Physical advantages of particles: protons and light ions

Abstract

Proton and ion beam therapy has been introduced in the Lawrence Berkeley National Laboratory in the mid-1950s, when protons and helium ions have been used for the first time to treat patients. Starting in 1972, the scientists at Berkeley also were the first to use heavier ions (carbon, oxygen, neon, silicon and argon ions). The first clinical ion beam facility opened in 1994 in Japan and since then, the interest in radiotherapy with light ion beams has been increasing slowly but steadily, with 13 centers in clinical operation in 2019. All these centers are using carbon ions for clinical application.

The article outlines the differences in physical properties of various light ions as compared to protons in view of the application in radiotherapy. These include the energy loss and depth dose properties, multiple scattering, range straggling and nuclear fragmentation. In addition, the paper discusses differences arising from energy loss and linear energy transfer with respect to their biological effects.

Moreover, the paper reviews briefly the existing clinical data comparing protons and ions and outlines the future perspectives for the clinical use of ions like oxygen and helium.

Introduction and historical perspective

Robert Wilson was the first to describe the use of proton beams for radiotherapy in his seminal paper from 1946.¹ In this paper, he already mentioned, that heavier ions like helium and carbon may be beneficial for radiotherapy due to their physical properties: The intense specific ionization of α particles … will probably make them the most desirable therapeutically, when such larger energies are attained. Heavier nuclei, such as very energetic carbon atoms, may eventually become therapeutically practical.

While there is an increasing number of facilities using proton therapy, with today more than 80 clinical facilities worldwide (see www.ptcog.ch/index.php/facilities-in-operation), there are still only 13 facilities offering beams of heavier ions¹ for clinical use, all of them providing carbon ion beams only. There is, however, a rationale using also other ion beams for therapeutic applications. Scientists at the Lawrence Berkeley National Laboratory (LBNL) were the first to exploit the potential of these light ions for radiotherapy, shortly after John Lawrence and Cornelius Tobias have started the first proton therapy treatments for pituitary gland treatments² at the 184-inch cyclotron in Berkeley. In 1957, the beam energy of the 184-inch cyclotron was increased to 920 MeV and the pituitary treatments at Berkeley were continued with Helium ions, simply because of the more suitable range of the helium ions at this energy.² Only in 1975 a higher energy machine, the Bevalac synchrotron became available at LBL and radiotherapy with various light and heavy ions was exploited. The majority of patients was treated with neon and helium ions, but also beams of carbon, silicon and argon were explored.^3,4 The pilot studies in Berkeley concluded that carbon is most suitable for therapy and all subsequent clinical facilities concentrated on carbon ions for radiotherapy. Recently, the interest in other ions beams has been rising again, as they have some advantages as compared to protons or carbon ions.⁵

In this contribution, the physical properties of different light ion beams (including protons as the lightest ion) are reviewed and compared in light of their potential clinical application.

Physical properties of light ions beams

In the following sections, the various physical properties of protons and other light ions are being compared starting with energy loss and the depth dose behavior, followed by the lateral scattering, nuclear interactions and finally the linear energy transfer, which is connected to the radiobiological effects if light ions.

Energy loss, energy loss straggling and depth dose

The depth dose curve of light ions is the main advantage as compared to high energy X-rays. It results primarily from the gradual energy loss of the charged particles, as compared to the exponential loss in fluence of X-rays, when penetrating tissue (Figure 1). The mean energy loss of ions per path length is given by the Bethe equation⁶ :

Figure 1. .

Relative absorbed dose of high energy X-rays (24 MV), protons (140 MeV) and carbon ions (270 MeV/u) as a function of depth in water (image: dkfz).

$${\displaystyle <\frac{dE}{dx}>=K\cdot z^2\cdot {\rho }_e\cdot \frac{1}{{\beta }^2}\left[\ln \left(\frac{2m_e{c}^2\cdot {\beta }^2\cdot W_{max}}{I^2\left(1-{\beta }^2\right)}\right)-{\beta }^2+corr.\right]}$$ (1)

where K = 0.307075 MeV cm² g⁻¹. z and $\beta$ are the charge and velocity of the projectile ion, ${\rho }_e$ is the electron density of the target medium, W_max is the maximum energy that the ion can transfer to an electron in a single collision and I is the mean excitation energy of the medium. The term corr. exhibits some additional corrections at very high and low energies.

