Dose and yield of secondaries

To obtain the dose and yield contribution due to the secondary particles pro-duced, the Hadrontherapy application has been modified retrieving single dose distributions curves related to each charged fragment produced along the carbon ions path. A PMMA cubic phantom, similar to that used for cells irradiation, has been simulated. The same methods of retrieving energy deposited in the sensi-tive detector and the same physical processes and parameters previously imple-mented (see section 5.1.2) have been used.

In order to have more readable plots, contributions of the isotopes have been summed, so that depth dose distributions for H, He, Li, Be and B fragments are shown in Figure 5.5, without distinguishing the mass number A. The dose con-tribution relative to carbon ions, which have undergone hadronic interaction along the path (¹⁰C, ¹¹C), have been also taken into account, separating this con-tribute from the depth dose distribution of the primary ¹²C ions. Moreover, total depth dose distribution (Bragg peak) and total dose due to the fragments are shown in the same plot. Semi-logarithmic scale has been used, otherwise dose contributions due to the secondaries and the fragment tail behind the peak would be not clearly visible⁷ (Figure 5.5).

A total number of 1·10⁶ primary events (¹²C) have been shot in the

7 At the this low energy (¹²C at 62 AMeV), effects of secondaries in dose and fluence are, indeed, much less visible than for higher energies (up to 400 AMeV).

134

tion in order to have statistical fluctuations on secondary particles production almost overall within 5%. Indeed, a huge number of primary particles is neces-sary in order to have relatively smooth depth dose curves also for the seconda-ries. A practical range of 9 mm has been found for primary particles.

In the overall plateau region, dose of secondary particles contribute only to about 1-3% on the total deposited dose registered at the same position and to the 0.5% on the peak. Thus, total dose (black line) and primary ¹²C dose (red line) practically coincide up to the peak position. Of course, just behind the Bragg peak total dose is only due the secondary particle (100%), indeed ¹²C dose dras-tically drop to zero.

Concerning the contribution of each particle on the total secondary dose, the percentage dose respect to the total dose due to the fragments at 1 mm behind the Bragg peak has been evaluated. As expected, the main part is due to the He fragments, which release the 56% of dose, followed by B fragments with 18%

and H with 15%. Contributions of other fragments are below 5%. Going more in depth the contribution is practically due only to H and He fragments which give a total dose which at 30 mm from the peak is still not negligible (~ 7% of the secondary dose obtained 1 mm behind the peak). This fact confirms what previ-ously found in chapter 4 and discussed for isotopes production in thin target ex-periments. Many alpha particles are, indeed, produced (together with H frag-ments) because of the specific alpha cluster structure characterizing carbon ions.

Moreover, the presence of light particles relatively far from the range of the pri-mary also confirms that projectile fragments are produced at velocities close to the primary particle ones, as expected according to the thin target results (see section 4.3).

It is also interesting to highlight that 1 mm before the Bragg peak the main contribution is given again by He fragments (46%), but in this case also C iso-topes give a not negligible contribution (25%).

An ambiguous step of He fragments in the entrance remains to be better un-derstood. It may be due to some nuclear processes which could be not activated for this specific energy range, but deeper investigations are needed in order to understand its cause.

5.2 Contributions of charged fragments

135 However, it must be stressed that the following plot represents just a calcula-tion of the physical dose, not giving detailed informacalcula-tion on where it is expected the major biological damage. To do that, the “beam quality” have to be globally considered and LET calculation can give, in this direction, more realistic re-sponses, as it will be discussed in the next section.

2 4 6 8 10 12

10² 10³ 10⁴ 10⁵ 10⁶ 10⁷

Depth [mm]

Arbitrary units

H He Li Be B C C12 Total Dose Dose of secondaries

Figure 5.5. Total depth dose distribution (Bragg curve, in black) and contribution of charged fragments (coloured lines) in PMMA. Dotted line represents the total contribu-tion from secondary particles.

More or less the same general comments are valid for the fluence distribu-tion (Figure 5.6). H and He ions are produced for overall the depth roughly with the same amount. This is, obviously, coherent with what previously found for the dose: He fragments, indeed, release about four time the dose released by H fragments, because of the Z² dependence of the stopping power (see sections 1.2.1 and A.1.1). Thus it has been found a released dose about 4 times higher.

Concerning the primary beam, about 82% of the incident carbon ions

136

reaches the peak region, because stripping of one or two neutrons produce re-spectively ¹¹C and ¹⁰C isotopes (mostly ¹¹C, which are about the 90% of secon-dary C fragments yield). As already pointed out, these isotopes are of great im-portance in hadrontherapy because they give the possibility to use the modern in-situ PET (Positron Emission Tomography) techniques for the monitoring of the delivered dose to the patient (see section 1.2.1).

A detailed calculation of the secondary particles yeild is crucial when calcu-lation of LET and its spatial distribution have to be evaluated for trying to relate the cellular damage to the “radiation quality”.

0 2 4 6 8 10 12

10¹ 10² 10³ 10⁴ 10⁵ 10⁶

Depth [mm]

Fluence

H He Li Be B C C12

Figure 5.6. Fluence depth distribution of primary and secondary particles in PMMA.