remains useful. Printing space does not permit a full description of these. For a summary of how these accelerators operate the reader should refer to short accounts such as Peach et al (2011), designed for hospital readers, with more complete accounts by Wilson (2001) in his excellent textbook, which contains ample worked examples concerning beam control, etc. Suffice it to say here that cyclotrons operating from a circular cavity arrangement accelerate protons to their peak energy on extraction. To produce lower energies that result in Bragg peaks at depths less than the maximum range, the beam must be degraded within metal or plastic strips of differing thicknesses (which become highly radioactive and must be situated sufficiently remote from the patient because of induced radiation including neutrons). Cyclotrons deliver high dose rates (0.5–1 Gy s⁻¹). For example 12 Gy in 24 s is not unusual.

In contrast, synchrotrons, which are used to accelerate protons or particles heavier than helium, occupy a much larger floor space and operate by a single radiofrequency accelerator combined with magnetic focusing and defocusing bending the beam around a geometrical arrangement of magnets, which leads the beam back to the original point for further acceleration. The magnetic field strength must be carefully increased to match the particle energies at each 'cycle'. When the desired energy is obtained the 'particle bunch' is extracted and then delivered.

There are two options for controlling beam size: the pencil beams delivered from the accelerator can be passively scattered by a filter to a wider area, but with a small neutron contamination, depending on the efficiency and composition of the filter. The alternative is to use the pencil beam and magnetically deflect the beam to the positions required (active scanning), which avoids neutron production and provides better conformity of dose to the intended targets.

In each case the energies delivered from these accelerators have a spread in terms of energy and in spatial properties. There are some useful terms to denote these.

Luminosity refers to the total energy emitted, often expressed per unit time.

Emittance measures the average spread of particle coordinates with respect to their position in 3D space and their momentum, with dimensions of length (e.g. metres) or length times angle (metres times radians). In a low-emittance particle beam, the particles are confined to a small distance and have nearly the same momentum. The probability of particle interactions will be greater, resulting in higher luminosity.

Also, further beam parameters include energy spread (in standard deviations), pulse repetition rate (f), bunches per macropulse (Mb) and effective bunch rate (fMb).

Proton range uncertainties

The study of the RBE of different radiation qualities is important, since the RBE concept is used in the dose prescription process of hadrontherapy. RBE is defined as:

$$\begin{eqnarray*}&&{\rm{RBE}}=\frac{\text{dose of control}\;(\text{low LET})\; \text{radiation}}{\text{dose of test}\; (\text{higher LET})\; \text{hadron radiation}}\end{eqnarray*}$$

for the same bio-effect, using each class of radiation.

The numerator dose becomes the number by which RBE is scaled from values of one upwards, the denominator being less than the numerator.

The RBE is dependent on the LET of the radiation, with an initial increase in RBE being followed by a reduction at higher LET values due to overkill/or cell killing inefficiency, the turnover point being dependent on the nuclear charge (z) of the ion, but not, apparently, the cell type. The RBE is also inversely related to dose for reasons related to differences in cellular radiosensitivities and the slope of the effectiveness curves between the reference (or control) low LET radiation and the higher LET state. This is illustrated in figure 1.3, based on the linear quadratic model of radiation effect (E) where E = αd + βd², d being the dose, α and β are biological coefficients, with subscripts L and H for the low and high LET states; further details regarding the radiobiology are given in following chapters. The RBE falls from 1.27 to 1.2 due to the geometry of the curves and such a change is an inherent feature of the linear-quadratic model providing that the LET-induced increment in α exceeds that in β (further discussed in chapters 8 and 9).

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The RBE concept was included in the dose prescription system for fast neutron therapy and continues to be important in proton and ion beam therapy; it is also potentially relevant in nuclear medicine and some forms of brachytherapy, but has not yet been used in their clinical application.

In experiments to determine the RBE, the choice of the control (or reference) radiation has varied considerably; examples include low-voltage x-rays (100–200 keV peak) and orthovoltage (200–350 keV peak), along with variable degrees of filtration to remove the lowermost keV x-rays within the x-ray spectrum. Other examples include 137-caesium or 60-Co gamma rays, megavoltage electrons and, more rarely, megavoltage x-rays in the clinical range 4–10 MeV. The lower the energy of any beam, the greater the LET; this applies to x- and γ-rays, protons, and all ions and electrons, because lower energies result in more localised energy release and absorption, and a higher LET, and also results in more clustered DNA damage. This will increase the RBE up to a saturation level beyond which the RBE falls at even higher LET values. Conversely, at higher energies of a particle or photon beam, then local LET and RBE are reduced, because the ionisations are not so spatially clustered.

