Experimental determination of particle range and dose distribution in thick targets through fragmentation reactions of stable heavy ions

In radiation therapy with highly energetic heavy ions, the conformal irradiation of a tumour can be achieved by using their advantageous features such as the good dose localization and the high relative biological effectiveness around their mean range. For effective utilization of such properties, it is necessary to evaluate the range of incident ions and the deposited dose distribution in a patient\u27s body. Several methods have been proposed to derive such physical quantities; one of them uses positron emitters generated through projectile fragmentation reactions of incident ions with target nuclei. We have proposed the application of the maximum likelihood estimation (MLE) method to a detected annihilation gamma-ray distribution for determination of the range of incident ions in a target and we have demonstrated the effectiveness of the method with computer simulations. In this paper, a water, a polyethylene and a polymethyl methacrylate target were each irradiated with stable 12C, 14N, 16O and 20Ne beams. Except for a few combinations of incident beams andtargets, the MLE method could determine the range of incident ions RMLE with a difference between RMLE and the experimental range of less than 2.0 mm under the circumstance that the measurement of annihilation gamma rays was started just after the irradiation of 61.4 s and lasted for 500 s. In the process of evaluating the range of incident ions with the MLE method, we must calculate many physical quantities such as the fluence and the energy of both primary ions and fragments as a function of depth in a target. Consequently, by using them we can obtain the dose distribution. Thus, when themean range of incident ions is determined with the MLE method, the annihilation gamma-ray distribution and the deposited dose distribution can be derived simultaneously. The derived dose distributions in water for the mono-energetic heavy-ion beams of four species were compared with those measured with an ionization chamber. The good agreement between the derived and the measured distributions implies that the deposited dose distribution in a target can be estimated from the detected annihilation gamma-ray distribution with a positron camera