B. Dörschel

Dynamic X-ray compensation for conformal radiotherapy by means of multi-leaf collimation

The application of a multiple fixed field technique employing individually shaped and intensity-modulated beams makes it possible to produce dose distributions of high conformity even in the case of concave target volumes. With the technique presented here arbitrary intensity-modulated beams for the practical solution of the inverse problem can be generated. It is also possible to omit wedges, blocks and compensators in conventional radiotherapy. A continuous unidirectional sweep of independently computer-controlled leaves of a multi-leaf collimator is used to modulate the primary uniform beam. A new algorithm is introduced that computes the leaf trajectories. Also, a method is presented that accounts for leaf penumbra and transmission, which causes the generated fluence distribution to deviate from the desired fluence distribution. An optimization algorithm minimizing this deviation is described. The algorithm calculating the leaf trajectories, as well as the method considering penumbra and transmission and the successive optimization technique are used to calculate examples. Treatment times are calculated and compared to those needed when using compensators. A relationship between the treatment time and the maximum leaf speed is also deduced. To achieve good performance the maximum leaf speed should be no less than 20 mm/s.

Measurement of the track etch rates along proton and alpha particle trajectories in CR-39 and calculation of the detection efficiency

Computation of the neutron response of CR-39 detectors needs to simulate the track formation by neutron induced charged particles taking into account the bulk etch rate and the track etch rate varying along the particle trajectories. The latter one was determined experimentally by track length measurement. The results allowed to derive the relationship between the track etch rate and the restricted energy loss of the charged particles. On this basis, the geometrical track parameters and track etch rates as well as the critical angle of particle incidence could be determined for protons and alpha particles in the energy range from 0.2 to 8.8 MeV. The energy dependence of the critical angle enabled to determine the detection efficiency for a charged particle of given energy and direction.

Intercomparative study of the detection characteristics of the CR-39 SSNTD for light ions : Present status of the Besancon-Dresden approaches

For the last few years, the Besancon and Dresden teams have been working in a parallel way on light ion (protons and alphas) registration characteristics for the CR-39 SSNTD. Even if the two groups use different approaches, the main part of both investigations concerns the study of the track etch rate (VT) and the consequences of the obtained results, which have provided us with greater understanding of detection limits. After recalling the methods used to determine the VT from both teams, will show how fundamental datal related to the registration properties of the CR-39 detector can be extracted. Indeed, the knowledge of an analytical relation for the VT enables the relationship between this velocity and the primary deposited energy to the examined with respect to the same spatial variable (the instantaneous depth of penetration (x) of the incoming particle). According to experimental uncertainties, the Bragg peak of the primary ionization coincides within a very close range with the maximum of the VT. Moreover, if increasing the etching parameters (C, T) increases the maximum VT value, these changes do not affect its position with respect to the instantaneous depth of penetration. Taking into account the reduced etch rate, the Dresden team found that both protons and alphas exhibit the same behavior when this rate is plotted versus the primary energy deposition rate. As a consequence, the corresponding reduced etch rate is always identical no matter what type of particle deposits a given amount of energy (e.g. proton or alpha). The Besancon team has corroborated the results obtained by the Dresden group for alphas and have extended the study to various etching conditions. From these results, the sensitivity of the CR-39 SSNTD is obtained in terms of critical LET and leads to a very low energy threshold for alpha particles. We will see throughout this paper that the lower threshold does not seem to depend on the etching parameters.

Dependence of the etch rate ratio on the energy loss of light ions in CR-39

Abstract Mathematical simulation of the etch pit evolution requires the knowledge of the relationship between the etch rate ratio and the restricted energy loss of charged particles. Whereas a unique correlation of both quantities independent of the kind of particle and its initial energy was found for protons, deuterons and alpha particles the results of the depth-dependent track etch rates for 7 Li , 11 B and 12 C ions indicated a different behaviour for heavier ions. A detailed analysis of the etch rate ratio in dependence on the restricted energy loss confirmed the existence of specific relationships for ions of different kind and initial energy. The spread of the corresponding curves is explained by the gradual increase of the track etch rate over a certain distance from the detector surface. The speed of this increase is the higher the lower the restricted energy loss is.

The program StopPow – A useful tool for computation of energy loss and range of light ions in SSNTDs

Abstract Energy loss along particle trajectories and ranges of light ions are needed for theoretical characterisation of tracks in solid state nuclear track detectors (SSNTDs). Computation of these data is possible using ion transport programs, e.g., the well-known TRIM program. Derived quantities necessary for the simulation of the track formation process can be calculated by these programs too. The practical use is, however, limited by the time-consuming data processing that the user has to perform. Therefore, the program StopPow was developed based on algorithms analogous to TRIM, but yielding direct output of interesting quantities such as restricted energy loss (REL) for different cut-off energies of delta electrons or energy shift due to ion passage through material layers of different thicknesses. Tests of the StopPow program were conducted by comparison of exemplary results with TRIM and International Commission on Radiation Measurements and Units (ICRU) data as well as with experimental results.