Due to the dependence on $\frac{1}{{\beta }^2},$ this leads to a remarkable increase of the energy loss per path length with decreasing velocity of the projectile, which results in the Bragg peak in the depth dose curve of ion beams (Figure 1). Beyond the Bragg peak, the ions will stop and the dose will sharply drop to zero. This is clearly seen for the proton curve. For heavier ions, a tail arises, which is due to a built-up of nuclear fragments with ranges longer than that of the primary ions (see below).

The mean energy loss per path length, ${\displaystyle <\frac{dE}{dx}>}$, is usually referred to as the linear stopping power, S, while the normalized value S/$\rho$ is called mass stopping power. It should also be noted, that S is strictly speaking only the collision stopping power, which is due to the inelastic collision of ions with the electrons of the target atoms. In principle, also radiative energy loss may arise, which is due to emission of Bremsstrahlung, but can be neglected for ion beams at the relatively low therapeutic energies. Finally, nuclear energy loss can occur, when the target nuclei obtain a recoil energy during the Coulomb scattering of an ion in the electric field of atomic nucleus. This contribution (which does not involve nuclear interactions) is relevant only at very low energies (typically below 1 MeV, i.e. in the stopping region of ions). Another effect of higher importance at very low kinetic energies is the fact, that ions will start to collect electrons and their charge will be reduced. This effect can be accounted for by introduction of an effective charge of the ion, which decreases the energy loss at energies below 1 MeV/u (Figure 2). Nuclear interactions between the two involved nuclei are not included in the energy loss, but are treated separately as a modification of the particle spectrum (see below).

Figure 2. .

Stopping power of different light ions as a function of energy are plotted as lines of different color: protons (purple), helium (red), carbon (green), oxygen (orange) and neon (blue) as calculated using ICRU data. Note the logarithmic scale of the energy axis. The residual range of protons at 1 MeV is less than 0.1 mm and even lower for the heavier ions (image: dkfz).

When comparing different ions in terms of energy loss, the main difference is resulting from the dependence of stopping power on the square of the charge of the projectile. This leads to a strong increase of the energy loss for heavier ions at the same velocity. For carbon ions, the energy loss is therefore a factor 36 larger than for protons at same energy per nucleon (as the kinetic energy scales with mass, ions at the same energy per nucleon, have the same velocity). This behavior is shown in Figure 2 for different ion types.

For therapy, it is more relevant to compare different ions at the same range, rather than same energy, which introduces an additional dependence on the velocity. The range R of different ions as a function of energy, can be obtained in the continuously slowing down approximation, by integrating the inverse of the stopping power over energy, up to the kinetic energy of the incident ion, T₀:

$${\displaystyle R_{csda}\left(T_0\right)\cong {\int }_0^{T_0}{\left(\frac{dE}{dx}\right)}^{-1}dE\propto E^{1.75}}$$ (2)

This relation exhibits that the range of different ions at the same energy per nucleon, scales approximately with: $R~\frac{\mathrm{m}}{z^2}$ . Consequently, helium ions have the same range as protons at the same energy per nucleon and carbon ions have one third of the range of protons at the same energy per nucleon. Figure 3 shows this dependence for different ion beams.

Figure 3. .

Range of ions in water as a function of energy per nucleon for protons, helium, carbon, oxygen and neon ions (image: dkfz).

A direct consequence from this relation is, that a facility for radiotherapy with carbon ions, yielding for the same range as a proton facility, will need an initial energy (per nucleon), which is three times higher. This results in the need for a significantly larger accelerator and higher costs for the facility.

