A mathematical approach to optimizing the radiation dose distribution in heterogeneous tumours.
A mathematical approach to optimizing the radiation dose distribution in heterogeneous tumours.
复制标题
优化异质肿瘤辐射剂量分布的数学方法。
作者：
N. Stavreva;Pavel Vassilev Stavrev;W. Round
本文提供了一种通用的剂量分布优化的数学方法，该方法允许考虑不同复杂程度的肿瘤。研究了两种不同的生物学准则--A)使肿瘤不同部分的控制概率(局部肿瘤控制概率)在整个肿瘤中保持一致；B)最小化传递到肿瘤的平均剂量。对于这两个标准，我们要求将整个肿瘤控制概率保持在特定的期望水平。证明了采用第一个判据需要剂量分布与细胞密度成对数，与细胞辐射敏感性的倒数成正比，而采用第二个判据则需要在细胞辐射感度不变的情况下剂量分布均匀。文中还给出了异质细胞辐射敏感性下的剂量分布公式。这两个标准在局部肿瘤控制概率和肿瘤的平均剂量方面进行了比较。结论是，保持恒定的局部肿瘤控制概率(标准A)可能比最小化平均剂量(标准B)具有更重要的临床意义。
This paper offers a general mathematical approach to dose distribution optimization which allows tumours with different degrees of complexity to be considered. Two different biological criteria - A) keeping the control probability of the different parts of the tumour (local tumour control probability) uniform throughout the tumour and B) minimizing the mean dose delivered to the tumour are studied. For both criteria we impose the requirement that the whole tumour control probability be kept on a certain desired level. It is proved that the adoption of the first criterion requires a dose distribution logarithmic with the cell density and proportional to the inverse of the cell radiosensitivity while the adoption of the second criterion necessitates a homogeneous dose distribution when the cell radiosensitivity is constant. The corresponding formula for the dose distribution in case of heterogeneous cell radiosensitivity is also given. The two criteria are compared in terms of local tumour control probability and mean dose delivered to the tumour. It is concluded that maintaining constant local tumour control probability (criterion A) may be of greater clinical importance then minimizing the mean dose (criterion B).