Since the reference radiation (sometimes called the control radiation) supplies the numerator dose for the RBE estimation, this must exceed the hadron radiation dose for the same bio-effect in order for the RBE to be greater than one. Should the control RBE irradiator have an LET that is greater than the test hadron LET then the RBE will be less than one. Choosing a control irradiator that has a higher LET than that of the photons/x-rays used in hospital clinics, will give a lower estimate of RBE than would be the case in the hospital setting for the same cellular system.

It follows that the choice of the reference radiation will have an important effect on the RBE ratio found. For example Hall and Gaccia (2011) quote typical LET values (keV μm⁻¹) of 2 for 250 keV (but the filtration is unspecified), 0.2 for 60-Co, 4.7 for 10 MeV protons and 0.5 for 150 MeV protons, while megavoltage photons are not mentioned. More comprehensive, but still incomplete, data can be found in ICRU report 16 (1970). These suggest, by extrapolation, that megavoltage photons in the clinical range of 4–8 MeV would have a LET value of around 0.2 keV μm⁻¹. A useful collation of data in Andrews (1978) shows a mean LET of 0.5 keV μm⁻¹ for 3 MeV photons and 60-cobalt irradiation, but stopping powers (or LET_∞) of 0.18 for 2 MeV electrons as well as being the theoretical minimum for any charged particle, and hence an important limit or baseline for relative biological effect studies. The average Compton electrons produced from 60-cobalt γ-rays have an LET_∞ of 0.26 keV μm⁻¹, so a slightly lower value around 0.2 keV μm⁻¹ would be expected from clinical range megavoltage photons.

Further information is contained in some publications, such as Spadinger and Palcic (1992), where an LET range of 5.5–6 keV μm⁻¹ is quoted for 25 keV x-rays and 1.7 keV μm⁻¹ for 122 KeV x-rays (the average value obtained with 250 KeV x-rays with 0.35 mm Cu and 0.4 mm Sn filtration), with a value of 0.2 keV μm⁻¹ for 11 MeV electrons, which are likely to closely resemble megavoltage photons in the clinical range.

From the above data, it seems reasonable to use a control radiation of either electrons of photons, according to the experiment being done, with an LET value of around 0.2 keV μm⁻¹, as would be achieved with a clinical photon or electron beam. The added value of having a megavoltage photon beam would be for comparative combined ballistic and radiobiological studies in humanoid phantoms between charged particles and clinically relevant photon energies.

Some important examples of the unsuitability of orthovoltage and lower voltage x-rays beams as the control/reference radiation are as follows.

• 1.  
  For the collated proton RBE data of Paganetti et al (2002), orthovoltage radiations, 14 low voltage or orthovoltage x-ray irradiations had an RBE of less than one and only one such experiment showed an RBE of just over one. The probability of this being due to chance or experimental error is low; use of the sign test provides the probability of there being no difference as p = 0.00061, a highly significant result.
• 2.  
  The literature contains a report by Amols et al (1986) who measured cell survival data in DLD-1 human tumour cells. Their results clearly demonstrate a statistically significant RBE difference between orthovoltage and megavoltage radiation (p = 0.001). A small difference was also measured in the RBE between megavoltage photons and megavoltage electrons, but the difference was not statistically significant (p = 0.25). All biological, dosimetric, and microdosimetric data were obtained under nearly identical geometric conditions, but using only one cell line.

The past literature contains many contributions that concentrate on the influence of lower photon energies in the low kilovoltage range on the RBE, but these are mainly in the context of radiation protection, because this class of x-rays are used so much in routine diagnostic medicine. Such work has confirmed that the RBE varies inversely with photon and particle energy (see, for example, the review by Hill 2004).

The RBE should be taken into account in clinical radiotherapy using positively charged particle beams, where RBEs can be significant even in the case of protons. Papers by Belli et al (2000), Britten et al (2013) and Marshall et al (2016), are examples of such work, containing well-documented experimental detail. There is presently a potential shift of opinion to include more flexible (or variable) RBE values than the constant values previously assumed in proton therapy, in order not to: (a) under-dose certain radiosensitive tumour classes and (b) over-dose late-reacting normal tissues of clinical importance. This is discussed in later chapters.