It is important to note, that eq. 1 is used to calculate the mean energy loss of many ions and that the energy loss of an individual ion is subject to statistical fluctuations. This phenomenon is called energy straggling as it leads to an energy distribution around this mean value. This energy straggling also leads to a variation in range, which is called range straggling. The range straggling distribution can be approximated for many practical applications by a Gaussian function, where the variance, σ_r, is increasing with range r, and may be approximated for different ions with atomic number, A, according to Chu et al⁷ by:

$${\displaystyle {\sigma }_r=\frac{0.012\cdot r^{0.951}}{\sqrt{A}}}$$ (3)

This increase of the width of the range leads to a broadening of the Bragg peaks as seen in Figure 1. Without energy, or range straggling, the Bragg peak would be much sharper. Eq. 3 also results in a significantly decreased range straggling for heavier ions, e.g. for carbon the straggling width is reduced by a factor of $\sqrt{12}\approx 3.5$ as compared to protons, which results in a sharper Bragg peak, including a sharper distal dose fall-off. Another important consequence of eq. 3 is, that range straggling is nearly linear to range and not depending on other material properties. This means, that one may derive the depth dose curve in any material by a simple scaling of the depth dose curve for water with the correct range. This crucial assumption is made in most treatment planning dose algorithms, meaning that only depth dose curves in water are required as input.

Multiple scattering and lateral penumbra

Coulomb scattering of the ions with the atomic nuclei of the target leads to a lateral scattering of the incident ions. The cross-section of the elementary scattering events is the well-known Rutherford scattering cross-section. The differential cross-section of an ion with charge z and energy E, at a target nucleus with charge Z for scattering into a solid angle dΩ is:

$${\displaystyle \frac{d\sigma }{d\mathrm{\Omega }}\sim \frac{z^2{Z}^2}{E^2}\cdot \frac{1}{si{n}^4\frac{\theta }{2}}}$$ (4)

The strong dependence on the scattering angle Θ leads to the suppression of large scattering angles. The effect of many subsequent Rutherford scattering events therefore is referred to as multiple small angle scattering and approximations for small scattering angles are usually introduced.

It is also seen from eq. 4, that lateral scattering for heavier ions will generally increase with the charge of the ion, but this increase is compensated by the much higher energies, needed to achieve the same range as compared to lighter ions.

For the transport of an ion beam through tissue, many subsequent scattering events have to be regarded and various transport theories exist (multiple scattering theories). The small angle approximation results in a Gaussian probability distribution P($\theta )$) of the scattering angle $\theta$ (projected on a plane) behind a thick target:

$${\displaystyle P\left(\theta \right)d\theta =\frac{1}{\pi \sqrt{2\pi }{\theta }_0^{}}exp\left(-{\theta }^2/2{\theta }_0^2\right)d\theta }$$ (5)

Here, ${\theta }_0$ is the width of the scattering angle distribution, approximately given by the so-called Highland formula⁸ :

$${\displaystyle {\theta }_0=14\left[\frac{MeV}{c}\right]\frac{z}{p\beta }\sqrt{\frac{r}{L_{rad}}}\left(1+\frac{1}{9}{\log }_{10}\frac{r}{L_{rad}}\right)}$$ (6)

where r is the penetration depth, z, p and β are the projectile charge, momentum and velocity, and L_rad is the radiation length of the material as defined for photons.

Due to the smaller scattering angles of heavier ions, the Gaussian small angle scattering approximation in eq. 5 is working better for light ions than for protons, where an underestimation of large scattering angles is seen. These latter are dominated by single scattering or few scattering events and follow the angular distribution of eq. 4. For protons, a more accurate formulation with the transport theory of Moliere⁹ is often used.

Eq. 6 may be used to estimate the variance of the scattering angles of different ions. At the same velocity, ${\theta }_0$ will scale approximately with $\frac{Z}{A}\sqrt{r},\mathrm{}\mathrm{o}\mathrm{r}\frac{1}{\sqrt{A}}$ (similar to range straggling). For carbons ions, this results in a reduction by a factor of ~1/3 as compared to protons at same velocity, or energy per nucleon. Since the energies needed to achieve the same range are higher for carbon, this reduces the scattering angles further. In Figure 4, the behavior of the lateral penumbra of different ion beams with same initial beam width is shown as a function of depth in water. This figure also demonstrates, that already helium ions do offer a significant reduction of the lateral scattering as compared to proton beams, which in fact produce a lateral penumbra larger than high energy X-rays at larger depths.

Figure 4. .

fwhm of beams of protons, helium and carbon as a function of depth in water, starting with the same initial fwhm of 4 mm (image: dkfz; data: courtesy of U. Weber). fwhm,full-width half-maximum.

In addition to Coulomb scattering, also the nuclear interactions and production of secondary particles lead to a broadening of the ion beam in depth as explained below.

