Robson R E, Brunger M J, Buckman S J, Garcia G, Petrović Z Lj, White R D
College of Science, Technology and Engineering, James Cook University, Townsville QLD 4810, Australia.
1] School of Chemical and Physical Sciences, Flinders University, Adelaide, SA 5001, Australia [2] Institute of Mathematical Sciences, University of Malaya, 5063 Kuala Lumpur, Malaysia.
Sci Rep. 2015 Aug 6;5:12674. doi: 10.1038/srep12674.
The kinetic theory of non-relativistic positrons in an idealized positron emission tomography PET environment is developed by solving the Boltzmann equation, allowing for coherent and incoherent elastic, inelastic, ionizing and annihilating collisions through positronium formation. An analytic expression is obtained for the positronium formation rate, as a function of distance from a spherical source, in terms of the solutions of the general kinetic eigenvalue problem. Numerical estimates of the positron range - a fundamental limitation on the accuracy of PET, are given for positrons in a model of liquid water, a surrogate for human tissue. Comparisons are made with the 'gas-phase' assumption used in current models in which coherent scattering is suppressed. Our results show that this assumption leads to an error of the order of a factor of approximately 2, emphasizing the need to accurately account for the structure of the medium in PET simulations.
通过求解玻尔兹曼方程，建立了理想化正电子发射断层扫描（PET）环境中非相对论性正电子的动力学理论，该理论考虑了通过正电子素形成的相干和非相干弹性、非弹性、电离和湮灭碰撞。根据一般动力学本征值问题的解，得到了正电子素形成率作为距球形源距离的函数的解析表达式。给出了液体水模型（人体组织的替代物）中正电子的正电子射程的数值估计，正电子射程是PET精度的一个基本限制。与当前模型中使用的“气相”假设进行了比较，在“气相”假设中相干散射被抑制。我们的结果表明，这种假设导致大约2倍的误差，强调了在PET模拟中准确考虑介质结构的必要性。
