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A Track Structure Model for Radial Dose Distributions of Energetic Heavy Ions

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A Track Structure Model for Radial Dose Distributions of Energetic Heavy Ions P-3b-S11 A TRACK STRUCTURE MODEL FOR RADIAL DOSE DISTRIBUTIONS OF ENERGETIC HEAVY IONS A.1Taymaz, T. 1Armagan, B.1Akkus, M.I. 1Bostan, M.H. 2Khalil, N. W. 3Eddy and C. 1Sencan 1Physics Division, Science Faculty, Istanbul University, Vezneciler Campus, 34459 Istanbul, Turkey 2Physics Department, Science Faculty, Ain Shams University, Cairo, Egypt 3Physics Department, Concordia University, 1455 de Maisonneuve Blvd. West, Montréal, Quebec H3G-1MB, Canada INTRODUCTION Linear Energy Transfer (LET) in its original definition (1) as energy imparted to matter per unit length of the primary particle track without micro-spatial event distribution specification is an insufficient criterion for microdosimetric definition. Depending on the kinetic energy of the ion a particle can transmit enough energy to its secondarily’s for travelling distance well exceeding the size of cell in tissue. Thus spreading the energy deposited “ locally ” a cylindrical volume of from few to several hundred-micron radiuses. In order to evaluate local damage in the molecule to the particular cell one must know local event distribution for a given type of ion irradiation. Considering the enormous complexity of the response of living matter to ionising radiation one must study the biological systems that have well defined sensitive areas in terms of the Target Theory. We do not intend to do this subject in this work, instead we will deal with microdosimetric aspects of the track structure for + + + + + Z equal to 2 , 6 , 8 , 10 and 18 , and interpret them for the radiobiology microdosimetrically in terms of y D , z D and dose D(r) deposited as a function of the distance r. Track structure models of Katz and Kobetich (2) describe the relationship between the spatial distribution of energy deposition in the form of positions of ionisation and excitation of target molecules whereas, the radial dose distribution D (3) about the path of the ion considered as the description parameter for the ion effects. In this investigation, we have used the model above, which it has the advantage of simplicity in considering the starlet geometry as a homogeneous site with respect the others (4, 5, 6, 7). The model provides a comparable description of the spatial distribution of ion track structure for both electrons and ions for tissue like target. Dealing with ionisation distribution in complex target geometry such as cellular and sub-cellular system track structure model could play an important role. However, the model is inadequate estimating the fluctuations in energy deposition. Obviously one should pay attention to the statistical fluctuations of dose D absorbed in cellular target, that dose D evenly distributed over the total volume of the cell. The cell will receive quite different “local” doses depending on the particular trajectory of electron, let’s say microdosimetrical variations of event distributions. These limitations of dose concept are, of course, by no means a special feature of heavy ion track structures. They hold for any kind of ionising radiation if one visualises sufficiently small target volume and constitute the fundamental difference between ionising and non-ionising radiation. MICRODOSIMETRIC EVENT SPECTRA The radial dose distribution computed using average track model of Katz and Kobetich, which consider the primary energy spectra from ion and its secondary from electron spectrum and given by 1 ∂ dn (r) = − ∑∫∫dΩ dω []E(r,ω)η(r,ω) ⋅ i (1) Dδ 2πr ∂r dωdΩ Where, E is the residual energy of an electron of initial electron energy ω after travelling distance r, and η(r,ω) is the transmission probability that an electron with starting energy ω penetrates a depth r. We have also included an angular distribution for the primary electrons with energy ω and solid angle Ω. δ indicates that it is the dose contribution from ionisation by secondary electrons at radial distance r from the path of ion. The last dn term i gives the number of electrons for given energy. dω dΩ Computational aspects of microdosimetry, whereas the program Monte-Carlo Code SRIM (8) was used in obtaining the stopping power together with the cross-section data library the ENDF/BV files and model of atomic and nuclear interactions as input for the calculations. The simulation takes into account the concept of the track structure of a particle in the medium and calculates the yd(y) dose distribution accordingly. The geometry, which is considered throughout this paper, is that of a pencil beam of monoenergetic ion normally incident on a volume of tissue equivalent material (9) of micrometric target sizes in which microdosimetric parameters were 1 P-3b-S11 estimated. Ions travel through the site undergoing small