The clinical relevance of the reduced lateral scattering is demonstrated in Figure 5 for a treatment plan for a skull base tumor comparing protons and carbon ions. The plans resulted from identical parameters (field configuration, calculation grid, prescription and organ at risk constraints), but different particle type (using clinical beam delivery parameters from the respective facility for the beam energies, initial beam width and scan grid).

Figure 5. .

Comparison of a treatment plan for a skull base patient calculated with the same field arrangement of protons (right) and carbon ions (left) as available in clinical facilities. The effects of the increased lateral penumbra of a proton beam are clearly visible. The proton plan was created for the MGH scanning beam, the carbon plan for the GSI facility (image: dkfz).

Nuclear interactions

Due to the relatively high energies of the incident ion beams, not only Coulomb interactions but also nuclear interactions between the colliding nuclei may occur. This may lead to a breakup of the binding of the nucleons and release of nuclear fragments of both, the projectile and the target nucleus. Since protons in this context are considered elementary particles, only target fragments may be produced during interactions of proton beams with matter. Due to the conservation of energy and momentum, light fragments are produced with higher momentum transfer and energy as compared to heavier fragments (in a central collision, all the kinetic energy minus the binding energy is transferred to a nucleon).

The secondary particle spectrum arising from a proton beam therefore consists mainly of secondary protons and neutrons and very few heavier fragments, like deuterons, tritons or helium nuclei etc. In addition, the remaining target nucleus will be in an excited stage and often unstable, which may lead to a subsequent β-decay or emission of γ−rays during de-excitation, which may be used for monitoring the dose deposition.

The proton–nucleon interaction cross-section is rather constant at high energies, reaches a maximum around 20 MeV (residual range ~0.5 cm) and then decreases quickly towards smaller energies. Secondary protons, neutrons and target activation are therefore mainly produced in the entrance region of a proton beam and their number drops close to the Bragg peak. This also leads to an increasing halo of secondary protons and more and more neutrons during traversal of the material or tissue.

The situation is quite different for all heavier ions. In this case, the fragmentation of the projectiles is more important in view of the generated secondary particle spectrum. This is due to that fact that the projectile fragments continue with approximately the same velocity as the primary ion. A secondary proton may be produced which has significant higher range than the primary ion. This gives rise to the dose tail of secondary ions, which is seen in Figure 1 beyond the Bragg peak of the primary carbon ions. Generally, lighter fragments are more abundant than heavier ones. Projectile fragments may have any charge number up to the charge of the primary. In case of carbon ions, secondary protons, helium, lithium, beryllium and boron ions may be produced. The target fragments are generally less important, since—due to the collision kinetics— their recoil energy is typically quite small and their range is consequently very short. For most situations, they are assumed to be absorbed at the point of production.

The secondary neutrons, which are produced in a light ion beam, generally have much higher energies as in proton beams and a momentum in the original beam direction. Although, the number of neutrons per incident ion may be significantly higher for carbon than than for protons, the overall number of neutrons is not, when treatments at the same relative biological effectiveness (RBE) weighted dose are considered. This is, because the stopping power of ions is higher than for protons and the number of ions needed to deliver the same RBE-weighted dose as compared to protons is about two orders of magnitude lower.

While in the case of protons only target activation occurs, also the secondary ions in a light ion beam may be radioactive. This is used, e.g. during in vivo monitoring of positron emitters with positron emission tomography cameras. Only for Z ≥ 6 relevant positron emitters are being produced. Therefore, only for carbon or heavier ions a β⁺-activation of the projectiles is achieved, which leads to an activation peak, which is close to the Bragg peak of the primaries. For all lighter ions, the activation is mainly in the entrance region of the ions and decreasing quickly towards the Bragg peak.

Generally, the momenta of secondary charged particles are forward peaked, but the emission angle is getting wider for lighter and slower particles. For heavier ions like carbon, this results in an outer halo of lower Z fragments and an inner halo of higher Z fragments. A consistent description of this pattern is only achieved by Monte Carlo algorithms. Since only few cross-section data are available for target materials other than water, most reaction cross-sections are being scaled by density to calculate the secondary particle spectrum resulting in human tissue.