Variations of the track etch rates along the alpha particle trajectories in two types of CR-39

The simulation of track formation processes in nuclear etched track detectors requires a quantitative formulation of registration criteria on the basis of the ratio of track etch to bulk etch rate. Whereas the bulk etch rate is measurable with sufficient accuracy by means of relatively simple techniques the track etch rate has been determined up to now indirectly by measuring the track diameters on the detector surface and assuming a constant etch rate along the particle trajectories. In deeper detector layers this assumption is, however, not valid because the energy loss strongly increases at the end of the particles range. The aim of the studies described was the direct experimental determination of the track etch rate as a function of the depth within the detector as well as the derivation of the relationship between the etch rate and the actual particle energy within the detector.

Variation of the track etch rate along the trajectories of light ions in CR-39

Abstract The track etch rate has been found to be described by a generalised function of the restricted energy loss in good approximation along the trajectories of protons, deuterons and alpha particles. Extending the studies to tracks of 7 Li , 11 B and 12 C ions, curves for the track etch rates as a function of the depth within the detector were obtained the shape of which is like that of the Bragg curve in principle. In detail, however, systematic deviations from a unique correlation of the track etch rate with the restricted energy loss are observed which are more distinct the heavier the ion and the lower its initial energy. This effect is explained by a gradual increase of the track etch rate to the value expected at a given restricted energy loss. At the beginning of the etching process the track etch rate is, therefore, lower than the value observed for larger depths when the same restricted energy loss is presumed.

Studies of SSNTDs made from LR-115 in view of their applicability in radiobiological experiments with alpha particles

Radiobiological studies on cell monolayers irradiated by charged particles need to determine the number and position of particle traversals. Solid state nuclear track detectors used as basic substrate for the cell layers are in principle suitable for this purpose. The detector foils must be as thin as possible but still guaranteeing mechanical stability. Two types of LR-115, red coloured and colourless, were tested in the present work. The studies aimed at optimisation of the etching conditions and determination of the registration efficiency for alpha particles in a wide range of energies and angles of incidence. Specific requirements have to be fulfilled for application of the detector foils under the environmental conditions of radiobiological experiments. Most important are biocompatibility between detector and cells and registration properties insensible against special treatments, as UV sterilisation and cell plating prior to irradiation as well as cell incubation after the irradiation. The experimental studies performed with alpha particles showed that environmental conditions of radiobiological experiments do not change the registration properties of LR-115 detectors significantly.

Computation of etched track profiles in CR-39 and comparison with experimental results for light ions of different kinds and energies

Abstract Computation of etched track profiles needs the knowledge of the variable track etch rates along the ion trajectories. Using the depth-dependent track etch rates experimentally determined for perpendicularly incident protons, deuterons and alpha particles as well as 7 Li , 11 B , 12 C , 14 N and 16 O ions of different energies simulations of the track development were performed. Two models of track etching were applied for that purpose recently published in literature. Although the models are based on the same physical fundamentals the results are slightly different. The reasons of the discrepancies were found by analysing the algorithms in detail. Comparison of the calculated track profiles with those determined experimentally from longitudinal sections of the etch pits showed good agreement for non-overetched as well as overetched tracks. The consistency of the whole experimental data set was checked by analysing the correlation of the track etch rates with geometric track parameters for all kinds of ions and etching times covered by the experiments.

3D computation of the shape of etched tracks in CR-39 for oblique particle incidence and comparison with experimental results

Abstract Computation of the shape of etch pits needs to know the varying track etch rate along the particle trajectories. Experiments with alpha particles and 7 Li ions entering CR-39 detectors under different angles showed that this function is not affected by the inclination of the particle trajectory with respect to the normal on the detector surface. Track formation for oblique particle incidence can, therefore, be simulated using the track etch rates determined for perpendicular incidence. 3D computation of the track shape was performed applying a model recently described in literature. A special program has been written for computing the x,y,z coordinates of points on the etch pit walls. In addition, the etch pit profiles in sagittal sections as well as the contours of the etch pit openings on the detector surface have been determined experimentally. Computed and experimental results were in good agreement confirming the applicability of the 3D computational model in combination with the functions for the depth-dependent track etch rates determined experimentally.