The urgent need to clarify RBEs in critical experimental normal tissues exposed to proton and other ionic beams will require careful choice of control radiation if the purpose of such studies is to provide information that will ultimately be useful for clinical purposes. Some potential forms of control radiations can easily be eliminated, as is the case for orthovoltage x-rays, despite their low expense and convenience, should be avoided, since they will lead to lower estimates of the RBE. 60-cobalt units also have some significant disadvantages. These include lower dose rates with time, since it is advisable to use the same exposure times (within differences of only 1–2 min at the most) for the control and test irradiations, due to ongoing repair of sub-lethal radiation damage. Longer treatments will have slightly lower bio-effectiveness and this will influence the estimated RBE ratio. Also, the need to compensate for radioactive decay on a weekly or monthly basis may sometimes be forgotten or wrongly applied; the LET can be lower than for megavoltage photons and there is drift of dose rate with time, and modification of source treatment distances to compensate for radiation decay, with accompanying changes in depth dose distributions. There are also problems associated with radiation protection of staff, shielding requirements, and source replacements required with time, are expensive, and have their own difficulties.

Some laboratories do have a 137-caesium irradiator, which is more compact, and delivers monoenergetic photons close to 0.5 MeV, which should have an LET close to that of cobalt beams. Again radioactive decay has to be compensated for and dose rate effects may accrue with time, although this can be overcome by using shorter source to target distances. Such a unit can be fitted into the size occupied by a large double refrigerator without additional shielding.

Megavoltage electrons are a reasonable choice for the control radiation in RBE studies. However, electron dosimetry, although much improved in recent years, has limitations due to its high scatter, especially for small field sizes, as well as an energy-dependent relationship of electron build-up with depth, which must be taken into account in any laboratory experiment. Electron fields are essentially SOBPs, often with lower RBEs than fields in megavoltage electron plateau regions, but there remains uncertainty as to their higher RBE values with fall off of dose and energy towards their end of range. It must not be forgotten that Auger electrons (from low energy radioactive emissions) can have very high RBEs. However a broad electron beam operating at, say, 8–10 MeV would give a satisfactory uniform dose for radiobiological experiments, but could not be used for beam ballistics combined with radiobiology comparisons.

There is interest in some particle therapy centres across Europe, including international laboratories like CERN, in addressing the clinically important RBE issue. For comparable results it is very important that the control radiation be standardised. The best standard to choose, despite the additional expense, would undoubtedly be megavoltage x-rays from a linear accelerator operating at typical energies used in the clinic. It is already the case that national radiation standards laboratories such NPL (Teddington, UK) contain a standard hospital linear accelerator for dosimetry comparisons and maintenance of standards. Likewise, laboratories that aim to contribute useful RBE data should use a control megavoltage linear accelerator with optional use of 4–10 MeV photons or electrons for their studies. A single 137-caesium source could also be useful.

Interestingly, since hospital linear accelerators are normally replaced every 10 years, it is relatively easy to obtain one that can be refurbished for experimental use. These would have a gantry for variable beam angles and collimation down to small field sizes.

In general, the RBE increases with depth due to the progressive increase in LET, especially within the Bragg peaks. However, there is evidence that if the same LET and dose is given at the same SOBP positions situated at markedly different depths, achieved by using a different incident energy, then the RBE is reduced in the deepest position. These intriguing experiments, led by V Megnin-Chanet (Institute Curie), were designed to study proton RBEs at various depths using the Orsay proton beams (Calugaru et al 2011), with two different incident energies of 76 and 201 MeV, with mid SOBPs at 20.5 and 160 mm, respectively, and also near the distal end of SOBPs at 26.9 and 185 mm, respectively, with identical LET characteristics towards their distal ends. The main physical differences appeared to be the beam widths: 3 and 12 cm diameters, respectively, indicating greater lateral dispersion at the increased depth after passive beam scattering. They observed a reduction in the RBE in two human cell lines from around the highest RBEs of 1.3–1.33 (at 3 cm depth) down to 1.0 (at 12 cm depth). Although the dose rates did differ with increasing depth, when DNA repair kinetics are considered the changes in minutes required to deliver the dose ranges used cannot account for the change in the RBE (the dose rate effect is discussed further in chapter 2).