Besides the built-up of a spectrum of secondary particles, nuclear interactions will lead to a loss of primary particles in the beam, which may be described by an exponential attenuation factor. The attenuation length λ is directly related to the total nuclear reaction cross-section and is defined by the decrease of incoming ions N₀ to a number N, after traversing a slab of thickness x:

$${\displaystyle \frac{N}{N_0}=ex{p}^{-\frac{x}{\lambda }}}$$ (7)

For carbon ions, the attenuation length λ is 259 mm, leading to an attenuation of the particle number by nearly 4% per cm range.¹⁰ For protons, attenuation is approximately 1,2% per cm range.¹¹ For heavier ions, the attenuation is increasing significantly, leading to a huge loss of incident ions and consequently to a decrease in dose between the entrance and the Bragg peak, as well as an increase of the tail dose.

This is seen, e.g. in Figure 6 for a neon beam. In this case, it becomes obvious, that the high energy transfer, which is connected to a high linear energy transfer (LET) (see below) is not only confined to the Bragg peak, but is present already in the entrance, leading to significant enhancement of skin dose and skin effects. This and the increased dose behind the Bragg peak, limits the clinical use of heavy ions (Z ≥ 10 as compared to light ions.

Figure 6. .

Measured depth dose of a 670 MeV/u Ne beam at GSI (black dots) in water together with calculated depth dose of the primary ions (red), secondary (blue) and tertiary (green) fragments.¹²

Linear energy transfer and radiobiological effects

The statistical nature of energy loss has been mentioned above in relation to range straggling. Another important effect of the energy loss straggling is the distribution of secondary electrons, which is arising from an ion beam. It generally has a very asymmetric form and is described by the Landau or Vavilov theory, as shown schematically in Figure 7. One can see that the most likely energy loss is in fact somewhat lower than the mean energy loss.

Figure 7. .

Relative probability of a certain amount of energy loss as a function of the energy loss Δ. The most probable, mean and maximum energy loss are also denoted (reprinted from¹³).

A difficulty of the Landau theory is, that the probability approaches zero, only in the limit of infinite energy loss. The maximal energy loss W_max in a single collision is, however, given by kinematics. When the electron mass relative to the mass of the incoming ion is neglected, it is given by:

$${\displaystyle W_{max}\cong 2m_e{c}^2\left(\frac{{\beta }^2}{1-{\beta }^2}\right)}$$ (8)

Consequently, the maximum energy loss for a proton and carbon ion with the same residual range of 15 cm in water is 350 and 750 keV, respectively. This is a relatively small difference, when the large difference in the total corresponding kinetic energy of the primary particle of 150 MeV (p) and 3600 MeV (C-12) is regarded.

Moreover, this maximum energy loss is roughly three orders of magnitude larger than the mean energy loss, which is around 800 eV, in the same situation. Since the range of secondary electrons at these low energies is only around 50 nm, most of the energy of high energetic protons and ions is deposited in direct vicinity of the track of the primary ion. The highly increased energy loss of higher Z particles as compared to protons then leads to an increased number of these low energy electrons, rather than higher energies of the electrons. The low energy of secondary electrons also explains why ions do not exhibit a built-up effect as compared to X-rays.

The production of a large number of short-ranged electrons is referred to as densely ionizing radiation and quantified by the term restricted LET, ${\displaystyle L_{\mathrm{\Delta }}}$ , or LET of a material. It is defined for a given particle type and energy by¹⁴:

$${\displaystyle L_{\mathrm{\Delta }}=\frac{d{E}_{\mathrm{\Delta }}}{dl}=S_{el}-\frac{d{E}_{ke,\mathrm{\Delta }}}{dl},}$$ (9)

where ${\displaystyle d{E}_{\mathrm{\Delta }}}$ is the mean energy lost by the ion due to electronic interactions in traversing the distance $dl$, minus the mean sum of the kinetic energies ${\displaystyle E_{ke,\mathrm{\Delta }}}$ , in excess of the energy Δ of all electrons released by the ions. The second part describes its relation to the electronic stopping power, where ${\displaystyle d{E}_{ke,\mathrm{\Delta }}}$ is the amount of energy ${\displaystyle E_{ke,\mathrm{\Delta }}}$ , released in traversing the distance $dl$. With ${\displaystyle \mathrm{\Delta }E=\mathrm{\infty }}$, the unrestricted LET, $L_{\infty }$ is resulting which is equivalent to $S_{el}$ . Since the mean energy of secondary electrons produced, is extremely low, it is common to use simply the unrestricted ${LET}_{\infty }$ for most practical purposes.