velocity changes and the energy deposited, ε, for a given path length Oand the frequency of linear energy distribution f(y) can be calculated from −1 dε f (y) = Of []y(O) (2) dO and = 2 y D ∫ y f (y)dy (3) Low velocity ions with insufficient range to traverse the site at a given path length will deposit all their energy in the site. However ion distributed lineal energy should be corrected for ion straggling and nuclear reaction effect for high-energy ions. Microdosimetric events of heavy ions were simulated for 0.1 nm to 1µm diameters of biological system. Dose distribution D(r) and dose mean specific energy z D was computed from the track distribution used in this model. The dose mean event spectrum y D described above may be converted to specific energy z D using the relationship 1 . 6 . 10 13 z D = y ⋅ O (4) V ⋅ ρ D Where V is the volume of the biological system and ρ, is the density of the target medium. Equation (4) is applicable to a single type of event, such as the traversal of a site by an incident ion. However, as the target size decreases or as the ion’s energy increases, the energy deposited in the site by secondary electrons that miss the target becomes increasingly important. The secondary electron of first order originate in centre of ion track, they travel in tortuous trajectory out to considerable lateral distance due to multiple scattering. The track of the secondary electron makes up the delta ray aura and is considered the microscopic signature of heavy ion in the target picture. Because of their irregular pathway, secondary electron can even return to centre of the ion path adding to the energy imparted to tissue by excitation and formation of higher secondaries (10). DISCUSSION AND CONCLUSION Heavy ions are expected to significantly improve the clinical results in tumour therapy due to their excellent dose deposition and their high biological effectiveness (11). The depth – dose distributions of heavy charged particles are characterised by a low dose plateau in the entrance channel and a sharp Bragg peak near the end of their ranges. For therapy planning and dose verification, it is therefore of great importance to have a detailed knowledge of these Bragg curves with increasing projectile energy and with increasing projectile size, we have performed calculation with different beams of a number of ions for several high energies. We have developed our dose program to calculate Microdosimetric parameters and total dose of heavy ion for a given medium. This program takes into account both the beam attenuation and the contributions from fragments of secondary and higher generation particles produced by nuclear reactions. Figure 1 shows computed radial dose for the ion of linear energy transfer (LET) of 150 keV/µm. The spectra shows some differences in radial energy deposited due to differences in track width, which is dependent on ion velocity. Such differences are expected to be important for specific target molecule sizes and spatial distribution of Figure 1.Computed radial dose distrubitions these molecules. The measurements of event spectra for 0.75 Me/amu alpha particle of 150 keV/µm. with TEPC agreed reasonably well with our computed spectra (11). Figure 2 shows y D and z D 2 P-3b-S11 values for He4, C12, N14, O16 ions and their secondary electrons as a function of energy in bone tissue of one micrometer. Figure 2. Comprasion of parametric model of mean y D and specific energy z D versus ions energy The specific energy mean spectra z D described above is shown in Figure 3, where z D is in Gy. Computation involved Z ≥ 2 incident ions, spherical sites of micrometric sizes and targets of non-interacting molecules. Figure 3. Calculation of mean specific energy as a function of simulated site size. Figure 4 shows the mean specific energy, z D as a function of the kinetic energy of the ion. The z D spectra are closely related to the response of the microdosimeter and provides a rough indication of biologically hazarful components of the radiation field. Comparison of the Figures 2 and 4 indicates a harder electron spectrum for lower energy ions. In computing the microdosimetric parameters such as D, y D and z D by using spatial pattern of energy deposition 3 P-3b-S11 105 4 10 Fe (26+) Ar (18+) 3 10 (Gy) Ne (10+) D Z 2 10 N (7+) C (6+) 1 10 d=1µm He (2+) 100 103 104 105 106 107 Energy T (keV) Figure 4. z D mean specific values as a function of ions energies and site size of 1µm. one can reproduce the detailed structure of y D event and/or of z D spectra. The stochastic effects (i.e. δ-ray electron), which caused from ionisation at a radial distance r from the path of ions are secondary contributor to the total dose D. The ion track width as well as the δ-ray effect are closely related to energy loss by straggling µ and especially important for the smaller target size which control the decrease in y D and z D from 0.1nm to 1 m.
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