This work presents an iterative method for the estimation of the absolute dose distribution in patients undergoing carbon ion therapy, via analysis of the distribution of positron annihilations resulting from the decay of positron-emitting fragments created in the target volume. The proposed method relies on the decomposition of the total positron-annihilation distributions into profiles of the three principal positron-emitting fragment species - ¹¹C, ¹⁰C and ¹⁵O. A library of basis functions is constructed by simulating a range of monoenergetic ¹²C ion irradiations of a homogeneous polymethyl methacrylate phantom and measuring the resulting one-dimensional positron-emitting fragment profiles and dose distributions. To estimate the dose delivered during an arbitrary polyenergetic irradiation, a linear combination of factors from the fragment profile library is iteratively fitted to the decomposed positron annihilation profile acquired during the irradiation, and the resulting weights combined with the corresponding monoenergetic dose profiles to estimate the total dose distribution. A total variation regularisation term is incorporated into the fitting process to suppress high-frequency noise. The method was evaluated with 14 different polyenergetic ¹²C dose profiles in a polymethyl methacrylate target: one which produces a flat biological dose, 10 with randomised energy weighting factors, and three with distinct dose maxima or minima within the spread-out Bragg peak region. The proposed method is able to calculate the dose profile with mean relative errors of 0.8%, 1.0% and 1.6% from the ¹¹C, ¹⁰C, ¹⁵O fragment profiles, respectively, and estimate the position of the distal edge of the SOBP to within an average of 0.7 mm, 1.9 mm and 1.2 mm of its true location.

这项工作提出了一种迭代方法，用于估计接受碳离子治疗的患者的绝对剂量分布，通过分析由目标体积中产生的正电子发射碎片的衰变引起的正电子湮没的分布。所提出的方法依赖于将总正电子湮没分布分解为三种主要的正电子发射碎片种类 - ¹¹ C、¹⁰ C 和¹⁵ O 的剖面。通过模拟一系列单能^{12构建基函数库}C 离子辐照均质聚甲基丙烯酸甲酯体模，并测量产生的一维正电子发射片段分布和剂量分布。为了估计在任意多能辐射期间传递的剂量，来自片段分布库的因子的线性组合迭代地拟合到在辐射期间获得的分解的正电子湮没分布，并且得到的权重与相应的单能剂量分布相结合以估计总剂量分布。在拟合过程中加入了一个总变化正则化项来抑制高频噪声。该方法用 14 种不同的多能¹²聚甲基丙烯酸甲酯靶标中的 C 剂量分布：一个产生平坦的生物剂量，10 个具有随机能量加权因子，三个具有不同的剂量最大值或最小值，分布在布拉格峰区域内。所提出的方法能够分别从¹¹ C、¹⁰ C、¹⁵ O 碎片剖面计算出平均相对误差为 0.8%、1.0% 和 1.6% 的剂量剖面，并估计 SOBP 远端边缘的位置到在距离其真实位置平均 0.7 毫米、1.9 毫米和 1.2 毫米的范围内。