LET is an important concept to quantify radiobiological effects, since it was noticed, that many parameters, like the RBE or the oxygen enhancing ratio (OER) of ions depend (besides other parameters) primarily on LET. Figure 8 shows a compilation of RBE data for various ions as a function of LET.

Figure 8. .

Compilation of RBE data for various ions and cell types. (Data from Sørensen et al¹⁵ image reproduced from Loeffler et al¹⁶). RBE,relative biological effectiveness.

It is, however, important to note, that LET, as defined above is a quantity, which is defined only for a simple radiation field, of a single ion type and energy. Whenever a mixture of energies or particles exists, the above definition is not applicable.

Instead, only a weighted average of LET can be calculated. Two concepts are mainly used for this purpose, the dose averaged or the track averaged LET, meaning, that LET contributions in a mixed particle spectrum are weighted with the dose contribution or the fluence contribution of the various particles at the point of interest, respectively.

The dose averaged LET_d, in a mixed energy field is defined as:

$${\displaystyle LE{T}_d(z)=\frac{{\int }_0^{\mathrm{\infty }}{S}_{el}(E)D(E,z)\text{d}E}{{\int }_0^{\mathrm{\infty }}D(E,z)\text{d}E}=\frac{{\int }_0^{\mathrm{\infty }}{S}_{el}^2(E)\mathrm{\Phi }(E,z)\text{d}E}{{\int }_0^{\mathrm{\infty }}{S}_{el}(E)\mathrm{\Phi }(E,z)\text{d}E}}$$ (10)

where the electronic stopping power is weighted by dose, integrated over the energy spectrum and normalized to the dose average. When dose is expressed by stopping power and fluence, the right part of the equation results. When different particle types are present, their contribution has to be summed up in addition in numerator and denominator.

The fluence, or track averaged LET_t, consequently is defined as:

$${\displaystyle LE{T}_t(z)=LE{T}_f(z)=\frac{{\int }_0^{\mathrm{\infty }}{S}_{el}(E)\mathrm{\Phi }(E,z)\text{d}E}{{\int }_0^{\mathrm{\infty }}\mathrm{\Phi }(E,z)\text{d}E}}$$ (11)

where the electronic stopping power is not weighted by dose, but by fluence instead.

One has to be careful, which LET value is specified, when using the concept of LET in a mixed radiation field. For most applications in treatment planning, an RBE calculation based on LET_d is used, while most experimental radiobiological data refer to a value of LET_t .

Generally, the use of an average LET value for treatment planning or RBE calculation has to be regarded as a purely empirical concept.

Monte Carlo simulations for protons using the two definitions above, demonstrate that subtle difference may arise for the LET distributions, as seen in Figure 9.

Figure 9. .

Monte Carlo simulations (Geant) of the dose and ratio of LET_d to LET_t for a proton beam of 5 cm range (reprinted from Guan et al¹⁷). The right panel shows the low energy region only. The parameter s refers to the simulated target size. LET,linear energy transfer.

The simulations for protons demonstrate that the target size is of crucial importance for the ratio of LET values, which is due to the dependence of LET_d on target size.¹⁷ Even for smaller targets, the two LET parameters may differ by 50% in the Bragg peak.

In general, RBE cannot be predicted by LET_d alone, but if an empirical relation of experimental RBE values and LET is derived, it should be carefully noted, how LET is defined for a mixed field.

Grün et al¹⁸ have shown that LET_d is a reasonable good predictor for RBE, only when the LET distributions are narrow. This is the case usually in scanned beams as compared to broad beams. LET_d is becoming less and less reliable as a predictor, when the distribution becomes broader or when heavier ions are considered, where fragmentation leads to broader spectra.