In contrast, Britten et al (2013) found no such effect in two cell lines with incident energies of 87 and 200 MeV at Bloomington, where scanned beams were used. Scanned beams, without metallic filter-related scatter, essentially consist of parallel tracks and so deliver the shorter inter-track separation distance (s) over most of their range. They exhibit little geometric dispersion, so s is relatively well preserved with depth, only being affected by mild coulombic scattering, which manifests itself mostly near to the extreme range when energy and velocity are reduced. Alternative explanations for the findings of the Paris and Bloomington experiments might include chance, or a cellular batch effect, or the cell types used. These latter hypotheses are unlikely, as each Institute had used two different cell lines with different radiobiological properties.

The most obvious physical explanation of this phenomenon, although speculative, is the increasing track separation caused by divergence in passively scattered beams. There can also be an associated loss of RBE with depth owing to increasing γ-ray contributions, but these are small and would be at least partly offset by neutron production in matter, and this should be much the same in both centres. The geometric scattering from a metallic scattering foil will result in ISL effects, emerging from an apparent point source, so that radiation fluence will fall sharply with increasing distance or depth.

If it is assumed that the RBE is proportional to inter-track distance, which decreases with depth (x) in passively scattered beams, all other factors being equal (dose, energy, LET), and if the rate of change of this effect depends on the operative RBE, then

$$\begin{eqnarray*}&&{\rm{d}}({\rm{\Delta RBE}})/{\rm{d}}x=-K{\rm{\Delta RBE}},\end{eqnarray*}$$

where ΔRBE represents the RBE value in excess of 1.

Integration then provides, for RBE values >1, 1 + RBE_x = 1 + RBE₀ e^−cx where RBE_x is the RBE value in excess of 1 at a specified depth of x cm, RBE₀ is the RBE value in excess of 1 at the smallest depth, and c is a constant assumed to be controlled by track separation.

For the Megnin-Chanet experiments, and using their pooled data for two different human cell lines, the above function provides a value of c = 0.009 and 0.013, respectively, for the mid SOBP and distal SOBP positions used for the comparisons, and so it is possible to plot the reduction in the RBE with increasing depth, as shown in figure 1.4. Further experiments are required at multiple depths to confirm this hypothesis and achieve a more robust value for parameter c.

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The other approach might be to use the inter-track distance (s). Using similar triangles, the radius of a divergent overall beam-field is proportional to the distance (x) that it traverses. For two different depth positions 1 and 2, indicated by the respective subscripts, the overall beam radii r₁ and r₂ are proportional to their respective depths (x₁ and x₂) due to the similar triangle rule; the areas A₁ and A₂ are given by $\pi {r}_{1}^{2}$ and $\pi {r}_{2}^{2}$. The inter-track distance, when squared, is s² = A/N, and since N remains constant, then the ratio of inter-track distances (s₁/s₂) at two different depths will be the same as x₁/x₂. Using one of the data examples in Calugaru et al 2011, from x = 2.69 to 18.5 cm, the inter-track separation ratio (SR) will change from the shallowest depth, where s₁ is normalised to 1, down to 2.69/18.5 = 0.145 (in the absence of precise knowledge of N or F). When this process is applied to the data, and by using a similar exponential function as in the above example, then the relationship between the RBE and the inter-track separation ratio (SR) can be expressed as 1 + 0.0055 e^(4.14SR), and this function is plotted in figure 1.5.

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Such exploratory data needs to be extended, with RBE estimations at many depths in a panel of cell lines in order to fully verify and extend this hypothesis, using further microdosimetry considerations.

Although speculative, if such a reduction in RBE with depth can occur in some cell lines with divergent beams, it may be possible to investigate reducing potential RBE problems in normal tissue adjacent to a tumour by electively increasing the path length (and energy) of the radiation and adding tissue equivalent material outside the skin (as shown in figure 1.6), aiming for the RBE to be close to one at the critical distance. The length of additional material would require careful calculation to produce the SOBP at the required tissue depth, but with loss of the RBE this could be advantageous where the local biological characteristics confer a high normal tissue RBE in a critical structure and which exceeds any critical normal tissue dose sparing advantage. The alternative way of reducing the normal tissue RBE is to increase the dose per fraction of the particle therapy (these aspects are discussed in later chapters).

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The possible detriment would be loss of electronic equilibrium build-up in skin and subcutaneous tissue due to the introduction of the artificial tissue, which allows the beam to diverge to the required extent to reduce the RBE.