Application of MLE method to range determination with induced β+ activity in hadron therapy

We proposed to apply the MLE method for determining the range of heavy ions and demonstrated the effectiveness of this method by experiments with 12C beams. We performed irradiation experiments with stable 12C ions of mono-energetic 290 MeV/u to a water, a polyethylene and a PMMA target. The theoretical ranges for 12C ions of 290 MeV/u in these targets are 160.5, 157.9 and 139.8 mm, respectively. The annihilation events from positron emitters generated by 12C ions were detected with a positron camera for 500 s just after the irradiation. To evaluate the range of 12C ions, the MLE method was applied to the annihilation gamma ray distribution. The derived ranges for the three targets were 160.6, 158.9 and 140.4 mm, respectively. Therefore, we can conclude that the range of 12C ions was determined within an accuracy of 1.0 mm for all targets.