When LET_d is calculated for a spread-out Bragg peak, it becomes clear, that LET_d is much lower in the entrance and beginning of the plateau region and only increases steeply towards the distal end. This is due to a dilution of the high LET in the peak by ions, passing with higher energy. This dilution is very much depending on the modulation depth or planning target volume size (Figure 10). Consequently, irradiation with light ions is becoming more and more similar to low LET treatment for larger and larger target volumes. In very large target volumes (e.g. sacral chordoma with >1 l volume) the high LET of light ions may therefore not be of any clinical relevance, unless a specific LET optimization is used, which tries to maximize LET in some sub volumes.

Figure 10. .

Dose averaged LET as a function of the size of a box shaped PTV, which is irradiated with four co-planar beams of carbon ions, spaced by 90°. Displayed are the minimum, maximum (dotted lines) and mean (full line) values of LET_d (reprinted from Bassler et al.¹⁹). Following the nomenclature of ICRU, all ions with a charge number Z < 10 will be referred to as light ions. This includes also protons with Z = 1. The use of heavy ions is restricted to ions with atomic charge 10 and above, i.e. for neon and all heaver ions. LET, linear energy transfer; PTV, planning target volume.

Consequently, it may be beneficial to combine, e.g. proton with carbon beams, in order to limit the high LET of carbon ions to resistant sub volumes of the target, as is suggested in.¹⁹

Another important aspect of high vs low LET radiation is the different microscopic dose distribution in the target and the much smaller number of carbon ions as compared to protons, which is needed to deliver the same dose (about a factor of 100 as mentioned above). This results in a highly inhomogeneous microscopic dose distribution, as only very few ions deliver a very high dose in very small, subcellular volumes. The relatively low number of ions needed, leads to significant statistical variation of the number of hits and dose per cell. In fact, the probability distribution of the dose to a cell nucleus is much broader for carbon ions as compared to protons as shown in.²⁰ Due to this statistics, some cells may be missed completely. This behavior certainly has important implications for radiobiological effects, which are not fully understood yet.

Clinical relevance of the physical characteristics

Several of the factors discussed above, indicate that there might be a clinical benefit in using heavier ions, like carbon or oxygen, as compared to protons or helium. There is, however, very limited, direct clinical evidence for such a benefit, which is due to the fact, that most clinical studies involving carbon ion therapy are retrospective single arm studies, not aiming at a direct comparison against proton therapy.

Currently, the Hyogo ion beam medical center in Japan is the only center in Japan offering proton and carbon ion therapy and is reporting most data on this issue,. They reported retrospective data for a number of treatment sites, with very favorable outcome as compared to historical results, but little to no statistically significant differences between proton and carbon therapy. These studies reported on primary sacral chordoma,²¹ partially resected bone and soft tissue sarcoma,²² sinonasal squamous cell carcinoma,²³ mucosal melanoma of the head and neck²⁴ and non-small cell lung cancer.²⁵ Only in adenoid–cystic carcinoma of the head and neck, a clear benefit was observed in the overall survival for patients treated with carbon, while local control was not different.²⁶ Overall, the results reported from Hyogo do therefore not indicate a significant difference between proton and ion beam therapy, but as stated in the related publications the statistical significance of this statement is weak. It should be noted, that the trials done at Hyogo are based on the same RBE-weighted dose and fractionation scheme applied for both modalities. When interpreting the results, it should be considered, that the applied doses may not necessarily be identical, due to the uncertainties in RBE.

Several randomized trials have been designed at the Heidelberg Ion Beam Therapy center to compare proton vs carbon ion therapy for chordoma and chondrosarcoma of the skull base,^27,28 sacrococcygeal chordoma²⁹ and for prostate cancer.³⁰ Only very limited results have been reported for these trials so far, which is due to slow recruitment and the long follow-up time needed. An interim analysis of 101 patients treated with protons and carbon ions for chondrosarcoma of the skull base has been reported,³¹ but revealed no statistical difference between both modalities. It resulted in slightly worse outcome for the carbon patients (92.9% vs 100% overall survival at 4 years). This may well be due to the different dose schemes prescribed for both modalities [60 Gy (RBE) at 3 Gy (RBE) for carbon vs 60 Gy (RBE) at 2 Gy (RBE) for protons], which was selected as best practice for both modalities in this study.

For the prostate cancer trial at HIT, some intermediate toxicity analysis was performed³² revealing overall slightly lower toxicity for carbon than for protons [at the same dose of 66 Gy (RBE) in 3.3 Gy (RBE) fractions], which again has to be interpreted carefully, as no control and survival rates have been presented yet.

As mentioned above, the general problem with all studies, is the modelling of radiobiological effects in treatment planning, which may result in substantial differences for RBE at different centers and makes it difficult to compare outcomes from various centers. The uncertainty of RBE should always be considered, when comparing clinical outcome from different modalities: a study leading to equal outcome for proton and carbon ions may result even if carbon ions are more effective, but RBE was overestimated. It is thus important to always compare tumor control as well as rate and severity of side-effects at the same time.

Another bias in clinical studies may arise from the reduced lateral penumbra of carbon ions, which may in some patients lead to a compromise in target dose and volumes for the proton patients.

Concerning other ions, there are no comparative clinical data available yet. A treatment planning study has been performed for proton vs helium treatments for meningeoma⁵ as part of the preparation for helium treatments at HIT. Generally, the differences found in this study are relatively small, but still may be significant. The main advantage of helium ions is due to the reduced lateral scattering and the resulting reduced doses to critical organs close to the target, e.g. up to 7 Gy (RBE) reduction in dose to the brain stem and optical nerves was found, when helium ions were compared with protons delivering a total dose of 54 Gy (RBE).

Concerning other high-LET effects, such as a reduced oxygen effect, which is observed in in-vitro studies for carbon ions, there is very little clinical evidence. A single study performed at HIMAC reports on 49 patients that were treated with carbon ions and where partial oxygen pressure was measured with a needle type electrode prior and after therapy.³³ The results showed no difference in outcome for patients with high or low partial oxygen pressure after carbon radiotherapy, while there was distinct difference in outcome for patients treated with X-rays. The study does, however, not demonstrate directly a benefit of this effect for the patients, as the two groups treated with either modality are very different with respect to the status of their disease.

Discussion

Light ions do have similar depth dose curves as compared to protons. The depth dose curve does exhibit a dose tail beyond the Bragg peak, which is due to secondary ions with larger range. This tail has to be regarded in treatment planning, but is typically considered not a clinical problem, as long as light ions are concerned. For heavy ions (neon and heavier), nuclear fragmentation leads to considerable loss of primaries, so that not only the dose tail is increasing, but also the high LET region is no longer limited to the Bragg peak.

A general advantage of light ions as compared to protons is their largely reduced lateral scattering, which makes helium an interesting choice, as its LET is only slightly higher than for protons.

Carbon ions are currently the only light ion in clinical use, which has mainly historical reasons. It has a significantly increased LET in the Bragg peak, which may lead to clinical benefits for resistant tumor cells, as indicated by in-vitro studies (see Durante and Loeffler³⁴ for an overview). The clinical efficacy of carbon ion therapy has been demonstrated in many tumors³⁵ but high-level clincal evidence is overall very limited (see Lazar et al³⁶ for a recent review). The same is in principle true for proton beam therapy, although the overall clincial evidence is somewhat stronger as compared to carbon ion therapy.³⁷ Consequently, there is also very little clinical evidence for demonstrating an additional benefit of light ions as compared to protons, as mentioned above.

As the dose averaged LET is decreasing strongly with larger target volumes, it may be interesting to increase LET by choosing heavier ions. In order to achieve a significant clinical difference in hypoxic tumors, it might be interesting to use, e.g. oxygen ions, as their LET is generally about a factor two higher than for carbon ions. Another important consideration is to mix high and low LET radiation and limit the target volume of light ions to small sub volumes, where resistant cells are present. By doing so, a higher LET in these smaller volumes is achieved, which may be beneficial. This will, however require a solid biological imaging for treatment planning.

Helium ions may be an interesting alternative to proton therapy, as helium ions show a significantly reduced lateral penumbra and a radiobiological behavior more similar to protons.⁵ Helium would also be less expensive than carbon ions, as they may be produced in cyclotrons rather than synchrotrons. Lastly, it is expected that the number of secondary neutrons is very low and the dose due to neutrons may even be lower than in proton therapy. This could be important for pediatric or pregnant patients, were secondary dose should be as low as possible. This is why helium beam therapy is under preparation at the HIT facility⁵ and considered in other facilities.